A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise

In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussia...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2021-10, Vol.23 (10), p.1351
Main Authors: Shan, Chenghao, Zhou, Weidong, Yang, Yefeng, Shan, Hanyu
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Bayesian analysis
Kalman filter
Kalman filters
measurement loss probability
mixture distribution
Noise
Noise measurement
non-stationary heavy-tailed measurement noise
Random variables
Sensors
State space models
State vectors
Time measurement
variational Bayesian
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Summary:In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23101351