Performance Improvement of Location Estimation Using Deviation on Received Signal Strength In Wireless Sensor Networks
Koichi Miyauchi a, Eiji Okamoto b, and Yasunori Iwanami c
Graduate School of Engineering, Nagoya Institute of Technology
Gokiso-cyo, Syowaku, Nagoya 466-8555, Japan
a miyauchi@rose.elcom.nitech.ac.jp c b,{okamoto, iwanami}@nitech.ac.jp
Abstract- We propose a performance improvement scheme
of location estimation using received signal strength (RSS)
method in wireless sensor networks. Reference nodes in
sensor networks receive RSS from a target node whose
location is unknown, calculate the RSS deviation score, and
eliminate the scattered RSS of edge-score. This improves
the estimation accuracy which is not high in RSS methods
in general. The simulation results show that the proposed
scheme enables better location estimation than the
conventional scheme under the small number of pre-RSS measurement situations.
Keywords- Received Signal Strength, Location Estimation, Deviation, Maximum Likelihood Estimation
I. INTRODUCTION
Recently, ad-hoc network communication systems, which do not require specific access points but provide various services, are drawing much attention. Especially, the wireless sensor network, in which the localization of a device is done by radio measurement and an advanced localized service is provided based on the estimated location, has been much studied [1-3]. In the location estimation, the received signal strength (RSS) method in which the location of unknown device (called ‘target node’) is estimated by multiple RSS at location known devices (called ‘anchor node’), is popular because this method is available for almost all wireless environments and the RSS mechanism is simple and low-cost [4,5]. However, RSS is not stable and the RSS value is changed even if the transmitter sends at a same power due to the influence of channel. It significantly degrades the performance of localization but there are few studies to tackle this problem. Therefore, we propose an improved location estimation scheme of RSS in which the deviation score of RSS is calculated and the RSS of edge-score is eliminated. The location is estimated by using the log-likelihood function based on the selected RSS. This scheme achieves less measurement of RSS and accurate estimation which enables low power consumption. In the following, we describe the algorithm of the proposed scheme and evaluate the performance through computer simulations.
i
P i P
relatively high for large
i
P
Fig. 1. RSS probability model of exponential distribution at
i-th anchor node.
II. RSS MODEL
The RSS can be modeled by probability distribution. If two-dimensional sensor field is assumed,the distance between the target node and i-th anchor node can be given by
2
2)
(
)
(i
i
i
y
y
x
x
r
(1) where ),(y x
T is the location of the target node and )
,
(i
i
y
x is the i-th of N anchor node location. Using this distance i r, the probability of RSS (received power) i P at anchor node i and the average RSS (average received power)
i
P calculated by the probability model are given by
E
D i
i
r
P, )
exp(
1
)
|
(
i
i
i
i
i
r P
P
P
r
P
p (2) where D and E are the channel coefficients configured by the sensor field environments [2]. From the left equation of (2), we can see that the average RSS i P is modeled by the target-anchor distance i r, and thus, the right equation shows what distance i r is likely when RSS i P is received at anchor node i. i r is changed according to the location of ),(y
x
T and the probability)|
(i i
r
r
P
p of i-th anchor node is also changed even if the same level of i P received. Fig. 1 shows an example of)|
(i
i
r r
P
p. From the exponential distribution property of (2), i P becomes nearly the average value of i P with high probability, but the probability of large value is not zero and sometimes the received RSS become large. This characteristic coincides the practical RSS model. The RSS method utilizes this difference of probability distribution and calculates the estimated location from multiple anchor nodes (at least three nodes).
III. MAXIMUM LIKELIHOOD LOCATION
ESTIMATION USING RSS
Each measured RSS of every anchor node modeled by (2)
is assumed as independent. The joint probability of p where the number of anchor nodes is N and i -th anchor node receives the power
i P is derived as
multiplication of (2) by
)|()|()|()|(2211N N r P p r P p r P p P p " T
(3)
This equation is a likelihood function and has a maximum value when T is most likely for the measured i P . In (3), each probability )|(i i r r P p is a function of the distance i r and this i r is determined by the position of target node ),(y x T . Hence, the likelihood function of (3) becomes maximum at the most likely position. The logalithm function )(T L of (3) after M times measurements of i P is given by
|
|
°?
