Gain-constrained filtering with probabilistic sensor delays and correlated noises

In this paper, the gain-constrained recursive filtering problem is investigated for a class of time-varying stochastic systems with probabilistic sensor delays and correlated noises. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step auto-correlated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraints. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.