Adaptive multinoulli-based Kalman filter with randomly unknown delayed and lost measurements

A novel adaptive multinoulli-based Kalman filter (AMKF) is proposed to address the filtering problem of a linear system with random one-step delays and unknown measurement loss and delay probabilities. By introducing four discrete random variables with multinoulli distribution, the weighted sum of four Gaussian distributions is converted into exponential multiplicative form. The AMKF exploits a hierarchical Gaussian probability density function, in which the variational Bayesian (VB) method is utilized to deal with the probability density function of the joint distribution. In the simulation, the proposed approach performs better in estimation accuracy in terms of unknown probability of delay and loss compared to the existing approach.