Optimal distributed filtering for nonlinear saturated systems with random access protocol and missing measurements: The uncertain probabilities case

The saturated-constrained distributed filtering problem is discussed for a class of discrete nonlinear systems with random access protocol (RAP) and missing measurements (MMs) under uncertain missing probabilities (UMPs). In order to prevent data congestions, the RAP is adopted to regulate the information transmission, where only one sensor is scheduled to have the communication right and transmit the information at each time step through a shared network. In addition, the phenomenon of MMs is considered, in which the UMPs are characterized by means of the nominal means and error bounds. The main purpose of this paper is to design a distributed filter under saturation constraint such that, for both RAP and MMs under UMPs, there exists an upper bound (UB) matrix of filtering error covariance and the corresponding distributed filter gain is constructed to minimize the trace of the received UB matrix by resorting to the matrix simplifying technique. Besides, the filtering algorithm performances are discussed regarding the boundedness and monotonicity of the presented distributed filtering scheme from the mathematical perspective. Finally, some comparisons are provided to illustrate the validity of the proposed time-varying distributed filtering algorithm.