Distributed parameter estimation with Markovian switching topologies and stochastic communication noises

This paper investigates the continuous-time distributed parameter estimation problem of sensor networks in uncertain sensing and communication environments. Each sensor uses a linear time-varying stochastic measurement model, and can only receive its neighbors´ estimation states corrupted by stochastic noises. The random switches between different communication topologies are described by Markov processes. We propose a continuous-time distributed estimation algorithm suitable for this kind of unreliable sensing and communication network. Under mild conditions on stochastic noises, gain function and topology-switching Markov chain, both the mean square and almost sure convergence of the designed algorithms are established by use of algebraic graph theory, stochastic differential equation theory, and Markov chain theory. The effect of sensor-dependent gain functions on the convergence of the algorithm is also analyzed.