A novel robust filter for non-stationary systems with stochastic measurement loss probabilities

This paper introduces an innovative variational Bayesian Kalman filtering method to tackle the filtering challenges posed by stochastic measurement losses and heavy-tailed noise in non-stationary linear systems. The non-stationary heavy-tailed noise is represented by a Bernoulli random variable that combines a Gaussian distribution with a heavy-tailed distribution. The Gaussian distribution has a high probability and nominal covariance, while the heavy-tailed distribution has a low probability and a covariance that can adapt to different situations. The Undisclosed nominal covariance is assumed to adhere to the distribution characteristics of the inverse Wishart. To construct a hierarchical Gaussian state space model, the measurement probability function is reshaped into an exponential product form through the utilization of extra Bernoulli random variable. Ultimately, the variational Bayesian technique is utilized to estimate the unknown random variables jointly. Simulation results show that the proposed algorithm has significant improvement in both filtering accuracy and measurement loss probability estimation.