Recursive Filtering with Stochastic Uncertainties and Incomplete Measurements

In this paper, the recursive filter is designed for a class of discrete time-varying nonlinear systems with stochastic uncertainties and incomplete measurements. By employing a stochastic Kronecker delta function, the phenomena of the incomplete measurements are characterized which contain the signal quantization and missing measurements in a unified framework. We design a new recursive filter such that, for both stochastic uncertainties and incomplete measurements, we obtain an upper bound of the filtering error covariance and then minimize such an upper bound by properly designing the filter gains. It is shown that the desired filter gain can be obtained in terms of the solutions to two Riccati-like difference equations, and therefore the proposed filtering algorithm is recursive suitable for online computations. Finally, an illustrative example is provided to demonstrate the feasibility and usefulness of the developed filtering scheme.