Localization of networks using various ranging bias models

Given a network of stations with incomplete and possibly imprecise inter-station range measurements, it is required to find the relative positions of the stations. Several models for the bias in the range estimates are discussed. We present a set of iterative algorithms that cope successfully with the various bias models and provide Maximum Likelihood position estimates. Proof of convergence is provided. A procedure, albeit designed for precise measurements, is also proposed for the initialization of the iterative algorithms. We also present compact, matrix form expression for the Cramér-Rao Bound (CRB). Numerical examples are provided to corroborate the results.