Distributed Parameter Estimation With Random Observation Matrices and Communication Graphs

The convergence of distributed parameter estimation algorithms is analyzed for a network of multiple nodes via information exchange with random observation matrices and communication graphs. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and the estimates of its neighbors, and an innovation term processing its own new measurement at each time step. By stochastic time-varying system, martingale convergence theories and the binomial expansion of random matrix products, the stochastic spatial-temporal persistence of excitation condition is established for mean square and almost sure convergence. Especially, it is shown that this condition holds for Markovian switching communication graphs and observation matrices, if the stationary graph is balanced with a spanning tree and the measurement model is spatially-temporally jointly observable. Furthermore, the quantitative bounds of mean square and almost sure convergence rates are both provided.