8 source location and depth estimation from digitized areomagnetic data

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㊀收稿日期:２０２２－１１－０８基金项目:安徽省教育厅高等学校科学研究项目(自然科学类)(２０２２ＡＨ０５２９２０)作者简介:王玉堂(１９８３－)ꎬ男ꎬ安徽涡阳人ꎬ硕士ꎬ副教授ꎬ研究方向:大数据及人工智能.㊀㊀辽宁大学学报㊀㊀㊀自然科学版第５０卷㊀第３期㊀２０２３年ＪＯＵＲＮＡＬＯＦＬＩＡＯＮＩＮＧＵＮＩＶＥＲＳＩＴＹＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎＶｏｌ.５０㊀Ｎｏ.３㊀２０２３基于深度学习的车辆前方障碍物距离估测王玉堂(安徽信息工程学院大数据与人工智能学院ꎬ安徽芜湖２４１１９９)摘㊀要:随着科技进步ꎬ自动驾驶系统的应用在未来必形成一种趋势ꎬ而车辆与障碍物之间的距离估测是自动驾驶系统中一个非常重要的技术.为了达到距离估测的目的ꎬ目前开发的自动驾驶系统大都需要依靠各式各样的距离传感器ꎬ例如激光雷达㊁雷达及超音波等ꎬ这些传感器在距离量测上通常具有高精度ꎬ但同时也伴随着高昂价格ꎬ这使自动驾驶系统的推广及普及变得越来越困难.本文提出了一个结合语义分割与深度估测的深度神经网络模型ꎬ其包含有相同卷积层数的编码器与解码器网络ꎬ将本文所提之网络架构在ＫＩＴＴＩ及Ｃｉｔｙｓｃａｐｅｓ资料集上进行训练ꎬ并在最后结合语义分割与深度估测等方法进行距离估测ꎬ实验结果证实ꎬ本文所提方法具有可行性.关键词:人工智能ꎻ深度估测ꎻ语义分割ꎻ深度学习中图分类号:ＴＰ３１１㊀㊀㊀文献标志码:Ａ㊀㊀㊀文章编号:１０００－５８４６(２０２３)０３－０２４８－１０ＤｉｓｔａｎｃｅＥｓｔｉｍａｔｉｏｎｏｆＯｂｓｔａｃｌｅｓｉｎＦｒｏｎｔｏｆＶｅｈｉｃｌｅｓＢａｓｅｄｏｎＤｅｅｐＬｅａｒｎｉｎｇＷＡＮＧＹｕ￣ｔａｎｇ(ＤｅｐａｒｔｍｅｎｔｏｆＢｉｇＤａｔａａｎｄＡｒｔｉｆｉｃｉａｌＩｎｔｅｌｌｉｇｅｎｃｅꎬＡｎｈｕｉＩｎｓｔｉｔｕｔｅｏｆＩｎｆｏｒｍａｔｉｏｎＴｅｃｈｎｏｌｏｇｙꎬＷｕｈｕ２４１１９９ꎬＣｈｉｎａ)Ａｂｓｔｒａｃｔ:㊀Ａｕｔｏｎｏｍｏｕｓｄｒｉｖｉｎｇｓｙｓｔｅｍｓａｒｅｔｈｅｗａｖｅｏｆｔｈｅｆｕｔｕｒｅꎻｆｏｒｓｕｃｈｓｙｓｔｅｍｓꎬｔｈｅｅｓｔｉｍａｔｉｏｎｏｆｔｈｅｄｉｓｔａｎｃｅｂｅｔｗｅｅｎｔｈｅｖｅｈｉｃｌｅａｎｄｓｕｒｒｏｕｎｄｉｎｇｏｂｓｔａｃｌｅｓｉｓｋｅｙ.ＭｏｓｔｃｕｒｒｅｎｔｄｉｓｔａｎｃｅｅｓｔｉｍａｔｉｏｎｍｅｔｈｏｄｓｒｅｌｙｏｎａｖａｒｉｅｔｙｏｆｄｉｓｔａｎｃｅｓｅｎｓｏｒｓꎬｓｕｃｈａｓＬｉＤＡＲꎬｒａｄａｒꎬｏｒｕｌｔｒａｓｏｎｉｃｓｅｎｓｏｒｓ.Ａｌｔｈｏｕｇｈｔｈｅｓｅｓｅｎｓｏｒｓｍｅａｓｕｒｅｄｉｓｔａｎｃｅａｃｃｕｒａｔｅｌｙꎬｔｈｅｉｒｈｉｇｈｃｏｓｔｈｉｎｄｅｒｓｔｈｅｐｏｐｕｌａｒｉｚａｔｉｏｎｏｆａｕｔｏｎｏｍｏｕｓｄｒｉｖｉｎｇｓｙｓｔｅｍｓ.Ｔｏｒｅｍｅｄｙｔｈｉｓｐｒｏｂｌｅｍꎬｔｈｉｓｐａｐｅｒｐｒｏｐｏｓｅｓａｄｅｅｐｎｅｕｒａｌｎｅｔｗｏｒｋ(ＤＮＮ)ｔｈａｔｃｏｍｂｉｎｅｓｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎａｎｄｄｅｐｔｈｅｓｔｉｍａｔｉｏｎ.ＴｈｅＤＮＮｉｎｃｌｕｄｅｓａｎｅｎｃｏｄｅｒａｎｄａｄｅｃｏｄｅｒꎬｂｏｔｈｏｆｗｈｉｃｈｈａｖｅｔｈｅｓａｍｅｎｕｍｂｅｒｏｆｃｏｎｖｏｌｕｔｉｏｎａｌｌａｙｅｒｓ.ＴｈｅｐｒｏｐｏｓｅｄｎｅｔｗｏｒｋａｒｃｈｉｔｅｃｔｕｒｅｗａｓｔｒａｉｎｅｄｏｎｂｏｔｈｔｈｅＫＩＴＴＩａｎｄＣｉｔｙｓｃａｐｅｓｄａｔａｓｅｔｓ.Ｔｈｅｐｒｏｐｏｓｅｄｍｅｔｈｏｄｐｒｏｖｉｄｅｄａｃｃｕｒａｔｅｄｉｓｔａｎｃｅｅｓｔｉｍａｔｉｏｎｉｎｅｖａｌｕａｔｉｏｎｔｅｓｔｓꎬｄｅｍｏｎｓｔｒａｔｉｎｇｉｔｓ㊀㊀ｆｅａｓｉｂｉｌｉｔｙ.Ｋｅｙｗｏｒｄｓ:㊀ａｒｔｉｆｉｃｉａｌｉｎｔｅｌｌｉｇｅｎｃｅꎻｄｅｐｔｈｅｓｔｉｍａｔｉｏｎꎻｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎꎻｄｅｅｐｌｅａｒｎｉｎｇ０㊀引言人工智能一直是人类向往的终极目标ꎬ而深度学习则是大家公认最接近人工智能的一种技术.近年来ꎬ深度学习在影像辨识㊁语音识别㊁医疗诊断和自动机器翻译等领域都有出色的表现ꎬ这都要归因于类神经网络的深度结构[１].计算机视觉常见的应用有:影像分类[２－３]㊁物体侦测[４－６]以及语义分割[７－１０]等.其中语义分割的任务是在像素等级上对整个影像进行实例分类ꎬ每个实例(或是类别)对应于影像中的物体或表示影像的一部分ꎬ例如人㊁车㊁道路及天空等.该任务也称为密集预测ꎬ该任务目标是用影像中的相应类别标记影像中的每个像素.语义分割对于场景理解非常的关键ꎬ可让深度学习模型更好地学习到环境中的全域视觉背景.对于机器人[１１]㊁自动驾驶[１２]㊁３Ｄ环境重建及增强现实[１３]等ꎬ深度感测是必要的技术.传统上ꎬ有关于道路前方障碍物的侦测与距离的判断ꎬ为了达到更可靠的感知能力ꎬ除了摄影机外ꎬ还需仰赖大量的传感器ꎬ其中包含超音波㊁雷达及激光雷达等.本文认为在这些传感器中ꎬ基于视觉感知的摄影机可提供车辆周遭环境最丰富的信息ꎬ其中包含颜色㊁纹理㊁物体形状以及外观等.这些都是其他形态的传感器所无法提供的.基于这个原因ꎬ本文提出一种基于行车记录仪摄影机的影像感知系统ꎬ利用摄影机所获取的影像来进行车辆前方的障碍物侦测与距离估算.由Ｌｏｎｇ等[１４]所提出的全卷积网络是第一个端到端(Ｅｎｄ￣ｔｏ￣ｅｎｄ)语义分割的网络架构.全卷积神经网络(ＦＣＮ)可使用任何大小的影像作为输入ꎬ并输出具有相同大小的分割影像.Ｌｏｎｇ等首先修改了当前流行的卷积神经网络(ＣＮＮ)架构ꎬ例如ＡｌｅｘＮｅｔ㊁ＶＧＧ１６和ＧｏｏｇＬｅＮｅｔ[１５]等.在文献[１４]中ꎬ他们采用卷积层替换所有的完全链接层ꎬ借以产生多个特征映射图ꎬ因此需要上采样(Ｕｐｓａｍｐｌｉｎｇ)来让输入的特征图产生与输入相同大小的输出.通常上采样是由具有大于１的行跨度(Ｓｔｒｉｄｅ)的卷积层所组成.这种方式通常又称为反卷积或转置卷积ꎬ因为它产生的特征图大小大于输入.在ＦＣＮ中ꎬ为了优化训练器ꎬ文中采用逐像素交叉熵损失来训练网络.此外ꎬ他们还在网络中添加了跳跃式连接的结构以产生更好的输出结果.在文献[１４]中ꎬ他们使用ＩｍａｇｅＮｅｔ资料集来训练语义分割模型ꎬ在２０１１年ＰａｓｃａｌＶＯＣ分类挑战中获得６２.２％平均交并比(ＭｅａｎｉｎｔｅｒｓｅｃｔｉｏｎｏｖｅｒｕｎｉｏｎꎬｍＩｏＵ)的评分.ＦＣＮ虽然具有较高的ｍＩｏＵꎬ但同时伴随着庞大的计算量.近年来ꎬ语义分割任务的成功有赖于大型标记资料集的开源ꎬ其中较知名的有Ｃａｍｖｉｄ资料集[１６]㊁Ｃｉｔｙｓｃａｐｅｓ资料集[１７]㊁ＭＳＣＯＣＯ资料集与ＰａｓｃａｌＶＯＣ２０１２资料集[１８]等.在国内ꎬ百度独创的资料集训练方法ꎬ被广泛应用在自动驾驶系统中ꎬ在一定程度上弥补了数据里程不足的问题.９４２㊀第３期㊀㊀㊀㊀㊀㊀王玉堂:基于深度学习的车辆前方障碍物距离估测㊀㊀语义分割研究基本上可分成以下几个类型.１)基于编码器－解码器的结构ꎬ其中比较著名的语义分割网络有ＦＣＮ㊁ＳｅｇＮｅｔ与Ｆａｓｔ－ＳＣＮＮ[１９]等ꎬ其在ＰａｐｅｒＷｉｔｈＣｏｄｅＢｅｎｃｈｍａｒｋｓ上有关Ｃｉｔｙｓｃａｐｅｓ资料集的ｍＩｏＵ分别为６５.３％㊁５７.０％与６８.０％等.２)基于注意力机制的结构ꎬ比较著名的方法有ＰＳＡＮｅｔ[２０]㊁ＣＡＡ(Ｃｈａｎｎｅｌｉｚｅｄａｘｉａｌａｔｔｅｎｔｉｏｎ)[２１]与ＭｕｌｔｉＳｃａｌｅＳｐａｔｉａｌＡｔｔｅｎｔｉｏｎ[２２]等ꎬ其在前述Ｂｅｎｃｈｍａｒｋｓ上有关Ｃｉｔｙｓｃａｐｅｓ数据库ｍＩｏＵ分别为８１.４％㊁８２.６％与８６.２％ꎬ其中文献[２２]结合多尺度架构ꎬ目前取得第一的佳绩.由此可见ꎬ基于注意力机制与多尺度架构成为未来语义分割研究的趋势.在单目深度估计(Ｍｏｎｏｃｕｌａｒｄｅｐｔｈｅｓｔｉｍａｔｉｏｎ)的研究上ꎬ比较重要的数据集包含有ＫＩＴＴＩ[２３－２４]㊁Ｍａｋｅ３Ｄ[２５]与ＮＹＵ－ＤｅｐｔｈＶ２[２６]等.近年来ꎬ有关深度估计方法ꎬ如运动结构恢复(ＳｔｒｕｃｔｕｒｅｆｒｏｍｍｏｔｉｏｎꎬＳｆＭ)[２７]以及立体视觉匹配(Ｓｔｅｒｅｏｖｉｓｉｏｎｍａｔｃｈｉｎｇ)[２８]ꎬ都是建立在多视点的特征对应(Ｆｅａｔｕｒｅｃｏｒｒｅｓｐｏｎｄｅｎｃｅｓ)上.深度估测方法基本上可分成以下几类:１)基于几何的方法:通过几何约束ꎬ从几幅影像中恢复场景３Ｄ结构ꎬ代表的方法有ＳｆＭ[２９]ꎬ可通过影像序列间的特征对应及几何约束来处理稀疏特征的深度估测问题.因此ꎬ前述方法在深度估测的准确性方面ꎬ很大程度上与精确的特征匹配和高质量的影像序列有关.２)基于传感器的方法:关于深度传感器ꎬ如ＲＧＢ－Ｄ相机和激光雷达ꎬ能够直接撷取影像的深度信息.ＲＧＢ－Ｄ相机能够直接撷取ＲＧＢ影像的像素级密集深度图ꎬ其缺点为有限的测量范围与光照敏感性.在自动驾驶应用上ꎬ激光雷达是比较常用的方法ꎬ但仅能产生稀疏的三维地图.３)基于深度学习的方法:这是目前最流行的深度估测方法ꎬ在ＫＩＴＴＩＢｅｎｃｈｍａｒｋｓ的评分排行榜上ꎬＶｉＰ－ＤｅｅｐＬａｂ[３０]在ＳＩＬｏｇ的评分指标上排行第２.ＶｉＰ－ＤｅｅｐＬａｂ是一个深度模型ꎬ其提出主要用来解决视觉中长期存在且具挑战性的反投影问题(Ｉｎｖｅｒｓｅｐｒｏｊｅｃｔｉｖｅｐｒｏｂｌｅｍ)ꎬ透过建模可从透视影像序列中恢复点云ꎬ同时为每个点提供深度信息.１㊀研究方法本文所提的深度神经网络如图１所示ꎬ在所提的网络架构中总共包含有６个主要的卷积区块ꎬ文中用Ｓｔａｇｅ来表示.对于同一个Ｓｔａｇｅꎬ每个卷积层输出的特征图具有相同的大小和通道数.在１－６的Ｓｔａｇｅ中ꎬ它们包含２－２－２－２－２－１层的卷积区块(Ｃｏｎｖ２Ｄｂｌｏｃｋ)ꎬ输出通道的数量分别是３２－６４－１２８－２５６－５１２－１０２４.在本文中ꎬ所有卷积层都使用带有可学习加权参数的卷积核.池化层使用ＭａｘＰｏｏｌｉｎｇ来缩小输出特征图的大小.在卷积层之后ꎬ应用批次正规化(ＢａｔｃｈｎｏｒｍａｌｉｚａｔｉｏｎꎬＢＮ)来归一化卷积层输出的数据ꎬ以避免在反向传播中出现梯度消失的现象ꎬ然后再使用ＲｅＬＵ(Ｒｅｃｔｉｆｉｅｄｌｉｎｅａｒｕｎｉｔ)活化函数ꎬ其可以保持正值不变ꎬ但会将负值设为０.现在ꎬ将注意力转向Ｄｅｃｏｄｅｒ网络的细节ꎬ其中每个Ｓｔａｇｅ对应于Ｅｎｃｏｄｅｒ网络的相同Ｓｔａｇｅ.在０５２㊀㊀㊀辽宁大学学报㊀㊀自然科学版２０２３年㊀㊀㊀㊀Ｄｅｃｏｄｅｒ网络中ꎬ每个卷积层表示为ＤＣ－Ｃｏｎｖ－ｍ－ｎꎬ其中ＤＣꎬｍ和ｎ分别表示Ｄｅｃｏｄｅｒ㊁Ｓｔａｇｅ和Ｌａｙｅｒ.对于语义分割结构的设计ꎬ大多数编码器网络都是相同的.唯一的区别在于解码器网络架构.在本文中ꎬ修改ＳｅｇＮｅｔ的Ｄｅｃｏｄｅｒ网络ꎬ同时引入跳跃连接的构架.这个想法的灵感主要来自Ｌｉｎ等[３１]提出的特征金字塔网络ꎬ该文确认了使用跳跃式连接结构时像素准确度(Ｐｉｘｅｌａｃｃｕｒａｃｙ)ꎬ具有较好的结果.为了更清楚描述本文所提跳跃连接的细部结构ꎬ以第４个Ｓｔａｇｅ为例来进行说明.首先ꎬ在Ｅｎｃｏｄｅｒ网络中选择第４个Ｓｔａｇｅ的最后一个卷积层ꎬ亦即ＥＣ－Ｃｏｎｖ－４－３ꎬ因为在同一个Ｓｔａｇｅ中最深的卷积层可以提取最具辨识度的特征ꎻ然后ꎬ在Ｄｅｃｏｄｅｒ网络中选择相应的卷积层ꎬ亦即ＤＣ－Ｃｏｎｖ－４－３ꎻ最后ꎬ再将这两个层进行跳跃连接ꎬ如图２所示.最后ꎬ再进行特征图放大以产生Ｕｐｓａｍｐｌｉｎｇ－３层.图１㊀本文所提具有对称Ｅｎｃｏｄｅｒ和Ｄｅｃｏｄｅｒ语义分割的网络构架１５２㊀第３期㊀㊀㊀㊀㊀㊀王玉堂:基于深度学习的车辆前方障碍物距离估测㊀图２㊀本文解码器跳跃连接结构示意图(ａ)串接方法ꎻ(ｂ)相加方法.㊀㊀本文在语义分割解码器的跳跃连接处加入注意力机制ꎬ如图３所示.在图中ꎬ特征图影像Ｘ(维度:ＢＳꎬＨꎬＷꎬＣ)为主干网络Ｓｔａｇｅ－３Ｌａｙｅｒ－３或Ｓｔａｇｅ－４Ｌａｙｅｒ－３的输出特征图.Ｙ(维度:ＢＳꎬＨꎬＷꎬＣ)为经注意力机制区块转换后之输出图ꎬ其大小与Ｘ相同ꎬ其中ＢＳ为批次量大小ꎬＨ与Ｗ分别为特征图的高与宽ꎬＣ为特征图之通道数量.注意力机制的设计理念:变异数与共变异数是统计学与机器学习中常用的统计量ꎬ其中变异数用来衡量随机变量与平均值间的平方偏差量ꎬ然而共变异数则是用来衡量两个随机变量间的相似性.基于此ꎬ随机变量间的分布愈相似ꎬ共变异数就愈大ꎻ相反ꎬ两者间的相似性愈低ꎬ共变异数就愈小.在本文中ꎬ可将特征图中的每一个像素点视为一个随机变量.因此ꎬ针对任一像素点(令为目标点)与所有其他像素点可计算其配对共变异数ꎬ如(ｘ１ꎬｘ２)的配对共变异数为(ｘ１－μ)(ｘ２－μ).图３㊀本文在编㊁解码器的跳跃连接中加入注意力机制内存块㊀㊀设Ｘ为输入特征图ꎬ先将ＸɪＲＨˑＷ的形状重新调整为ａɪＲＮˑ１ꎬ其中Ｎ＝ＨˑＷꎬＨ与Ｗ分别表示特征图的高与宽.令ａ＝ｂ＝ｃ＝[ｘ１ꎬｘ２ꎬ ꎬｘｎ]Ｔꎬ并令μ为平均值ꎬ因此共异变数ＣｏｖＮˑ１＝(ａ－μ)(ｂ－μ)Ｔꎬ进一步可计算注意力机制特征图为ｄＮˑ１＝ＣｏｖＮˑＮｃＮˑ１⇒ＹＨˑＷꎬ最终特征图为原特征图与注意力机制特征图相加.２５２㊀㊀㊀辽宁大学学报㊀㊀自然科学版２０２３年㊀㊀㊀㊀㊀２㊀结果与讨论本文实验系统采用ＬｉｎｕｘＵｂｕｎｔｕ１８.０４ꎬ开发环境为Ｐｙｔｈｏｎ３.７.０ꎬ安装的函数库ＴｅｎｓｏｒＦｌｏｗ２.３.０和Ｏｐｅｎｃｖ－ｐｙｔｈｏｎ３.２.０.８.本文在Ｃｉｔｙｓｃａｐｅｓ资料集上进行所提深度神经网络在语义分割上的性能评估.而深度估测方面则在ＫＩＴＴＩ资料集上进行训练及评估.本数据集有大量的道路行车记录数据且包含大量的传感器记录的真实数据.在语义分割方面ꎬ本文采用ｍＩｏＵ指标评估影像中各个类别的分割效能.而深度估测评估度量则是采用ＲＭＳＥ(Ｒｏｏｔｍｅａｎｓｑｕａｒｅｅｒｒｏｒ)及准确性.在本文中ꎬ使用ＴｅｎｓｏｒＦｌｏｗ来实现本文所提的深度神经网络架构.本文所提架构在Ｃｉｔｙｓｃａｐｅｓ资料集上进行及ｍＩｏＵ评分分别定义如公式(１)和(２)所示.ＰＡ＝ðＣｉ＝０ＰｉｉðＣｉ＝０ðＣｊ＝０Ｐｉｊ(１)ｍＩｏＵ＝１Ｃ＋１ðＣｉ＝０ＰｉｉðＣｊ＝０Ｐｉｊ＋ðＣｊ＝０Ｐｊｉ－Ｐｉｉ(２)式中:Ｃ是要预测的总类别数ꎬ由于背景也需要考虑进来ꎬ因此总类别数将增加为Ｃ＋１ꎻＰｉｉ表示该像素属于第ｉ个类别ꎬ且被识别为第ｉ类ꎬ因此它是真阳性ꎻＰｉｊ表示像素属于第ｉ个类别ꎬ但却被错误地辨识为第ｊ个类别ꎬ故其属于伪阴性ꎻＰｊｉ则是将第ｊ个类别错误地标示为第ｉ个类别ꎬ故其属于伪阳性.为了评价深度估测网络的性能ꎬ本文采用ＣＮＮ估计单目图像深度[３２]的评价方法ꎬ该评价方法有以下５个评价指标:ＲＭＳＥ㊁ＲＭＳＥｌｏｇ㊁ＡｂｓＲｅｌ㊁ＳｑＲｅｌ及Ａｃｃｕｒａｃｙꎬ其定义分别如下:ＲＭＳＥ＝１ＮðｉɪＩｄｉ－ｄ∗ｉ２(３)ＲＭＳＥｌｏｇ＝１ＮðｉɪＩｌｏｇ(ｄｉ＋１)－ｌｏｇ(ｄ∗ｉ－１) ２(４)ＡｂｓＲｅｌ＝１ＮðｉɪＩ｜ｄｉ－ｄ∗ｉ｜ｄ∗ｉ(５)ＳｑＲｅｌ＝１ＮðｉɪＩｄｉ－ｄ∗ｉ２ｄ∗ｉ(６)Ａｃｃｕｒａｃｙ＝％ｏｆｄｉｓ.ｔｍａｘｄｉｄ∗ｉꎬｄ∗ｉｄｉæèçöø÷＝δ<ｔｈｒ(７)式中:ｄｉ与ｄ∗ｉ分别表示图像深度的预测值与真值ꎻＩ为图像ꎻＮ是图像的总点数ꎻｔｈｒ分别采用１.２５㊁１.２５２及１.２５３.以上指标主要用于评价图像深度真实值(Ｇｒｏｕｎｄｔｒｕｔｈ)与预测值(Ｐｒｅｄｉｃｔｅｄｖａｌｕｅｓ)间接近的程度ꎬ其中ＲＭＳＥ㊁ＲＭＳＥｌｏｇ㊁ＡｂｓＲｅｌ及ＳｑＲｅｌ等指标的值愈小代表深度网络的估测性能愈好ꎻ反之ꎬＡｃｃｕｒａｃｙ指标是愈大愈好.表１为在深度神经网络是否加入注意力机制对于语义分割性能的影响.由表可知ꎬ加入一层注３５２㊀第３期㊀㊀㊀㊀㊀㊀王玉堂:基于深度学习的车辆前方障碍物距离估测㊀㊀意力机制内存块优于不加入注意力机制的内存块.同样ꎬ从图４(ｂ)与图４(ｃ)中看出ꎬ加入注意力机制内存块的语义分割性能是优于没有加入注意力内存块的.同时ꎬ由表１中亦可看出ꎬ当加入更多层的注意力机制内存块反而会劣化语义分割性能.表１㊀针对深度神经网络构架中跳跃连接层是否加入注意力机制在Ｃｉｔｙｓｃａｐｅｓ数据集的ｍＩｏＵ和Ｐｉｘｅｌａｃｃｕｒａｃｙ的评分结果ＭｅｔｈｏｄｍＩｏＵＰｉｘｅｌａｃｃｕｒａｃｙＮｏａｔｔｅｎｔｉｏｎ０.７９５８０.８８５６Ａｔｔｅｎｔｉｏｎ/Ｓｔａｇｅ４０.７９６１０.８８８４Ａｔｔｅｎｔｉｏｎ/Ｓｔａｇｅ３＆４０.６８５７０.８１１５图４㊀本文所提构架在解码器增加注意力机制在语义分割方面的视觉结果比较(ａ)原图ꎻ(ｂ)加入注意力机制之语义分割图ꎻ(ｃ)无注意力机制之语义分割图.㊀㊀在语义分割方面ꎬ本文所提出的构架在Ｃｉｔｙｓｃａｐｅｓ数据集上进行了训练与测试ꎬ并对本文提出的深度网络估测结果与文献[７]㊁[１４]和[１９]中相应的数据进行了比较.从表２中可以看出ꎬ本方法的ｍＩｏＵ值为７９.６ꎬ优于ＳｅｇＮｅｔ的５７.０ꎬＦＮＣ的６５.３以及Ｆａｓｔ－ＳＣＮＮ的６８.０.表２㊀本文所提方法与现代语义分割方法的ｍＩｏＵ评分比较ＡｐｐｒｏａｃｈｍｌｏＵ/％Ｆａｓｔ－ＳＣＮＮ[１９]６８.０ＦＣＮ[１４]６５.