Abstract
In maneuvering target tracking applications, the performance of the traditional interacting multiple model (IMM) filter deteriorates seriously under heavy-tailed measurement noises which are induced by outliers. A robust IMM filter utilizing Student’s t-distribution is proposed to handle the heavy-tailed measurement noises in this paper. The measurement noises are treated as Student’s t-distribution, whose degrees of freedom (dof) and scale matrix are assumed to be governed by gamma and inverse Wishart distributions, respectively. The mixing distributions of the target state, dof, and scale matrix are achieved through the interacting strategy of IMM filter. These mixing distributions are used for the initialization of time prediction. The posterior distributions of the target state, dof, and scale matrix conditioned on each mode are obtained by employing variational Bayesian approach. Then, the target state, dof, and scale matrix parameters are jointly estimated. A variational method is also given to estimate the mode probability. The unscented transform is utilized to solve the nonlinear estimation problem. Simulation results show that the proposed filter improves the estimation accuracy of target state and mode probability over existing filters under heavy-tailed measurement noises.
Highlights
The Kalman filter is widely used for target tracking due to the low computational complexity for real time processing and the statistic optimality under a linear state space model with Gaussian noises
We propose a robust interacting multiple model (IMM) filter against heavy-tailed measurement noises for maneuvering target tracking
The heavy-tailed measurement noises are treated as Student’s t-distribution, and the unknown dof and scale matrix are assumed to be governed by Gamma and inverse Wishart distributions, respectively
Summary
The Kalman filter is widely used for target tracking due to the low computational complexity for real time processing and the statistic optimality under a linear state space model with Gaussian noises. The variational Bayesian (VB) based Student’s t filter [27,28,29,30] represents the Student’s t-distribution of noises as an infinite mixture of Gaussians, and employs VB approach to jointly estimate the state and the unknown parameters of the Student’s t-distribution. As far as we know, Shen et al [31] considered utilizing Student’s t-distribution to improve the robustness of IMM filter for the first time They modeled the heavy-tailed measurement noises as Student’s t-distribution and employed IMM and VB approaches to estimate the target state, the probability of motion mode and the parameters of noises. The growth of dof estimates is prevented and the estimation accuracy of state is improved over existing filters under heavy-tailed measurement noises as shown in our simulation example
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