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

Abstract

The aim of so-called range-only target motion analysis (ROTMA) is to estimate the trajectory of a target by a single platform collecting range-only measurements. We focus on the observability analysis when the target is in constant-velocity motion. More precisely, the observability conditions are established when the observer's trajectory is composed of one or several legs. We establish a link between the Fisher information matrix (FIM), and the observability, after having proven the similarity of this matrix with the FIM encountered in bearingsonly target motion analysis (BOTMA). We compare observability statuses in BOTMA and ROTMA all along the paper.

Performance of range-only TMA

“…In [8], we showed that when the observer is in CV motion, the trajectory of the target is observable up to an isometry (rotation or axial symmetry). We characterized the set of targets (true target and ghost-targets) O in the same range as the target of interest:…”

“…1 depicts the scenario and the 500 estimates (O and T are for the initial positions of the observer and the target, respectively). Because the FIM is singular [8], the CRLB cannot be computed; therefore in Table I the Numerous other simulations with various scenarios allow us to conclude that the MLE is unbiased. But we cannot claim that the MLE reaches the CRLB, because for such scenarios, the FIM is singular.…”

“…Here, despite the presence of a ghost, the MLE is efficient. Note that adding a third leg does not guarantee observability [8]. (m/s).…”

“…Local observability was analysed by the rank of the Fisher information matrix (FIM) [7]. Global observability conditions were proposed recently in [8] and [9]. In the same vein, we present here some aspects of estimation (which was not addressed in [8] and [9]), in particular for scenarios where observability is not acquired and for which the FIM is fullranked, or conversely for scenarios where the trajectory of the target is observable, but the FIM is singular.…”

“…In section IV, the observer's trajectory is composed of two legs. Here, the target's trajectory can be observable or not [8]. Section V presents a case where the order of the observer's kinematic model is greater than that of the target, and still the trajectory of the target is unobservable [9].…”