３ＳｅｇＮｅｔ[７]５７.０Ｐｒｏｐｏｓｅｄ(Ａｔｔｅｎｔｉｏｎ/Ｓｔａｇｅ４)７９.６㊀㊀在深度估测方面ꎬ本文所提出的构架在ＫＩＴＴＩ数据集上进行了训练与测试ꎬ评价图像深度真实值(Ｇｒｏｕｎｄｔｒｕｔｈ)与预测值(Ｐｒｅｄｉｃｔｅｄｖａｌｕｅｓ)间接近的程度.将本文提出的深度网络估测结果与相关文献进行了比较ꎬ其中ꎬ在选用相同Ｄｅｐｔｈ的基础上ꎬ４５２㊀㊀㊀辽宁大学学报㊀㊀自然科学版２０２３年㊀㊀㊀㊀ＲＭＳＥꎬＲＭＳＥｌｏｇ指标小于参考文献[３１－３２]中的数据ꎬＡＲＤ(Ａｖｅｒａｇｅｒｅｌａｔｉｖｅｄｅｖｉａｔｉｏｎｓ)ꎬＲＳＤ(Ｒｅｌａｔｉｖｅｓｔａｎｄａｒｄｄｅｖｉａｔｉｏｎｓ)等指标均高于参考文献[３１－３２]中的数据.由表３可看出本文所提出的深度神经网络架构在深度估测的各项评价结果都优于参考文献[３１－３２].表３㊀本文所提方法与相关文献在深度估测性能方面比较ＬｏｗｅｒｉｓｂｅｔｔｅｒＨｉｇｈｅｒｉｓｂｅｔｔｅｒＡｐｐｒｏａｃｈＤｅｐｔｈ/ｍＲＭＳＥＲＭＳＥｌｏｇＡＲＤＲＳＤδ<１.２５δ<１.２５２δ<１.２５３Ｃｏａｒｓｅ[３２]０~８０７.２１６０.２７３０.１９４１.５３１０.６７９０.８９７０.９６７Ｃｏａｒｓ＋Ｆｉｎｅ[３２]０~８０７.１５６０.２７００.１９０１.５１５０.６９２０.８９９０.９６７ＤＣＮＦ－ＦＣＳＰ[３１]０~８０７.０４６０.２１７０.６５６０.８８１０.９５８Ｐｒｏｐｏｓｅｄ０~８０４.８７９０.２３１０.１５８１.１０１０.７８４０.９３３０.９７３㊀㊀注:测试的数据集为ＫＩＴＴＩＤａｔａｓｅｔ㊀㊀最后本文在车辆与前方障碍物距离估测方面ꎬ从语义分割图像中取得分割目标物ꎬ再对深度图像中取得相应位置的深度数值由小到大进行排序ꎬ取得前２０％深度数值作为该物体的距离估测数值ꎬ如图５所示ꎬ从图５(ａ)中可以看到本文所提方法能有效地估测出本车与前方障碍物间的距离.图５㊀车辆与前方目标物间的距离估测图(ａ)原图ꎻ(ｂ)深度图像图ꎻ(ｃ)目标分割二值图像图.３㊀结论本文提出了一种对称式Ｅｎｃｏｄｅｒ和Ｄｅｃｏｄｅｒ的深度神经网络架构ꎬ并在深度估测方面采用ＫＩＴＴＩ资料集进行训练ꎬ在语义分割方面则是采用Ｃｉｔｙｓｃａｐｅｓ资料集[３３]来进行训练.实验结果显示ꎬ本文所提障碍物距离估测方法具有可行性.本文所提出的网络架构与其他相似的深度估测网络架构ꎬ在相同的训练及测试条件下ꎬ前者在准确率方面也有不错的表现.在未来的工作中ꎬ将研究不同的解码器架构以及更强健的障碍物侦测方法ꎬ以达成目标物的距离估测ꎬ同时持续改善本文所提深度估测网络的准确度.５５２㊀第３期㊀㊀㊀㊀㊀㊀王玉堂:基于深度学习的车辆前方障碍物距离估测㊀㊀参考文献:[１]㊀ＨｏｃｈｒｅｉｔｅｒＳꎬＳｃｈｍｉｄｈｕｂｅｒＪ.Ｌｏｎｇｓｈｏｒｔ￣ｔｅｒｍｍｅｍｏｒｙ[Ｊ].ＮｅｕｒａｌＣｏｍｐｕｔａｔｉｏｎꎬ１９９７ꎬ９(８):１７３５－１７８０.[２]㊀ＫｒｉｚｈｅｖｓｋｙＡꎬＳｕｔｓｋｅｖｅｒＩꎬＨｉｎｔｏｎＧＥ.ＩｍａｇｅＮｅｔｃｌａｓｓｉｆｉｃａｔｉｏｎｗｉｔｈｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓ[Ｃ]//ＮＩＰＳᶄ１２:Ｐｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅ２５ｔｈＩｎｔｅｒｎａｔｉｏｎａｌＣｏｎｆｅｒｅｎｃｅｏｎＮｅｕｒａｌＩｎｆｏｒｍａｔｉｏｎＰｒｏｃｅｓｓｉｎｇＳｙｓｔｅｍｓ.ＮｅｗＹｏｒｋ:ＣｕｒｒａｎＡｓｓｏｃｉａｔｅｓＩｎｃ.ꎬ２０１２:１０９７－１１０５.[３]㊀ＳｉｍｏｎｙａｎＫꎬＺｉｓｓｅｒｍａｎＡ.Ｖｅｒｙｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｔｗｏｒｋｓｆｏｒｌａｒｇｅ￣ｓｃａｌｅｉｍａｇｅｒｅｃｏｇｎｉｔｉｏｎ[ＥＢ/ＯＬ].(２０１４－０９－０４)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１４０９.１５５６.[４]㊀ＲｅｄｍｏｎＪꎬＤｉｖｖａｌａＳꎬＧｉｒｓｈｉｃｋＲꎬｅｔａｌ.Ｙｏｕｏｎｌｙｌｏｏｋｏｎｃｅ:Ｕｎｉｆｉｅｄꎬｒｅａｌ￣ｔｉｍｅｏｂｊｅｃｔｄｅｔｅｃｔｉｏｎ[Ｃ]//２０１６ＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ.ＬａｓＶｅｇａｓ:ＩＥＥＥꎬ２０１６:７７９－７８８.[５]㊀ＲｅｎＳＱꎬＨｅＫＭꎬＧｉｒｓｈｉｃｋＲꎬｅｔａｌ.ＦａｓｔｅｒＲ￣ＣＮＮ:Ｔｏｗａｒｄｓｒｅａｌ￣ｔｉｍｅｏｂｊｅｃｔｄｅｔｅｃｔｉｏｎｗｉｔｈｒｅｇｉｏｎｐｒｏｐｏｓａｌｎｅｔｗｏｒｋｓ[ＥＢ/ＯＬ].(２０１５－０６－０４)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１５０６.０１４９７.[６]㊀ＳｅｒｍａｎｅｔＰꎬＥｉｇｅｎＤꎬＺｈａｎｇＸꎬｅｔａｌ.ＯｖｅｒＦｅａｔ:Ｉｎｔｅｇｒａｔｅｄｒｅｃｏｇｎｉｔｉｏｎꎬｌｏｃａｌｉｚａｔｉｏｎａｎｄｄｅｔｅｃｔｉｏｎｕｓｉｎｇｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｔｗｏｒｋｓ[ＥＢ/ＯＬ].(２０１３－１２－２１)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１３１２.６２２９.[７]㊀ＢａｄｒｉｎａｒａｙａｎａｎＶꎬＫｅｎｄａｌｌＡꎬＣｉｐｏｌｌａＲ.ＳｅｇＮｅｔ:Ａｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｅｎｃｏｄｅｒ￣ｄｅｃｏｄｅｒａｒｃｈｉｔｅｃｔｕｒｅｆｏｒｉｍａｇｅｓｅｇｍｅｎｔａｔｉｏｎ[Ｊ].ＩＥＥＥＴｒａｎｓａｃｔｉｏｎｓｏｎＰａｔｔｅｒｎＡｎａｌｙｓｉｓａｎｄＭａｃｈｉｎｅＩｎｔｅｌｌｉｇｅｎｃｅꎬ２０１７ꎬ３９(１２):２４８１－２４９５.[８]㊀ＨａｒｉｈａｒａｎＢꎬＡｒｂｅｌａｅｚＰꎬＧｉｒｓｈｉｃｋＲꎬｅｔａｌ.Ｈｙｐｅｒｃｏｌｕｍｎｓｆｏｒｏｂｊｅｃｔｓｅｇｍｅｎｔａｔｉｏｎａｎｄｆｉｎｅ￣ｇｒａｉｎｅｄｌｏｃａｌｉｚａｔｉｏｎ[Ｃ]//ＰｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ.Ｂｏｓｔｏｎ:ＩＥＥＥꎬ２０１５:４４７－４５６.[９]㊀ＨｅＫＭꎬＧｋｉｏｘａｒｉＧꎬＤｏｌｌáｒＰꎬｅｔａｌ.ＭａｓｋＲ￣ＣＮＮ[Ｃ]//２０１７ＩＥＥＥＩｎｔｅｒｎａｔｉｏｎａｌＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎ(ＩＣＣＶ).Ｖｅｎｉｃｅ:ＩＥＥＥꎬ２０１７:２９８０－２９８８.[１０]㊀ＫｕｈｎｅｒｔＫＤꎬＳｔｏｍｍｅｌＭ.Ｆｕｓｉｏｎｏｆｓｔｅｒｅｏ￣ｃａｍｅｒａａｎｄＰＭＤ￣ｃａｍｅｒａｄａｔａｆｏｒｒｅａｌ￣ｔｉｍｅｓｕｉｔｅｄｐｒｅｃｉｓｅ３Ｄｅｎｖｉｒｏｎｍｅｎｔｒｅｃｏｎｓｔｒｕｃｔｉｏｎ[Ｃ]//２００６ＩＥＥＥ/ＲＳＪＩｎｔｅｒｎａｔｉｏｎａｌＣｏｎｆｅｒｅｎｃｅｏｎＩｎｔｅｌｌｉｇｅｎｔＲｏｂｏｔｓａｎｄＳｙｓｔｅｍｓ.Ｂｅｉｊｉｎｇ:ＩＥＥＥꎬ２００６:４７８０－４７８５.[１１]㊀ＨｏｒｎＢＫＰ.Ｒｏｂｏｔｖｉｓｉｏｎ[Ｍ].Ｂｏｓｔｏｎ:ＴｈｅＭＩＴＰｒｅｓｓꎬ１９８６.[１２]㊀ＲｉｂｌｅｒＲＬꎬＶｅｔｔｅｒＪＳꎬＳｉｍｉｔｃｉＨꎬｅｔａｌ.Ａｕｔｏｐｉｌｏｔ:Ａｄａｐｔｉｖｅｃｏｎｔｒｏｌｏｆｄｉｓｔｒｉｂｕｔｅｄａｐｐｌｉｃａｔｉｏｎｓ[Ｃ]//ＰｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅＳｅｖｅｎｔｈＩｎｔｅｒｎａｔｉｏｎａｌＳｙｍｐｏｓｉｕｍｏｎＨｉｇｈＰｅｒｆｏｒｍａｎｃｅＤｉｓｔｒｉｂｕｔｅｄＣｏｍｐｕｔｉｎｇ(Ｃａｔ.Ｎｏ.９８ＴＢ１００２４４).Ｃｈｉｃａｇｏ:ＩＥＥＥꎬ１９９８:１７２－１７９.[１３]㊀ＭｉｌｇｒａｍＰꎬＴａｋｅｍｕｒａＨꎬＵｔｓｕｍｉＡꎬｅｔａｌ.Ａｕｇｍｅｎｔｅｄｒｅａｌｉｔｙ:Ａｃｌａｓｓｏｆｄｉｓｐｌａｙｓｏｎｔｈｅｒｅａｌｉｔｙ￣ｖｉｒｔｕａｌｉｔｙｃｏｎｔｉｎｕｕｍ[Ｃ]//ＰｒｏｃＳＰＩＥ２３５１ꎬＴｅｌｅｍａｎｉｐｕｌａｔｏｒａｎｄＴｅｌｅｐｒｅｓｅｎｃｅＴｅｃｈｎｏｌｏｇｉｅｓ.Ｂｏｓｔｏｎ:ＳＰＩＥꎬ１９９５ꎬ２３５１:２８２－２９２.[１４]㊀ＬｏｎｇＪꎬＳｈｅｌｈａｍｅｒＥꎬＤａｒｒｅｌｌＴꎬｅｔａｌ.Ｆｕｌｌｙｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｔｗｏｒｋｓｆｏｒｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎ[Ｃ]//２０１５ＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ(ＣＶＰＲ).Ｂｏｓｔｏｎ:ＩＥＥＥꎬ２０１５:３４３１－３４４０.[１５]㊀ＳｚｅｇｅｄｙＣꎬＬｉｕＷꎬＪｉａＹＱꎬｅｔａｌ.Ｇｏｉｎｇｄｅｅｐｅｒｗｉｔｈｃｏｎｖｏｌｕｔｉｏｎｓ[Ｃ]//２０１５ＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ(ＣＶＰＲ).Ｂｏｓｔｏｎ:ＩＥＥＥꎬ２０１５:１－９.[１６]㊀ＢｒｏｓｔｏｗＧꎬＦａｕｑｕｅｕｒＪꎬＣｉｐｏｌｌａＲ.Ｓｅｍａｎｔｉｃｏｂｊｅｃｔｃｌａｓｓｅｓｉｎｖｉｄｅｏ:Ａｈｉｇｈ￣ｄｅｆｉｎｉｔｉｏｎｇｒｏｕｎｄｔｒｕｔｈｄａｔａｂａｓｅ[Ｊ].ＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎＬｅｔｔｅｒｓꎬ２００９ꎬ３０(２):８８－９７.[１７]㊀ＬｉｎＴＹꎬＭａｉｒｅＭꎬＢｅｌｏｎｇｉｅＳꎬｅｔａｌ.ＭｉｃｒｏｓｏｆｔＣＯＣＯ:Ｃｏｍｍｏｎｏｂｊｅｃｔｓｉｎｃｏｎｔｅｘｔ[Ｃ]//ＣｏｍｐｕｔｅｒＶｉｓｉｏｎ–ＥＣＣＶ２０１４.Ｚｕｒｉｃｈ:ＳｐｒｉｎｇｅｒꎬＣｈａｍꎬ２０１４:７４０－７５５.[１８]㊀ＥｖｅｒｉｎｇｈａｍＭ.ＴｈｅＰａｓｃａｌＶｉｓｕａｌＯｂｊｅｃｔＣｌａｓｓｅｓＣｈａｌｌｅｎｇｅ２０１２(ＶＯＣ２０１２)[Ｒ/ＯＬ].(２０１２－０４－０１)[２０２２－１２－１５].ｈｔｔｐｓ://ｐｊｒｅｄｄｉｅ.ｃｏｍ/ｍｅｄｉａ/ｆｉｌｅｓ/ＶＯＣ２０１２＿ｄｏｃ.ｐｄｆ.６５２㊀㊀㊀辽宁大学学报㊀㊀自然科学版２０２３年㊀㊀㊀㊀[１９]㊀ＰｏｕｄｅｌＲＰＫꎬＬｉｗｉｃｋｉＳꎬＣｉｐｏｌｌａＲ.Ｆａｓｔ￣ＳＣＮＮ:Ｆａｓｔｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎｎｅｔｗｏｒｋ[ＥＢ/ＯＬ].(２０１９－０２－１２)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１９０２.０４５０２.[２０]㊀ＺｈａｏＨＳꎬＺｈａｎｇＹꎬＬｉｕＳꎬｅｔａｌ.ＰＳＡＮｅｔ:Ｐｏｉｎｔ￣ｗｉｓｅｓｐａｔｉａｌａｔｔｅｎｔｉｏｎｎｅｔｗｏｒｋｆｏｒｓｃｅｎｅｐａｒｓｉｎｇ[Ｃ]//ＥｕｒｏｐｅａｎＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎ.Ｍｕｎｉｃｈ:Ｃｈａｍꎬ２０１８:２７０－２８６.[２１]㊀ＨｕａｎｇＹꎬＫａｎｇＤꎬＪｉａＷＪꎬｅｔａｌ.Ｃｈａｎｎｅｌｉｚｅｄａｘｉａｌａｔｔｅｎｔｉｏｎ￣ｃｏｎｓｉｄｅｒｉｎｇｃｈａｎｎｅｌｒｅｌａｔｉｏｎｗｉｔｈｉｎｓｐａｔｉａｌａｔｔｅｎｔｉｏｎｆｏｒｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎ[ＥＢ/ＯＬ].(２０２１－０１－１９)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/２１０１.０７４３４.[２２]㊀ＳａｇａｒꎬＡꎬＳｏｕｎｄｒａｐａｎｄｉｙａｎＲＫ.Ｓｅｍａｎｔｉｃｓｅｇｍｅｎｔａｔｉｏｎｗｉｔｈｍｕｌｔｉｓｃａｌｅｓｐａｔｉａｌａｔｔｅｎｔｉｏｎｆｏｒｓｅｌｆｄｒｉｖｉｎｇｃａｒｓ[ＥＢ/ＯＬ].(２０２０－０６－３０)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/２００７.１２６８５.[２３]㊀ＧｅｉｇｅｒＡꎬＬｅｎｚＰ.Ａｒｅｗｅｒｅａｄｙｆｏｒａｕｔｏｎｏｍｏｕｓｄｒｉｖｉｎｇ?ＴｈｅＫＩＴＴＩｖｉｓｉｏｎｂｅｎｃｈｍａｒｋｓｕｉｔｅ[Ｃ]//ＰｒｏｃｅｅｄｉｎｇｓｏｆＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ.ＮｅｗＹｏｒｋ:ＩＥＥＥꎬ２０１２:３３５４－３３６１.[２４]㊀ＧｅｉｇｅｒＡꎬＬｅｎｚＰꎬＳｔｉｌｌｅｒＣꎬｅｔａｌ.Ｖｉｓｉｏｎｍｅｅｔｓｒｏｂｏｔｉｃｓ:ＴｈｅＫＩＴＴＩｄａｔａｓｅｔ[Ｊ].ＴｈｅＩｎｔｅｒｎａｔｉｏｎａｌＪｏｕｒｎａｌｏｆＲｏｂｏｔｉｃｓＲｅｓｅａｒｃｈꎬ２０１３ꎬ３２(１１):１２３１－１２３７.[２５]㊀ＳａｘｅｎａＡꎬＳｕｎＭꎬＮｇＡＹ.Ｍａｋｅ３Ｄ:Ｌｅａｒｎｉｎｇ３Ｄｓｃｅｎｅｓｔｒｕｃｔｕｒｅｆｒｏｍａｓｉｎｇｌｅｓｔｉｌｌｉｍａｇｅ[Ｊ].ＩＥＥＥＴｒａｎｓａｃｔｉｏｎｓｏｎＰａｔｔｅｒｎＡｎａｌｙｓｉｓａｎｄＭａｃｈｉｎｅＩｎｔｅｌｌｉｇｅｎｃｅꎬ２００９ꎬ３１(５):８２４－８４０.[２６]㊀ＳｉｌｂｅｒｍａｎＮꎬＨｏｉｅｍＤꎬＫｏｈｌｉＰꎬｅｔａｌ.ＩｎｄｏｏｒｓｅｇｍｅｎｔａｔｉｏｎａｎｄｓｕｐｐｏｒｔｉｎｆｅｒｅｎｃｅｆｒｏｍＲＧＢＤｉｍａｇｅｓ[Ｃ]//ＥＣＣＶᶄ１２:Ｐｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅ１２ｔｈＥｕｒｏｐｅａｎＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎ.Ｆｌｏｒｅｎｃｅ:Ｓｐｒｉｎｇｅｒꎬ２０１２:７４６－７６０.[２７]㊀ＬｉｕＦＹꎬＳｈｅｎＣＨꎬＬｉｎＧＳꎬｅｔａｌ.Ｌｅａｒｎｉｎｇｄｅｐｔｈｆｒｏｍｓｉｎｇｌｅｍｏｎｏｃｕｌａｒｉｍａｇｅｓｕｓｉｎｇｄｅｅｐｃｏｎｖｏｌｕｔｉｏｎａｌｎｅｕｒａｌｆｉｅｌｄｓ[Ｊ].ＩＥＥＥＴｒａｎｓａｃｔｉｏｎｓｏｎＰａｔｔｅｒｎＡｎａｌｙｓｉｓａｎｄＭａｃｈｉｎｅＩｎｔｅｌｌｉｇｅｎｃｅꎬ２０１６ꎬ３８(１０):２０２４－２０３９.[２８]㊀ＹｏｎｅｄａＫꎬＴｅｈｒａｎｉＨꎬＯｇａｗａＴꎬｅｔａｌ.Ｌｉｄａｒｓｃａｎｆｅａｔｕｒｅｆｏｒｌｏｃａｌｉｚａｔｉｏｎｗｉｔｈｈｉｇｈｌｙｐｒｅｃｉｓｅ３￣Ｄｍａｐ[Ｃ]//２０１４ＩＥＥＥＩｎｔｅｌｌｉｇｅｎｔＶｅｈｉｃｌｅｓＳｙｍｐｏｓｉｕｍＰｒｏｃｅｅｄｉｎｇｓ.Ｄｅａｒｂｏｒｎ:ＩＥＥＥꎬ２０１４:１３４５－１３５０.[２９]㊀ＶｉｊａｙａｎａｒａｓｉｍｈａｎＳꎬＲｉｃｃｏＳꎬＳｃｈｍｉｄＣꎬｅｔａｌ.ＳｆＭ￣ｎｅｔ:Ｌｅａｒｎｉｎｇｏｆｓｔｒｕｃｔｕｒｅａｎｄｍｏｔｉｏｎｆｒｏｍｖｉｄｅｏ[ＥＢ/ＯＬ].(２０１７－０４－２５)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１７０４.０７８０４.[３０]㊀ＱｉａｏＳＹꎬＺｈｕＹＫꎬＡｄａｍＨꎬｅｔａｌ.ＶｉＰ￣ＤｅｅｐＬａｂ:Ｌｅａｒｎｉｎｇｖｉｓｕａｌｐｅｒｃｅｐｔｉｏｎｗｉｔｈｄｅｐｔｈ￣ａｗａｒｅｖｉｄｅｏｐａｎｏｐｔｉｃｓｅｇｍｅｎｔａｔｉｏｎ[ＥＢ/ＯＬ].(２０２０－１２－０９)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/２０１２.０５２５８.[３１]㊀ＬｉｎＴＹꎬＤｏｌｌáｒＰꎬＳｅｒｇｅＪ.ｅｔａｌ.ＦｅａｔｕｒｅｐｙｒａｍｉｄＮｅｔｗｏｒｋｓｆｏｒｏｂｊｅｃｔｄｅｔｅｃｔｉｏｎ[Ｃ]//２０１７ＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ(ＣＶＰＲ).Ｈｏｎｏｌｕｌｕ:ＩＥＥＥꎬ２０１６:９３６－９４４.[３２]㊀ＥｉｇｅｎＤꎬＰｕｈｒｓｃｈＣꎬＦｅｒｇｕｓＲ.Ｄｅｐｔｈｍａｐｐｒｅｄｉｃｔｉｏｎｆｒｏｍａｓｉｎｇｌｅｉｍａｇｅｕｓｉｎｇａｍｕｌｔｉ￣ｓｃａｌｅｄｅｅｐｎｅｔｗｏｒｋ[ＥＢ/ＯＬ].(２０１４－０７－０９)[２０２２－１２－１５].ｈｔｔｐｓ://ａｒｘｉｖ.ｏｒｇ/ａｂｓ/１４０６.２２８３.[３３]㊀ＣｏｒｄｔｓＭꎬＯｍｒａｎＭꎬＲａｍｏｓＳꎬｅｔａｌ.Ｔｈｅｃｉｔｙｓｃａｐｅｓｄａｔａｓｅｔｆｏｒｓｅｍａｎｔｉｃｕｒｂａｎｓｃｅｎｅｕｎｄｅｒｓｔａｎｄｉｎｇ[Ｃ]//２０１６ＩＥＥＥＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉｓｉｏｎａｎｄＰａｔｔｅｒｎＲｅｃｏｇｎｉｔｉｏｎ.ＬａｓＶｅｇａｓ:ＩＥＥＥꎬ２０１６:３２１３－３２２３.(责任编辑㊀郭兴华)７５２㊀第３期㊀㊀㊀㊀㊀㊀王玉堂:基于深度学习的车辆前方障碍物距离估测。

