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

Abstract

Range-only target motion analysis (ROTMA) consists of estimating the trajectory of a target using a single platform collecting range-only measurements. Observability analysis is carried out when the target is in constant-velocity motion and the observer maneuvers gently (a constant turn motion or a constant acceleration motion). We compare observability in bearings-only target motion analysis (BOTMA) and ROTMA throughout the paper, together with the rank of the Fisher information matrix. In each case, we establish necessary and sufficient observability conditions and we identify the virtual (or ghost) targets giving the same measurements when the system is not observable.

Performance of range-only TMA

“…Note that the observer and the target are on a rendezvous route. In this case the FIM is singular [9]. The estimates and the performance are given in Table III.…”

“…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]. We end with a more favourable case: the observer's trajectory contains an arc of a circle and this suffices to guarantee observability [9].…”

“…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.…”

Adaptive Robust Guidance Scheme Based on the Sliding Mode Control in an Aircraft Pursuit-Evasion Problem

“…At the same time, one must select a target's motion model, like the current statistical model, the Singer model, or the interactive multi-model scheme [3]. For polishing up the estimating performance of the target's maneuvers, observability of the interception problem with LOS angular velocity measurement is analyzed [4]. It concludes that current homing guidance schemes result in a decrease in observability of tracking the target.…”

“…Because relative distance cannot be observed from the line-of-sight measurement, it is necessary to use a special type of self-motion to solve this problem. Thus, the method of introducing LOS angular oscillatory motion is presented in [4] to improve the observability. The oscillatory motion of the LOS angle improves observability, but the trajectories generated by the guidance schemes are inevitably influenced by this motion mode and affect final guidance precision.…”