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摘要:
微惯性测量单元（MIMU）的标定技术是低精度惯性导航领域中的重要研究方向，传统标定方法操作复杂，标定精度严重依赖转台精度。为解决大批量MIMU快速标定的问题，提出了一种基于自适应遗传算法（GA）的微机电系统（MEMS）加速度计快速标定方法，将加速度计标定问题转化为参数优化问题。首先，利用模观测原理构造目标优化函数；然后，分析系统可观测度确定最优标定编排方案；最后，采用全局搜索的自适应遗传算法优化标定参数。实验结果表明：与牛顿迭代法相比，标定精度提升1~3个数量级，运算速度提高61%。标定后解算的水平姿态角误差小于0.1°，可实现与传统标定方法相同量级的姿态精度，验证了所提方法的优越性和实用性。
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.
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表 1 多位置下可观测性判别矩阵的秩和奇异值
Table 1. Rank and singular value of observable matrix under multi-position
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 
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表 2 本文方法与牛顿迭代法的标定结果对比
Table 2. Comparison of calibration results between proposed method and Newton's iteration
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。
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表 3 本文方法与牛顿迭代法的运算时间对比
Table 3. Comparison of operational time between proposed method and Newton's iteration
方法 运算时间/s 本文方法 164.28 牛顿迭代法 421.92
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表 4 水平姿态角误差均值
Table 4. Mean 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
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