Robust recursive filtering for uncertain systems with finite-step correlated noises, stochastic nonlinearities and autocorrelated missing measurements

In this paper, the robust recursive filtering problem is studied for a class of uncertain systems with finite-step correlated noises, stochastic nonlinearities and autocorrelated missing measurements. The correlated noises and stochastic nonlinearities are simultaneously considered, where process noises and measurement noises are arbitrary finite-step autocorrelated and cross-correlated. The missing measurements appear in a random way which is governed by missing rates obeying a certain probability distribution. The autocorrelation of missing rates, for the first time, is introduced to reflect the interaction of network bandwidth at adjacent sampling times. The aim of the addressed filtering problem is to design an unbiased robust recursive filter such that, for the uncertain systems, the filtering error is minimized at each sampling time. It is shown that the filter gain is obtained by solving a recursive matrix equation. A numerical simulation example is presented to illustrate the effectiveness of the proposed algorithm.