Properties of range-only target motion analysis

In this paper, we address the problem of the range-only target motion analysis (RO-TMA) of a source whose velocity is constant when the trajectory of the observer is composed of two legs. By lack of room, we only illustrate the fact that the trajectory of the source is observable if and only if the bearings are constant. We end up with an apparent paradox: the Fisher information matrix (FIM) is singular if and only if the trajectory of the source is observable. Although it has received little attention so far, this technique of TMA is particularly interesting for it provides one with an instructive example of the nonequivalence between the notions of estimability (i.e. the Fisher information matrix is invertible) and of observability (i.e. the uniqueness of the solution). Finally, the classical maximum likelihood estimator is proposed and its efficiency is illustrated via Monte-Carlo simulations.