Non-linear least squares estimation via network gossiping

Various estimation problems can be formulated as non-linear least squares (NLLS) problems, which can be solved using the Gauss-Newton algorithm. In this paper, we use gossiping to implement the Gauss-Newton algorithm in a fully distributed fashion, and show the convergence of this Gossip-based Gauss-Newton (GGN) algorithm. As an example, we show by simulations that the GGN algorithm is effective and robust in solving power system state estimation, and that the Mean Square Error (MSE) performance remains comparable to the centralized scheme and degrades gracefully even with random link/node failures.