°??°ˉ
°
?-??1·¨¨?§ N
i i M
k ik
i P M
P P M
L 1
1
)1log()(T
(4)
where ik P
is the k -th received power of i -th anchor
node. The )?,?(?y x
T which has the maximum )(T L is the estimated location. Here, as shown in (4), equations of (2) and (3) can be represented using the sampling average
power | M
k ik M P 1instead of the receive RSS i P . This is the maximum likelihood (ML) estimation of RSS localization.
IV . PROPOSED ESTIMATION SCHEME
As shown in (2), the probability distribution of RSS is an exponential distribution with the mean i P and variance 2i P . From (2), D and E are constant and 2i P have large values as i r is shortened. Fig. 2 shows an example of five RSS samples causing the estimation error. An extremely large receive RSS (e.g.2i P in Fig. 2) enlarges the difference between the average power i P of the model
in (2) and the sampling average power | M
k ik M P 1. From (4), this difference makes a fluctuation of )(T L for T . Thus, when a scattered RSS from the mean i P is obtained in measurement, )|(i i r P r p is affected and the accuracy of (4) is degraded. This is the problem of the RSS localization scheme decreasing the accuracy and is expected to be solved. Therefore, we consider the elimination of noisy RSS. For each anchor node i after M times measurements of ik P , the deviation score ik T of ik P can be derived using the sample average
| M
k ik i M P 1P and the standard deviation i V of the sample by
M k N
i P T i
i ik ik ,...,1,...,1)(10
V P (5)
ik
P sampling average power of model average power in (2) i
P 1i P 2
i P This gap degrades the estimation accuracy
extremely large RSS
i
P 0
4i P 3i
P 5
i P
Fig. 2. Example of receive RSS samples degrading
estimation accuracy where M=5.
:model average power 1i P 2
i P eliminating outside of the effective diviation range.
i
P 0effective range of deviation
i P gap is decreased
max T min T 1i T i
P :sampling average power of ik
P :sampling average power after eliminating ineffective RSS.4i P 3i P 5
i P 4i T 3i T 5
i T 2
i T
Fig. 3. Elimination of ineffective RSS where M=5.
We introduce the upper and lower limits as max T and min T , respectively, for ik T . The receive RSS ik P whose ik T is within the range between min T and max T is used for calculation of (4) and the accuracy can be improved without an extra measurement. Fig. 3 shows the example of eliminating effect. By eliminating the receive RSS having extremely large or small value, the sampling
average power | M
k ik M P 1approaches the model average i P
and the gap is decreased. This improvement will raise the estimation accuracy of location.
V ?ALGORITHM OF PROPOSED SCHEME AND
NUMERICAL RESULTS
A. Performance comparison with regard to RSS
measurements
The algorithm of proposed scheme is illustrated in Fig. 4. Using this algorithm, the performance is evaluated in the 4 x 4 m sensor field with linear anchor node location as shown in Fig. 5. The range of deviation score is 85max T and 15min T , and the channel parameters are assumed as 71026.5 u D and 5.2 E This deviation range is configurated by a heuristic search. The actual location of target node is set to )5.1,5.1(),( Y X M . In this simulation,
the root mean square error (RMSE) between M and T ?
is compared as the evaluation function which is given by
22)?()?(y Y x
X RMSE (6) The RMSE performance for each measurement number M from 3 to 12 is calculated by the average of 10000 times trial. Table 1 shows the simulation conditions and Table 2 shows the simulation results.
RSS measurement Standard score calculation
Is within threshold?
Yes
No
ik T Remove from
likelihood function and M ?M-1
ik P Is all checked?
No
Yes
Estimation RMSE calculation
ik T 1
k k 1
k
Fig. 4. Algorithm of proposed scheme.
4[m]
4[m]
(0.0,3.5)(0.0,0.5)
(0.0,1.5)(0.0,2.5)(0.5,0.0)
(1.5,0.0)
(2.5,0.0)
(3.5,0.0)
Target node Anchor node
(1.5,1.5)
Fig. 5. Sensor field in the study.
