Convergence properties of normalized random incremental gradient algorithms for least-squares source localization

Michael G. Rabbat, Angelia Nedic

Abstract: We consider the problem of localizing a single source using received signal strength measurements gathered at a number of sensors. We assume that the measurements follow the standard path loss model and are corrupted by additive white Gaussian noise. Under this model, the maximum likelihood solution to the source localization problem involves solving a non-linear least squares optimization problem. We study the convergence property of a normalized incremental gradient method for solving this problem. Remarkably, despite the fact that the problem is non-convex, the normalized incremental gradient method generates a sequence of iterates which are attracted to the global optimum under some mild conditions.