基于TheoH方差的陀螺随机误差系数动态提取

朱战辉; 汪立新; 陈伟峰; 薛亮

doi:10.13700/j.bh.1001-5965.2016.0048

基于TheoH方差的陀螺随机误差系数动态提取

doi: 10.13700/j.bh.1001-5965.2016.0048

朱战辉^{1, 2},
汪立新^1, ,,
陈伟峰²,
薛亮¹

1.
火箭军工程大学控制科学与工程系, 西安 710025
2.
中国人民解放军 96401部队, 宝鸡 721006

基金项目:

国家自然科学基金 61503390

详细信息

作者简介:
朱战辉,男,博士研究生,工程师。主要研究方向:惯性系统及测试、数字信号处理

通讯作者:
汪立新,男,博士,教授,博士生导师。主要研究方向:惯性技术及测试。E-mail:wanglixin066@sina.cn.

中图分类号: V241.5
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出版历程
- 收稿日期: 2016-01-13
- 录用日期: 2016-03-18
- 网络出版日期: 2017-01-20

Dynamic extraction of stochastic error coefficients for gyro based on TheoH variance

ZHU Zhanhui^{1, 2},
WANG Lixin^{1
, ,},
CHEN Weifeng²,
XUE Liang¹

1.
Department of Control Science and Engineering, Rocket Force University of Engineering, Xi'an 710025, China
2.
Unit 96401 of the Chinese People's Liberation Army, Baoji 721006, China

Funds:

National Natural Science Foundation of China 61503390

More Information

Corresponding author: E-mail:wanglixin066@sina.cn

摘要

摘要:
针对运用动态Allan方差提取陀螺随机误差系数时，用截断窗截取原始信号造成方差估计置信度降低的问题，提出运用混合理论方差（TheoH方差）来代替Allan方差对截断窗内的数据进行分析，并提取出随时间变化的陀螺随机误差系数。TheoH方差改善了Allan方差计算时相关时间只能达到信号总时间的二分之一及长相关时间下方差估计置信度降低的问题，其计算的相关时间可以达到数据总时间的四分之三，有效改善了动态算法因数据截取造成误差系数估计置信度下降的缺陷。从对仿真信号和光学陀螺实测数据处理结果上来看，本文方法既能准确地对动态条件下陀螺量测信号的随机误差进行细化辨识，又能大幅提高中、长相关时间下方差估计的置信度。
- 陀螺 /
- 随机误差系数 /
- 动态Allan方差 /
- 混合理论方差(TheoH方差) /
- 窗函数
Abstract:
To solve the problem that the confidence on the estimate is poor when the dynamic Allan variance is used to analyze stochastic error of gyro, due to the reduced amount of data captured by the truncation windows, a new algorithm based on high confidence and hybrid theoretical variance (TheoH variance) is proposed. The Allan variance which is used to analyze the data in the truncation windows is replaced by TheoH variance in the proposed dynamic algorithm. The problems that the averaging time calculated with Allan variance is half of total data length and the confidence decreases at long-term averaging time are perfectly solved, the correlation time of the calculation can reach 3/4 of the total time of data, and the defect that the confidence level of the error coefficient estimates decreased is effectively improved, which is caused by the dynamic algorithm data interception. The measured data of dynamic test for optical gyroscope and simulation data are analyzed with the proposed algorithm and dynamic Allan variance. The results show that the proposed algorithm can describe the non-stationary of gyroscope more effectively and greatly improve the confidence of variance estimation at middle-term and long-term correlation time.
- gyro /
- stochastic error coefficients /
- dynamic Allan variance /
- hybrid theoretical variance(TheoH variance) /
- window function

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图 1 Theo1方差的采样原理

Figure 1. Sampling principle of Theo1 variance

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图 2 TheoH标准差的合成过程

Figure 2. Forming process of TheoH deviation

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图 3 DAVAR方法设计流程图

Figure 3. Flowchart of DAVAR method design

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图 4 陀螺输出随机误差仿真模型

Figure 4. Stochastic error simulation model of gyro output

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图 5 仿真信号的Allan标准差、Theo1标准差和TheoH标准差分析

Figure 5. Analysis by Allan deviantion，Theo1 deviantion and TheoH deviantion for simulated signal

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图 6 实测信号的DAVAR、DHVAR-A和DHVAR分析

Figure 6. Analysis by DAVAR,DHVAR-A andDHVAR for measured signal

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图 7 零偏不稳定性的动态提取

Figure 7. Dynamic extraction of bias instability

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图 8 陀螺随机误差输出

Figure 8. Output of stochastic error of gyro

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图 9 陀螺实测信号随机误差的DHVAR分析

Figure 9. DHVAR analysis of gyro measued signal stochastic error

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图 10 各随机误差系数随时间变化曲线

Figure 10. Time-variant curves of different stochasticerror coefficients

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图 11 零偏不稳定性的DAVAR和DHVAR动态提取

Figure 11. Dynamic extraction of bias instabilitywith DAVAR and DHVAR

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表 1 各种动态方法下随机误差系数的方差估计值

Table 1. Variance estimation of stochastic error coefficientsby different dynamic methods

系数	单位	期望值	DAVAR	DHVAR-A	DHVAR
Q	μrad	0.006 3	0.006 7	0.006 8	0.006 7
N	( )/h^1/2	0.001 0	0.001 1	0.001 1	0.001 1
B	( )/h	0.026 5	0.035 4	0.030 8	0.029 9
K	(°)/h^3/2	0.451 9	1.052 9	0.735 7	0.706 2
R	(°)/h²	1.119 3	9.797 3	5.806 5	5.622 4

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表 2 稳定条件下随机误差系数的估计值

Table 2. Estimation of stochastic error coefficient under steady condition

系数	单位	量纲	期望值	DAVAR	DHVAR-A	DHVAR
Q	μrad	×10^-3	0.400	0.047	0.043	0.041
N	(°)/h^1/2	×10^-4	0.011	0.011	0.011	0.011
B	( )/h	×10^-2	0.520	0.732	0.545	0.533
K	( )/h^3/2		14.1	38.9	20.7	18.3
R	(°)/h²		106	735	256	219

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