Table 1. Simulation condition of location estimation at
(1.5,1.5) of target node.
Size of Sensor field
4[m] x 4[m] Target node location (1.5,1.5)
Number of anchor node N =8
Anchor node location Fig. 5
Trans. mode parameters 5.2,1026.57 u E D Effective deviation range max T =85, min T =15
Number of RSS measurement M =3 to 12
Number of trial to calculate RMSE
10000 times
Table 2. Comparison of RMSE between two schemes.
M:Number of RSS measurement
RMSE of conventional ML[m]
RMSE of proposed ML w/ removing RSS[m]
30.2839924 0.279515740.2388926 0.236479350.2079692 0.207790360.1889015 0.188784670.1734935 0.173493580.1624253 0.162425390.1539064 0.1539064100.1453188 0.1453188110.1392523 0.139252312
0.1327633
0.1327633
The results of the performances of the proposed scheme are better than conventional ML with M from 3 to 6. This means that in the less measurement situation, the noisy RSS degrades the performance and the proposed scheme effectively eliminates them so that the probability model at anchor nodes becomes closer to (2). Meanwhile, after sufficient measurements over 7 of M , the performances of both schemes coincide because the distribution model of measured RSS is already close to (2). By this fact, the performance is not improved even if the edge RSS is eliminated. Therefore, the proposed scheme contributes the performance improvement in relatively fewer measurements.
B. Performance comparison with regard to target node
location
From the results of the previous simulation, it is found that the performance of the propose scheme is better at a less RSS measurement region. Then, we compare the performance with regard to anchor node location at a small number of RSS measurements. The performance of algorithm of Fig. 4 is calculated and compared with the conventional ML scheme under the condition of Table 3. The location of target node ),(y x T changes throughout the sensor field per 0.1[m] in x and y directions, and the effective region where the RMSE of the proposed scheme is smaller than conventional scheme is drawn.
Table 3. Simulation conditions for calculating effective
region at M =3, 5, and 7.
Size of Sensor field
4[m] x 4[m] Grid size of simulation
0.1[m]
Number of anchor node N
=8
Anchor node location Fig. 5
Trans. Mode parameters 5.2,1026.57 u E D
Effective deviation range
(a)max T =85, min T =15
(b)max T =85, min T =25
Number of RSS measurement M =3, 5, and 7.
Number of trial to calculate RMSE
10000 times
Fig. 6. Effective region of proposed scheme where M =3
and the deviation range is (a).
Fig. 7. Effective region of proposed scheme where M =5
and the deviation range is (a).
Fig. 8. Effective region of proposed scheme where M =7
and the deviation range is (a).
Fig. 9. Effective region of proposed scheme where M =7
and the deviation range is (b).
Fig. 6 to 9 show the results. At M =3 of Fig. 6, the small number of RSS samples makes its distribution unstable (see Fig. 3) and the proposed eliminating scheme works well. As a result, the effective region is large as shown Fig. 6, especially at a far side from anchor nodes. As the number of RSS measurements increase, the effective region gradually becomes smaller as shown in Figs. 7 and 8. Although the values of RMSE are decreased in both schemes, the sampling average power gets closer to the model average power i P and the effect of the proposed scheme is decreased. However, we can see that the proposed scheme works well at the far side of sensor field even with M =7, and it is expected the proposed scheme is effective where the target node is not close to anchor nodes.
In Fig. 8, the performance is not improved at the center area of the censor field because the sampling average power is stable there. From the simulation result, it is found that )(T L of the target node which is approximately equally distant from anchor nodes is stable. Therefore, we enhanced the elimination range of RSS deviation and calculated the performance. Fig. 9 shows the result of elimination range extension from Fig. 8 of M=7. The effect of elimination is raised and the performance is improved. Thus, the parameter optimization may enhance the efficiency of the proposed scheme.
