哈工大导航原理大作业

《导航原理》作业

(惯性导航部分)

姓名

班级 1104103

学号

一、题目要求

A fighter equipped with SINS is initially at the position of 35 NL

and 122 EL,stationary on a motionless carrier. Three

gyrosXG,YG,ZG,and three accelerometers, XA,YA,ZA are installed

along the axes bX,bY,bZ of the body frame respectively.

Case 1:stationary onboard test

The body frame of the fighter initially coincides with the

geographical frame, as shown in the figure, with its pitching

axisbXpointing to the east,rolling axis bY to the north, and azimuth

axisbZupward. Then the body of the fighter is made to rotate step by step

relative to the geographical frame.

(1) 10around bX

(2) 30around bY

(3) 50-around bZ

After that, the body of the fighter stops rotating. You are required

to compute the final output of the three accelerometers on the fighter,

using both DCM and quaternion respectively,and ignoring the device errors.

It is known that the magnitude of gravity acceleration is 2/8.9gsm.

Case 2:flight navigation

Initially, the fighter is stationary on the motionless carrier with

its board 25m above the sea level. Its pitching and rolling axes are both

in the local horizon, and its rolling axis is45on the north by east,

parallel with the runway onboard. Then the fighter accelerate along the runway and take off from the carrier.

The output of the gyros and accelerometers are both pulse numbers,Each

gyro pulse is an angular increment of secarc1.0,and each accelerometer

pulse is g6e1,with 2/8.9gsm.The gyro output frequency is 10 Hz,and

the accelerometer’s is 1Hz. The output of gyros and accelerometers within

5400s are stored in MATLAB data files named and , containing matrices

gm of 35400 and am of 35400 respectively. The format of data as shown

in the tables, with 10 rows of each matrix selected. Each row represents

the out of the type of sensors at each sample time.

The Earth can be

seen as an ideal

sphere, with radius

and spinning rate

rad/s10292.75-, The

errors of sensors are

ignored, so is the

effect of height on the magnitude of gravity. The output of the gyros are

to integrated every . The rotation of geographical frame is to be updated

every 1s, so are the velocities and position of the figure. You are

required to:

(1)Compute the final attitude quaternion, longitude, latitude, height,

and east, north, vertical velocities of the fighter.

(2)Compute the total horizontal distance traveled by the fighter.

(3)Draw the latitude-versus-longitude trajectory of the fighter, with

horizontal longitude axis.

(4)Draw the curve of the height of fighter, with horizontal time axis.

二、Case1解答

方向余弦阵法

（1） 绕Xb轴转过ψ10

10cos10sin010sin10cos0001cossin0sincos0001C

（2） 绕Yb轴转过30

30cos030sin01030sin030coscos0sin010sin0cosC

（3） 绕Zb轴转过50

1000）50（cos）50（sin-0）50（sin）50（cos1000cossin-0sincosC

所以变换后的坐标

XEYCCCNZ

由于初始时刻有

009.8EN

所以计算得

三个加速度计的输出分别是 ,/4504.42xsmA

,/6027.22ysmA

smA/3581.8z2

计算程序见附录一

四元数法

（1）绕Xb轴转过ψ10

i2sin2cosq

（2）绕Yb轴转过30

j2sin2cosq

（3）绕Zb轴转过50

k2sin2cosq

则合成四元数

)2sin2(cos)2sin2(cos)2sin2(coskjiqqqq

合成四元数的逆

1123qpipjpk

由公式 qNEqZYX1

计算得

三个加速度计的输出分别是 ,/4504.42xsmA

,/6027.22ysmA

smA/3581.8z2

由两种计算方法的计算结果可以看出，方向余弦阵法和四元数法的计算结果是一致的。

计算程序见附录二

三、Case2解答

程序流程图

源程序详见附录三

仿真及结果

运行程序可得：

（1）战斗机相对当地地理坐标系的姿态四元数为：

4841.00023.00054.08750.0Q

（2）经度= 8757.122

纬度=35.0694 高度=8061.24

（3）战斗机的东部，北部和垂直速度

smV/7716.393e

smV/5612.267n

smV/1583.3u

（4）战斗机总水平距离为：m103822.26

运行程序，绘制纬度-经度战斗机轨迹（以经度为横轴，纬度为纵轴）；如图：

运行程序，绘制战斗机的高度的曲线（以时间为横轴，高度为纵轴），如图：

四、心得体会

通过本次的大作业，我对比力、四元数等惯性导航技术中涉及的基本概念有了更深的理解，同时再次复习方向余弦矩阵法和四元数法求解捷联惯导系统，更加熟练地掌握其算法。

除此之外，本次大作业中所有程序均要涉及Matlab编程，在编写程序时，四元数的初始化非常重要，如果四元数的初始化错误，会导致所有的运算结果错误。在编程过程中，每当遇到问题，我就会上网查一些资料，并与周边同学进行深入讨论，学习并解决问题。这进一步提高了我的自学能力和对知识综合应用的能力。

五、参考/协助确认

本文是根据本人研究成果，并参考相关文献资料整合而成，非本人完全独立研究完成，编程部分很大程度上参考了百度百科及周边同学的研究成果。另外，报告形式上借鉴了上届学长学姐的形式。本人对作业中的某些结论不负完全责任，特此声明。