存在非高斯重尾分布噪声的纯方位目标跟踪算法

doi:10.12382/bgxb.2022.0058

摘要/Abstract

摘要：

纯方位目标跟踪是目标跟踪研究中的热点问题,针对目标跟踪方程中的非高斯重尾分布噪声问题,提出了一种针对非高斯重尾分布噪声的卡尔曼滤波算法。该方法通过建立基于存在异常值的高斯分布的层次高斯模型来近似未知的非高斯重尾分布系统过程噪声和测量噪声,并使用变分贝叶斯推断来学习混合概率,解决混合概率不确定带来的滤波性能下降的问题,从而提高滤波的鲁棒性。同时针对纯方位目标跟踪模型的非线性,结合修正增益卡尔曼滤波来降低量测方程非线性的影响。数值仿真结果表明,相对于EKF、UKF和变分贝叶斯卡尔曼滤波PEKF-VB、VBEKF,新算法VBMGEKF估计精度分别提高了69.31%、58.08%、127.84%和9.36%,具备更好的鲁棒性与精度。

关键词: 纯方位目标跟踪, 变分贝叶斯, 层次高斯模型, 重尾分布噪声, 修正增益卡尔曼滤波

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

刘灿, 王辉, 林德福, 崔晓曦, 徐晗晖. 存在非高斯重尾分布噪声的纯方位目标跟踪算法[J]. 兵工学报, 2023, 44(5): 1469-1481.

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.

图/表 20

图1 层次高斯SSM

Fig.1 Hierarchical Gaussian State Space Model

图2 三维空间目标定位示意图

Fig.2 Schematic diagram of 3D spatial target positioning

图3 跟踪目标轨迹场景示意图

Fig.3 Diagram of target tracking trajectory scene

图4 目标跟踪距离误差RMSE(a=300)

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

图5 目标跟踪相对误差RMSE (a=300)

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

图6 目标跟踪速度误差RMSE(a=300)

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

图7 目标跟踪加速度误差RMSE (a=300)

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

图8 目标跟踪距离误差RMSE(a=500)

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

图9 目标跟踪相对误差RMSE (a=500)

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

图10 目标跟踪速度误差RMSE(a=500)

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

图11 目标跟踪加速度误差RMSE(a=500)

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

图12 目标跟踪距离误差RMSE(a=700)

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

图13 目标跟踪相对误差RMSE (a=700)

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

图14 目标跟踪速度误差RMSE(a=700)

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

图15 目标跟踪加速度误差RMSE(a=700)

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

表1 不同噪声分布下的平均RMSE

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

图16 目标跟踪距离误差RMSE (a=N(1000,1000))

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

图17 目标跟踪相对误差RMSE (a=N(1000,1000))

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

图18 目标跟踪速度误差RMSE(a=N(1000,1000))

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

图19 目标跟踪加速度误差RMSE(a=N(1000,1000))

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

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