Optimal range-difference-based localization considering geometrical constraints

This paper proposes a new type of algorithm aimed at finding the traditional maximum-likelihood (TML) estimate of the position of a target given time-difference-of-arrival (TDOA) information, contaminated by noise. The novelty lies in the fact that a performance index, akin to but not identical with that in maximum likelihood (ML), is a minimized subject to a number of constraints, which flow from geometric constraints inherent in the underlying problem. The minimization is in a higher dimensional space than for TML, and has the advantage that the algorithm can be very straightforwardly and systematically initialized. Simulation evidence shows that failure to converge to a solution of the localization problem near the true value is less likely to occur with this new algorithm than with TML. This makes it attractive to use in adverse geometric situations.