Linear optimal filtering for time-delay networked systems subject to missing measurements with individual occurrence probability

In this paper, we discuss the problem of optimal filter design for a class of networked stochastic systems subject to state delay and missing measurements. Both the random perturbations and the missing measurements are addressed in the system model, where the random perturbations are characterized by the multiplicative noises and the addressed phenomena of the missing measurements are modeled by a series of mutually independent Bernoulli random variables with individual occurrence probability. In view of the innovative analysis approach and the recursive projection formula, we design an optimal filter for networked systems with multiplicative noises and missing measurements such that the filtering error is minimized in mean square error sense. The main advantage of the proposed result lies in its recursive form applicable for online computations. In addition, we can see that the filter parameter can be obtained by solving some recursive equations. Finally, we give a numerical simulation example to illustrate the effectiveness of the filtering method proposed in this paper.