Journal of Shanghai Jiaotong University ›› 2020, Vol. 54 ›› Issue (9): 881-889.doi: 10.16183/j.cnki.jsjtu.2020.99.014

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A Variational Bayes-Based Filter with Uncertain Heavy-Tailed Noise

DONG Xiangxiang, LÜ Runyan, CAI Yunze*()   

  1. Department of Automation; Key Laboratory of System Control and Information Processing of the Ministry of Education; c. Key Laboratory of Marine Intelligent Equipment and System of the Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2020-01-06 Online:2020-09-28 Published:2020-10-10
  • Contact: CAI Yunze*


An adaptive Pearson Type VII based filter was proposed to deal with measurement noise with heavy tailed distribution and uncertain statistical characteristics in nonlinear filtering. In view of the fact that the scale matrix and degree-of-freedom (DOF) parameters of traditional robust Kalman filter are fixed, which cannot adjust adaptively. The Pearson Type VII distribution was selected to model the heavy tailed noise to realize the adaptive estimation of 2-DOF parameters based on Cubature Kalman filter (CKF). Inverse Wishart and Gamma distributions were used to describe prior distributions of the scale matrix, 2-DOF parameters, and auxiliary parameters. Besides, time updating of these parameters was performed through a forgetting factor. Based on the variational Bayesian theory, the variational iteration of joint posterior probability density function formed by states together with the 2-DOF parameters and auxiliary parameters was performed, and the states and noise parameters were estimated simultaneously. The simulation results show that this algorithm has a higher filtering accuracy than the traditional robust CKF under the condition of uncertain heavy tailed noise.

Key words: heavy tailed noise, Pearson Type VII distribution, variational Bayesian (VB), joint estimation, Cubature Kalman filter (CKF)

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