Solving the Source Localization Problem via Global Distance Continuation

A new optimization algorithm is presented for the solution of the range-based source-localization problem employing a least-squares (LS) multidimensional scaling (MDS) formulation over non-squared distances. The algorithm is based on an progressive objective-smoothing technique known as global distance continuation (GDC). The fundamental requirements to implement a GCD method, namely, expressions for the smoothed cost-function and its derivatives, and lower bound on the starting value of the smoothing parameter lambda, are all derived analytically. The GDC method is known to be stable, fast and insensitive to initial point. Since distance measurement errors are a major cause of degradation in localization systems, by providing a GDC algorithm that does not require squaring measured distances we add to the latter advantages further robustness to noise. The performance of the resulting linear-distance GDC algorithm is evaluated via extensive Monte Carlo analysis and comparisons to a) the conventional squared-distance GDC algorithm, b) a Newton-based optimization technique of similar complexity, and c) the (impractical) grid-based exhaustive search method, i.e., maximum-likelihood (ML) estimator. The results reveal that the linear-distance GDC algorithm outperforms the considered alternatives and achieves the performance of the ML estimator.