Bearings-Only Target Tracking Algorithm with Non-Gaussian Heavy-Tailed Distributed Noise

doi:10.12382/bgxb.2022.0058

Abstract

Abstract:

The bearings-only target tracking is a classic problem in the reserach on target tracking. Focusing on the problem of non-Gaussian heavy-tailed distributed noise in the model of target tracking, this paper proposes a new Kalman filter algorithm. Firstly, the hierarchical Gaussian model is established to approximate the unknown process noise and measurement noise of the non-Gaussian heavy-tailed distributed system. Next, the variational Bayesian inference is used to learn Mixture Probability to solve the problem of the filter’s performance degradation caused by the uncertainty of Mixture Probability, so as to improve the robustness of the filter. At the same time, for the nonlinearity of the bearings-only target tracking model, Modified Gain Kalman filter is used to reduce the influence of nonlinearity on the observation equation. The numerical simulations have verified that the proposed filter has better estimation accuracy and robustness than EKF, UKF and the variational Bayesian Kalman filters PEKF-Vb and VBEKF. The estimation accuracy of the proposed algorithm VBMGEKF is improved by 69.31%, 58.08%, 127.84% and 9.36%.

Key words: bearings-only target tracking, variational Bayes, hierarchical Gaussian model, heavy-tailed distributed noise, modified gain Kalman filter

LIU Can, WANG Hui, LIN Defu, CUI Xiaoxi, XU Hanhui. Bearings-Only Target Tracking Algorithm with Non-Gaussian Heavy-Tailed Distributed Noise[J]. Acta Armamentarii, 2023, 44(5): 1469-1481.

Figures/Tables 20

Fig.1 Hierarchical Gaussian State Space Model

Fig.2 Schematic diagram of 3D spatial target positioning

Fig.3 Diagram of target tracking trajectory scene

Fig.4 RMSE in distance error of target tracking (a=300)

Fig.5 RMSE inrelative distance error of target tracking (a=300)

Fig.6 RMSE in velocity error of target tracking (a=300)

Fig.7 RMSE in acceleration error of target tracking (a=300)

Fig.8 RMSE in distance error of target tracking (a=500)

Fig.9 RMSE in distance relative error of target tracking (a=500)

Fig.10 RMSE in velocity error of target tracking (a=500)

Fig.11 RMSE in acceleration error of target tracking (a=500)

Fig.12 RMSE in distance error of target tracking (a=700)

Fig.13 RMSE in relative distance error of target tracking (a=700)

Fig.14 RMSE in velocity error of target tracking (a=700)

Fig.15 RMSE in acceleration error of target tracking (a=700)

Table 1 Average RMSE under different noise distributions

算法	平均RMSE/m
算法	a=300	a=500	a=700	a=N(1000,1000)
EKF	11577	13501	16512	21623
UKF	10928	12606	14881	18819
PEKF-VB	11359	18168	27171	44173
VBEKF	7773	8721	10176	12805
本文算法	7156	7974	9241	11575

Fig.16 RMSE in distance error of target tracking (a=N(1000,1000))

Fig.17 RMSE in relative distance error of target tracking (a=N(1000,1000))

Fig.18 RMSE in velocity error of target tracking (a=N(1000,1000))

Fig.19 RMSE in acceleration error of target tracking (a=N(1000,1000))

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