Approximate MLE Algorithm for Source Localization Based

Approximate MLE Algorithm for Source Localization Basedon TDOA Measurements∗Guoxiang GuDepartment of Electrical and Computer EngineeringLouisiana State University,Baton Rouge,LA70803-5901July2006,Revised January2007ABSTRACTSource localization is investigated based on noisy measurements of TDOA(time-diﬀerence of arrival)in which the measurement noises are assumed to be Gauss distributed.The solution to the constrained WLS(weighted least-squares)is derived and applied to the source localization problem based on TDOAs.The proposed algorithm is shown to be an approximate MLE(maximum likelihood estimation)algorithm under some mild condition.The simulation results show that the proposed approximate MLE algorithm compares favorably with the existing solution methods for source localization based on TDOA measurements.Keywords:Passive source localization,TDOA,AOA,MLE,constrained LS1.INTRODUCTIONPassive source localization has been an important research topic in the signal processing society.It has received greater attention in recent years due to the renewed interest in wireless location(cf.Sayed et al.11and the references therein).This paper considers source localization based on TDOA measurements that has been studied in several papers from Abel and Smith1to Friedlander,6in Hahn and Tretter,8in papers from Ho and Xu10to Schau and Robinson,12and in Torrieri.15Despite the fact that the measurement noises are additive and Gaussian,such a source localization problem is nonlinear in nature and the exact MLE solution is diﬃcult to compute.For this reason,the problem was initially investigated for the case when the sensors are arranged in a linear fashion1,2,8where diﬀerent optimum processing techniques are proposed under various assumptions. When the sensors are distributed irregularly,the optimum solutions are much harder to obtain.A linearization approach based on Taylor series is proposed in5,15to compute the optimum solution iteratively.Because of the existence of local minima,the Taylor series method requires an initial solution close to the global minimum.A more appealing approach is the quasi-linear method employed in6,12,13that converts the nonlinear measurement equations into quasi-linear measurement equations by treating the nonlinear term as a parameter.Two diﬀerent procedures are developed independently in6,13that turn out be mathematically equivalent.A further progress is made in3,10which treats the nonlinear term as an independent variable to be estimated that is solved via WLS procedure together with the location variables.A second WLS is then introduced to minimize the mismatch between the nonlinear term and the location estimate.This two-step WLS procedure is shown to be more eﬀective and closer to the true optimum solution than other existing approaches.In this paper we consider the same passive source localization problem using the same quasi-linear measure-ment equations.Diﬀerent from the existing solution methods,the nonlinear term in the quasi-linear measurement ∗This research is supported in part by US Air Force.Further author information E-mail:ggu@,Telephone:(225)578-5534Wireless Sensing and Processing II, edited by Raghuveer M. Rao, Sohail A. Dianat, Michael D. Zoltowski,Proc. of SPIE Vol. 6577, 657707, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.719865equations is treated as a constraint which is in fact a quadratic constraint.A numerical procedure based on simultaneous diagonalization9is developed to compute the WLS solution under the quadratic constraint.This new procedure is shown to be an approximate MLE solution under the assumption that the ratios of the distances between all but one sensor and the target to the noise variance in TDOA measurements are suitably large.The assumption is rather mild and is satisﬁed so long as the relative distances among all the sensors are suitably large and the noise variance is suitably small which hold in practice for localization based on TDOA measurements. Our results are fairly complete and complement the existing ones in the literature.The simulation results il-lustrate the eﬀectiveness of the proposed solution procedures that compare favorably with the existing results. However due to the space limite,the simulation results are not presented which are available in.72.PROBLEM FORMULATION AND PRELIMINARY ANALYSISFor simplicity we consider only two-dimensional localization although the results are applicable to the three-dimensional case as well.Denote(x k,y k)as the position of the k th sensor and(x T,y T)as the position of the stationary target.Our goal is to estimate the position(x T,y T)based on the TDOA measurement data collected by n sensors located at{(x k,y k)}n k=1.LetR k,T=(x T−x k)2+(y T−y k)2,R T=R1,T,(1)be the distance between the target and the k th sensor.Then the TDOAs are deﬁned by∆t k,1:=(R k,T−R T)/c=T−x k2T−y k2−T−x12T−y12/c(2)for k=2,3,···,n with c the speed of light.The target location is embedded in TDOAs or∆t k,1=∆t k,1(x T,y T). As in the literature we assume that the measurements of TDOAs are given by∆ˆt k,1=∆t k,1(x T,y T)+δt k,1(3)where{δt k,1}n k=2are uncorrelated Gaussian random variables with mean zero and varianceσ2t.That is,the measurement noises have the joint probability density function(PDF)asp∆(δt;x T,y T)=1(2π)n−1σn−1texp−nk=212σ2t∆ˆt k,1−∆t k,1(x T,y T)2.(4)It follows that source localization based on TDOAs is a nonlinear estimation problem.For the joint PDF in(4),an MLE solution to the source localization problem seeks(x T,y T)such that p(δt;x T,y T)achieves its global maximum that is an unbiased estimate under some regularity condition.14The well-known Cram´e r-Rao bound dictates that the error covariance associated with any unbiased estimate is bounded below by the inverse of the corresponding FIM(Fisher information matrix).The computation of the FIM can be complex but has simpler formulas in the case of Gaussian random variables.For source localization based on TDOA measurements,the corresponding FIM can be obtained by applying the Slepian formula14that leads toFIM(∆t)=nk=21c2σ2tcos(βk)−cos(β1)sin(βk)−sin(β1)cos(βk)−cos(β1)sin(βk)−sin(β1)(5)whereβk is the bearing parameter given byβk=tan−1[(y T−y k)/(x T−x k)]and1≤k≤n.Denoteρk=x2k+y2k and rewrite(2)equivalently as(x T−x k)2+(y T−y k)2=(x T−x1)2+(y T−y1)2+c∆t k,12.(6)Then with appropriate scaling we arrive at the following equation:1√cρ2k−ρ21=2√cx k−x1y k−y1xTy T+c√c∆t2k,1+2√cR T∆t k,1(7)for2≤k≤n.The TDOA data in(3)can be substituted in to obtain a quasi-linear model as in.3,6,12,13Indeeddenotea k=1√cρ2k−ρ21−c2(∆ˆt2k,1+µσ2t),ηk=−2√c(R T+c∆ˆt k,1)δt k+c√c(δt2k−µσ2t)(8)for2≤k≤n whereµ≥0.Letθ=x T y T R Tbe the location parameter vector.Thena=Hθ+η⇐⇒⎡⎢⎢⎢⎢⎣a2a3...a n⎤⎥⎥⎥⎥⎦=2√c⎡⎢⎢⎢⎢⎣x2−x1y2−y1c∆ˆt2,1x3−x1y3−y1c∆ˆt3,1.........x n−x1y n−y1c∆ˆt n,1⎤⎥⎥⎥⎥⎦⎡⎢⎣x Ty TR T⎤⎥⎦+⎡⎢⎢⎢⎢⎣η2η3...ηn⎤⎥⎥⎥⎥⎦(9)The above is the same as the quasi-linear model in the literature with{a k}pseudo-measurements and{ηk}the corresponding noises.However it imposes a constraint to the parameter vectorθas(θ−θ0) Q(θ−θ0)=0,Q=diag(1,1,−1),(10)whereθ0=x1y10.Denote E{·}and E{·|·}as the expectation and conditional expectation.Forµ=1,E{ηk|∆ˆt k,1}=0,E{η2k|∆ˆt k,1}=4c(R T+c∆ˆt k,1)2σ2t+2c3σ4t(11) where E{δt3k}=0and E{δt4k}=3σ4t are used.The question is under what condition{ηk}are Gauss distributed, assuming that{δt k}are Gauss distributed with zero mean.The next lemma is useful.Lemma2.1.Let Z=−2αV+V2−σ2whereα>0and Z is a Gauss random variable with mean zero and varianceσ2.If the ratio ofαtoσis suﬃciently large,then Z is approximately Gauss distributed in the neighborhood of−σ2with mean zero and variance4α2σ2.Proof:It is easy to verify that E{Z}=0andσ2Z=E{Z2}=4α2σ2+2σ4=2σ2(2α2+σ2).(12) By noting that Z=(V−α)2−(σ2+α2),we haveV=−α±22Z≥−(σ2+α2).(13)Since V is Gauss distributed,the PDF of Z is given byp Z(z)=1√2πσ2⎧⎨⎩e−12σ2α−√z+(σ2+α2)22z+(σ2+α2)+e−12σ2α+√z+(σ2+α2)22z+(σ2+α2)⎫⎬⎭.(14)Figure1.PDF p Z(z)versus Gauss PDF with x-axis scaled byσ−1,y-axis byσ,andα=10σLet U=22The integral of theﬁrst term in p Z(z)isI1=1√2∞−(σ2+α2)e−12σ2α−√z+(σ2+α2)2222dz=1√∞−ασe−v2/2dv=:Qασ.Hence it is concluded that ifασis suﬃciently large,then I1≈1and thus p Z(z)is dominated by theﬁrst term.It is also easy to see that whenασis suﬃciently large,σ2Z is dominated by4α2σ2.In the case of z+σ2= withclose to zero,we havep Z(z)≈1√2⎧⎨⎩e−12σ2α−√z+(σ2+α2)2222⎫⎬⎭≈1√22exp−(z+σ2)28σα(15)concluding that Z is approximately Gauss distributed in the neighborhood of z=−σ2.Although Lemma2.1states that Z is approximately Gauss distributed near−σ2,it does not imply that its PDF peaks at Z=−σ2.In fact it can be shown by straightforward calculation that the PDF of Z peaks at −3σ2,E{Z}≈0,and E{Z2}≈(2ασ)2provided thatασ>>1.Figure1shows the approximate PDF of Z given byp Z(z)≈1√2⎧⎨⎩e−12α−√ 2222⎫⎬⎭(16)in solid line and the PDF of Gauss random variable with mean−σ2and variance(2ασ)2in dashed line where α=10σis used.Therefore Z is approximately Gaussian not only in the neighborhood of Z=−σ2but in a much greater interval.We comment that the approximate PDF of Z and the exact of PDF of Z are indistinguishable for the caseα≥10σ.We note that Z is Gauss distributed if and only ifγZ is Gauss distributed withγa nonzero constant.In addition it is reasonable to assume that∆ˆt k,1≈∆t k,1for2≤k≤n.Hence by applying Lemma2.1to theelements of the noise vector in(9)we can conclude that{ηk}are approximately Gauss distributed provided thatασ=R T+c∆ˆt k,1cσt≈R T+c∆t k,1cσt=R k,Tcσt>>1.(17)Such a condition holds as long as the relative distances among all the sensors are suitably large and the noise variance is suitably small.It is thus concluded that by takingµ=0,{ηk}in(9)are approximately Gauss distributed and can be well approximated by Gauss variable with mean zero and variance4c(R k,T+c∆ˆt k,1)2σ2t≈4cR2k,Tσ2t provided that the condition in(17)holds.In factµ=0is what employed in.3,10 Because{ηk}are approximately Gauss distributed with mean zero and variance{4cR2k,Tσ2t}in the caseµ=0, the joint PDF in(4)can be replaced by the following PDFp Z(η;x T,y T)≈1(2π)n−1det(Σ)exp−12(a−Hθ) Σ−1(a−Hθ)(18)whereΣ≈4cσ2t diagR22,T,R23,T,···,R2n,T.Recall the constraint(10)for the parameter vector.Hence anapproximate MLE for the location parameter vectorθis the one that minimizesJ=12(a−Hθ) Σ−1(a−Hθ)(19)subject to the constraint(10)under the condition in(17).A solution will be provided in the next section to such constrained WLS problems.In the following we provide an approximate expression of the FIM for the quasi-linear model(9)when{ηk}are approximately Gaussin distributed.Lemma2.2.Suppose that the noise vector in the quasi-linear model(9)admits an approximate joint PDF in (18).Then the associated FIM with respect to the location parameter(x T,y T)is approximately the same as in(5).Proof:DenoteθT=x T y T.Then Hθ=H1θT+bR T whereH1=2√c⎡⎢⎢⎢⎢⎣x2−x1y2−y1x3−x1y3−y1......x n−x1y n−y1⎤⎥⎥⎥⎥⎦,b=2√c⎡⎢⎢⎢⎢⎣∆ˆt2,1∆ˆt3,1...∆ˆt n,1⎤⎥⎥⎥⎥⎦.(20)Thus the quadratic function in(19)that is the exponent of the joint PDF in(18)has the formJ=12(a−bR T−H1θT) Σ−1(a−bR T−H1θT).(21)Because both Hθ=bR T+H1θT andΣin the joint PDF involve the location parameters(x T,y T),the Slepian-Bangs formula14can be applied to compute the associated FIM that is given byFIM=nk=2c24R2k,Tσ2t2x kc2+b k cos(β1)2y kc2+b k sin(β1)2x kc2+b k cos(β1)2y kc2+b k sin(β1)+nk=22R2k,Tcos(β1)sin(β1)cos(β1)sin(β1).(22)Under the condition(17),the above is dominated by theﬁrst summation leading toFIM≈nk=214c2σ2t R2k,T2x k+c2b k cos(β1)2y k+c2b k sin(β1)2x k+c2b k cos(β1)2y k+c2b k sin(β1)=nk=21c2σ2tcos(βk)−cos(β1)sin(βk)−sin(β1)cos(βk)−cos(β1)sin(βk)−sin(β1)(23)that is identical to the expression in(5).We comment that the second summation in(22)is resulted from the Bangs’formula.Under the condition(17), it is insigniﬁcant compared with theﬁrst summation implying thatFIM is insensitive to(x T,y T)embedded in the covarianceΣ.In addition Lemma2.2shows thatFIM associated with the quasi-linear model is approximately the same as the FIM associated with the nonlinear measurement model.This fact justiﬁes the formulation of the constrained WLS for computing an approximate MLE solution to source localization based on TDOA measurements.3.SOLUTION TO THE CONSTRAINED WLS PROBLEMMinimization of J in(19)subject to the constraint(10)has been tackled in6,12,13and in.3,10Several solution procedures have been developed but they all bypass the diﬃculty in solving the constrained WLS problem directly.In this section,we provide a general solution tomin θ Qθ=012(a−Hθ) Σ−1(a−Hθ)(24)The solution to the above constrained WLS is applicable to the case when the constraint is given by(θ−θ0) Q(θ−θ0)=0withθ0=0.See Remark3.2.In(24),the matrix Q is an indeﬁnite nonzero matrix with size × and matrix H has rank that is its number of columns.We employ the method of Lagrange multiplier to solve(24).Letλbe real and considerJ=12(Hθ−a) Σ−1(Hθ−a)+θ Qθ.(25)Then the necessary condition for optimality yields the conditionH Σ−1[Hθ−a]+λQθ=0⇐⇒θ=[H Σ−1H+λQ]−1H Σ−1a.(26) An optimal solution needs to satisfy the constraintθ Qθ=0leading toa Σ−1H[H Σ−1H+λQ]−1Q[H Σ−1H+λQ]−1H Σ−1a=0.(27)The solution algorithm hinges to the computation of the real rootλfrom the above equation and there can be more than one such real root.The result of simultaneous diagonalization in9can be employed for this purpose. BecauseΣ=Σ >0and Q=Q ,there exists a nonsingular matrix S such that H Σ−1H=SDΣS and Q=SD Q S where DΣand D Q are both diagonal.It is noted that DΣand D Q have the same inertia asΣand Q,respectively.It follows that(27)is equivalent to(S−1H Σ−1a) (λI+DΣD−1Q )−1D−1Q(λI+DΣD−1Q)−1(S−1H Σ−1a)=0.(28)Let D −1Q =diag(q 1,q 2,···,q ).Then it has the same number of negative and positive elements as D =D ΣD −1Q =diag(d 1,d 2,···,d )by the positivity of Σand D Σ.In fact q i d i >0.The matrices S and D can be obtained by eigenvalue decomposition of A Σ−1AQ −1=SDS −1.Let v i be the i th element of S −1H Σ−1a .Then (28)is equivalently converted into the following:(S −1H Σ−1a ) (λI +D −1Q D Σ)−1D −1Q (λI +D ΣD −1Q )−1(S −1H Σ−1a )=i =1q i v 2i (λ+d i )2=0.(29)Because Q is indeﬁnite,there is at least one strictly positive and one strictly negative element from {q i } i =1.Hence the above equation has at least one real root.However there are only ﬁnitely many real λvalues satisfying(29).In fact all the roots of the nonlinear equation in (29)are roots of the following polynomial with degree 2( −1):i =1q i v 2i k =i(λ+d k )2=0.(30)For source localization based on TDOAs,the constraint is given by (10)in which case =3implying that the computational complexity due to the roots computation is rather modest.Denote {λk }r k =1as the r real roots of (30).Now by (26),Hθ−a =[H (H Σ−1H +λk Q )−1H Σ−1−I ]a = HQ −1(λk I +H Σ−1HQ −1)−1H Σ−1−I a = (λk I +HQ −1H Σ−1)−1HQ −1H Σ−1−I a=−λk (λk I +HQ −1H Σ−1)−1a =−λk Σ(λk Σ+HQ −1H )−1aSubstituting the above into the performance index leads toJ =12λ2k a (λk Σ+HQ −1H )−1Σ(λk Σ+HQ −1H )−1a.(31)Let λopt be one of the r real roots that minimizes J over {λk }r k =1.Then in light of (26),the optimal θis obtained as θ=θopt given by θopt =[H Σ−1H +λopt Q ]−1H Σ−1a.(32)The above solution procedure is summarized into the following theorem.Theorem 3.1.Consider the constrained WLS in (24).Let H Σ−1HQ −1=SDS −1be the eigenvalue decompo-sition with {d i }eigenvalues.Then there holdH Σ−1H =SD ΣS ,Q =SD Q S ,(33)with D Σand D Q diagonal and D =D ΣD −1Q.Denote v =S −1H Σ−1a and {λk }as real roots of (30).If λopt minimizes J in (31)over {λk },then the solution to the constrained WLS is given by (32).Remark 3.2.If the quadratic constraint is δθ Qδθ=(θ−θ0) Q (θ−θ0)=0which involves θ0=0,then by Hθ=Hθ0+Hδθ,we may consider to solve alternativelymin δθ Qδθ=012[(a −Hθ0)−Hδθ] Σ−1[(a −Hθ0)−Hδθ].The above is identical to the constrained WLS in (24)with δθas unknown to which the solution procedure developed earlier is applicable.After the optimal δθopt is available,θopt =δθopt +θ0can also be obtained.It is noted that in applying the solution procedure in Theorem3.1to source localization based on TDOAs, the noise covariance matrixΣis unavailable that depends on the target location(x T,y T).As in the literature, we may setΣ=I to compute an initial location solution(ˆx(0)T,ˆy(0)T)via the constrained WLS procedure which can then be substituted intoΣto compute the solutionθopt to the corresponding constrained WLS.Although further iterations can be employed to obtain a more accurate solution,simulation results show that they are unnecessary.In fact by the proof of Lemma2.2,the second summation in the expression ofFIM in(23)is due to the Bang’s formula obtained by computing derivative ofΣwith respect to(x T,y T).This term is insigniﬁcant compared with theﬁrst summation implying that the minimum achievable error variance by unbiased estimators is insensitive to the location parameter(x T,y T)embedded inΣ.Therefore it is adequate to compute the solution to the constrained WLS twice.Finally we would like to comment that the constrained WLS solution is an approximate MLE solution to the source localization problem based on TDOAs by treating measured TDOAs{∆ˆt k,1}n k=2as deterministic quantities.That is,it is an approximate MLE solution conditioned on the measured TDOAs.However it is also important to observe that even if we treat{∆ˆt k,1}n k=2as random,the constrained WLS solution is still an approximate MLE solution.Recall that a WLS solution can be obtained by choosing a perturbation vectorˆ∆a that has the smallest Euclidean norm such that16rankΣ−1/2HΣ−1/2a+ˆ∆a=rankΣ−1/2H(34)and then solveΣ−1/2Hθ=Σ−1/2a+ˆ∆a.Basically the imperfect measurements in a are removed byˆ∆a.It is noted that the third column of H,or b in(20),involves imperfect measurements as well.However the variance of the measurement noise in vector b is only4cσ2t,much smaller than4cσ2t R2k,T(variances ofηk)under the condition(17).Hence it is unnecessary to introduce the perturbation to the third column of H that does not aﬀect the approximate MLE estimate that is validated in our simulation study,although not reported here.4.CONCLUDING REMARKSThe problem of passive localization has been investigated based on TDOA measurements which is a nonlinear estimation problem.It has been shown that the nonlinear term in the quasi-linear measurement equations can be treated as a constraint which is in fact a quadratic constraint.A numerical procedure based on simultaneous diagonalization is developed to compute the weighted LS(LS)solution under the quadratic constraint.This new procedure is shown to be an approximate MLE solution under the assumption that the ratios of the distances between all but one sensor and the target to the noise variance in TDOA measurements are suitably large.Because of the space limit,the simulation results are not presented in the present conference version.As concluding remarks,we comment that the assumption on uncorrelated TDOA measurement noises can be removed.Such an assumption is in fact not used in deriving the constrained WLS solution.That is,the solution procedure summarized in Theorem3.1is applicable to the case whenΣis an arbitrary symmetric positive deﬁnite matrix. See also the results in3for the derivation of the various covariance matrices when the TDOA measurement noises are correlated.We also comment that the moving source localization studied in10involves two quadratic constraints to which a similar constrained WLS solution can be derived.However it involves roots computation for two2-variate polynomials which has high complexity.How to bypass such a high complexity is currently under study.REFERENCES1.J.S.Abel and J.O.Smith,“Source range and depth estimation from multipath range diﬀerence measure-ments,”IEEE Trans.Acoust.Speech,Signal Processing,vol.37,pp.1157-1165,Aug.1989.2.G.C.Carter,“Time delay estimation for passive sonar signal processing,”IEEE Trans.Acoust.Speech,Signal Processing,vol.29,pp.463-470,June1981.3.Y.T.Chan and K.C.Ho,“A simple and eﬃcient estimator for hyperbolic location,”IEEE Trans.SignalProcessing,vol.42,pp.1905-1915,Aug.1994.4.B.T.Fang,“Simple solutions for hyperbolic and related positionﬁxes,”IEEE Trans.Aerosp.Electron.Syst.,vol.26,pp.748-753,Sept.1990.5.W.H.Foy,“Position-location solutions by Taylor-series estimation,”IEEE Trans.Aerosp.Electron.Syst.,vol.12,pp.187-194,Mar.1976.6.B.Friedlander,“A passive localization algorithm and its accuracy analysis,”IEEE J.Ocean.Eng.,vol.12,pp.234-245,Jan.1987.7.G.Gu,“Target localization based on TDOAs and FDOAs,”Quarterly report to Sensor Directorate,WPAFB,March2006.8.W.R.Hahn and S.A.Tretter,“Optimum processing for delay-vector estimation in passive signal arrays,”IEEE rm.Theory,vol.19,pp.608-614,Sept.1973.9.R.A.Horn and C.R.Johnson,Matrix Analysis,Cambridge University Press,reprinted in1999.10.K.C.Ho and W.Xu,“An accurate algebraic solution for moving source location using TDOA and FDOAmeasurements,”IEEE Trans.Signal Processing,vol.52,pp.2453-2463,Sept.2004.11.A.H.Sayed,A.Tarighat,and N.Khajehnouri,“Network-based wireless location,”IEEE Signal ProcessingMagazine,vol.22,pp.24-40,July2005.12.H.C.Schau and A.Z.Robinson,“Passive source localization employing intersecting spherical surfaces fromtime-of-arrival diﬀerences,”IEEE Trans.Acoust.Speech,Signal Processing,vol.35,pp.1223-1225,Aug.1987.13.J.O.Smith and J.S.Abel,“Closed-form least-squares source location estimation from range-diﬀerence mea-surements,”IEEE Trans.Acoust.Speech,Signal Processing,vol.35,pp.1661-1669,Dec.1987.14.P.Stoica and R.Moses,Introduction to Spectral Analysis,Prentice-Hall,Upper-Saddle River,NJ,1997.15.D.J.Torrieri,“Statistical theory of passive location systems,”IEEE Trans.Aerosp.Elect.Syst.,vol.20,pp.183-198,Mar.1984.16.S.van Huﬀel and J.Vandewalle,The Total Least Squares problem:Computational Aspects and Analysis,SIAM Publisher,1991.。

