Denis Pillon

Bearings-Only Maneuvering Target Motion Analysis from a Nonmaneuvering Platform

In bearings-only target motion analysis (BOTMA), the common hypothesis is that the observer maneuvers while the source is traveling according to a constant speed and course. But there is no reason that the roles of each protagonist cannot be exchanged. In this paper, we consider an uncommon scenario: the trajectory of the target is composed of two legs (i.e., a target brutally changes its heading while keeping its speed) and the observer does not maneuver. We prove that the trajectory of the target is observable under nonrestrictive conditions. A batch estimator is proposed, and its performance is compared with the classic Cramer-Rao lower bound (CRLB). Monte-Carlo simulations reveal the efficiency of the estimator. The robustness to a nonbrutal heading change is evaluated. Then an adhoc estimate taking the correct model into account is proposed and applied to simulated data. Again, its performance is compared with the CRLB, and its robustness is evaluated when the speed of the target changes. Finally, the respective performances of the target motion analysis (TMA) made by each mobile are compared.

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

The passive target motion analysis (TMA) of a source in constant turn (CT) motion by a platform moving with a constant velocity (CV) vector is addressed. The observer acquires either bearing measurements or bearing and frequency measurements. Firstly the bearings-only (BO)-TMA is investigated. The observability conditions are established, and the performance is analyzed with the Cramer-Rao lower bound (CRLB). The behavior of the maximum likelihood estimator (MLE) 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 BO-TMA to evaluate the improvement brought about by frequency measurements in some typical scenarios. Tactical aspects are also investigated.

New Observability Criterion in Target Motion Analysis

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),..., te [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.

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

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 (CV) motion. More precisely, the observability conditions are established when the observers 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 bearings-only target motion analysis (BOTMA). We compare observability statuses in BOTMA and ROTMA in the paper.

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

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 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.

A statistical fusion for a leg-by-leg bearings-only TMA without observer maneuver

In previous papers, we addressed the problem of bearings-only tracking of targets whose trajectory is composed of several legs from a non-maneuvering observer. We named it bearings-only maneuvering target motion analysis (BOMTMA). We proposed two estimates when the number of legs is equal to two: the classic maximum likelihood estimate (MLE) and an estimate based on a geometric fusion of leg-by-leg tracking. In this paper we introduce an estimate constructed on a statistical fusion whose main advantage, unlike the two previous ones, is that it can be easily extended to the case where the trajectory of the source is composed of three or more legs.