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MEMS陀螺随机误差特性研究及补偿

张玉莲 储海荣 张宏巍 张明月 陈阳 李银海

张玉莲, 储海荣, 张宏巍, 张明月, 陈阳, 李银海. MEMS陀螺随机误差特性研究及补偿[J]. 中国光学, 2016, 9(4): 501-510. doi: 10.3788/CO.20160904.0501
引用本文: 张玉莲, 储海荣, 张宏巍, 张明月, 陈阳, 李银海. MEMS陀螺随机误差特性研究及补偿[J]. 中国光学, 2016, 9(4): 501-510. doi: 10.3788/CO.20160904.0501
ZHANG Yu-lian, CHU Hai-Rong, ZHANG Hong-wei, ZHANG Ming-yue, CHEN Yang, LI Yin-hai. Characterists and compensation method of MEMS gyroscope random error[J]. Chinese Optics, 2016, 9(4): 501-510. doi: 10.3788/CO.20160904.0501
Citation: ZHANG Yu-lian, CHU Hai-Rong, ZHANG Hong-wei, ZHANG Ming-yue, CHEN Yang, LI Yin-hai. Characterists and compensation method of MEMS gyroscope random error[J]. Chinese Optics, 2016, 9(4): 501-510. doi: 10.3788/CO.20160904.0501

MEMS陀螺随机误差特性研究及补偿

doi: 10.3788/CO.20160904.0501
基金项目: 

国家自然科学基金资助项目 No.51305421

详细信息
    通讯作者:

    张玉莲(1991-),女,山东济宁人,硕士,研究实习员,主要从事惯性导航系统方面的研究。E-mail:yulian-2009@163.com

  • 中图分类号: V249.322

Characterists and compensation method of MEMS gyroscope random error

Funds: 

National Natural Science Foundation of China No.51305421

More Information
  • 摘要: 为了提高MEMS陀螺输出角速度的精度,采用Allan分析法以及Kalman滤波算法对MEMS陀螺仪进行随机误差分析和补偿。由Allan方差分析陀螺的输出数据,对Allan方差进行最小二乘法拟合,得到各项随机噪声的定量评价指标;对陀螺的输出数据使用AR模型进行数学建模,采用AIC准则确定了AR模型的阶次,建立了陀螺零漂数据的离散时间表达式;在AR模型所建立的陀螺随机误差模型的基础上,设计了Kalman滤波器,对陀螺输出数据使用Kalman算法进行了滤波处理,对陀螺的随机误差进行了补偿;通过Allan方差对Kalman算法对陀螺随机误差的补偿效果进行分析。实验结果表明:角速率随机游走Kalman滤波前为0.1487°/$\sqrt{h}$,Kalman滤波补偿后为0.0041°/$\sqrt{h}$,通过补偿可减小97.24%的角速率随机游走误差;零偏不稳定性Kalman滤波前为1.9408°/h,Kalman滤波补偿后为0.0542°/h,通过补偿可减小97.21%的零偏不稳定性误差;速率随机游走Kalman滤波前为2.6985°/h$\frac{3}{2}$,Kalman滤波补偿后为0.3343°/h$\frac{3}{2}$,通过补偿可减小87.61%的速率随机游走误差。Kalman滤波适用于MEMS陀螺的滤波处理,可有效降低陀螺的随机误差。
  • 图  1  陀螺随机误差辨识典型Allan方差曲线

    Figure  1.  Typical Allan variance curve of Gyro random error identification

    图  2  陀螺仪测试原理框图

    Figure  2.  Principle frame chart of gyro test

    图  3  MEMS陀螺仪测试平台

    Figure  3.  Test platform of MEMS gyro

    图  4  MSG1100D陀螺输出原始数据

    Figure  4.  Output raw data of MSG1100D gyro

    图  5  MSG1100D的Allan标准差及其拟合曲线

    Figure  5.  MSG1100D′s Allan standard deviation and it′s fitting curve

    图  6  MEMS陀螺随机误差Kalman滤波效果图

    Figure  6.  Kalman filtering of MEMS Gyro random error

    图  7  Kalman滤波前后Allan标准差对比曲线

    Figure  7.  Allan standard deviation contrast curves before and after Kalman filtering

    图  8  动态下MEMS陀螺随机误差Kalman滤波效果图

    Figure  8.  Kalman filtering effect of MEMS gyro random error under dynamic condition

    表  1  MSG1100D陀螺的各项随机误差统计表

    Table  1.   Random error statistics of MSG1100D gyro

    随机误差项结果
    量化噪声Q/urad3.643 1×10-5
    角随机游走N/(°/ $\sqrt{h}$ )0.148 7
    零偏不稳定性B/(°/h)1.940 8
    速率随机游走K/(°/h $\frac{3}{2}$ )2.698 5
    速率斜坡R/(°/h2)24.167 9
    下载: 导出CSV

    表  2  AR模型拟合系数

    Table  2.   Fitting coefficients of AR model

    Modelφ1φ2φ3AIC
    AR(1)0.123 500-7.341 6
    AR(2)0.123 70.001 90-7.341 6
    AR(3)0.1240.017 760.128 1-7.358 1
    下载: 导出CSV

    表  3  滤波前后数据均值和方差对比

    Table  3.   Comparison of mean values and variance before and after filtering

    参数均值/(°/s)方差/(°/s)2
    滤波前7×10-36.087 8×10-4
    滤波后1.952 4×10-43.737 3×10-7
    下载: 导出CSV

    表  4  Kalman滤波后陀螺的各项随机误差统计表

    Table  4.   Statistics of gyro random errors after Kalman filter

    随机误差项滤波后结果随机误差降低百分比/%
    量化噪声Q/urad4.1×10-688.75
    角随机游走N/(°/ $\sqrt{h}$ )0.004197.24
    零偏不稳定性B/(°/h)0.054 297.21
    速率随机游走K/(°/h $\frac{3}{2}$ )0.334 387.61
    速率斜坡R/(°/h2)6.156 374.53
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-02-29
  • 修回日期:  2016-04-14
  • 刊出日期:  2016-08-01

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