激光与视觉融合的透视平面检测与深度预测研究

计算机测量与控制．２０２１．２９（１１）　犆狅犿狆狌狋犲狉犕犲犪狊狌狉犲犿犲狀狋牔犆狅狀狋狉狅犾　·２９　·收稿日期：２０２１０３１７；　修回日期：２０２１０５０６。

基金项目：国家自然科学基金（６１７０２０２０）；北京市自然科学基金（４１７２０１３）；北京市自然科学基金－海淀原始创新联合基金（Ｌ１８２００７）。

作者简介：赵宇琦（１９９７），男，北京人，硕士生，主要从事机器视觉，三维重建方向的研究。

引用格式：赵宇琦，连晓峰，王宇龙，等．激光与视觉融合的透视平面检测与深度预测研究［Ｊ］．计算机测量与控制，２０２１，２９（１１）：２９３４．文章编号：１６７１４５９８（２０２１）１１００２９０６ＤＯＩ：１０．１６５２６／ｊ．ｃｎｋｉ．１１－４７６２／ｔｐ．２０２１．１１．００６中图分类号：ＴＰ３９１．４１文献标识码：Ａ激光与视觉融合的透视平面检测与深度预测研究赵宇琦１，连晓峰１，王宇龙２，田梓薇１，徐晨星１（１．北京工商大学人工智能学院，北京　１０００４８；２．中国兵器工业信息中心，北京　１０００８９）摘要：针对单一的激光传感器或视觉传感器无法检测到透视三维平面的问题，提出一种基于激光传感器与视觉传感器融合的透视平面检测与深度预测算法；首先采用透视平面检测网络，在二维彩色图像中对透视平面进行图像分割；其次应用单一图像反射去除算法，在分割得到的透视平面区域分离背景信息，并使用ＭｅｇａＤｅｐｔｈ算法进行深度预测，得到相对深度图；最后结合激光传感器的深度数据，采用抽样一致性算法，计算深度标尺，并使用对透视平面进行深度赋值，将相对深度图转化为绝对深度图，进而完成对透视平面的深度预测；实验结果表明该算法能成功检测并分割透视平面，且能得到正确的透视平面绝对深度信息。

关键词：视觉与激光融合；数据融合；平面检测；深度估计；随机抽样一致性犚犲狊犲犪狉犮犺狅狀犌犾犪狊狊犘犾犪狀犲犇犲狋犲犮狋犻狅狀犪狀犱犇犲狆狋犺犘狉犲犱犻犮狋犻狅狀犅犪狊犲犱狅狀犉狌狊犻狅狀狅犳犔犪狊犲狉犪狀犱犆犪犿犲狉犪ＺＨＡＯＹｕｑｉ１，ＬＩＡＮＸｉａｏｆｅｎｇ１，ＷＡＮＧＹｕｌｏｎｇ２，ＴＩＡＮＺｉｗｅｉ１，ＸＵＣｈｅｎｘｉｎｇ１（１．ＳｃｈｏｏｌｏｆＡＩ，ＢｅｉｊｉｎｇＴｅｃｈｎｏｌｏｇｙａｎｄＢｕｓｉｎｅｓｓＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ　１０００４８，Ｃｈｉｎａ；２．ＣｈｉｎａＯｒｄｎａｎｃｅＩｎｄｕｓｔｒｙＩｎｆｏｒｍａｔｉｏｎＣｅｎｔｅｒ，Ｂｅｉｊｉｎｇ　１０００８９，Ｃｈｉｎａ）犃犫狊狋狉犪犮狋：Ａｉｍｉｎｇａｔｔｈｅｐｒｏｂｌｅｍｔｈａｔａｓｉｎｇｌｅｌａｓｅｒｓｅｎｓｏｒｏｒｖｉｓｉｏｎｓｅｎｓｏｒｃａｎｎｏｔｄｅｔｅｃｔｔｈｅｐｅｒｓｐｅｃｔｉｖｅｔｈｒｅｅ－ｄｉｍｅｎｓｉｏｎａｌｐｌａｎｅ，ａｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅｄｅｔｅｃｔｉｏｎａｎｄｄｅｐｔｈｐｒｅｄｉｃｔｉｏｎａｌｇｏｒｉｔｈｍｂａｓｅｄｏｎｔｈｅｆｕｓｉｏｎｏｆｌａｓｅｒｓｅｎｓｏｒａｎｄｖｉｓｉｏｎｓｅｎｓｏｒｉｓｐｒｏｐｏｓｅｄ．Ｆｉｒｓｔｌｙ，ｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅｄｅｔｅｃｔｉｏｎｎｅｔｗｏｒｋｉｓｕｓｅｄｔｏｓｅｇｍｅｎｔｔｈｅｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅｉｎａｔｗｏ－ｄｉｍｅｎｓｉｏｎａｌｃｏｌｏｒｉｍａｇｅ；ｓｅｃｏｎｄｌｙ，ａｓｉｎｇｌｅｉｍａｇｅｒｅｆｌｅｃｔｉｏｎｒｅｍｏｖａｌａｌｇｏｒｉｔｈｍｉｓａｐｐｌｉｅｄｔｏｓｅｐａｒａｔｅｔｈｅｂａｃｋｇｒｏｕｎｄｉｎｆｏｒｍａｔｉｏｎｉｎｔｈｅｓｅｇｍｅｎｔｅｄｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅａｒｅａ，ａｎｄｔｈｅＭｅｇａＤｅｐｔｈａｌｇｏｒｉｔｈｍｉｓｕｓｅｄｆｏｒｄｅｐｔｈｐｒｅｄｉｃｔｉｏｎｔｏｏｂｔａｉｎａｒｅｌａｔｉｖｅｄｅｐｔｈｍａｐ；ａｎｄｆｉｎａｌｌｙｃｏｍｂｉｎｉｎｇｔｈｅｄｅｐｔｈｄａｔａｏｆｔｈｅｌａｓｅｒｓｅｎｓｏｒ，ｔｈｅｓａｍｐｌｉｎｇｃｏｎｓｉｓｔｅｎｃｙａｌｇｏｒｉｔｈｍｉｓｕｓｅｄｔｏｃａｌｃｕｌａｔｅｔｈｅｄｅｐｔｈｓｃａｌｅ，ａｎｄｔｈｅｄｅｐｔｈａｓｓｉｇｎｍｅｎｔｔｏｔｈｅｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅｉｓｕｓｅｄｔｏｃｏｎｖｅｒｔｔｈｅｒｅｌａｔｉｖｅｄｅｐｔｈｍａｐｉｎｔｏａｎａｂｓｏｌｕｔｅｄｅｐｔｈｍａｐ，ａｎｄｔｈｅｎｃｏｍｐｌｅｔｅｔｈｅｄｅｐｔｈｐｒｅｄｉｃｔｉｏｎｏｆｔｈｅｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅ．Ｔｈｅｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅａｌｇｏｒｉｔｈｍｃａｎｓｕｃｃｅｓｓｆｕｌｌｙｄｅｔｅｃｔａｎｄｓｅｇｍｅｎｔｔｈｅｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅ，ａｎｄｃａｎｏｂｔａｉｎｔｈｅｃｏｒｒｅｃｔａｂｓｏｌｕｔｅｄｅｐｔｈｉｎｆｏｒｍａｔｉｏｎｏｆｔｈｅｐｅｒｓｐｅｃｔｉｖｅｐｌａｎｅ．犓犲狔狑狅狉犱狊：ｃａｍｅｒａａｎｄｌａｓｅｒｆｕｓｉｏｎ；ｄａｔａｆｕｓｉｏｎ；ｐｌａｎｅｄｅｔｅｃｔｉｏｎ；ｄｅｐｔｈｅｓｔｉｍａｔｉｏｎ；ｒａｎｄｏｍｓａｍｐｌｅｃｏｎｓｅｎｓｕｓ（ＲＡＮＳＡＣ）０　引言透视平面通常具有广泛的实用和装饰用途，由于其透光无色的特性，通常是一种非晶态的无定形的固体，其透光无色的特性会对现有的计算机视觉系统与激光传感器系统造成严重的干扰（如深度预测［１］和激光测距［２］）：视觉传感器及其算法无法分辨透视平面，且由于视觉传感器提供的图像只有二维的信息，所以通常会误判透视平面后的信息；又由于透视平面通常为无色透光平面，会对激光传感器测量的距离信息造成严重影响，使其接收错误的深度信息。

基于单目深度估计的输电线路防外破监测方法

TECHNOLOGY AND INFORMATION科学与信息化2023年11月下 73基于单目深度估计的输电线路防外破监测方法*陈华超1 李刚领2（通讯作者）廖承就1 张惠荣1 张磊21. 广东电网有限责任公司惠州供电局广东惠州 516000；2. 广州中科智巡科技有限公司广东广州 510623摘要基于单目摄像机，提出一种结合目标检测与单目深度估计的输电线路防外破监测方法，在采用目标检测模型获取图像内施工机械位置信息的基础上，结合Transformer编码器（一种采用自注意力机制的深度学习模型）和CNN解码器（一种采用卷积神经网络的深度学习模型）的强大性能，直接建立RGB彩色像素与深度值之间的关系映射，在单一图像上进行深度估计。

关键词 Transformer编码器；CNN解码器；深度估计模型Monitoring Method for Transmission Line External Breakage Prevention Based on Monocular Depth Estimation Chen Hua-chao 1, Li Gang-ling 2(corresponding author), Liao Cheng-jiu 1, Zhang Hui-rong 1, Zhang Lei 21. Guangdong Power Grid Corporation Huizhou Power Supply Bureau, Huizhou 516000, Guangdong Province, China;2. Guangzhou Zhongke I-Inspection Technology Company Ltd., Guangzhou 510623, Guangdong Province, ChinaAbstract Based on the monocular camera, a transmission line external breakage prevention monitoring method is proposed, which uses the object detection model to obtain the position information of construction machinery in the image, combines with the powerful performance of Transformer encoder (a deep learning model using self-attention mechanism) and CNN decoder (a deep learning model using convolutional neural network), the relationship mapping between RGB color pixels and depth values is directly established to perform depth estimation on a single image.Key words Transformer encoder; CNN decoder; depth estimation model引言目前输电线路防外破监测的方式主要为视频监控，利用网络摄像机实时回传线路的监控画面，由工作人员判断线路是否存在外力破坏隐患，可以实现了输电线路状态与外力破坏风险的集中监测。

基于深度学习的单目图像深度估计

摘要图像深度估计是计算机视觉领域中一项重要的研究课题。

深度信息是理解一个场景三维结构关系的重要组成部分，准确的深度信息能够帮助我们更好地进行场景理解。

在真三维显示、语义分割、自动驾驶及三维重建等多个领域都有着广泛的应用。

传统方法多是利用双目或多目图像进行深度估计，最常用的方法是立体匹配技术，利用三角测量法从图像中估计场景深度信息，但容易受到场景多样性的影响，而且计算量很大。

单目图像的获取对设备数量和环境条件要求较低，通过单目图像进行深度估计更贴近实际情况，应用场景更广泛。

深度学习的迅猛发展，使得基于卷积神经网络的方法在单目图像深度估计领域取得了一定的成果，成为图像深度估计领域的研究热点。

但是单目深度估计仍面临着许多挑战：复杂场景中的复杂纹理和复杂几何结构会导致大量深度误差，容易造成局部细节信息丢失、物体边界扭曲及模糊重建等问题，直接影响图像的恢复精度。

