Recursive Filtering with Fading Measurements, Sensor Delays, and Correlated Noises

In this chapter, the recursive filtering problem is firstly investigated for a class of discrete-time non-linear stochastic systems with random parameter matrices, multiple fading measurements, and correlated noises. The phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval. The purpose of the addressed filtering problem is to design an unbiased, recursive, and optimal filter in the minimum variance sense. Intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation. Based on the proposed filter approach, the gain-constrained recursive filtering problem is studied for a class of non-linear time-varying stochastic systems with probabilistic sensor delays and correlated noises. 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 prespecified filter gain constraint.