VI. CONCLUSION
In this study, we proposed a performance improvement scheme of RSS location estimation in wireless sensor networks. By adopting the deviation score of receive RSS and eliminating the scattered values, the accuracy of localization is improved in a few measurement cases without an extra measurement. Numerical results showed that the performance was better than the conventional scheme at several RSS measurement cases and the deviation range optimization raised the performance. In future studies, a performance improvement scheme for various power distributions other than exponential model and an autonomous elimination range control along to environments will be developed.
Acknowledgment
This research was partially supported by KDDI foundation.
References
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[3] Ismail Guvenc and Ghia-Chin Chong,’A Survey on TOA Based Wireless Localization and NLOS Mitigation Techniques’,IEEE Communications Surveys & Tutorials, V ol. 11, No. 3. (21 August 2009), pp. 107-124.
[4] Charalampos Papamanthou, Franco P Preparata, and Roberto Tamassia,’Algorithms for Location Estimation Based on RSSI Sampling’, Fourth International Workshop, ALGOSENSORS 2008, Reykjavik, Iceland, Revised Selected Papers, p.72-86, July 2008.
[5] C.Savarese, J.Rabaey, and J.Beutel, ’Locationing in Distributed Ad-Hoc Wireless Sensor Networks.’, In Proc. ICASSP, pp.2037-2040, May.2001.
jquery对象访问。 Jq对象（dom对象集合）的Eq方法和jq选择器返回的都是是jquery对象，只能使用jquery 方法；Jq对象（dom集合）的get方法和“jq对象[i]”返回的是dom元素对象，只能使用dom方法。 Jq对象的find（selector |obj|ele）和children用来查找子对象和后代对象 Jq对象的find方法用于查找当前jq对象（dom集合）的后代对象，Jq对象的children方法用于查找当前jq对象（dom集合）的子对象对象。这两个方法都只能使用jq对象（dom对象集合）来调用，并且他们返回的也是jq对象。 Jq手册中的api方法都是js对象（dom集合）对象或者$对象的方法。只能使用jq对象（dom 集合）或者$来调用。如each，attr、val，find，children等等 Jq对象的index方法搜索当前集合中的匹配的元素，并返回相应元素的索引值，从0开始计数 如果不给index方法传递参数，那么返回值就是这个jQuery对象集合中第一个元素相对于其同辈元素的位置。 如果参数是一组DOM元素或者jQuery对象，那么返回值就是传递的元素相对于原先集合的位置。 如果参数是一个选择器，那么返回值就是原先元素相对于选择器匹配元素中的位置。如果找不到匹配的元素，则返回-1。 Jq选择器 1、个基本选择器： 基本选择器可以拼接一起来选择某组元素，原则： 对同一个元素描述的多个基本选择器中间没有任何间隔。 如div[name=aa]表示name属性等于aa的div元素（元素名选择器div和属性选择器[name=aa]中间没有任何间隔）。 div.cval表示class值等于cval的div元素，表示class值等于cval是div元素（类选择器.cval 和元素名选择器div之间同样没有任何间隔） #id值 .class值 元素名 //属性 [attr]具有aaa属性