针对上述问题，本文主要研究基于深度学习的单目图像深度估计方法。

主要工作包括以下两个方面：（1）针对室内场景中复杂纹理和复杂几何结构造成的物体边界扭曲、局部细节信息丢失等问题，提出一种基于多尺度残差金字塔注意力网络模型。

首先，提出了一个多尺度注意力上下文聚合模块，该模块由两部分组成：空间注意力模型和全局注意力模型，通过从空间和全局分别考虑像素的位置相关性和尺度相关性，捕获特征的空间上下文信息和尺度上下文信息。

该模块通过聚合特征的空间和尺度上下文信息，自适应地学习像素之间的相似性，从而获取图像更多的全局上下文信息，解决场景中复杂结构导致的问题。

然后，针对场景理解中物体的局部细节容易被忽略的问题，提出了一个增强的残差细化模块，在获取多尺度特征的同时，获取更深层次的语义信息和更多的细节信息，进一步细化场景结构。

在NYU Depth V2数据集上的实验结果表明，该方法在物体边界和局部细节具有较好的性能。

（2）针对已有非监督深度估计方法中细节信息预测不够准确、模糊重建等问题，结合Non-local能够提取每个像素的长期空间依赖关系，获取更多空间上下文的原理，本文通过引入Non-local提出了一种新的非监督学习深度估计模型。

测绘类词汇中英文对照(2)

测绘类词汇中英文对照（２）开采沉陷观测mining subsidence observation开采沉陷图map of mining subsidence开窗windowing勘测设计阶段测量survey in reconnaissance and design stage 勘探基线prospecting baseline勘探网测设prospecting network layout勘探线测量prospecting line survey勘探线剖面图prospecting line profile map康索尔海图Consol chart康索尔海图Consol chart抗差估计，*稳健估计robust estimation考古摄影测量archaeological photogrammetry克拉索夫斯基椭球Krasovsky ellipsoid克莱罗定理Clairaut theorem克莱罗定理Clairaut theorem刻绘scribing刻图仪scriber坑道平面图Adit planimetric坑探工程测量Adit prospecting engineering survey空基系统space-based system空间大地测量学space geodesy空间改正free-air correction空间后方交会space resection空间前方交会space intersection空间试验室Spacelab空间数据管理系统spatial database management system空间数据基础设施SDI空间数据基础设施spatial data infrastructure空间数据转换spatial data transfer空间信息可视化visualization of spatial information空间异常free-air anomaly空中导线测量aerophotogonometry空中三角测量aerotriangulation空中水准测量aeroleveling控制测量control survey控制测量control survey控制点control point控制点control point库容测量reservoir storage survey跨河水准测量river-crossing leveling块状图block diagram快门shutter矿产图map of mineral deposits矿场平面图mining yard plan矿区控制测量control survey of mining area矿区控制测量control survey of mining area矿山测量mine survey矿山测量交换图exchanging documents of mining survey 矿山测量图mining map矿山测量学mine surveying矿山经纬仪mining theodolite矿体几何[学] mineral deposits geometry矿体几何制图geometrisation of ore body框标fiducial mark框幅摄影机frame camera拉普拉斯点Laplace point拉普拉斯方位角Laplace azimuth兰勃特投影Lambert projection蓝底图blue key浪花Breaker勒夫数Love's number雷达测高仪radar altimeter雷达覆盖区radar overlay雷达应答器radar responder雷达指向标radar ramark类别视觉感受perceptual groupings类型地图typal map离心力centrifugal force离心力centrifugal force离心力位potential of centrifugal force礼炮号航天站Salyut Space Station理论地图学theoretical cartography理论最低低潮面lowest normal low water理论最高潮面highest normal high water历史地图historic map历元平极mean pole of the epoch立标Beacon立井导入高程测量induction height survey through shaft 立井定向测量shaft orientation survey立井激光指向[法] laser guide of vertical shaft立体测图仪stereoplotter立体地图relief map立体观测stereoscopic observation立体观测模型stereoscopic model立体镜stereoscope立体判读仪stereointerpretoscope立体摄影测量stereophotogrammetry立体摄影机stereocamera立体摄影机stereometric camera立体视觉stereoscopic vision立体像对stereopair立体坐标量测量stereocomparator粒子加速器测量particle accelerator survey 连接点tie point连续调continuous tone连续调continuous tone连续对比successive contrast连续方式continuous mode连续方式continuous mode连续减光板continuous attenuator连续减光板continuous attenuator帘幕式快门，*焦面快门curtain shutter帘幕式快门，*焦面快门curtain shutter帘幕式快门，*焦面快门focal plane shutter 联测比对comparison survey联测比对comparison survey联合平差combined adjustment联合平差combined adjustment联盟号宇宙飞船Soyuz Spacecraft联系测量connection survey联系测量connection survey联系三角形法connection triangle method 联系三角形法connection triangle method 联系数correlate联系数correlate亮度lightness量测摄影机metric camera量底法quantity base method量化quantization量化quantizing裂缝观测fissure observation邻带方里网grid of neighboring zone邻图拼接比对comparison with adjacent chart邻图拼接比对comparison with adjacent chart邻元法neighborhood method邻元法neighborhood method林业测量forest survey林业基本图forest basic map零[位]线改正correction of zero line零[位]线改正correction of zero line零漂改正correction of zero drift零漂改正correction of zero drift零相位效应zero-phase effect领海基线测量territorial sea baseline survey六分仪sextant鲁洛夫斯太阳棱镜Roelofs solar prism陆地卫星Landsat滤光片Filter旅游地图tourist map略最低低潮面，*印度大潮低潮面Indian spring low water 略最低低潮面，*印度大潮低潮面lower low water罗经[校正]标compass adjustment beacon罗经[校正]标compass adjustment beacon罗兰-C定位系统Loran-C positioning system罗兰海图Loran chart罗盘经纬仪compass theodolite罗盘经纬仪compass theodolite罗盘仪compass罗盘仪compass罗盘仪测量compass survey罗盘仪测量compass survey逻辑兼容，*逻辑一致性logical consistency芒塞尔色系Munsell color system锚地Anchorage锚位anchorage berth卯酉面prime vertical plane卯酉圈prime vertical卯酉圈曲率半径radius of curvature in prime vertical 蒙绘mask artwork蒙绘，*透写图tracing蒙片mask面水准测量area leveling面状符号area symbol瞄直法sighting line method名义量表nominal scaling名义量表nominal scaling明礁bare rock模糊分类法fuzzy classifier method模糊影像fuzzy image模拟磁带analog tape模拟地图analog map模拟法测图analog photogrammetric plotting模拟空中三角测量analog aerotriangulation模拟立体测图仪analog stereoplotter模拟摄影测量analog photogrammetry模式识别pattern recognition模型连接bridging of model模型缩放scaling of model模型置平leveling of model莫洛坚斯基公式Molodensky formula莫洛坚斯基理论Molodensky theory墨卡托海图Mercator chart墨卡托投影Mercator projection目标发射器target reflector目标区target area目视判读visual interpretation目视天顶仪visual zenith telescope内部定向interior orientation能见度visibility能见敏锐度visibility acuity拟稳平差quasi-stable adjustment逆转点法reversal points method年平均海面annual mean sea level鸟瞰图bird's eye view map欧洲遥感卫星ERS欧洲遥感卫星Europe Remote Sensing Satellite 偶然误差accident error偶然误差random error判读，*判释，*解释interpretation判读仪interpretoscope旁向倾角lateral tilt旁向倾角roll旁向重叠lateral overlap旁向重叠side lap旁向重叠side overlap偏角法method of deflection angle偏振光立体观察vectograph method of stereoscopic viewing 频率误差frequency error频偏frequency offset频漂frequency drift平板仪plane-table平板仪测量plane-table survey平板仪导线plane-table traverse平差值adjusted value平衡潮equilibrium tide平极mean pole平均地球椭球mean earth ellipsoid平均海[水]面mean sea level平均海面归算seasonal correction of mean sea level平均曲率半径mean radius of curvature平均误差average error平均运动mean motion平面控制点horizontal control point平面控制网，*水平控制网horizontal control network平面曲线测设plane curve location平面图plane平面坐标horizontal coordinate平时钟mean-time clock平行圈parallel circle平移参数translation parameters平整土地测量survey for land consolidation平整土地测量survey for land smoothing屏幕地图screen map坡度测设grade location坡面经纬仪slope theodolite剖面图Profiles普拉烈系统PRARE普拉烈系统Precise Range and Rangerate Equipment 普通地图general map普通地图集general atlas普通海图general chart曝光exposure气体激光器gas laser气象代表误差meteorological representation error恰可察觉差JND恰可察觉差just noticeable difference千米尺kilometer scale铅垂线plumb line前方交会[forward] intersection钱德勒摆动Chandler wobble钱德勒摆动Chandler wobble浅地层剖面仪sub-bottom profiler浅色调tint浅滩shoal桥墩定位location of pier桥梁测量bridge survey桥梁控制测量bridge construction control survey桥梁轴线测设bridge axis location切线支距法tangent off-set method切向畸变tangential distortion切向畸变tangential lens distortion倾斜观测tilt observation倾斜位移tilt displacement倾斜仪clinometer倾斜仪clinometer清绘fair drawing求积仪planimeter求积仪platometer球面投影stereographic projection球心投影，*大环投影gnomonic projection区划地图regionalization map区域地图集regional atlas区域地质调查regional geological survey区域地质图regional geological map区域网平差block adjustment曲线光滑line smoothing全景畸变panoramic distortion全景摄影panoramic photography全景摄影机panorama camera全景摄影机panoramic camera全能法测图universal method of photogrammetric mapping 全球导航卫星系统Global Navigation Satellite System全球导航卫星系统GLONASS全球定位系统global positioning system全球定位系统GPS全色红外片panchromatic infrared film全色片panchromatic film全息摄影hologram photography全息摄影holography全息摄影测量hologrammetry全组合测角法method in all combinations权weight权函数weight function权矩阵weight matrix权逆阵inverse of weight matrix权系数weight coefficient热辐射thermal radiation热红外线图像thermal infrared imagery热红外线图像thermal IR imagery人工标志[点] artificial target人机交互处理interactive processing人口地图population map人文地图human map人仪差personal and instrumental equation认知制图cognitive mapping认知制图cognitive mapping任意比例尺arbitrary scale任意投影arbitrary projection任意轴子午线arbitrary axis meridian日月引力摄动lunisolar gravitational perturbation 冗余码redundant code冗余信息redundant information儒略日Julian Day三边测量trilateration survey三边网trilateration network三差相位观测triple difference phase observation 三杆分度仪three-arm protractor三角测量triangulation三角点triangulation point三角高程测量trigonometric leveling三角高程导线polygonal height traverse三角高程网trigonometric leveling network三角基座tribrach三角锁triangulation chain三角网triangulation network三脚架tripod三维地景仿真three-dimensional terrain simulation 三维网three-dimensional network扫海测量sweep扫海测量wire drag survey扫海测深仪sweeping sounder扫海具sweeper扫海区swept area扫海深度sweeping depth扫海趟sweeping trains扫雷区mine-sweeping area扫描数字化scan-digitizing扫描仪scanner色彩管理系统color management system色彩管理系统color management system色调tone色环color wheel色环color wheel色盲片achromatic film色相hue森林分布图forest distribution map晒版plate copying晒版printing down闪闭法立体观察blinking method of stereoscopic viewing 扇谐系数coefficient of sectorial harmonics扇谐系数coefficient of sectorial harmonics熵编码entropy coding上下视差vertical parallax上下视差y-parallax摄谱仪spectrograph摄影比例尺photographic scale摄影测量畸变差，*畸变差photogrammetric distortion摄影测量内插photogrammetric interpolation摄影测量学photogrammetry摄影测量仪器photogrammetric instrument摄影测量与遥感学photogrammetry and remote sensing 摄影测量坐标系photogrammetric coordinate system摄影处理photographic processing摄影分区flight block摄影航线flight line of aerial photography摄影机检校camera caliberation摄影机检校camera caliberation摄影机主距principal distance of camera摄影基线air base摄影基线photographic baseline摄影经纬仪camera transit摄影经纬仪camera transit摄影经纬仪photo theodolite摄影学photography摄站camera station摄站camera station摄站exposure station伸缩仪extensometer深度基准sounding datum深度基准面保证率assuring rate of depth datum深色调shade甚长基线干涉测量very long baseline interferometry生物量指标变换biomass index transformation生物医学摄影测量biomedical photogrammetry声呐扫海sonar sweeping声呐图像sonar image声速改正correction of sounding wave velocity声速改正correction of sounding wave velocity声速计velociment声图判读interpretation of echograms声学多普勒海流剖面仪acoustic Doppler current profiler 声学多普勒海流剖面仪ADCP声学水位计acoustic water level失锁loss of lock施工测量construction survey施工测量construction survey施工方格网square control network施工控制网construction control network施工控制网construction control network石英弹簧重力仪quartz spring gravimeter石油勘探测量petroleum exploration survey时号time signal时号改正数correction to time signal时号改正数correction to time signal时钟频率clock frequency时钟频率clock frequency识别码identification code实时处理real-time processing实时摄影测量real-time photogrammetry 实用地图学applied cartography矢量绘图vector plotting矢量数据vector data矢量重力测量vector gravimetry世界地图集world atlas世界时universal time世界时UT市政工程测量public engineering survey 示坡线slope line视差Parallax视场对比simultaneous contrast视地平线apparent horizon视距sighting distance视距乘常数stadia multiplication constant 视距导线stadia traverse视距加常数stadia addition constant视觉变量visual variable视觉层次visual hierarchy视觉对比visual contrast视觉分辨敏锐度resolution acuity视觉立体地图stereoscopic map视觉平衡visual balance视模型perceived model视线高程elevation of sight视准线法collimation line method视准线法collimation line method适淹礁rock awash适应性水平adaptation level收时time receiving手持水准仪hand level首曲线intermediate contour艏向heading输电线路测量power transmission line survey输油管道测量petroleum pipeline survey鼠标[器] mouse竖盘指标差index error of vertical circle竖盘指标差vertical collimation error竖曲线测设vertical curve location竖直摄影vertical photography数量感quantitative perception数学地图学mathematical cartography数值地籍numerical cadastre数值地籍numerical cadastre数字地图产品标准product standard of digital map双标准纬线投影projection with two standard parallels 双介质摄影测量two-medium photogrammetry双曲线导航图hyperbolic navigation chart双曲线定位，*测距差定位hyperbolic positioning双曲线定位系统hyperbolic positioning system双曲线格网hyperbolic positioning grid双色激光测距仪two-color laser ranger双向航道two-way route水尺tide staff水库测量reservoir survey水库淹没线测设setting-out of reservoir flooded line水雷[危险]区mine [dangerous] area水利工程测量hydrographic engineering survey水面水准surface level水平角horizontal angle水平折光差horizontal refraction error水汽辐射仪water vapor radiometer水深soundings水深测量sounding水深测量自动化系统automatic hydrographic survey system 水声定位acoustic positioning水声定位系统acoustic positioning system水声全息系统acoustic holography system水声应答器acoustic responder水铊lead水听器hydrophorce水位water level水位分带改正correction of tidal zoning水位分带改正correction of tidal zoning水位改正correction of water level水位改正correction of water level水位曲线curves of water level水位曲线curves of water level水位遥报仪communication device of water level水位遥报仪communication device of water level水文观测，*水文测验hydrometry水文要素hydrologic features水下摄影测量underwater photogrammetry水下摄影机underwater camera水准测量leveling surveying水准尺leveling staff水准点Benchmark水准路线leveling line水准面level surface水准器Bubble水准网leveling network水准仪，*水准器level水准原点leveling origin瞬间地图twinkling map瞬时极instantaneous pole瞬时视场IFOV瞬时视场instantaneous field of view丝网印刷silk-screen printing斯托克斯公式Stokes formula斯托克斯理论Stokes theory撕膜片peel-coat film四色印刷four color printing似大地水准面quasi-geoid搜索区searching area岁差precession隧道测量tunnel survey穗帽变换tasseled cap transformation缩微地图microfilm map缩微摄影microcopying缩微摄影microphotography缩小仪photoreducer塔尔科特测纬度法Talcott method of latitude determination台链station chain太阳辐射波谱solar radiation spectrum太阳光压摄动solar radiation pressure perturbation太阳同步卫星sun-synchronous satellite态势地图posture map特殊水深special depth特征feature特征编码feature coding特征码feature codes特征码清单feature codes menu特征提取feature extraction特征选择feature selection特种地图particular map体素voxel天波干扰sky-wave interference天波修正sky-wave correction天顶距zenith angle天顶距zenith distance天球坐标系celestial coordinate system天球坐标系celestial coordinate system天文大地垂线偏差astro-geodetic deflection of the vertical 天文大地网astro-geodetic network天文大地网平差Adjustment of astrogeodetic network天文点astronomical point天文定位系统astronomical positioning system天文方位角astronomical azimuth天文经度astronomical longitude天文经纬仪astronomical theodolite天文年历astronomical almanac天文年历astronomical ephemeris天文水准astronomical leveling天文纬度astronomical latitude天文重力水准astro-gravimetric leveling天文坐标测量仪astronomical coordinate measuring instrument 天线高度antenna height田谐系数coefficient of tesseral harmonics田谐系数coefficient of tesseral harmonics条幅[航带]摄影机continuous strip camera条幅[航带]摄影机continuous strip camera条幅[航带]摄影机strip camera条件方程condition equation条件方程condition equation条件平差condition adjustment条件平差condition adjustment铁路工程测量railroad engineering survey通用横墨尔卡投影Universal Transverse Mercator projection 通用极球面投影Universal Polar Stereographic projection通用极球面投影UPS通用墨卡尔投影UTM同步观测simultaneous observation同步验潮tidal synobservation同名光线corresponding image rays同名光线corresponding image rays同名核线corresponding epipolar line同名核线corresponding epipolar line同名像点corresponding image points同名像点corresponding image points同名像点homologous image points统计地图statistic map投影变换projection transformation投影差height displacement投影差relied displacement投影方程projection equation投影器Projector投影器主距principal distance of projector投影晒印projection printing透光率transmittance透明负片transparent negative透明正片transparent positive透明注记stick-up lettering透视截面法perspective traces透视投影perspective projection透视旋转定律，*沙尔定律Chasles theorem透视旋转定律，*沙尔定律Chasles theorem透视旋转定律，*沙尔定律rotation axiom of the perspective 透视旋转定律，*沙尔定律rotational theorem图幅mapsheet图幅编号sheet designation图幅编号sheet number图幅接边edge matching图幅接合表index diagram图幅接合表sheet index图根点mapping control point图根控制mapping control图解纠正graphical rectification图解图根点graphic mapping control point图廓edge of the format图廓map border图历簿mapping recorded file图例legend图面配置map layout图象picture图像编码image coding图像变换image transformation图像处理image processing图像分割image segmentation图像分析image analysis图像复合image overlaying图像几何纠正geometric rectification of imagery 图像几何配准geometric registration of imagery 图像理解image understanding图像描述image description图像识别image recognition图像数字化image digitization图像增强image enhancement图形graphics图形-背景辨别F-G discrimination图形-背景辨别Figure-ground discrimination图形符号graphic symbol图形记号graphic sign图形权倒数weight reciprocal figure图形元素graphic elements土地规划测量land planning survey土地利用现状图present landuse map土地信息系统land information system土地信息系统LIS推荐航线recommended route托帕可斯卫星T/P托帕克斯卫星TOPEX/POSEIDON拖底扫海aground sweeping陀螺定向光电测距导线gyrophic EDM traverse陀螺方位角gyro azimuth陀螺经纬仪gyro theodolite陀螺经纬仪gyroscopic theodolite陀螺仪定向测量gyrostatic orientation survey椭球扁率flattening of ellipsoid椭球长半轴，*地球长半轴semimajor axis of ellipsoid 椭球短半轴，*地球短半轴semiminor axis of ellipsoid 椭球面大地测量学ellipsoidal geodesy椭球偏心率eccentricity of ellipsoid拓扑地图topological map拓扑关系topological relation拓扑检索topological retrieval外部定向exterior orientation网点stipple网格地图grid map网格法grid method网格结构grid structure网屏screen网纹片transparent foil网线ruling危险界限limiting danger line微波测距仪microwave distance measuring instrument 微波辐射microwave radiation微波辐射计microwave radiometer微波图像microwave imagery微波遥感microwave remote sensing微波遥感器microwave remote sensor微重力测量microgravimetry维纳频谱Winer spectrum维宁•曼尼斯公式V ening-Meinesz formula伪彩色图像pseudo-color image伪等值线地图pseudo-isoline map伪距测量pseudo-range measurement卫星测高satellite altimetry卫星大地测量satellite geodesy卫星定位satellite positioning卫星多普勒[频移]测量satellite Doppler shift measurement卫星多普勒定位satellite Doppler positioning卫星高度satellite altitude卫星跟踪卫星技术satellite-to-satellite tracking卫星跟踪卫星技术SST卫星跟踪站satellite tracking station卫星共振分析analysis of satellite resonance卫星构形satellite configuration卫星-惯导组合定位系统satellite-inertial guidance integrated positioning sy卫星轨道改进improvement of satellite orbit卫星激光测距satellite laser ranging卫星激光测距，侧视雷达SLR卫星激光测距仪satellite laser ranger卫星-声学组合定位系统satellite-acoustics integrated positioning system卫星受摄运动perturbed motion of satellite卫星像片图satellite photo map卫星星下点sub-satellite point卫星运动方程equation of satellite motion卫星重力梯度测量satellite gradiometry卫星姿态satellite attitude位置[线交]角intersection angle of LOP位置函数，*坐标函数position function位置精度positional accuracy位置线line of position位置线LOP位置线方程equation of LOP文化地图cultural map文化地图cultural map纹理分析texture analysis纹理增强texture enhancement沃尔什变换Walsh transformation无线电定位radio positioning无线电航行警告radio navigational warning无线电指向标，*电指向radio beacon无线电指向标表list of radio beacon五角棱镜pentaprism物镜分辨力resolving power of lens物理大地测量学，*大地重力学physical geodesy 误差检验error test误差理论theory of errors误差椭圆error ellipse雾[信]号fog signal系列地图series maps系统集成system integration系统误差systematic error弦线支距法Chord off-set method弦线支距法Chord off-set method显微摄影photomicrography现势地图up-to-data map线路平面图route plan线路水准测量route leveling线路中线测量center line survey线路中线测量center line survey线路中线测量location of route线纹米尺，*日内瓦尺standard meter线形锁linear triangulation chain线形网linear triangulation network线性调频脉冲Chirp线性调频脉冲Chirp线阵遥感器linear array sensor线阵遥感器pushbroom sensor线状符号line symbol限差tolerance限航区restricted area乡村规划测量rural planning survey相对定位relative positioning相对定向relative orientation相对定向元素element of relative orientation相对航高relative flying height相对论改正relativistic correction相对误差relative error相对重力测量relative gravity measurement相干声呐测深系统interferometric seabed inspection sonar 相关平差Adjustment of correlated observation相关器correlator相关器correlator相位传递函数phase transfer function相位传递函数PTF相位多值性phase ambiguity相位模糊度解算phase ambiguity resolution相位漂移phase drift相位稳定性phase stability相位周，*巷lane相位周，*巷phase cycle相位周值，*巷宽lane width相位周值，*巷宽phase cycle value镶嵌索引图index mosaic巷道验收测量footage measurement of workings象限仪quadrant象形符号replicative symbol像场角angular field of view像等角点isocenter of photograph像底点photo nadir point像地平线，*合线horizon trace像地平线，*合线image horizon像地平线，*合线vanishing line像幅picture format像空间坐标系image space coordinate system像片photo像片photograph像片比例尺photo scale像片地质判读，*像片地质解译geological interpretation of photograph 像片方位角azimuth of photograph像片方位元素photo orientation elements像片基线photo base像片纠正photo rectification像片内方位元素elements of interior orientation 像片判读photo interpretation像片平面图photoplan像片倾角tilt angle of photograph像片外方位元素elements of exterior orientation 像片镶嵌photo mosaic像片旋角swing angle像片旋角yaw像片主距principal distance of photo像平面坐标系photo coordinate system像移补偿image motion compensation像移补偿IMC像元pixel像主点principal point of photograph像主纵线principal line [of photograph]销钉定位法stud registration小潮升neap rise小潮升neap rise小角度法minor angle method小像幅航空摄影SFAP小像幅航空摄影small format aerial photography 协调世界时coordinate universal time协调世界时coordinate universal time协调世界时UTC协调世界时时号time signal in UTC协方差函数covariance function协方差函数covariance function心象地图mental map新版海图new edition of chart新版海图new edition of chart信号杆signal pole信息量contents of information信息量contents of information信息提取information extraction信息属性information attribute星载遥感器satellite-borne sensor行差run error行星大地测量学planetary geodesy行政区划图administrative map修版retouching虚地图virtual map虚拟地景virtual landscape序惯平差sequential adjustment悬式经纬仪hanging theodolite旋转参数rotation parameters选取限额norm for selection选取限额norm for selection选取指标index for selection选权迭代法iteration method with variable weights寻北器north-finding instrument寻北器north-finding instrument寻北器polar finder压力验潮仪pressure gauge亚太区域地理信息系统基础设施常设委员会PCGIAP亚太区域地理信息系统基础设施常设委员会Permanent Committee on GIS Infrastructure for Asia and the Pacific严密平差rigorous adjustment沿海测量coastwise survey沿海测量coastwise survey颜色空间color space颜色空间color space验潮tidal observation验潮仪tide-meter验潮站tidal station验潮站零点zero point of the tidal阳像positive image遥感remote sensing遥感测深remote sensing sounding遥感模式识别pattern recognition of remote sensing 遥感平台remote sensing platform遥感数据获取remote sensing data acquisition遥感制图remote sensing mapping野外地质图field geological map野外填图field mapping因瓦基线尺invar baseline wire阴像negative image阴像negative image引潮力tide-generating force引潮位tide-generating potential引航图集pilot atlas引力gravitation引力位gravitational potential引水锚地pilot anchorage引张线法method of tension wire alignment印刷版printing plate荧光地图fluorescent map影像image影像imagery影像地质图geological photomap影像分辨力image resolution影像分辨力resolving power of image 影像复原image restoration影像金字塔image pyramid影像匹配image matching影像融合image fusion影像数据库image database影像相关image correlation影像镶嵌image mosaic影像质量image quality游艇用图smallcraft chart游艇用图yacht chart渔礁fishing rock渔堰fishing haven渔业用图fishing chart渔栅fishing stake宇宙制图cosmic mapping宇宙制图cosmic mapping预报地图Prognostic map预打样图pre-press proof预制符号preprinted symbol预制感光板，*PS 版presensitized plate 原子钟atomic clock圆曲线测设circular curve location圆曲线测设circular curve location圆-圆定位，*距离-距离定位range-range positioning圆柱投影cylindrical projection圆柱投影cylindrical projection圆锥投影conic projection圆锥投影conic projection远程定位系统long-range positioning system远海测量pelagic survey月平均海面monthly mean sea level月球轨道飞行器lunar orbiter运动方程分析解analytical solution of motion equation 运动方程数值解numerical solution of motion equation 运动方程数值解numerical solution of motion equation 运动线法Arrowhead method晕滃法hachuring晕渲法hill shading载波相位测量carrier phase measurement载波相位测量carrier phase measurement再分结构subdivisional organization凿井施工测量construction survey for shaft sinking凿井施工测量construction survey for shaft sinking栅格绘图raster plotting栅格数据raster data站心坐标系topocentric coordinate system章动nutation章动nutation照相排字机phototypesetter照相制版镜头printer lens照相制版镜头process lens照准点sighting point照准点归心sighting centring真地平线，*真水平线true horizon真实孔径雷达real-aperture radar真误差true error真子午线true meridian整体大地测量integrated geodesy整体感associative perception整体结构extensional organization正常高normal height正常高normal height正常水椭球，*水准椭球normal level ellipsoid 正常水椭球，*水准椭球normal level ellipsoid 正常引力位normal gravitation potential正常引力位normal gravitation potential正常重力normal gravity正常重力normal gravity正常重力场normal gravity field正常重力场normal gravity field正常重力公式normal gravity formula正常重力公式normal gravity formula正常重力位normal gravity potential正常重力位normal gravity potential正常重力线normal gravity line正常重力线normal gravity line正方形分幅square mapsubdivision正片positive正象right-reading正直摄影normal case photography正直摄影normal case photography正轴投影normal projection正轴投影normal projection郑和航海图Zheng He's Nautical Chart政治地图political map支水准路线spur leveling line直方图规格化histogram specification直方图均衡histogram equalization直角坐标网rectangular grid志田数Shida'a number制图分级cartographic hierarchy制图分级cartographic hierarchy制图简化cartographic simplification制图简化cartographic simplification制图精度mapping accuracy制图夸大cartographic exaggeration制图夸大cartographic exaggeration制图专家系统cartographic expert system制图专家系统cartographic expert system制图资料cartographic document制图资料cartographic document制图资料source material质底法quality base method质量感qualitative perception秩亏平差rank defect adjustment置信度Confidence置信度Confidence中程定位系统medium-range positioning system中国测绘学会Chinese Society of Geodesy, Photogrammetry and Cartog中国测绘学会CSGPC中国测绘学会Chinese Society of Geodesy, Photogrammetry and Cartog中国测绘学会CSGPC中国大地测量星表CGSC中国大地测量星表Chinese Geodetic Stars Catalogue中国大地测量星表CGSC中国大地测量星表Chinese Geodetic Stars Catalogue中华人民共和国测绘法Surveying and Mapping Law of the People's Republic of中天法transit method中误差RMSE中误差root mean square error中心式快门between-the-lens shutter中心式快门lens shutter中星仪transit instrument中性色调，*灰色调middle tone中央子午线central meridian中央子午线central meridian钟偏clock offset钟偏clock offset钟速clock rate钟速clock rate重采样resampling重力gravity重力测量gravity measurement重力场gravity field重力潮汐改正correction of gravity measurement for tide重力潮汐改正correction of gravity measurement for tide 重力垂线偏差gravimetric deflection of the vertical重力垂直梯度vertical gradient of gravity重力点gravimetric point重力固体潮观测gravity observation of Earth tide重力归算gravity reduction重力基线gravimetric baseline重力基准gravity datum重力数据库gravimetric database重力水平梯度horizontal gradient of gravity重力梯度测量gradiometry重力梯度测量gravity gradient measurement重力梯度仪gradiometer重力位gravity potential重力仪gravimeter重力异常gravity anomaly周期误差periodic error周跳cycle slip周跳cycle slip轴颈误差error of pivot主垂面principal plane [of photograph]主垂面principal vertical plane主动式遥感active remote sensing主分量变换Principal component transformation主合点principal vanishing point主核面principal epipolar plane主核线principal epipolar line主检比对main/check comparison主台main station。

