基于Masreliez-Martin的鲁棒分数阶容积卡尔曼滤波算法及应用

doi:10.12305/j.issn.1001-506X.2023.01.27

摘要/Abstract

摘要：

针对具有非高斯量测噪声的分数阶离散时间非线性系统的状态估计问题, 提出一种基于Masreliez-Martin(简称为M-M)方法的鲁棒分数阶容积卡尔曼滤波器。在分数阶离散非线性动态系统基础上, 使用三阶容积原则推导了状态预测公式, 并使用M-M方法实现状态的量测更新, 构成了基于M-M方法的鲁棒分数阶容积卡尔曼跟踪算法。将提出的算法应用到再入目标的状态估计中, 仿真结果表明, 基于M-M方法的鲁棒分数阶容积卡尔曼滤波器优于分数阶无迹滤波器和分数阶容积卡尔曼滤波器。最后, 分析了不同程度的量测污染噪声对鲁棒分数阶容积卡尔曼滤波算法的估计性能影响, 验证了所提算法的鲁棒性。

关键词: 分数阶微积分, 容积卡尔曼滤波器, 状态估计, Masreliez-Martin方法

Abstract:

Aiming at the state estimation problem of discrete fractional-order nonlinear system with non-Gaussian measurement noise, a robust fractional-order cubature Kalman filter based on the Masreliez-Martin (M-M) method is proposed. Using the third-order cubature rule to derive the state prediction and refining the measurement update using M-M method, the M-M method based robust fractional cubature Kalman filter for the fractional discrete nonlinear dynamic system is derived. The proposed algorithm is applied to state estimation of the re-entry ballistic target. The simulation results show that the M-M method based robust fractional cubature Kalman filter is better than the fractional unscented filter and fractional cubature Kalman filter. Finally, the influence of contaminated measurement noise on the estimation performance of the M-M based robust fractional cubature Kalman filter algorithm is analyzed, and the results show that the proposed algorithm has good effectiveness and robustness.

Key words: fractional calculus, cubature Kalman filter (CKF), state estimation, Masreliez-Martin (M-M) method

中图分类号:

TP273

穆静, 严东升, 蔡远利, 王长元. 基于Masreliez-Martin的鲁棒分数阶容积卡尔曼滤波算法及应用[J]. 系统工程与电子技术, 2023, 45(1): 234-240.

Jing MU, Dongsheng YAN, Yuanli CAI, Changyuan WANG. Masreliez-Martin method based robust fractional cubature Kalman filtering algorithm and its applications[J]. Systems Engineering and Electronics, 2023, 45(1): 234-240.

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