New Observability Criterion in Target Motion Analysis

Abstract

In the literature different observability concepts can be found sometimes far from the initial concept introduced by Kaiman in 1960. In this paper, we will consider only the original concept i.e. the one concerning linear deterministic systems. A system is so-called observable on the interval [t0, t1] if and only if a continous measurement set Y(t),..., tε [t0, t1] allow the calculus of the initial state vector X (to). Three remarks should be made: 1. This concept is independant of the coordinate system. 2. For a linear stochastic system with normally noised measurements, the observability concept is equivalent to the inversability of the Fisher information matrix. 3. For non-linear systems, things are not so simple: a criterion (often very tedious) exists for each observability concept (weak, observability, uniform observability, local observability, ...). This is the case of T.M.A. for which systems are naturally non-linear.