针对参数不确定系统的高效离群值抑制算法

戚壮壮 ,  何秋生 ,  宋亚楠

科学技术与工程 ›› 2025, Vol. 25 ›› Issue (34) :14742-14750

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科学技术与工程 ›› 2025, Vol. 25 ›› Issue (34) :14742-14750 DOI: 10.12404/j.issn.1671-1815.2409743
电子技术、通信技术

针对参数不确定系统的高效离群值抑制算法

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Efficient Outlien Suppression Algorithm for Uncertain Parameter Systems

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摘要

针对全球卫星导航系统使用过程中因受到测量离群值影响导致状态估计不准确的问题,研究了一种离群值抑制鲁棒卡尔曼滤波(robust Kalman filtering with outlier suppression, RKFOF)技术。首先假设系统和测量模型的所有矩阵都受到范数有界参数不确定性的影响,采用纯粹的确定性观点并应用惩罚函数使其转变为鲁棒正则化最小二乘估计问题。然后利用新息向量正态分布的特性来确定离群值的动态阈值,最后对协方差矩阵求导得出最优卡尔曼增益。通过将偏移离群值同化到测量模型中,利用离群值偏移量统计来减轻其影响。与RKF算法、WKF算法和ORF算法等进行比较,实验表明:当离群值率小于30%时,几种算法效果相近;当离群值数量大于30%时,RKFOF算法的均方根误差相比于以上算法分别降低了42.3%、16.3%和13.1%以上。

Abstract

Aiming at the problem of inaccurate state estimation caused by measurement outliers during the use of the global navigation satellite system, a RKFOF(robust Kalman filtering with outlier suppression) technology was studied. Firstly, it was assumed that all matrices of the system and measurement models were affected by norm-bounded parameter uncertainties. A purely deterministic perspective was adopted, and a penalty function was applied to transform it into a robust regularized least squares estimation problem. Then, the characteristic of the normal distribution of the innovation vector was used to determine the dynamic threshold of outliers. Finally, the optimal Kalman gain was obtained by differentiating the covariance matrix. By assimilating offset outliers into the measurement model, the influence of outliers was mitigated through the statistics of the outlier offset. Compared with algorithms such as RKF(robust Kalman filter), WKF(weighted Kalman filter), and ORF(outlier rejection filter), experiments show that when the outlier rate is less than 30%, the effects of these algorithms are similar. When the number of outliers is greater than 30%, the root mean square error of the RKFOF algorithm is reduced by more than 42.3%, 16.3%, and 13.1% respectively compared with the above algorithms.

关键词

状态估计 / 全球卫星导航系统 / 离群值抑制 / 鲁棒卡尔曼滤波 / 范数有界

Key words

state estimation / GNSS / outlier suppression / RKF(robust Kalman filter) / norm-bounded

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戚壮壮, 何秋生, 宋亚楠. 针对参数不确定系统的高效离群值抑制算法[J]. 科学技术与工程, 2025, 25(34): 14742-14750 DOI:10.12404/j.issn.1671-1815.2409743
QI Zhuang-zhuang, HE Qiu-sheng, SONG Ya-nan. Efficient Outlien Suppression Algorithm for Uncertain Parameter Systems[J]. Science Technology and Engineering, 2025, 25(34): 14742-14750 DOI:10.12404/j.issn.1671-1815.2409743

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基金资助

国家自然科学基金(52274160)

太原市“双百攻关行动”第一批“揭榜挂帅”项目(2024TYJB0133)

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