基础地理信息术语（中英文对照）

基础地理信息术语（中英文对照）absolute reference frame绝对参考坐标系adjacency analysis相邻分析adjoining sheets邻接图幅agglomeration（制图分类中的）聚合方法aggregation聚合；聚集altitude tinting分层设色animated mapping动画制图animation动画application program应用程序Application ProgrammingInterface(API)应用程序界面applications package应用软件包Applications ProgramInterface应用程序接口applications system应用系统applied cartography应用地图学auto-cartography自动制图automated cartography自动制图学automated data dictionary自动数据字典automated data processing自动数据处理Automated DigitizingSystem(ADS)自动数字化系统automated featurerecognition自动特征识别azimuth coordinate system方位坐标系base map of topography地形底图base map/cadastre底图／地籍图Beijing geodetic coordinatesystem 1954１９５４年北京坐标系block数据块；信息组；程序块block correction区域改正border边缘；界限；边界线；邻接；图廓间border figure图廓数据border information图廓注记border line图廓线border matching边缘匹配B-splineB-tree二叉树；二元树cadaster地政局；地籍图cadastral attribute地籍特征cadastral data base地籍数据库cadastral features地籍特征cadastral information地籍信息cadastral informationsystem地籍信息系统cadastral inventory地籍调查cadastral layer地籍信息层cadastral lists地籍册cadastral management地籍管理cadastral map地籍图cadastral map series地籍图册cadastral mapping地籍制图cadastral survey地籍测量 carrier frequency(GPS)载波频率（全球定位系统）cartographic analysis地图分析cartographic classification地图分类cartographic communication地图传输cartographic data base地图数据层cartographic data base management system地图数据库管理系统cartographic data model地图数据模型cartographic expert system制图专家系统cartographic generalization制图综合cartographic projection地图投影cartographic(al) analysis地图分析cartography地图制图学；地图学chorographic map时序图choropleth map等值区域图class分类，分级class interval分级间距；分类间距class list分类清单classification rule分类规则cluster聚类分析compaction压缩completeness完整性computer-graphicstechnology计算机图形技术congruent image叠合图象contour等高线，等值线，轮廓contouring display分层显示coverage［GIS］图层cover-ID层标识符data数据data access security数据存取安全性data accessibility数据可达性data acquisition数据获取data analysis数据分析data architecture数据结构data base；database数据库data capture数据采集data catalogue数据目录data communications数据通信data conversion数据转换data definition数据定义data editing数据编辑data element数据要素data encoding数据编码data entry数据输入Data Exchange Format数据交换格式data extraction数据提取data file数据文件data handling数据处理data item数据项data layering数据分层data manipulation数据操作data model数据模型data product数据产品data quality数据质量data quality数据质量data reality数据真实性data records数据记录data reduction数据整理data reduction；datacompression数据压缩data redundancy数据冗余度data representation数据表示data retrieval数据查询data schema数据模式data security数据安全性data sensitivity数据灵敏性data set数据集data set quality数据集质量data smoothing数据平滑data snooping数据探测法data sources数据源data storage数据贮存data structure数据结构data structure conversion数据结构转换data transfer数据传输data transmission数据传输data type数据类型data updating数据更新data vectorization数据矢量化datum transformation基准变换descriptive data描述数据desktop GIS桌面地理信息系统differential GlobalPositioning System；DGPS差分全球定位系统digigtizing cursor数字化鼠标digital数字的digital cartography数字地图制图digital correlation数字相关digital data数据；数字资料digital data collection数字数据存贮系统Digital Data CommunicationMessage Protocol数字化数据通讯消息协议Digital Data System数字化数据系统Digital ElevationMatrix(DEM)数字高程矩阵digital encoding数字编码digital exchange format数据转换标准Digital Field Update System数字化外业更新系统digital filessynchronization数字化文件同步化Digital GeographicInformation数字化地理信息交换标准digital image数字影（图）象digital image processing数字图象处理Digital Landscape Model数字景观模型Digital Line Graph；DLG数字线划图digital map数字地图digital map registration数字地图套合digital mapping数字测图digital mosaic数字镶嵌digital mosaicing数字镶嵌digital number；DN数字值digital orthoimage数字正射影象digital orthoimagery数字正射影象digital orthophoto数字正射影象Digital Orthophotoquads；DOQ数字正方形正射象片图digital photogrammetry数字摄影测量digital process数字化过程digital rectification数字纠正digital simulation数字模拟digital surface model；DSM数字表面模型digital tablet数字化板Digital Terrain Model；DTM数字地面模型Digital to Analog Converter数／模转换器digital tracing table数控绘图桌digital value数字化值digital voice数字化声音digital-analog数字模拟digitalyzer模数转换器digitization数字化digitize maps数字化地图digitized data数字化数据digitized file数字化文件digitized image数字化影象digitized terrain data数字化地面数据digitized video数字影（图）象digitizer数字化仪digitizer accuracy数字化仪精度digitizer resolution数字化仪分辨率digitizer workstation数字化工作站digitizing数字化digitizing board数字化板digitizing edit数字化编辑digitizing table；tablet数字化板digitizing threshold数字化阀值digraph有向图disk磁盘disk space磁盘空间disk storage磁盘存储diskette软磁盘distributed architecture分布式体系结构Distributed ComputingEnvironment分布式计算环境Distributed Data Processing分布式数据处理Distributed Database ；DDB分布式数据库Distributed DatabaseManagement System,DDBMS分布式数据管理系统distributed processing分布式处理Distributed Relational分布式关系数据库结构districe coding地区编码districting分区（空间聚合）disturbed orbit卫星轨道升交点document file文档文件Document ImagePeocessing(DIP)文件影象处理document window文档窗口document/page reader光符识别仪器documentation drawing二维绘图document-file icon文档文件图标download文件（程序）传输（从中心机到个人微机）downloadable font可传输字符draft草图；草案drafting绘制；绘图；草拟drafting scale绘图比例尺drainage水系；水文要素；排水设备drainage map水系图；流域图drainage pattern水系类型；水网类型drape两维数据在表面叠加产生透视图draping两维数据叠加在透视图上drawing绘图drawing board绘图板drawing entities绘图实体Drawing Exchange Format图形交换格式drawing extents绘图范围drawing file绘图文件drawing grid绘图格网drawing interchange format绘图交换格式drawing limits绘图限制drawing registration绘图对齐；绘图定位drawing sizes图面大小；图幅尺寸drawing unit绘图单元drum plotter滚筒式绘图机drum scanner滚筒式扫描机duobinary coding双二进制编码DX 90水文地理数据格式dynamic-Link Library,DLL动态链接库earth gravity model地球重利模型Earth Resources InformationSystem；ERIS地球资源信息系统earth satellite thematicsensing地球卫星专题遥感earth shape；figure of theearth地球形状Earth spheroid地球椭球体Earth spherop地球椭球面earth surface地球表面earth synchronous orbit地球同步轨道earth window地球数据窗口Earth-centered ellipsoid地心椭球Earth-fixed coordinatesystem站心坐标系EarthResource TechnologySatellite地球资源技术卫星Earthwatch地球监视卫星Eclogically SustainableDevelopment生态平衡的持续发展ecosystem生态系统edge join边缘匹配edge matching边缘匹配edge of the format；mapborder图廓edit编辑；修改edit verification编辑核实edit/display on input输入编辑/显示edit/display on output输出编辑/显示editing编辑effective radius of theEarth地球有效半径eigenvector特征向量eigenvector analysis特征向量分析EIS process环境影响评价过程Electric Chart and Display电子图形显示信息系统electric mail；e-mail电子邮件electronic bearing电测方位electronic chart电子海图electronic chart database；ECDB电子海图数据库Electronic Data Collection电子数据集合Electronic Data Interchange(EDI)电子数据交换Electronic DataInterchange；EDI电子数据交换electronic drawing tablet电子绘图板electronic engraver电子刻图机electronic imaging system电子成像系统electronic line scanner电子扫描机electronic map电子地图electronic publishingsystem电子印刷系统Embedded QUEL内嵌式查询embedded SQL镶嵌式查询语言emergency run地图翻印encipher；encode；encoding编码enclosing rectangle(最小)封闭四边形encoding code model编码模型encoding scheme编码方法End Of Line文件结束标志End Of Text行结束标志end points文本结束标志end user终端用户end user participation终端用户参与Enhanced graphicsAdapter(EGA)增强图形适配器enhanced imagery增强图象enhanced mode增强模式entity实体entity实体,组织,结构entity classes实体类entity classes实体分类entity instance实体样品entity object实体对象entity point实体定位点entity relationship datamodel实体关系数据模型entity relationshipdiagram；ERD实体关系图Entity Relationship Model；E-R Model实体关系模型entity set实体集entity set model实体集模型entity subtype/supertype实体子类型/母类型entity type实体类型Entity-RelationshipApproach E-R法entropy熵(平均信息量)entropy coding熵编码ent-to-end data system终端站间数据系统environmental analysis环境分析environmental assessment环境评价environmental cadastre环境地籍图environmental capacity环境容量environmental data base环境数据库environmentaldata/information环境数据/信息environmental map环境地图environmental mapping data环境制图数据environmental overlays环境图environmental planning环境规划environmental qualityassessment环境质量评价environmental remotesensing环境遥感equation item方程项E-R diagram E-R图EROS地球资源观测系统European TransferFormat(ETF)欧洲传输格式executable file执行文件execution执行(程序指令)extended color扩展彩色Extended GraphicsAdapter(EGA)增强图形适配卡Extended Graphics Array扩展图形矩阵Extensional Database扩展数据库external attribute table外部属性表external data storage外部数据存储(相对于数据库) external database file外部数据库文件external margin外图廓external polygon外部多边形external program外部程序external schema外部模式external storage外部存储设备facilities设施；装备facility data设施数据facility instrument设施设备facility map设施图facility network设施网络facility splice设施接合fast Fourier transform快速傅立叶变换feature特征Feature and AttributeCoding Catalogue地物与属性编码目录feature attribute table特征属性表feature bounded边界标识地物feature class特征分类feature codes特征码feature codes menu特征码清单feature coding特征编码feature extraction特征提取feature ID特征标识符feature identifier特征标识符feature instance特征实例feature item特征项feature marked有标记特征feature number特征标识符feature selection特征选择feature separation特征分类feature spanned跨区特征feature supported支持特征feature user-ID特征用户标识码Federal InformationProcessing联邦信息处理标准Federal InformationProcessing Standards/联邦信息处理标准／空间数据转换标准field［数据］域file［计算机］文件file activity文件活动file attribute文件属性file compression文件压缩file format文件格式file fragmentation文件分段存储file indexing文件管理索引file integrity文件完整性file name文件名file name extension文件扩展名file protection文件保护file server文件服务器file server protocol文件服务器协议file set文件集file specification文件说明；文件说明表file structure文件结构file system文件系统file transfer文件转换File Transfer Protocol文件传输协议file-by-file compression文件压缩filename extension文件后缀名fill pattern填充模式fixed length record format定长记录格式flag标志；特征flair point识别点；明显地物点flap叠置floppy disk；floppy软盘form line地表形态线format格式format conversion格式转换format line格式行format model格式模型formatted model格式化模型formatting格式化formatting function格式化函数；格式编排formfeed换页；格式馈给forms interface格式界面forms processing表格处理fractal分数的；分形；分数维fractional map scale分数地图比例尺fractional scale分数比例尺frequency band频段；频带frequency bias频偏frequency curve频率曲线frequency demodulation鉴频frequency distribution频率分布full-resolution picture全精度影（图）象，高分辨率影（图）象fully concatenated key全连串码fully digital mapping全数字化制图function library功能库functional data base功能数据库functional mapping功能制图functional structure功能结构fuzzy模糊的；失真的fuzzy analysis模糊分析fuzzy classifier method模糊分类法fuzzy C-means模糊聚类法fuzzy distance模糊距离fuzzy intersection concept模糊交叉概念fuzzy tolerance模糊容限Gauss plane coordinate高斯平面坐标Gaussian coordinate高斯坐标Gauss-Kruger coordinate高斯－克吕格坐标Gauss-Kruger grid高斯－克吕格格网Gauss-Kruger map projection高斯－克吕格地图投影gazetteer地名录general scale基本比例尺generic term地理通名Geo Based InformationSystem基于地学的信息系统geo-analysis地理分析geobase地区库geobase system地区系统geobased information system地区信息系统geobotanical cartography地植物学制图geocartography地理制图geocode地理编码geocoded virtual map地理编码虚拟图geocodes地理编码geocoding地理编码geocoding system地理编码系统geo-defined unit地理定义单元geo-distribution地理分布Geographer's Line地理坐标网geographic地理的；地理学的geographic aggregation地理聚合geographic analysis地理分析Geographic Analysis andDisplay System(GADS)地理分析显示系统Geographic AnalysisPackage(GAP)地理分析软件geographicanalysis/modelingcapability地理分析／模拟能力geographic area boundaries地理面积边界Geographic Area CodeIndex(GACI)地理面积编码索引Geographic Base File(GBF)地理基础文件Geographic Base File/Dual地理底图基础文件／双重独立地图编码Geographic Base InformationSystem(GBIS)地理基础信息系统Geographic Base System(GBS)地理基础系统geographic boundaries地理边界geographic boundary data地理边界数据geographic calibration地理标准geographic classification地理分类geographic codes地理坐标码geographic coding地理编码geographic coordinate地理坐标geographic coordinates地理坐标geographic coverage地理层geographic data地理数据geographic data base地理数据库geographic data set地理数据集geographic data structure地理数据结构Geographic Database地理数据库geographic display system地理显示系统geographic entity地理实体geographic feature地理特征geographic feature data地理特征数据geographic graticule地理坐标网geographic grid地理网格geographic identifiers地理标识符geographic indexed file地理索引文件geographic indexes地理索引geographic information system地理信息系统geographic inverse地理位置反算geographic landscape地理景观geographic latitude地理纬度geographic location地理位置geographic longitude地理经度geographic meridian地理子午线geographic modeling地理模拟geographic name地理名称geographic net地理坐标格网geographic numbering system地理编号系统geographic object地理对象geographic pole地极geographic position地理位置geographic reference地理参考geographic reference system地理参考系统geographic referencing地理参考过程geographic standardization地理标准化geographic survey地理测量geographic value地理坐标值geographical地理的geographical coordinate地理坐标geographical data base地理数据库geographical general name地理通名geographical map地理图geographical name index地名索引geographical name；placename地名geographical network地理格网geographical pole地极geographical position地理位置geographical referencesystem地理坐标参考系geographical viewingdistance地理视距geographical zones地理带geographical-explorationtraverse地理勘测路线geographics limits细线；内图廓线geography地理学Geomatics（加拿大）地球信息学geometric rectification几何校正geometric registration几何配准geomorphic map地貌类型图geomorphological map地貌图geomorphological mapping地貌制图geomorphology地貌学geo-politic data base行政区划数据库geoprocessing application地理处理应用geoprocessing approach地理处理方法geoprocessing functions地理处理函数geoprocessing modeling 地理处理模拟geoprocessing operations地理处理操作geoprocessing productivity地理处理率geoprocessing system地理处理系统geoprocessing virtual mapsystem地理处理虚拟图系统Geoprocessing(GP)地理处理过程geoprocessor地理处理器GEOREF世界地理坐标参考系GEOREF coordinate system世界地理坐标参考系GEOREF grid世界地理坐标参考网格georeference 地理坐标参考georeference system地理坐标参考系georeferenced 地理坐标参考的geo-referenced informationsystem地理参考信息系统georeferencing地理坐标参考过程georelational model地理相关模型geosphere地理圈geostatistics地理统计GIS/LIS地理信息系统／土地信息系统global全球的Global EnvironmentalMonitoring System(UNEP)全球环境监测系统（联合国环境项目）global land informationsystem(GLIS)全球土地信息系统global positioning全球定位Global PositioningSystem(GPS)全球定位系统global rediation总辐射global satellite system全球卫星系统Global TelecommunicationsSystem全球远程通讯系统gopographic landform地形graph图；图形graphic图形的；图示的graphic compose图形合成graphic data base图形数据库graphic data base file图形数据库文件graphic data concept图形数据概念graphic illustration图解说明；图解例证graphic input procedure图形输入法graphic input unit图形输入设备Graphic Interchange Format图形交换格式graphic interpolation图解内插法graphic limits图形边界graphic manipulation图形维护graphic map features图示地图特征graphic map manipulation图示地图操作graphic map scale图解地图比例尺graphic mapping controlpoint图解图根点graphic menu图示菜单graphic modes图示模式graphic object图形对象graphic output unit图形输出设备graphic overlay图形叠加graphic plane图示面graphic presentation图形显示graphic primitive图形元素graphic product图形产品graphic production图形生成graphic rectification图形校正graphic representation图形表示graphic scale图解比例尺graphic sign图形记号graphic superimposition图形叠加graphic symbol图形符号graphic symbols/symbology图形符号／符号表示graphic system components图形系统组成graphic tablet图形数字化板graphic terminal图形终端graphic text string图形文本串graphic trace图形跟踪graphic variable图形变量graphical screen interface图形屏幕界面graphical userinterface(GUI)图形用户界面graphics图形graphics accelerator图形加速卡graphics cursor图形光标graphics display units图形显示单元graphics inquiry图形查询graphics languages图形语言graphics mode图形模式graphics page图形页Graphics PerformanceCharacterization(GPC)图形工作特性graphics resolution图形分辨率graphics screen图形屏幕界面graphics software图形软件graphics tablet图形数字化板graticule格网graticule十字丝；地理坐标网grating光栅grid格网grid栅格，格网；坐标网grid amplitude格网幅度grid azimuth坐标方位角grid bearing坐标方位角grid cell格网元素；网眼grid cell compositing网眼组成grid cell data网眼数据结构grid cell data structure网眼数据结构grid cell lattice三维网眼格数据结构grid cell map网眼地图grid cell map-record format网眼地图记录格式grid cell modeling网眼模拟grid cell search网眼搜寻grid convergence坐标纵线收敛角grid coordinate system格网坐标系grid coordinates格网坐标系grid data格网数据grid declination格网真北偏角grid equator格网赤道grid factor格网因子grid format格网格式grid interval网格间距grid inverse网格反算grid length坐标网距grid lines/codes格网线／码grid magnetic angle格网磁偏角grid map格网地图grid meridian坐标网纵线grid method格网法grid of neighboring zone邻带方里网grid origin坐标格网原点grid structure网格结构grid system格网系统grid tick格网标记grid variation格网磁偏角grid zone坐标带grid/raster data格网／栅格数据gridded data格网数据gridiron layout格网平面图gridiron pattern格网图形grid-point method网点板法gridsystem直角坐标格网grips数据转换程序halftone screen半色调屏幕header标题header file头文件header label头标header line标题行header record首记录hextree分级图象数据模型hidden attribute隐含属性hidden file隐含文件hidden line removal隐线消除hidden surfaces隐面hidden variable隐含变量hierarchical分级的；层次的hierarchical data分级数据hierarchical data base分级数据库hierarchical data model层次数据模型hierarchical data structure 分级数据结构hierarchical database分层数据库hierarchical districts层次分区hierarchical file structure分级文件结构hierarchical file system分级文件系统hierarchical model分级模型hierarchical organization等级结构hierarchical relationship分级关系式（数据文件结构）hierarchical sequence层次序列hierarchical spatialrelationship分级空间关系hierarchical storage分级存储hierarchical structure分级结构hierarchization分级High Level Data LinkControl高级数据连接控制High Memory Area高位地址内存区histogram直方图；柱状图；频率图history命令记录Huffman code霍夫编码hull TIN表面Human Computer Interaction人机交互Human Computer Interface人机界面hypertext电子文本；超级文本I channel同相信道；I通路I notation parameter整数记号参数I/O addresses输入／输出地址I/O CharacterRecognition(I/O CR)输入／输出字符识别I/O error输入／输出错误I/O port输入／输出端口I-beam I指针image象，象片；影象，图象；镜象图形image coding图象编码image compression影（图）象压缩image contrast影象反差image coordinate影象坐标image correlation影象相关image data影（图）象数据image data base影象数据库image data collection图象数据收集image data compaction图象数据压缩image data retrieval图象数据检索image data storage图象数据存储image definition影象清晰度（分辨力）image degradation影（图）象退化；影（图）象衰减image description影象描绘image digitization图象数字化image displacement影象位移image distortion影（图）象失真image integrator图象综合image intensifier影（图）象增强器；变象管；象亮化器image intensity图象强度image interpretation影象判读image magnification影（图）象放大image matching影象匹配image processing图象处理校正复原image processingrectification图象处理校正复原image ray象点投影线image recognition影（图）象识别image reconstruction影（图）象重建image reconstructor影象再现装置image registration图象配准image representation影（图）象显示；影（图）象再现image resolution；groundresolution影象分辨力image scale影象比例尺image size影（图）象尺寸；影（图）象范围image space象空间image space coordinatesystem象空间坐标系image stack影（图）象栈image transform影（图）象变换image transformation图象变换image translator影（图）象转换器image；imagery影象imagery feature影象特征index指标；指数；索引index to Names地名索引indexed索引化的indexed sequential file顺序索引文件indexing索引；加下标；变址informatics信息学information area信息区information bit信息位information center信息中心information collection信息采集information content信息量information explosion信息爆炸information extraction信息提取information float信息浮动information format信息格式information management信息管理information network信息网information overlays信息叠加information rate信息传输速率Information requirement(IR)请求信息information revolution信息革命information science信息科学information system信息系统information technology(IT)信息技术information theory信息论information window信息窗口infowmation信息input输入input area输入区input data输入数据input device输入设备input image(inimage)输入影（图）象input/outpu model输入／输出模型input/output analysis输入／输出分析Input/Output(I/O)输入／输出inquiry查询insert插入；嵌入integrated data base集成数据库integrated data layer集成数据层Integrated GeographicalInformation System集成化地理信息系统integrated GIS/technologies综合地理信息系统／技术integrated informationsystem综合信息系统integrated spatial system综合空间信息系统integrated system综合系统interactive交互式interactive digitizing人机交互数字化interactive display人机交互显示interactive drafting交互式绘图interactive editing交互式编辑interactive graphics交互式制图Interactive Graphics andRetrieval System交互图形与恢复系统Interactive Graphics DesignSystem交互式图形设计系统Interactive GraphicsSystem/Interactive交互式制图系统／交互式制图子系统interactive imageprocessing system人机对话影（图）象处理系统interactive mode交互式模式Interactive Multimedia交互式多媒体interactive processing人机交互处理interactive processing交互式处理interactive processing mode人机交互模式interactive restoration人机对话复原Interactive SurfaceModeling交互式地表建摸interactive topology交互式拓扑。

