An Overdispersed Black-Box Variational Bayesian-Kalman Filter with Inaccurate Noise Second-Order Statistics.

Lin Cao,Zongmin Zhao,Chuyuan Zhang,Kangning Du,Chong Fu,Jianfeng Gu,Dongfeng Wang

doi:10.3390/s21227673

Abstract

Aimed at the problems in which the performance of filters derived from a hypothetical model will decline or the cost of time of the filters derived from a posterior model will increase when prior knowledge and second-order statistics of noise are uncertain, a new filter is proposed. In this paper, a Bayesian robust Kalman filter based on posterior noise statistics (KFPNS) is derived, and the recursive equations of this filter are very similar to that of the classical algorithm. Note that the posterior noise distributions are approximated by overdispersed black-box variational inference (O-BBVI). More precisely, we introduce an overdispersed distribution to push more probability density to the tails of variational distribution and incorporated the idea of importance sampling into two strategies of control variates and Rao–Blackwellization in order to reduce the variance of estimators. As a result, the convergence process will speed up. From the simulations, we can observe that the proposed filter has good performance for the model with uncertain noise. Moreover, we verify the proposed algorithm by using a practical multiple-input multiple-output (MIMO) radar system.

Highlights

The design of robust filters has been one of the most popular topics in modern radar systems and multiple-input multiple-output (MIMO)-based radar system in particular
For target B, the average performance of Kalman filter based on posterior noise statistics (KFPNS) is 29.62% and 41.56% higher than that of intrinsically Bayesian robust Kalman filter (IBRKF) and the classical Kalman filter separately
A Bayesian robust Kalman filter based on posterior noise statistics is designed by adding the calculation method of posterior noise

Summary

Introduction

The design of robust filters has been one of the most popular topics in modern radar systems and MIMO-based radar system in particular. It is impossible or prohibitively expensive to design an optimal filter by obtaining and/or understanding accurate models in the real world, which makes some nominally optimal filters suffer significant degradations in performance even if small deviations from the assumed models occur. The Bayesian-based robust approach has attracted significant attention in the design of robust filters due to the use of information with respect to the prior distribution of models in providing more accurate knowledge on the statistical model. The meaning of a Bayesian criterion is as follows: The average cost is the least. Θl ], θ ∈ Θ, where Θ is the set of all possible parameters, called the uncertain class These parameters can be obtained by solving the corresponding posterior distribution; the Bayesian robust filter can be expressed as follows: ψΘ (yk ) = arg minEθ [ Cθ (xk , ψ(yk )) |Yk ],

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Results

Conclusion