A mixed time-scale algorithm for distributed parameter estimation : Nonlinear observation models and imperfect communication

The paper considers the algorithm NLU for distributed (vector) parameter estimation in sensor networks, where, the local observation models are nonlinear, and inter-sensor communication is imperfect, in the sense, that the network links fail randomly and inter-sensor transmission is quantized. The paper introduces the class of separably estimable observation models, which generalizes the notion of observability in centralized linear estimation to distributed nonlinear estimation. We show that the NLU algorithm leads to consistent and asymptotically unbiased estimates of the parameter at each sensor for separably estimable observation models. In other words, the sensors reach consensus almost sure (a.s.) to the true parameter value. The algorithm NLU is a mixed time scale stochastic algorithm, characterized by two different decreasing weight sequences associated with the consensus and innovation updates. The analysis of the NLU algorithm, thus, does not follow under the purview of standard stochastic approximation, making the analysis developed in the paper of independent theoretical interest.