双目三角测量原理

双目三角测量原理The principle of binocular triangulation is a fundamental concept in the field of computer vision, which is used to calculate the depth and 3D structure of objects in a scene. 双目三角测量原理是计算机视觉领域的一个基本概念，用于计算场景中物体的深度和三维结构。

By using the parallax between the two images captured by two different cameras, the distance to objects in the scene can be estimated. 通过使用两个不同摄像头拍摄的两个图像之间的视差，可以估算出场景中物体的距离。

One of the key advantages of binocular triangulation is its ability to provide precise and detailed 3D information about a scene or objects within it. 双目三角测量的一个关键优势是它能够提供关于场景或其中物体的精确和详细的三维信息。

This information can be used in a wide range of applications, including 3D modeling, augmented reality, object recognition, and depth estimation for autonomous vehicles. 这些信息可以应用于广泛的领域，包括三维建模、增强现实、物体识别以及自主车辆的深度估算。

From a technical perspective, binocular triangulation works by using the geometric relationship between the two camera viewpoints andthe image coordinates of corresponding points in the scene. 从技术角度来看，双目三角测量是通过利用两个摄像头视角之间的几何关系以及场景中对应点的图像坐标来工作的。

利用光场进行深度图估计（DepthEstimation）算法之一——聚焦算法

利⽤光场进⾏深度图估计（DepthEstimation）算法之⼀——聚焦算法前⾯⼏篇博客主要说了光场相机，光场相机由于能够记录相机内部整个光场，可以实现重聚焦(模糊线索)和不同视⾓的变换(视差线索)，同时也可以利⽤这个特性进⾏深度估计（Depth Estimation）。

先说⼀下利⽤重聚焦得到的不同聚焦平⾯图像获取深度图（模糊线索 ,defocus），其实这个原理⾮常简单。

1. 以聚焦范围为0.2F-2F为例，alpha∈(0.2,2)，取Depth Resolution=256, 那么步长就为(2-0.2)/256，我们通过重聚焦算法可以获取得到这个范围内的256幅重聚焦图像。

2. 对每⼀幅重聚焦的图像进⾏求梯度的操作，得到梯度图，⽐如使⽤matlab中的Gradient2D()函数，得到256幅梯度图。

注意，都是三通道的，所以求梯度也要在每⼀个通道进⾏。

⽤C++实现的gradient2D的代码如下：1void gradient2D(Mat input, Mat& output)2 {3 Mat Ix(input.size(), CV_32F);4 Mat Iy(input.size(), CV_32F);5//get Iy6for (int nrow = 0; nrow < input.rows; nrow++)7 {8for (int ncol = 0; ncol < input.cols; ncol++)9 {10if (ncol == 0)11 {12 Ix.at<float>(nrow, ncol) = abs(input.at<uchar>(nrow, 1) - input.at<uchar>(nrow, 0));13 }14else if (ncol == input.cols - 1)15 {16 Ix.at<float>(nrow, ncol) = abs(input.at<uchar>(nrow, ncol) - input.at<uchar>(nrow, ncol - 1));17 }18else19 {20 Ix.at<float>(nrow, ncol) = abs((input.at<uchar>(nrow, ncol + 1) - input.at<uchar>(nrow, ncol - 1)) / 2.0);21 }22 }23 }24//get Ix25for (int nrow = 0; nrow < input.rows; nrow++)26 {27for (int ncol = 0; ncol < input.cols; ncol++)28 {29if (nrow == 0)30 {31 Iy.at<float>(nrow, ncol) = abs(input.at<uchar>(1, ncol) - input.at<uchar>(0, ncol));32 }33else if (nrow == input.rows - 1)34 {35 Iy.at<float>(nrow, ncol) = abs(input.at<uchar>(nrow, ncol) - input.at<uchar>(nrow - 1, ncol));36 }37else38 {39 Iy.at<float>(nrow, ncol) = abs((input.at<uchar>(nrow + 1, ncol) - input.at<uchar>(nrow - 1, ncol)) / 2.0);40 }41 }42 }43 magnitude(Ix, Iy, output);44 }View Code3.对每⼀幅梯度图在局部窗⼝内进⾏均值滤波，相当于参考每⼀个像素点处的邻域梯度值，增加鲁棒性。

