﻿ 小视场星敏感器量测延时滤波算法<sup>*</sup>
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Filtering algorithm of NFOV star sensor measurement delay
QIAN Huaming, WANG Di, WU Yonghui, HUANG Zhikai
College of Automation, Harbin Engineering University, Harbin 150001, China
Received: 2018-05-17; Accepted: 2018-08-24; Published online: 2018-09-05 09:34
Foundation item: National Natural Science Foundation of China (61573113)
Corresponding author. QIAN Huaming, E-mail:qianhuam@sina.com
Abstract: Aimed at measurement delay in the narrow field of view (NFOV) star sensor used for attitude estimation, a robust extended Kalman filter (REKF) algorithm is proposed to solve the measurement delay. According to the minimum mean square error criterion, the minimum upper bound of the variance is solved and the filter gain is determined by the minimum upper bound. The designed REKF algorithm can effectively solve the problem of measurement delay and improve the accuracy of attitude estimation. Finally, the simulation results show that the algorithm is superior to the conventional additive robust extended Kalman filter (AEKF), robust finite-horizon filter (RFHF) and robust Kalman filter (RKF) algorithm, which can better solve the problem of measurement delay in nonlinear systems, and the effectiveness of the algorithm is verified.
Keywords: narrow field of view (NFOV) star sensor     attitude estimation     extended Kalman filter (EKF)     robust filtering     measurement delay

1 组合姿态算法设计 1.1 系统模型

1.1.1 陀螺的量测模型

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1.1.2 星敏感器的量测模型

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1.2 状态方程与量测方程

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ωk为满足均值为零、方差为Qk= 的高斯白噪声；为乘性噪声项，s取3，ηik表示均值为零、方差为1的噪声，Aik表示有适当阶数的确定矩阵：

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Γk=diag{pk, 1  pk, 2…  pk, m}，由Γk的分布特性可知，是一个零均值的随机矩阵序列。由文献[11]可知，h(xk)满足:

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2 鲁棒扩展卡尔曼滤波算法

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2.1 估计误差方差

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2.2 算法设计

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3 仿真实验与分析 3.1 仿真环境

3.2 仿真分析

1) 情况1

 图 1 情况1时姿态角均方根误差对比 Fig. 1 Comparison of root mean square error of attitude angle in Case 1
 图 2 情况1时姿态角误差对比 Fig. 2 Comparison of attitude angle error in Case 1

2) 情况2

 图 3 情况2时姿态角均方根误差对比 Fig. 3 Comparison of RMSE of attitude angle in Case 2
 图 4 情况2时姿态角误差对比 Fig. 4 Comparison of attitude angle error in case 2
4 结论

1) 建立带有延时不确定项的误差模型，该模型考虑到非线性系统同时存在乘性噪声及量测模型延时的情况，对REKF滤波算法进行改进。

2) 在算法设计时，根据最小均方误差准则要求，通过求取预测误差方差和滤波更新误差方差的最小上界进而确定滤波增益的最优值。REKF算法的性能在于不确定性模型来表示实际系统，从而达到状态估计误差最小，精度最高。

3) 仿真结果表明，REKF滤波算法可以有效解决量测延时问题，提高姿态估计的精度。

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#### 文章信息

QIAN Huaming, WANG Di, WU Yonghui, HUANG Zhikai

Filtering algorithm of NFOV star sensor measurement delay

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(2): 234-242
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0279