Globally optimal Kalman filtering with correlated noises, random one-step sensor delay and multiple packet dropouts

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In this paper, we investigate the globally optimal Kalman filtering problem for uncertain stochastic systems with one-step autocorrelated process noises, cross-correlated noises, random one-step sensor delay and multiple packet dropouts. The multiplicative noises are used to characterize the random disturbances existing in systems. Random one-step sensor delay and multiple packet dropouts are characterized by employing two Bernoulli distributed random variables with known conditional probabilities. By separating the random variables from the non-random terms in the transmission and measurement matrices of the addressed dynamical systems, the process noises and measurement noises in the augmented systems depend on the state and the stochastic uncertain perturbations. The process noises are one-step autocorrelated and cross-correlated with the measurement noises. For this complicated systems, a globally optimal Kalman filtering algorithm is developed in the minimum mean square error (MMSE) sense. Finally, we provide a simulation example to illustrate the performance of the proposed filtering approach.