Active, wideband detection and localization in an uncertain

Active,wideband detection and localization in an uncertain multipath environmentM.WazenskiDigital System Resources,12450Fair Lakes Circle,Suite500,Fairfax,Virginia22033D.AlexandrouSACLANT Undersea Research Centre,Viale San Bartolomeo,400,19138La Spezia,Italy͑Received19January1996;accepted for publication21October1996͒Active,wideband detection and localization of targets in a dense multipath environment isapproached via optimal detection and estimation theory in conjunction with a received signal modeldescribed by weighted,delayed,and phase-shifted replicas of the transmitted signal.Thesemultipath signal parameters are known to vary with acoustic medium properties includingsound-speed proﬁle,bottom composition and topography,and sea surface state.The optimumreceiver is a time domain processor based on the statistical properties of the multipath parameters.An acoustic propagation model drives the optimum receiver by mapping acoustic mediumparameters to multipath signal parameters through Monte Carlo simulation.The generic sonarmodel͑GSM͒software package provides the required simulation environment.Illustrative detectionand localization examples are presented in the form of receiver operator characteristics͑ROC͒andlocalization ROCs,respectively.Results demonstrate signiﬁcant improvement in detection andlocalization over standard matchedﬁltering,even with uncertainty of the physical environment andrandom effects of boundary scattering.©1997Acoustical Society of America.͓S0001-4966͑97͒01403-3͔PACS numbers:43.30.Vh,43.30.Wi͓MBP͔INTRODUCTIONTraditionally,detection and localization of targets via active sonar has been approached through matchedﬁltering. In dense multipath environments͑e.g.,shallow water͒,this approach produces a multitude of temporally smeared corre-lation peaks,making detection and localization difﬁcult.In this paper,we approach this problem through application of optimum physics-based signal processing which merges sta-tistical physical modeling of the propagation medium and stochastic descriptions of environmental uncertainty within a Bayesian decision-theoretic framework.This approach pro-duces a robust matchedﬁeld method of detection and is ad-ditionally capable of localizing the target.The sensitivity of traditional matchedﬁeld processing ͑MFP͒to environmental mismatch is well documented.1,2 Our approach provides an explicit means of expressing un-certainty regarding the acoustic environment,resulting in the best possible processor given the extent of knowledge of propagation conditions.Previous applications of optimum physics-based signal processing include robust passive source localization by Richardson and Nolte with the optimal uncertainﬁeld processor͑OUFP͒.3Application of the OUFP in a random scattering environment has been presented by Haralabus et al.4and Premus et al.5The present work ex-tends application to active wideband scenarios.Our approach amounts to a time domain matchedﬁeld technique in that we endeavor to describe the target echo through acoustic modeling.Utilizing all available a priori information regarding the environment,we build a probabi-listic description of the acoustic medium.The acoustic model converts this acoustic medium information to a description of the target echo waveform at the receiver.A detection de-cision is based on the resulting stochastic description of the received target echo.A key consideration in the present development is the representation of the target echo at the receiver.Here we employ a signal model described by weighted,delayed,and phase-shifted replicas of the transmitted signal.This model provides an efﬁcient parametric method for representing the target echo waveform using information inherently known in an active sonar application,namely the type of signal and time of transmission.Successful application of time domain matchedﬁeld to real data has been reported by Michalopou-lou et al.6for broadband source localization.Detection techniques which employ a multipath signal model for the received target echo have been reported by Lourtie and Carter for both ad hoc7and optimal8approaches. While these works integrate a priori descriptions of multi-path propagation into the detector,no means of obtaining such prior information is provided.As an alternative to com-prehensive signal modeling,Giannakis and Tsatsanis devel-oped a general detection method for random non-Gaussian signals in additive Gaussian noise using third-order cumulant sums.9Techniques which attempt to acquire an understand-ing of multipath propagation include neural nets trained with in situ data,10and adaptive algorithms such as blind deconvolution.11For the present approach,we obtain de-scriptions of the physical environment,utilizing current in situ measurements as well as relevant historical data. Through acoustic modeling,these prior physical descriptions are converted to a probabilistic description of multipath pa-rameters.The paper is organized as follows.In Sec.I,a discussionand supportive reasoning for choosing the signal model is presented.Section II presents a theoretical development and functional description of the detector.In Sec.III,we discuss the simulation environment and associated implementation issues.Results of simulation are reported in Sec.III C.I.SIGNAL MODELINGThe signal model employed assumes the received pres-sure ﬁeld can be adequately described as the sum of complex weighted and delayed replicas of the transmitted signal.12,8,13The complex baseband signal is expressed asr ͑n ͒ϭ͚i ϭ0M Ϫ1␣i s ͑n Ϫ␶i ͒e Ϫj ␪i ,͑1͒where s is the complex baseband transmit signal and ␣,␶,and ␪,are the amplitudes,delays,and phase shifts over M multipaths,respectively.The signal model makes no as-sumption as to the nature of the transmit signal.Thus,con-stant wave ͑CW ͒,FM,pulse trains,and other signals with unique range/Doppler properties can be accommodated.The primary value of this signal model is that it provides an efﬁcient means of characterizing the acoustic channel in-dependent of the frequency regime employed.Moreover,this model provides a physically meaningful method of translat-ing uncertain physical descriptions of the ocean to a stochas-tic representation of the acoustic signal.The assumed signal model has restricted application in certain ocean scenarios with large bandwidth signals.In par-ticular,this signal model does not account for dispersive ef-fects in the ocean.Generally,there are two sources of dis-persion in an ocean waveguide.Intrinsic dispersion,a relatively minor effect,results from frequency-dependent at-tenuation in the medium.12The more signiﬁcant source of dispersion is geometrical dispersion.In situations where the ocean depth is on the order of an acoustic wavelength,group velocity is strongly frequency dependent.14Thus,the modelis most accurately employed in situations where the acoustic wavelength is at least an order of magnitude smaller that the ocean waveguide depth.If,for a particular application,dis-persive effects are signiﬁcant,such effects,which are gener-ally deterministic,can be accounted for by adjusting the sig-nal,s ,in the signal model.Another potential limitation of the signal model con-cerns boundary scattering.In the general situation,a number of multipaths propagate via surface and/or bottom interac-tion.Generally,boundary scattering is frequency dependent due to multiscale roughness features that may exist.Since the signal model assumes frequency-independent scattering,application is limited to environments exhibiting small scale roughness,where the frequency dependence of scattering is minimal.II.DETECTOR DEVELOPMENTFor an arbitrary array of elements,the observation vec-tor x is deﬁned as the set of complex pressure signals,base-banded from some center frequency f 0and comprised of N discrete time samples over K different receiver elements.The vector x k represents the received waveform at the k th element,and thus,x ϭ͓x 1T Ӈx 2T Ӈ...Ӈx K T ͔T͑2͒is the column vector containing NK complex signal samples.The detection problem begins with the standard two hy-pothesis approach,H 0:x ϭn ͑⌿͒,͑3͒H 1:x ϭr ͑⌽͒ϩn ͑⌿͒,͑4͒in which the observation vector x falls under either hypoth-esis H 1in which both signal and noise are present or hypoth-esis H 0in which noise alone is observed.The observed noise n is expressed as a function of physical environmentparam-FIG.1.Functional diagram of the optimal multipath detector showing a preprocessed multipath database and iterative integration.eters,⌿.The signal vector r is expressed as a function of acoustic channel parameters,⌽.In our case,⌽is deﬁned as the set of multipath amplitudes␣,delays␶,and phases␪for each receiver element.Although not explicitly stated,it should be noted that the set of␣,␶,and␪vary as a function of the physical environment and the target location,denoted by the set parameters⌿and⌶,respectively.⌿represents measurable and meaningful ocean proper-ties affecting acoustic propagation.Such properties include a description of the sound-speed proﬁle,surface roughness, and bottom composition and roughness.In the general case,⌿affects the propagation of noise through the ocean,ulti-mately affecting the statistical properties of the received noise.Indirectly,⌿also affects the received multipath signal since␣,␶,and␪are determined by the physical environ-ment.This indirect inﬂuence on the received multipath signal holds for⌶as well.The optimal detector for any reasonable cost function is the likelihood ratio15␭͑x͒ϵp͑x͉H1͒p͑x͉H0͒.͑5͒For signal or noise parameters which are uncertain,the opti-mal receiver requires integration over the unknowns and their associated a priori distributions,16yielding␭͑x͒ϭ͐⌶͐⌿͐⌽p͑x͉⌽,⌿,⌶,H1͒p͑⌽,⌿,⌶͉H1͒͐⌿p͑x͉⌿,H0͒p͑⌿͉H0͒.͑6͒Since the observed noise varies as a function of the physical ocean environment,our detector is a doubly composite hy-pothesis problem,requiring integration over the noise envi-ronment separately under each hypothesis.By deﬁnition under the H1hypothesis,x depends on⌽and⌿only.Thus,the above conditional pdf simpliﬁes to, p͑x͉⌽,⌿,⌶,H1͒ϭp͑x͉⌽,⌿,H1͒.͑7͒Through the deﬁnition of conditional probability,we sepa-rate⌽from⌿and⌶.Thus,we have,p͑⌽,⌿,⌶͉H1͒ϭp͑⌽͉⌿,⌶,H1͒p͑⌿,⌶͉H1͒.͑8͒Using the above expressions,Eq.͑6͒can be rewritten as ␭͑x͒ϭ͐⌶͐⌿͐⌽p͑x͉⌽,⌿,H1͒p͑⌽͉⌿,⌶,H1͒p͑⌿,⌶͉H1͒͐⌿p͑x͉⌿,H0p⌿͉H0.͑9͒Finally,substituting for⌽the set of multipath param-eters,␣,␶,and␪,the expression for our detectorbecomes␭͑x͒ϭ͐⌶͐⌿͐␣͐␶͐␪p͑x͉␣,␶,␪,⌿,H1͒p͑␣,␶,␪͉⌿,⌶,H1͒p͑⌿,⌶͉H1͒͐⌿p͑x͉⌿,H0͒p͑⌿͉H0͒.͑10͒In addition,we assume that the noise process is Gauss-ian.Thus,the conditional probabilities are given byp͑x͉␣,␶,␪,⌿,H1͒ϭ12␲N/2͉⌳⌿͉1/2ϫexp͓Ϫ12…xϪr͑␣,␶,␪͒…H⌳͑⌿͒Ϫ1…xϪr͑␣,␶,␪͒…͔͑11͒andp͑x͉⌿,H0͒ϭ1͑2␲͒N/2͉⌳͑⌿͉͒1/2expͩϪ12x H⌳͑⌿͒Ϫ1xͪ,͑12͒where⌳is the complex covariance matrix of the noise pro-cess.Equations͑10͒–͑12͒deﬁne the optimum uncertain mul-tipath receiver͑OUMR͒.Note that the replica signal r is speciﬁed by the multipath signal parameters.Also,the noise covariance depends on the acoustic environment.For the purposes of this paper,we focus on propagation effects on the target signal and treat the noise environment as white both spatially and temporally.Thus,we eliminate de-pendence of the conditional pdf’s for both hypotheses on⌿and simplify Eq.͑10͒to␭͑x͒ϭ͵⌶͵⌿͵␣͵␶͵␪p͑x͉␣,␶,␪,H1͒p͑x͉H0ϫp͑␣,␶,␪͉⌿,⌶,H1͒p͑⌿,⌶͉H1͒.͑13͒Recognizing the deﬁnition of the likelihood ratio,we simplify our detector as␭͑x͒ϭ͵⌶͵⌿͵␣͵␶͵␪␭͑x͉␣,␶,␪͒ϫp͑␣,␶,␪͉⌿,⌶,H1͒p͑⌿,⌶͉H1͒.͑14͒The conditional likelihood ratio in Eq.͑14͒is simply the likelihood function of a signal known exactly͑SKE͒.16Thus,␭͑x͉␣,␶,␪͒ϭexpͫ1␴n2Re͑x H r͑␣,␶,␪͒͒Ϫ12␴n2…r͑␣,␶,␪͒H r͑␣,␶,␪͒…ͬ,͑15͒where␴n2is the variance of the noise for all receivers.Accurate prior distributions of multipath parameters are critical for effective operation of our detector.Previous works assume these distributions are either known a priori7,8 or completely unknown,requiring either in situmeasurements,10or adaptive estimation.11Our approach,in-stead,takes advantage of information available about the physical environment,however uncertain or incomplete. Through acoustic modeling,we convert this information to a probabilistic description of multipath parameters.The mechanism that allows the acoustic model to drive the OUMR is the conditional pdf,p͑␣,␶,␾͉⌿,⌶,H1͒.This function maps speciﬁcations of target location,⌶,and envi-ronment parameters,⌿,to probabilistic descriptions of sig-nal parameters,␣,␶,and␪.A key consideration here is the treatment of acoustic propagation as a random process.This allows a proper treatment for such effects as boundary scat-tering and internal waves.In addition,this treatment accom-modates the type and scope of physical parameters used to describe the environment.By and large,one can only make general descriptions of physical properties,supportable by historical databases and sparse in situ measurements.These descriptions give rise to an ensemble of possible ocean real-izations.For example,it is reasonable to assume a general seasonal SSP description,which supports an entire family of sound-speed proﬁles.Thus,⌿contains the set of physical parameters describing an ensemble of possible oceans,lead-ing to a statistical description of multipath parameters.A distinction should be made between the conditional pdf given above and the prior pdf,p͑⌿,⌶͉H1͒.This function describes the uncertainty of the physical parameters them-selves;the conditional pdf describes the uncertainty of the multipath parameters given a deterministic set of physical parameters.Thus,two layers of uncertainty are treated within the OUMR.We refer to the uncertainty of the physical pa-rameters as the outer layer,and the uncertainty of the multi-path parameters as the inner layer.A functional description of the detector is shown in Fig.rmation about the acoustic environment is used to pro-duce realizations of the propagation medium.Through an acoustic propagation model,descriptions of the multipath’s amplitude,delay,and phase can be obtained and stored in a database.From the multipath database,a multipath replica is generated and correlated with the received array signals.This process is repeated in order to properly integrate over the uncertain and random ocean conditions.Once integration is completed,a detection decision is made based on a chosen threshold.Since the target’s location is an additional uncertainty, we integrate over potential target locations for optimal detec-tion.As is typical with matchedﬁeld methods,the received multipath signal is highly dependent on target location,and hence,offers the opportunity to accurately estimate a target’s location.In our approach,such an estimate is obtained di-rectly from the detector without additional processing.This beneﬁt is explored through simulation in the next section. III.SIMULATIONSimulations of the optimal detector were performed in a relatively shallow water environment where moderately dense multipath conditions were expected.For the purposes of simulation,we limited ourselves to an azimuthally homo-geneous,range independent environment.It is important to note that our approach is valid for the general situation where the ocean environment changes as a function of azi-muth and range.This,however,requires a more comprehen-sive propagation model.We considered a moderately shallow water waveguide of300-m depth.A vertical array ofﬁve elements operating at a center frequency of250Hz served as both the transmitter and receiver platform.The array spanned50–130m in depth with20-m spacing between elements.A single target was placed at2000m in range and150m in depth.The sound-speed proﬁle͑SSP͒was considered uncertain in our simulation.We operated under the assumption that a mean summer Mediterranean proﬁle was valid but a degree of uncertainty existed due to dynamic ocean processes. These effects were modeled by adding Gaussian noise to the mean sound-speed proﬁle,the variance of which decreased from2.5m/s at the surface to0.05m/s at the bottom.In order to produce a realistic SSP,a correlation coefﬁcient of 0.5was introduced between successive points along the pro-ﬁle.The summer Mediterranean proﬁle was characterized by strong thermal gradient near the surface,a sound channel axis at about100m,and a pressure gradient below the sound channel axis.Boundary interaction was considered as a random pro-cess in our simulation.The surface model employed was derived from a2D scattering simulation reported by Harala-bus et al.4which uses the Kirchoff approximation to the Helmholtz integral equation as developed by Thorsos.17The rms wave height was0.56m corresponding to a sea state of two.Figure2shows histograms for the specular reﬂection coefﬁcient in amplitude and phase.The bottom was similarly modeled but made slightly smoother and lossy.Figure3 shows histograms for the bottom.Notice that phase pertur-bations are smaller indicating a smoother bottom.The reﬂec-tion coefﬁcient magnitude is also smaller,indicating greater loss.A.Acoustic propagation modelingThe acoustic propagation software selected for simula-tion was the generic sonar model͑GSM͒which utilizes ray theory.Ray methods are ideal because they work in synergy with the signal model in providing the necessary multipath parameters.Frequency domain propagation models such as normal mode,parabolic equation,or fast-ﬁeld program͑FFP͒are applicable;however,acquiring the necessary multipath parameters is less efﬁcient with these methods since they require a Fourier synthesis.Alternative time domain propa-gation models,including time-marched FFP18and time do-main parabolic equation,12offer similar beneﬁts to ray meth-ods.In order to conﬁrm the applicability of ray theory to the selected simulation scenario,an initial comparison between ray theory͑GSM͒and normal mode propagation,using SNAP19was performed.A test simulation was carried out using a1-s linear FM signal centered at250Hz and sweep-ingϮ64Hz.The selected SSP was that of a mean summer Mediterranean proﬁle,and the boundaries were speciﬁed as smooth with the bottom composed of gravel.12This pro-moted moderate multipath propagation.Figure4shows the one-way transfer function for both models at70-m depth foran active source located 2000-m away and 150-m deep.Good agreement between GSM and SNAP was observed.Differences in amplitude were the primary source of dis-agreement,which is ray theory’s main deﬁciency.Figure 5shows the corresponding received signal.A correlation coef-ﬁcient of 0.85was observed between the two waveforms.Further simulations were performed for both a softer bottom ͑silty sand ͒and harder bottom ͑basalt ͒.The softer bottom demonstrated less multipath propagation due to higher bot-tom loss.A correlation coefﬁcient of 0.93was observed in this case.Conversely,the harder bottom demonstrated sig-niﬁcantly more multipath propagation.A correlation coefﬁ-cient of 0.61was observed.These results suggest that ampli-tude prediction differences become more signiﬁcant with denser multipath environments.That withstanding,the agreement observed is supportive of the use of ray methods for propagation modeling.Active propagation for the main simulation was per-formed in two steps.Rays were ﬁrst traced from the source to the target and then from the target to the receiver.The overall source-target-receiver transfer function was obtained through convolution of the two one-way propagation paths.The target was modeled as a point scatterer of arbitrary scat-tering strength.B.Monte Carlo integrationIntegration over the uncertain environment parameters is generally very costly computationally.Monte Carlo integra-tion techniques provide a powerful tool for approximating integrals.Generally,computations can be reduced by orders of magnitudes.Such techniques have been applied previ-ously by Shorey and Nolte,20Haralabus et al.,4and Premus et al.5The application of Monte Carlo integration generally re-quires summation of the integrand for randomly selected val-ues of the integral.As the number of random computations increases,the variance of the error approaches zero in a 1/ͱn fashion.21The number of iterations required depends on the sensitivity of the integrand to the variable and gener-ally cannot be determined analytically.In practice,one in-vestigates the change in the solution as iterations increase.As an example,Fig.6shows ROC performance as a function of the number of Monte Carlo trials.The ﬁgureillustratesFIG.2.Histograms of amplitude and phase variations in the surface reﬂection coefﬁcient in the forward scatteringdirection.FIG.3.Histograms of amplitude and phase variations in the bottom reﬂection coefﬁcient in the forward scattering direction.that suitable convergence is achieved after300trials.For thesimulation results reported here,1000trials were used toensure adequate convergence.C.Detection resultsDetection results from our multipath detector are sum-marized in the form of receiver operator characteristics ͑ROC͒.To facilitate a direct comparison with standard rep-lica correlation͑matchedﬁltering with the transmit wave-form͒,we consider a target of known location.Theﬁrst ROC results were generated using a1-s CWpulse at250Hz.Additive white Gaussian was included toproduce a signal-to-noise ratio͑SNR͒of11.0dB.Figure7shows a set of typical ocean transfer functions for the arrayof elements,obtained through GSM simulation.By convolv-ing these functions with the transmit waveform,a set of re-ceived basebanded signals is shown in Fig.8.Figure9shows the ROC results for optimal,ideal,mis-matched,and matchedﬁlter processors.The ideal processoris one which operates without uncertainty regarding acousticpropagation.It essentially matchﬁlters the received signalwith the complete multipath waveform and serves as the ab-solute upper bound for our problem.Differences in perfor-mance between the ideal and optimal processors are due tothe uncertainty in prior knowledge and random behavior ofacoustic propagation.The mismatched result is derived from a processor which accounts only for the mean acoustic propagation,ignoring the statistical effects of boundary in-teraction.In situations where the actual propagation condi-tions closely approximate the mean conditions,the mis-matched result will approximate the ideal;however,in the general situation,where actual propagations conditions devi-ate from the mean,the mismatched performance is poor. This processor demonstrates the classic sensitivity issue re-garding MFP techniques and demonstrates the importance of treating acoustic propagation as a random phenomena.The matchedﬁlter result,a replica correlator using the transmit waveform as the replica,is also shown.In the narrow-band case above,the small time–bandwidth product of the transmit signal correlates satisfac-tory with the multipath signal.Thus the performance differ-ence between optimal detection and replica correlation is not too signiﬁcant—about2.5dB.Repeating the above simula-tion with a1-s linear FM signal of100-Hz sweep,a set of received basebanded signals shown in Fig.10.ROC perfor-mance for this wideband signal is shown in Fig.11for an SNR of11.0dB.In this wideband case,substantial improve-ment in detectability by about25dB is demonstrated over replica correlation.For a probability of false alarm at10Ϫ3, the probability of detection rises from about1%to nearly 80%.Moreover,the optimal result demonstrates robust per-formance when compared to the mismatchedresult. parison of transfer functions using SNAP͑upper graph͒with GSM͑lower graph͒.D.Localization resultsIn normal situations,target location is uncertain.Thus,operation of the optimal detector requires integration over potential target locations.When a detection decision intheparison of received multipath waveforms using SNAP ͑upper graph ͒with GSM ͑lower graph ͒.A correlation coefﬁcient of 0.85was observed between thesewaveforms.FIG.6.ROC performance given as a function of Monte Carlo trials.Con-vergence is demonstrated when increased trials incrementally improve per-formance.FIG.7.Impulse response ͑two-way ͒of the simulation ocean environment.Solid lines denote in-phase,dotted lines denotes quadrature.afﬁrmative is made,the range/depth cell that maximizes the integrand can be used as a maximum likelihood estimate of the target’s position.22As an example,Fig.12shows the log-likelihood ratio as a function of target range and depth.The peak near the center represents the true target location—this for a nearly noise free situation.In order to gauge the localization performance in typical noise situations,trials were iterated to produce localization ROCs or LROCs.23Figure 13shows the localization perfor-mance using the linear FM signal for an SNR of 11dB.The maximum probability in correctly localizing the target is about 92%for the ideal case in which the environment is known exactly and about 80%for the optimal processor which accounts for the uncertain knowledge of the ocean.Repeating LROC analysis for various detection indices,the probability of correct localization ͑PCL ͒can be plotted as afunction of SNR PCL curves for this simulation is shown in Fig.14.In this simulation,90%probability of correct local-ization of the target was observed for an SNR of 12dB.IV.CONCLUSIONTemporal smearing of match ﬁlter output associated with traditional active detection systems inhibits the detec-tion of low SNR targets and reduces the accuracy of range estimation in dense multipath environments.In this paper,we have applied optimum physics-based signal processing in an effort to improve detection performance and extend local-ization capability under these conditions.We have shown through simulation that an optimal approach using acoustic propagation modeling can improve active detection in a dense multipath environment and offer localization in both range and depth in a manner similar to matched ﬁeldmeth-FIG.8.Array of received signals in the absence of noise using a CW transmit waveform.Solid lines denote in-phase,dotted lines denotes quadra-ture.FIG.9.ROC performance using a CWsignal.FIG.10.Array of received signals in the absence of noise using an FM transmit waveform.Solid lines denote in-phase,dotted lines denotes quadra-ture.FIG.11.ROC performance using an FM signal.ods.Furthermore,the approach demonstrates robust perfor-mance with respect to uncertainty surrounding the true acoustic environment.Efﬁcient implementation of optimal methods was of foremost importance in our approach.The selected time do-main signal model provides a reasonably accurate and efﬁ-cient means of describing the acoustic return from a target in all but signiﬁcantly dispersive environments.When com-bined with ray models and Monte Carlo integration tech-niques,the OUMR demonstrated improved detection and lo-calization performance with moderate computational requirements.The development of the detection/localization algorithm yielded two layers of stochastic processing—an outer layer and an inner layer.The outer layer expresses the uncertainty in knowledge of the true physical environment.As demon-strated by simulation ͑i.e.,ideal versus optimal ͒,system per-formance correlates with the certainty inenvironmentalFIG.12.Plot of the log-likelihood ratio,ln …␭͑x ͒…,as a function of target range and depth.The peak is shown at the correct location ͑150m,2000m ͒.FIG.13.LROC performance for an SNR of 11dB.FIG.14.Localization performance given as a function of overall SNR.。

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J.A. Olowofela, *B.S. Badmus, S.A. Ganiyu, O.T. Olurin, and P. Babatunde
Department of Physics, University of Agriculture, Abeokuta, Nigeria
Email: *badmusbs@
2
2
∂T Where ∂y is the vertical gradient of the field. (b) The Horizontal gradient magnitude
The horizontal gradient magnitude (HGM) method (Blakely and Simpson, 1986, Nasreddine and Haydar, 2001) is perhaps the simplest approach of estimating magnetic contact locations and depths because it does not require the calculation of vertical derivatives but only the calculation of the two first-order horizontal derivatives of the field. Thus, for a grid of magnetic field value T (x, y), the HGM is given by:
Where θ is the local phase of the total field, (Thurston and Smith,1997) Location of the Study Area The study was carried out in Ibadan area of Oyo State, South western Nigeria. The area is located within longitude 30 30’ E to 40 00’ E and latitude 70 00’ N to 7030’ N covering an area 55km X 55km, which is 3,025 square kilometers. The location and contour maps of Ibadan area are shown in Fig. 1 and Fig. 2 respectively. Geological Set up The area falls within the basement complex of South-western Nigeria characterised by the basement complex rocks of the Precambrian age consists of various granites and the metasedimentary rocks (Adetoyinbo et al., 2010). Ibadan area is composed of biotite granitic 137
(c) The Local Wavenumber
2
2
The local wavenumber k(x, y) is given by:
k (x, y) =
θ=
∂θ ∂θ + and ∂x ∂y ∂T ∂Z
2 2
2
2
∂T ∂T + ∂x ∂y
Introduction Most geophysical data like aeromagnetic data are interpreted to determine the locations, depths and forms of the sources responsible for the observed magnetic anomalies. The process of determining the location and depth of a magnetic source from gridded potential field data begins with the construction of a function from the data such that the function peaks over the magnetic source. Examples of such functions are analytic signal amplitude (ASA), local wavenumber (LWN) and the Horizontal gradient magnitude (HGM). (Nabighian, 1972, 1984; Roest et al., 1993). In this study, a digitized aeromagnetic data of Ibadan area, south western part of Nigeria as obtained by Nigerian Geological Survey Agency in 2009 were employed to determine the locations and depths to sources using the ASA, LWN, and HGM methods. Theory: (a) The Analytic signal amplitude
The analytic signal or total gradient is formed through the combination of first order horizontal and vertical gradients of the magnetic anomaly. The analytic signal is independent of magnetization direction and the direction of the Earth’s magnetic field. (Milligan and Gunn, 1997). The function used in this method is the analytic signal amplitude (ASA) defined by:
Fig. 1: Location map of ibadan area. Result and Discussion Result: Source Locations and Depth: The location and depth solutions are shown in Figs. 4a, b and c for the HGM, LWN and ASA respectively. Using a maximum standard error of 35% on each of the methods, depths were computed for the sources from the total intensity field of the study area. The results obtained from the HGM revealed depth range limit of 0.588-2.310 km. while the AS gave an estimated depth to the magnetic sources to range from 0.263-4.28 km. LWN method revealed an estimated depth to range from 0.607 -2.480 km. For each of the diagrams, the centre of each circle coincides with the location of a maximum for that function, while the diameter of the circle is proportional to the depth estimated for the source at that point.
Source Location and Depth Estimation from Digitized Aeromagnetic Data Acquired from a Basement Complex Formation: Olowofela et al.
2
ASA (x, y) =
∂T ∂T ∂T + (Roest and Pilkington, 1992) + ∂x ∂y ∂Z
Open access e-Journal
Earth Science India,
eISSN: 0974 – 8350 Vol. 4(III), July, 2011, pp. 136-142 /
Source Location and Depth Estimation from Digitized Aeromagnetic Data Acquired from a Basement Complex Formation
Abstract
Locations and depths to magnetic contacts were estimated from the total intensity magnetic field using horizontal gradient magnitude (HGM), Analytic signal amplitude (ASA) and local wavenumber (LWN). The digitized magnetic data of Ibadan area, south-western Nigeria were analyzed to estimate depths to magnetic sources as well as source locations. The results obtained showed a shallow depth range limit for the HGM and LWN while the ASA method overestimated shallow source depths when compared with HGM and LWN functions. Keywords: Horizontal gradient magnitude, analytic signal, local wavenumber, source location, source depth, aeess e-Journal