This paper addresses the problem of locating an acoustic source using a sensor network in a distributed manner, i.e., without transmitting the full data set to a central point for processing. This problem has been traditionally addressed through the maximum likelihood framework or nonlinear least squares. These methods, even though asymptotically optimal under certain conditions, pose a difficult global optimization problem. It is shown that the associated objective function may have multiple local optima and hence local search methods might stagnate at a sub-optimal solution. In this paper, we treat the problem in its convex feasibility formulation. We propose the aggregated projection onto convex sets (APOCS) method, which, in contrast to the original POCS method, converges to a meaningful limit even when the problem is infeasible without requiring a diminishing step size. Simulation results show convergence to the global optimum with significantly faster convergence rates compared to the previous methods.
Blatt and Hero REF describe the aggregated projection onto convex sets (APOCS) method by treating the localization problem in its convex feasibility formulation.
APOCS: a rapidly convergent source localization algorithm for sensor networks
IEEE/SP 13th Workshop on Statistical Signal Processing, 2005
IEEE/SP 13th Workshop on Statistical Signal Processing, 2005
Mathematics