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A New Variational Bayesian-based Kalman Filter with Random Measurement Delay and Non-Gaussian Noises

Chenghao Shan, Weidong Zhou*, Hanyu Shan, and Lu Liu
International Journal of Control, Automation, and Systems, vol. 20, no. 8, pp.2594-2605, 2022

Abstract : To improve the estimation accuracy of the Kalman filter in the scenario of random measurement delay and non-Gaussian process and measurement noises, a new variational Bayesian (VB)-based Kalman filter is proposed in this paper. First, the state expansion method and Bernoulli random variable (BRV) are utilized to characterize random measurement delay. Second, the one-step predicted probability density function (PDF) and measurement noise vectors are modeled as Student’s t (ST) distributions. Third, the likelihood function of two ST distributions is converted from a weighted sum to an exponential product to establish a hierarchical Gaussian state space model (HGSSM). Finally, the system state, BRV and intermediate random variables (IRV) are simultaneously estimated using the variational Bayesian (VB) method. Simulation experiment results indicate that the proposed filter has superior estimation performance to current filters to address the filtering problem of random measurement delay and non-Gaussian process and measurement noises.

Keyword : Kalman filter, non-Gaussian noise, random measurement delay, variational Bayesian (VB).

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