Target Motion Analysis of a Source in a Constant Turn from a Nonmaneuvering Observer

Abstract

The passive target motion analysis (TMA) of a source in constant turn motion by a platform moving with a constant velocity vector is addressed in this paper. The observer acquires either bearing measurements or bearing and frequency measurements. Firstly the bearings-only TMA is investigated. The observability conditions are established and the performance is analyzed with the Cramér-Rao lower bound. The behavior of the maximum likelihood estimator is evaluated using Monte-Carlo simulations, for various typical scenarios. The bearings and frequencies TMA is subsequently analyzed in the same way. Its performance is compared with that of the bearings-only TMA to evaluate the improvement brought about by frequency measurements, in some typical scenarios.Tactical aspects are also investigated.

Observability: range-only vs. bearings-only target motion analysis for a leg-by-leg observer's trajectory

“…This study could be extended in several directions: firstly, the observability when the observer has a constant acceleration vector, or when it travels in an arc of a circle, must be investigated, together with the extension to 3D space. Secondly, it is known (see [8] and [9]) that in BOTMA, when the observer does not maneuver, the target is observable in special situations; for example, when the target is traveling in an arc of a circle, or according to a two-leg motion model at constant speed. It is legitimate to wonder whether this conclusion in BOTMA remains valid in ROTMA; in particular, is the observer's maneuver unnecessary?…”

Observability: Range-Only Versus Bearings-Only Target Motion Analysis When the Observer Maneuvers Smoothly

“…This is a proof that the problem of ROTMA cannot be expressed under a linear form (otherwise the set of ghost-targets would be a linear subspace and hence uncountable). Obviously, we do not claim to have achieved a complete study of observability in ROTMA; for example, the cases when the observer's trajectory is composed of a CA motion followed by a CV motion, or when the motion of the observer is polynomial of order greater than two, or when the observer does not maneuver whereas the target does (which we studied in BOTMA in [2] and [9]), and so on must be investigated.…”

“…The square 2 y  being positive or null and the right hand side term being negative or null, we have 2 0    . That yields the vector…”

Performance of range-only TMA

“…When several solutions exist (presence of ghost-targets), we are able to give the other solution(s) from the one returned by the algorithm. This study could be extended to the case of maneuvering targets as in [10].…”