Novel closed-form ML position estimator for hyperbolic location

Geolocation of mobile terminals has become in the last decades an important issue in mobile networks. In the literature, there have been presented several closed-form position estimators based on time-difference-of-arrival (TDOA) measurements. Only Fang's estimator can be considered optimum in the maximum likelihood (ML) sense. Unfortunately, it can only be applied to the particular case of two TDOA measurements for the two dimensional (2D) location case. This paper presents an extension of this closed-form estimator to be applied to an arbitrary number of TDOA measurements by means of a transformation in the maximum likelihood function. This allows the ML function minimization to be split in several partial ML minimizations which only consider a subset of the available measurements, where the original Fang's estimator can be applied. Numerical simulations show that the proposed algorithm, that can be considered asymptotically the ML-estimator, attains the theoretical limits for all range of reasonable SNR values and has a low implementation complexity.