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Variational Bayesian filtering algorithm based on M-estimation with its application in bearing-only target tracking

delete2026-06-18
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PRE
AI
H
Haoran Chen
C
Chenxi Tang
G
Gang Wang *
DOI：10.1016/j.sigpro.2026.110766delete
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Abstract

Abstract

En 中文
In bearing-only tracking scenarios, the observation equation exhibits strong nonlinearity, and noise statistics are often unknown, time-varying, and accompanied by abrupt outliers. Traditional filters are prone to issues such as initial value sensitivity, geometric amplification, and confidence imbalance. This paper constructs a progressive filtering framework, sequentially integrating pseudolinear strategies, M-estimation methods, and variational Bayesian inference: first, linearizing the orientation observations through a single algebraic transformation to form a low-computation pseudo-linear structure; then, employ the variational Bayesian method to achieve online estimation of the measurement noise variance. Simultaneously, embed the Huber M-estimation within each variational iteration for iterative weighting, to suppress the impact of burst outliers and initial value jumps on state updates, completing a fused closed-loop of "variance adaptive estimation, outlier robust processing, and state recursive update." The corresponding algorithm is called the pseudo-linear Kalman filter combined with variational Bayesian and M-estimation (PMVBKF). On this basis, to further eliminate the inherent systematic bias of pseudo-linearization, this paper introduces a bias compensation mechanism and proposes BC-PMVBKF (Bias-Compensated PMVBKF). This algorithm adds a bias correction step based on the three-step closed-loop of PMVBKF, effectively solving the estimation bias problem caused by the correlation between measurements and states. Experiments demonstrate that under various platform quantity and noise intensity, the BC-PMVBKF consistently maintains the lowest RMSE and exhibits minimal error fluctuation against both geometric degradation and random outliers.
Keywords:
Bearing-only tracking
Pseudolinear transformation
Huber M-estimation
Variational Bayesian
Kalman filter
Bias compensation

Journal

Signal Processing cover
Signal Processing
IF:
3.6
Papers:
9.9K
Citations:
1.7W

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