Gaussian-consensus filter for nonlinear systems with randomly delayed measurements in sensor networks

•The Gaussian filter is presented for nonlinear systems with delayed measurements.•The delay in the measurement equation obeys a Markov chain.•The posterior probability of delay is estimated based on the multiple model method.•A Gaussian-consensus filter gives a decentralized fusion in sensor networks.

This paper presents the decentralized state estimation problem of discrete-time nonlinear systems with randomly delayed measurements in sensor networks. In this problem, measurement data from the sensor network is sent to a remote processing network via data transmission network, with random measurement delays obeying a Markov chain. Here, we present the Gaussian-consensus filter (GCF) to pursue a tradeoff between estimate accuracy and computing time. It includes a novel Gaussian approximated filter with estimated delay probability (GEDPF) online in the sense of minimizing the estimate error covariance in each local processing unit (PU), and a consensus strategy among PUs in processing network to give a fast decentralized fusion. A numerical example with different measurement delays is simulated to validate the proposed method.