Time-difference-of-arrival regularised location estimator for multilateration systems

A new version of an open form localisation algorithm, called regularised location estimator (RLE), for time difference of arrival (TDOA) multilateration systems is proposed. This algorithm is based on Tikhonov regularisation and on maximum-likelihood estimation. It is aimed to solve the localisation problem for both well-conditioned and ill-conditioned situations. It provides solutions that are statistically and numerically efficient, in contrast to the algorithms in the literature providing solutions that are only efficient in one sense and that do not solve the ill-conditioned situations, which can be found in some operational conditions. A recursive formulation for estimating the regularisation parameter is provided and some mathematical analyses about the proposed estimator are also presented. A comparison with a large number of open and closed form algorithms in the literature is performed with both simulated and real data. The results show that the novel TDOA-RLE provides superior performance even in the case of well-conditioned situations.