Consensus+Innovations Distributed Estimation with Random Network Graphs, Observation Matrices and Noises

We analyze the convergence of distributed consensus+innovations parameter estimation algorithms over uncertain networks with communication noises. The linear observation of the unknown parameter by each agent, the underlying noisy communication network, and the noises therein are respectively characterized by a sequence of randomly time-varying observation matrices, random digraphs, and random variables. At each time step, every agent updates its estimation upon its measurement and interaction with its neighbors iteratively. By martingale convergence, algebraic graph and stochastic time-varying system theories, we prove that the algorithm gains can be designed properly such that all agents' estimates converge to the real parameter in mean square if the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition.