A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student’s t-inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN.
In this article, a new Gaussian-Student's t mixing distribution-based Kalman filter is presented to investigate the filtering issue for linear stochastic system with unknown measurement random delay rate and non-stationary heavy-tailed measurement noise. Firstly, by employing a Bernoulli distributed variable and introducing system state extension method, the form of measurement likelihood function of double measurement noise distributions is converted from the weighted sum to an exponential product. Secondly, the non-stationary heavy-tailed measurement noises of current time and last time are modeled as Gaussian-Student's t mixing distributions by introducing extra Bernoulli distributed variables. Thirdly, the variational Bayesian technique is utilized to jointly infer the system state, the Bernoulli distributed variables of measurement noises, distribution mixing probabilities, the intermediate random variables, the Bernoulli distributed variable of measurement delay and the unknown measurement random delay rate. Finally, the effectiveness of the proposed Kalman filter is demonstrated by a target tracking simulation experiment.
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