Probability-Guaranteed Distributed Estimation for Two-Dimensional Systems Under Stochastic Access Protocol

This paper studies the probability-guaranteed distributed estimation problem for a kind of two-dimensional shift-varying sensor networks under the stochastic access protocol (SAP). The considered system is affected by unknown-but-bounded perturbations and sector bounded nonlinearity. The communication architecture of a multi-node network is expressed by a digraph. Due to the limited communication channel, each moment allows only one adjacent node to send its measurement data and schedules the signal transmission of the addressing system using the SAP, characterized by a series of independent random variables. For each smart sensor, we designed a distributed estimator based on the network topology as well as the SAP and derived sufficient conditions to ascertain the probability of the estimation error located in the desired ellipsoid being not less than the predetermined value. Collection of these probability ellipsoids acquired at each position is then minimized by solving a set of convex optimization problems in the meaning of matrix trace. Finally, efficiency of the estimator design strategy proposed is demonstrated using a numerical example.