三段判别域与最小二乘拟合的抗差滤波算法

doi:10.12305/j.issn.1001-506X.2021.05.23

摘要/Abstract

摘要：

组合导航系统卫星信号在传播过程中容易受到干扰导致卫星导航观测值出现故障。对于此问题, 提出一种基于最小二乘拟合原理的抗差滤波算法, 根据检测量的分布状态将故障分为三段判别域, 分别为无故障、偏差和超差的情况。无故障时不做处理, 出现偏差时对观测值进行降权处理, 对于超差情况, 用前几个时刻的观测值组成的拟合函数进行一个时刻的外延, 代替当前时刻的故障观测值。仿真结果表明, 三段判别域相对于两段判别域多了对偏差情况的处理, 提高了导航精度。连续时间内发生超差情况时, 相比于使用降权法, 基于最小二乘拟合的抗差滤波算法导航精度更高, 稳定性更好。

关键词: 组合导航, 卡尔曼滤波, 卡方检验, 最小二乘拟合

Abstract:

The satellite signal of integrated navigation system is susceptible to interference during the propagation process, which causes the satellite navigation observation value to fail. For this problem, according to the distribution state of the detection quantity, a robust filtering algorithm based on the principle of least squares fitting ia proposed, and the fault is divided into three discriminant domains, which are respectively no fault, deviation and out of tolerance. No processing is performed when there is no fault. When there is a deviation, the observation value is reduced in weight. For out of tolerance, a fitting function composed of the measured values at the previous few moments is used to extend a moment, instead of the fault observation value at the current moment. The simulation results show that the three discriminant domain has more processing for deviation than the two discriminant domain, and the navigation accuracy is improved. When an out of tolerance situation occurs in a continuous time, compared to the use of the reduced weight method, the robust filtering algorithm based on the least square fitting has higher navigation accuracy and better stability.

Key words: integrated navigation, Kalman filtering, chi-square test, least square fitting

中图分类号:

V448

蔡保杰, 邵雷. 三段判别域与最小二乘拟合的抗差滤波算法[J]. 系统工程与电子技术, 2021, 43(5): 1346-1353.

Baojie CAI, Lei SHAO. Robust filtering algorithm based on three discriminant domain and least squares fitting[J]. Systems Engineering and Electronics, 2021, 43(5): 1346-1353.

图/表 21

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显著性水平α	阈值T(1)
0.975	0.001
0.950	0.004
0.900	0.016
0.750	0.102
0.250	1.323
0.100	2.706
0.050	3.841
0.025	5.024
0.010	6.635
0.005	7.879

	抗差滤波	无抗差滤波
东向位置误差/m	-11.8~6.06	-25.8~32.6
北向位置误差/m	-6.64~7.54	-20.5~34.9
天向位置误差/m	-2.62~2.57	-7.9~13.9
东向速度误/(m/s)	-0.3~0.3	-1.16~1.11
东向速度误差/(m/s)	-1.3~1.2	-1.8~5.2
东向速度误差/(m/s)	-0.2~0.3	-0.8~1.11

	降权法	拟合法
东向位置误差/m	-6.86~5.41	-8.11~12.09
北向位置误差/m	-4.89~9.74	-8.26~8.58
天向位置误差/m	-2.72~6.52	-3.65~2.37
东向速度误差/(m/s)	-0.30~0.25	-0.38~0.41
东向速度误差/(m/s)	-0.63~0.68	-0.67~1.06
天向速度误差/(m/s)	-0.15~0.11	-0.17~1.18

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