Sensor network source localization via projection onto convex sets (POCS)

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 nonlinear least squares or maximum likelihood framework. 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 saddle points and hence any local search method might stagnate at a sub-optimal solution. In this paper, we formulate the problem as a convex feasibility problem and apply a distributed version of the projection onto convex sets (POCS) method. We give a closed form expression for the projection phase, which usually constitutes the heaviest computational aspect of POCS. Conditions are given under which, when the number of samples increases to infinity or in the absence of measurement noise, the convex feasibility problem has a unique solution at the true source location. In general, the method converges to a limit point or a limit cycle in the neighborhood of the true location. Simulation results show convergence to the global optimum with extremely fast convergence rates compared to the previous methods.