Analysis of an Elliptic Localization Algorithm Using Fixed Point Iteration

A recent research on a fixed point iteration (FPI) algorithm for elliptic localization has shown tremendous promise in terms of reduced implementation complexity than existing algorithms without sacrificing performance [1]. However, no theoretical analysis was provided in this study. In this article, we present a thorough theoretical analysis of the FPI algorithm’s convergence and performance. These analyses show that: 1) the optimum estimate of the maximum likelihood estimation (MLE) problem is found in a sphere; 2) the FPI estimator is unbiased and its covariance matrix achieves the Cramér-Rao lower bound (CRLB) matrix when the measurement noise is small enough.