2 极大似然参数辨识方法 极大似然参数估计方法是以观测值的出现概率为最大作为准则的，这是一种很普遍的参数估计方法，在系统辨识中有着广泛的应用。 2.1 极大似然原理 设有离散随机过程}{k V 与未知参数θ有关，假定已知概率分布密度)(θk V f 。如果我们得到n 个独立的观测值,21,V V …n V ,，则可得分布密度)(1θV f ，)(2θV f ，…,)(θn V f 。要求根据这些观测值来估计未知参数θ，估计的准则是观测值{}{k V }的出现概率为最大。为此，定义一个似然函数 ) ()()(),,,(2121θθθθn n V f V f V f V V V L = （2.1.1） 上式的右边是n 个概率密度函数的连乘，似然函数L 是θ的函数。如果L 达到极大值，}{k V 的出现概率为最大。因此，极大似然法的实质就是求出使L 达到极大值的θ的估值∧ θ。为了便于求∧ θ，对式（2.1.1）等号两边取对数，则把连乘变成连加，即 ∑== n i i V f L 1)(ln ln θ （2.1.2） 由于对数函数是单调递增函数，当L 取极大值时，lnL 也同时取极大值。求式（2.1.2）对θ的偏导数，令偏导数为0，可得 0ln =??θL （2.1.3） 解上式可得θ的极大似然估计ML ∧ θ。 2.2 系统参数的极大似然估计 设系统的差分方程为 )()()()()(1 1 k k u z b k y z a ξ+=-- （2.2.1） 式中 111()1...n n a z a z a z ---=+++ 1101()...n n b z b b z b z ---=+++ 因为)(k ξ是相关随机向量，故（2.2.1）可写成 )()()()()()(1 11k z c k u z b k y z a ε---+= （2.2.2） 式中 )()()(1 k k z c ξε=- （2.2.3） n n z c z c z c ---+++= 1 11 1)( （2.2.4） )(k ε是均值为0的高斯分布白噪声序列。多项式)(1-z a ，)(1-z b 和)(1-z c 中的系数n n c c b b a a ,,,,,10,1和序列)}({k ε的均方差σ都是未知参数。 设待估参数
极大似然辨识及其MATLAB 实现 摘 要：极大似然参数估计方法是以观测值的出现概率为最大作为准则的，这是一种很普遍的参数估计方法，在系统辨识中有着广泛的应用。本文主要探讨了极大似然参数估计方法以及动态模型参数的极大似然辨识并且对其进行了MATLAB 实现。 关键词：极大似然辨识 MATLAB 仿真 迭代计算 1 极大似然原理 设有离散随机过程}{k V 与未知参数θ有关，假定已知概率分布密度)(θk V f 。如果我们得到n 个独立的观测值,21,V V …n V ,，则可得分布密度)(1θV f ，)(2θV f ，…,)(θn V f 。要求根据这些观测值来估计未知参数θ，估计的准则是观测值{}{k V }的出现概率为最大。为此，定义一个似然函数 ) ()()(),,,(2121θθθθn n V f V f V f V V V L = （1.1） 上式的右边是n 个概率密度函数的连乘，似然函数L 是θ的函数。如果L 达到极大值，} {k V 的出现概率为最大。因此，极大似然法的实质就是求出使L 达到极大值的θ的估值∧ θ。为了 便于求∧ θ，对式（1.1）等号两边取对数，则把连乘变成连加，即 ∑== n i i V f L 1 )(ln ln θ （1.2） 由于对数函数是单调递增函数，当L 取极大值时，lnL 也同时取极大值。求式（1.2）对θ的偏导数，令偏导数为0，可得 ln =??θ L （1.3） 解上式可得θ的极大似然估计ML ∧ θ。 2 系统参数的极大似然估计 设系统的差分方程为 )()()()()(1 1k k u z b k y z a ξ+=-- （2.1） 式中 1 1 1()1...n n a z a z a z ---=+++ 11 01()...n n b z b b z b z ---=+++ 因为)(k ξ是相关随机向量，故（2.1）可写成 )()()()()()(1 11k z c k u z b k y z a ε---+= （2.2） 式中 )()()(1 k k z c ξε=- （2.3）
北京工商大学 《系统辨识》课程上机实验报告（2014年秋季学期） 专业名称：控制工程 上机题目：极大似然法进行参数估计专业班级： 2015年1 月
