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We analyze convergence of decentralized cooperative online estimationalgorithms by a network of multiple nodes via information exchanging in anuncertain environment. Each node has a linear observation of an unknownparameter with randomly time-varying observation matrices. The underlyingcommunication network is modeled by a sequence of random digraphs and issubjected to nonuniform random time-varying delays in channels. Each node runsan online estimation algorithm consisting of a consensus term taking a weightedsum of its own estimate and neighbours' delayed estimates, and an innovationterm processing its own new measurement at each time step. By stochastictime-varying system, martingale convergence theories and the binomial expansionof random matrix products, we transform the convergence analysis of thealgorithm into that of the mathematical expectation of random matrix products.Firstly, for the delay-free case, we show that the algorithm gains can bedesigned properly such that all nodes' estimates converge to the true parameterin mean square and almost surely if the observation matrices and communicationgraphs satisfy the stochastic spatiotemporal persistence of excitationcondition. Secondly, for the case with time delays, we introduce delay matricesto model the random time-varying communication delays between nodes. It isshown that under the stochastic spatio-temporal persistence of excitationcondition, for any given boundeddelays, proper algorithm gains can be designedto guarantee mean square convergence for the case with conditionally balanceddigraphs.

Decentralized Cooperative Online Estimation With Random Observation Matrices, Communication Graphs and Time Delays