2. Recursive Filtering with Missing Measurements and Quantized Effects

In Chap. 2, the recursive filtering problems are investigated for non-linear systems with missing measurements over a finite horizon. Firstly, the EKF problem with multiple missing measurements is studied. Both deterministic and stochastic non-linearities are included in the system model. The phenomenon of measurement missing occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0, 1]. The aim of the addressed filtering problem was to design a filter such that, in the presence of both the stochastic non-linearities and multiple missing measurements, an upper bound is obtained for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. Secondly, the proposed recursive filtering strategy is extended to deal with the filtering problem for systems with missing measurements, quantization effects, and multiplicative noises. A set of parallel results is obtained by using the similar techniques.