一 实验目的 通过实验掌握极大似然法在系统参数辨识中的原理和应用。 二 实验原理 1 极大似然原理 设有离散随机过程}{k V 与未知参数θ有关，假定已知概率分布密度)(θk V f 。如果我们得到n 个独立的观测值,21,V V …n V ,，则可得分布密度)(1θV f ，)(2θV f ，…,)(θn V f 。要求根据这些观测值来估计未知参数θ，估计的准则是观测值{}{k V }的出现概率为最大。为此，定义一个似然函数 ) ()()(),,,(2121θθθθn n V f V f V f V V V L = （1.1） 上式的右边是n 个概率密度函数的连乘，似然函数L 是θ的函数。如果L 达到极大值，}{k V 的出现概率为最大。因此，极大似然法的实质就是求出使L 达到极大值的θ的估值∧ θ。为了便于求∧ θ，对式（1.1）等号两边取对数，则把连乘变成连加，即 ∑== n i i V f L 1 )(ln ln θ （1.2） 由于对数函数是单调递增函数，当L 取极大值时，lnL 也同时取极大值。求式（1.2）对 θ的偏导数，令偏导数为0，可得 0ln =??θL （1.3） 解上式可得θ的极大似然估计ML ∧ θ。 2 系统参数的极大似然估计 Newton-Raphson 法实际上就是一种递推算法，可以用于在线辨识。不过它是一种依每L 次观测数据递推一次的算法，现在我们讨论的是每观测一次数据就递推计算一次参数估计值得算法。本质上说，它只是一种近似的极大似然法。 设系统的差分方程为
第一部分HTML DOM简介 1 DOM简介 HTML文档对象模型 HTML文档对象模型（Document Object Model）定义了访问和处理 HTML 文档的标准方法。HTML DOM 把 HTML 文档呈现为带有元素、属性和文本的树结构（节点树）。 什么是 DOM？ 通过JavaScript，您可以重构整个HTML文档。您可以添加、移除、改变或重排页面上的项目。 要改变页面的某个东西，JavaScript 就需要获得对 HTML 文档中所有元素进行访问的入口。这个入口，连同对 HTML 元素进行添加、移动、改变或移除的方法和属性，都是通过文档对象模型来获得的（DOM）。 DOM 被分为不同的部分（核心、XML及HTML）和级别（DOM Level 1/2/3） DOM 可被 JavaScript 用来读取、改变 HTML、XHTML 以及 XML 文档。 ?Core DOM 定义了一套标准的针对任何结构化文档的对象 ?XML DOM定义了一套标准的针对XML 文档的对象 ?HTML DOM定义了一套标准的针对HTML 文档的对象 2 DOM节点 节点 根据 DOM，HTML 文档中的每个成分都是一个节点。
DOM 是这样规定的： ?整个文档是一个文档节点 ?每个HTML 标签是一个元素节点 ?包含在HTML 元素中的文本是文本节点 ?每一个HTML 属性是一个属性节点 ?注释属于注释节点 Node层次 节点彼此都有等级关系。 HTML 文档中的所有节点组成了一个文档树（或节点树）。HTML 文档中的每个元素、属性、文本等都代表着树中的一个节点。树起始于文档节点，并由此继续伸出枝条，直到处于这棵树最低级别的所有文本节点为止。 下面这个图片表示一个文档树（节点树）： 3 DOM节点树 文档树（节点数）
什么是DOM？ 通过JavaScript，您可以重构整个HTML文档。您可以添加、移除、改变或重排页面上的项目。 要改变页面的某个东西，JavaScript就需要对HTML文档中所有元素进行访问的入口。这个入口，连同对HTML元素进行添加、移动、改变或移除的方法和属性，都是通过文档对象模型来获得的（DOM）。 在1998年，W3C发布了第一级的DOM规范。这个规范允许访问和操作HTML页面中的每一个单独的元素。 所有的浏览器都执行了这个标准，因此，DOM的兼容性问题也几乎难觅踪影了。 DOM可被JavaScript用来读取、改变HTML、XHTML以及XML文档。 DOM被分为不同的部分（核心、XML及HTML）和级别（DOM Level 1/2/3）： Core DOM 定义了一套标准的针对任何结构化文档的对象 XML DOM 定义了一套标准的针对XML文档的对象 HTML DOM 定义了一套标准的针对HTML文档的对象。 HTML DOM 节点 HTML文档中的每个成分都是一个节点。 节点 根据DOM，HTML文档中的每个成分都是一个节点。 DOM是这样规定的： ?整个文档是一个文档节点 ?每个HTML标签是一个元素节点 ?包含在HTML元素中的文本是文本节点 ?每一个HTML属性是一个属性节点
注释属于注释节点 Node 层次 节点彼此都有等级关系。 HTML文档中的所有节点组成了一个文档树（或节点树）。HTML文档中的每个元素、属性、文本等都代表着树中的一个节点。树起始于文档节点，并由此继续伸出枝条，直到处于这棵树最低级别的所有文本节点为止。 文档树（节点数） 请看下面这个HTML文档：