Distributed Constrained Nonlinear Least-Squares Estimation Algorithm Over Unbalanced Directed Networks

This article deals with the problem of distributed constrained nonlinear least-squares (LS) estimation over multi-agent networks, where each agent sequentially obtains noisy and local observations about an unknown parameter vector over time. The communication between agents over the network is described by an unbalanced directed graph, and each agent only knows its own local objective function subject to a closed convex set constraint. In this context, a novel projection-type distributed LS estimation algorithm is developed by marrying the recent gradient tracking and push-sum techniques. It is shown that all local estimates converge almost surely to the true parameter vector. Unlike most existing projection-based distributed estimation algorithms which only work with diminishing step-sizes, the proposed algorithm can afford constant step-sizes and therefore enjoys a faster convergence rate. Performances of the proposed algorithm with regards to the asymptotic mean and covariance of the weighted estimation error are shown to be consistent with those of the centralized method. Finally, numerical examples are provided to demonstrate the proposed algorithm.