R-means localization: A simple iterative algorithm for range-difference-based source localization

In this paper, we present a simple iterative algorithm for range-difference (RD) based localization. The RD-based localization is a kind of nonlinear optimization problem and generally it has no closed-form solution. Through auxiliary function approach, we derive iterative update rules without any tuning parameters, which just consists of 1) averaging source-sensor distances, 2) averaging the source positions estimated by updating source-sensor distance on each sensor with the source-direction fixed. Due to the resemblance of the iterative averaging to k-means clustering, we call it r-means localization. The convergence of the algorithm is guaranteed. The acceleration of the convergence is also investigated.