运动机构中传感器信号的数字滤波处理算法研究与仿真

论文总字数：32510字

摘 要

运动机构中，通常用位置信息的差分来表征其速度，但是测试得到的数据有一定误差。本文基于以上实际背景，对减小转动机构的速度测量误差的方法进行了研究。首先，提出使用滤波减小误差，对相关滤波方法进行了理论研究，介绍了以上方法的具体流程，并从数学的角度对递归滤波器进行了详细分析。然后，对理论分析中提到的方法分析进行线性和非线性系统，静态和动态波形的仿真，指出在参数合适的情况下递归滤波器有较好的滤波性能，非递归的小波变换滤波动态特性较好，静态特性一般，并最终决定在转动机构中使用卡尔曼滤波和最小二乘滤波。对递归滤波器的相关参数进行了分析，发现递归滤波器需要平衡延时特性和滤波性能的影响，以使其工作在最佳状态。最后，将滤波方法运用于实际系统中，首先对激光雷达数据进行了离线滤波，初步判断滤波器的滤波性能。然后将最小二乘滤波和卡尔曼滤波运用于转动机构中，分别进行匀速和变速运动的信号处理并和低通滤波器性能进行对比，实验结果表明，最小二乘滤波和卡尔曼滤波的实时处理性能都优于传统的低通滤波，且通过实验数据处理可得，卡尔曼滤波的效果更好，更适用于信号的实时处理和分析。

关键词：运动机构，卡尔曼滤波，最小二乘滤波，实时处理

Abstract

In motion mechanism, the velocity is usually measured by the differential of position. However, the data obtained when measuring has some error. Based on the existing issue above, the way to reduce the error in velocity measurement in motion mechanism is studied in this article. First, using filtering to reduce the error is put forward and relevant methods of filtering are studied theoretically and the procedures of them are introduced. Recursive filter is analyzed in detail from the angle of mathematic. Then, the simulation in linear and non-linear, steady and dynamic system is performed based on the method mentioned above. It is suggested that the recursive filter has good performance when the parameter is given properly and that non-recursive wavelet transform filter has good performance in dynamic system while it is poor in steady one. The final decision is made that least square filter and Kalman filter are used separately in the motion mechanism. What’s more, related parameter is analyzed in recursive filter, it is founded that the latency and the filter performance should be balanced so that the filter itself can work in the best state. At last, the filtering methods are used in real-world system. Above all the offline filtering is performed based on data measured by Lidar and the performance of the filter is proved preliminarily. And then, the uniform and variable velocity signal measurement are processed using least square filter and Kalman filter, which are compared by the performance of low pass filter. The result shows that the least square filter and Kalman filter both have better performance than low pass filter in the real-time processing of signal. Besides, the effect of Kalman filter is better than least square filter through the processing of the data to follow. So it is concluded that Kalman filter has a better performance thus fitter in real-time processing and analyzing of the signal.

Key words: motion mechanism, Kalman filter, least square filter, real-time processing

目 录

摘要......................................................................................................................................................... Ⅰ

Abstract....................................................................................................................................................II

第一章 绪论 1

1.1 背景和意义 1

1.2 研究方法 1

1.3 光电编码器简述 1

1.4 光电编码器误差来源 2

1.5 国内外研究现状 3

1.6 本文组织结构 4

1.7 本章小结 5

第二章 滤波方法介绍 6

2.1 低通滤波器 6

2.2 自适应递归滤波器 8

2.2.1 贝叶斯滤波 8

2.2.2 卡尔曼滤波 9

2.2.3 其他形式的卡尔曼滤波 11

2.2.4 粒子滤波 13

2.3 小波变换滤波 14

2.4 本章小结 16

第三章 滤波方法仿真与结果分析 17

3.1 线性系统的仿真 17

3.2 非线性系统的仿真 19

3.3 小波变换滤波仿真 20

3.4 参数对滤波器性能的影响 21

3.4.1 参数对卡尔曼滤波器的影响 22

3.4.2 参数对粒子滤波的影响 24

3.5 滤波器的可行性分析 25

3.6 本章小结 25

第四章 运动机构实际测试与结果分析 27

4.1 激光雷达距离数据的滤波 27

4.2 对转动机构的实时处理 29

4.2.1 实验平台介绍 29

4.2.2 对恒定速度的实时滤波 32

4.2.3 对变化速度的实时滤波 36

4.2.4 结论 39

4.3 本章小结 39

第五章 总结与展望 40

参考文献（References） 41

附录A 软件程序清单 42

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