﻿ 基于自适应遗传算法的MEMS加速度计快速标定方法<sup>*</sup>
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Rapid calibration method of MEMS accelerometer based on adaptive GA
GAO Shuang, ZHANG Ruoyu
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100083, China
Received: 2019-01-29; Accepted: 2019-04-26; Published online: 2019-06-17 15:35
Corresponding author. GAO Shuang, E-mail: gaoshuang@buaa.edu.cn
Abstract: MEMS inertial measurement unit (MIMU) calibration is one of an important research direction in low-precision inertial navigation. Traditional calibration method has complex operating procedures and depends most on turntable accuracy. In order to overcome the problem of MIMU calibration in batch production, this paper presents a rapid micro-electro-mechanical system (MEMS) accelerometer calibration method based on adaptive genetic algorithm (GA), which converts calibration task to parameter optimization. Firstly, the principle of norm observation is adopted to establish the objective optimization function. Secondly, the optimal calibration scheme is designed on the basis of system observability analysis. Finally, calibration parameters can be optimized through adaptive GA with global search capability. Experimental results demonstrate that, compared with Newton's iteration, the proposed method can improve calibration accuracy by 1-3 orders of magnitude and increase operational speed by 61%. After the proposed calibration, the horizontal attitude error is less than 0.1° and its accuracy can reach the same order of magnitude as that in traditional method, which verifies its superiority and practicability.
Keywords: micro-electro-mechanical system (MEMS)     accelerometer     genetic algorithm (GA)     norm observation     calibration     observability analysis

1 加速度计标定模型 1.1 加速度计输出模型

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1.2 模观测标定原理

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2 基于自适应遗传算法的标定参数求解

 图 1 遗传算法流程 Fig. 1 Flowchart of genetic algorithm
2.1 初始种群与编码

2.2 适应度计算

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2.3 选择、交叉与变异

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3 最优标定编排设计

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 图 2 静态多位置标定编排方案 Fig. 2 Static multi-position calibration scheme

 位置 秩 奇异值 3 8 29.861 29.713 29.562 29.405 29.405 29.405 4.220 2.969 1.715×10-7 4 9 41.585 41.585 41.585 29.716 29.562 29.405 6 5.168 4.198 5 9 41.585 41.585 41.585 41.585 41.585 29.564 6.708 6.708 5.968 6 9 41.805 41.585 41.585 41.585 41.585 41.585 7.348 4 7.348 4 5.968 3 7 9 51.106 46.513 41.693 41.585 41.585 41.585 7.937 2 7.819 6 6.006 3 8 9 55.280 46.533 46.513 46.493 46.493 41.657 8.374 9 8.263 3 6.033 1 9 9 59.063 55.107 50.992 46.596 46.493 46.493 8.649 9 8.394 6 6.451 9 10 9 64.408 57.427 50.991 48.495 48.261 46.572 9.154 2 9.122 3 8.204 8 11 9 68.476 58.829 55.023 50.931 50.931 47.303 9.882 8 9.832 8 9.463 6 12 9 72.041 65.751 58.810 51.012 50.931 50.931 10.392 10.392 9.881 7 13 9 72.041 67.576 58.813 58.810 52.764 50.951 10.816 10.765 10.605 14 9 72.041 68.973 62.385 62.377 55.011 55.011 11.178 11.149 11.132 15 9 72.041 68.973 65.779 62.394 62.394 62.377 11.458 11.456 11.439

4 实验结果分析

 图 3 MTi-1系列惯性测量组合 Fig. 3 MTi-1 series inertial measurement unit

 图 4 适应度函数变化曲线 Fig. 4 Curves of fitness function variation
 图 5 误差参数标定结果 Fig. 5 Calibration results of error parameters

 误差参数 传统标定方法标定结果 牛顿迭代法 本文方法 标定结果 相对误差/% 标定结果 相对误差/% Bx/(m·s-2) 0.116 46 0.116 29 -0.146 0.116 44 -0.017 By/(m·s-2) 0.036 1 0.035 9 -0.554 0.036 107 0.019 Bz/(m·s-2) 0.136 44 0.138 42 1.451 0.136 37 -0.051 Sxx 9.805 18 9.805 2 0.000 204 9.805 9 0.007 Syy 9.787 18 9.788 2 0.010 4 9.787 6 0.004 Szz 9.771 07 9.811 5 0.414 9.771 1 0.000 3 Mxy -0.005 8 0.276 8 × -0.006 42 10.69 Mxz 0.005 22 0.405 1 × 0.002 42 -53.64 Myx 0.006 07 —— —— —— —— Myz 0.003 93 -0.768 9 × 0.003 09 -21.37 Mzx -0.003 6 —— —— —— —— Mzy -0.006 2 —— —— —— —— 注：“×”表示无相对误差结果；“——”表示无此项安装误差。

 方法 运算时间/s 本文方法 164.28 牛顿迭代法 421.92

 图 6 水平姿态角误差曲线 Fig. 6 Curves of horizontal attitude errors

 方法 俯仰角误差/(°) 横滚角误差/(°) 传统标定方法 0.015 0.109 牛顿迭代法 0.24 -0.191 本文方法 0.062 -0.051

1) 能够准确标定出MEMS加速度计的全部误差参数，与牛顿迭代法相比，标定精度提升1~3个数量级，运算速度提升61%，本文方法可有效应用于MEMS加速度计的快速标定。

2) 标定后解算的水平姿态角误差小于0.1°，能达到与传统标定方法相同量级的精度，验证了本文方法在实际导航中的应用价值。

5 结论

1) 本文针对传统标定方法标定时间长、标定精度依赖转台精度等问题，提出了一种基于自适应遗传算法的MEMS加速度计快速标定方法，实现对全部误差参数的快速准确标定。根据模观测原理，将标定问题转化为非线性方程组的优化求解问题；以系统可观测性分析为依据，设计最优标定路径。采用自适应交叉和变异概率，提升遗传算法的全局搜索和收敛性能。

2) 实际测试结果表明，与牛顿迭代法相比，本文方法具有标定精度高、标定速度快等优点，标定后能达到与传统标定方法相同量级的姿态精度，验证了本文方法的优越性和有效性。

3) 本文方法缩短标定时间，降低标定成本，具有重要的理论研究和工程应用价值。同时，由于遗传算法的参数选取直接影响标定精度及运算速度，如何通过适应度函数的动态变化及对选择、交叉、变异算子的改进以提升遗传算法的寻优精度和收敛速度是未来工作中值得进一步研究的问题。

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#### 文章信息

GAO Shuang, ZHANG Ruoyu

Rapid calibration method of MEMS accelerometer based on adaptive GA

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(10): 1982-1989
http://dx.doi.org/10.13700/j.bh.1001-5965.2019.0040