Low-complexity weighted pseudolinear estimator for TDOA localization with systematic error correction

A closed-form pseudolinear estimation algorithm for time-difference-of-arrival (TDOA) emitter localization was previously proposed by replacing TDOA hyperbolae with their asymptotes, effectively transforming the TDOA localization problem into a bearings-only localization problem. Despite having a good mean-square error (MSE) performance and low computational complexity, this algorithm was observed to suffer from systematic errors arising from the large misalignment between TDOA hyperbolae and asymptotes particularly in the near field and for poor geometries, resulting in increased estimation bias. To address the bias problem, this paper presents a systematic error correction technique based on a two-stage estimation process in which the estimation errors due to asymptote misalignment are computed from an initial location estimate and then subsequently corrected. The superior performance of the new algorithm compared with the maximum likelihood estimator is demonstrated with simulation examples.