On the Maximum Likelihood Estimation of Position

In this paper, we obtain the Maximum Likelihood Estimator (MLE) of position in the framework of Global Navigation Satellite Systems (GNSS) for an antenna array based receiver. This theoretical result sets the basis of a completely different approach to the positioning problem, in contrast to the conventional two-steps position estimation, consisting of estimating the synchronization parameters of the in-view satellites and then performing a position estimation with that information. To the authors' knowledge, this is a novel approach which copes with signal fading and it mitigates multipath and jamming interferences. If a satellite link is severely affected by channel characteristics, the rest of the in-view constellation can overcome the nuisance in the joint estimate. The resulting multivariate ML cost function to optimize is shown under several environments and some computer simulation results are provided comparing the proposed method, both for a single antenna and an antenna array based receivers, with common single point navigation solution in terms of positioning errors, showing an increased performance.