Recursive filtering for two-dimensional systems with missing measurements subject to uncertain probabilities

This paper addresses the recursive filtering problem for a class of two-dimensional systems suffering from missing measurements. The phenomenon of missing measurements occurs randomly and is depicted by a series of uncorrelated stochastic variables obeying individual Bernoulli distributions with uncertain probabilities. The main purpose is to design a recursive filter such that, in the presence of uncertain rates of the missing measurements, an upper bound is guaranteed and then minimized for the actual filtering error variance. The dynamics of the error variances are presented firstly. Then, by utilizing the stochastic analysis and inductive method, we establish an upper bound for the filtering error variance and subsequently achieve the minimal one at each time step by choosing a suitable filter gain. The desired upper bound can be obtained recursively by solving two sets of Riccati-like equations. Finally, a simulation example shows the effectiveness of the designed filter scheme.