When the primary measurement sensor is passive in nature--by which we mean that it does not directly measure range or range rate--there are well-documented challenges for target state estimation. Most estimation schemes rely on variations of the Extended Kalman Filter (EKF), which, in certain situations, suffer from divergence and/or covariance collapse. For this and other reasons, we believe that the Kalman filter is fundamentally ill-suited to the problems that are inherent in target state estimation using passive sensors. As an alternative, we propose a bounded-error (or set-membership) approach to the target state estimation problem. Such estimators are nearly as old as the Kalman filter, but have enjoyed much less attention. In this study we develop a practical estimator that bounds the target states, and apply it to the two-dimensional case of a submarine tracking a surface vessel, which is commonly referred to as Target Motion Analysis (TMA). The estimator is robust in the sense that the true target state does not escape the determined bounds; and the estimator is not unduly pessimistic in the sense that the bounds are not wider than the situation dictates. The estimator is--as is the problem itself--nonlinear and geometric in nature. In part, the simplicity of the estimator is maintained by using redundant states to parameterize the target's velocity. These redundant states also simplify the incorporation of other measurements that are frequently available to the system. The estimator's performance is assessed in a series of simulations and the results are analyzed. Extensions of the algorithm are considered.

Les méthodes de trajectographie conventionnelles par mesures d’angle supposent que la source est en mouvement rectiligne uniforme tandis que l’observateur est manœuvrant. Dans cette thèse, nous remettons en cause cette hypothèse en proposant un autre modèle de cinématique de la source : le mouvement circulaire uniforme. Nous prouvons qu’une telle trajectoire est observable à partir d’un observateur en mouvement rectiligne uniforme. Puis, nous étudions l’apport de mesures additionnelles de fréquence ou la faisabilité de la trajectographie par mesures de distances. Le cas d’une source en mouvement rectiligne uniforme et d’un observateur manœuvrant est étudié pour ce dernier type de mesures. Chaque cas donne lieu à une analyse de l’observabilité de la trajectoire de la source et à la mise au point de l’estimateur du maximum de vraisemblance. Nous montrons que ce dernier s’avère le plus souvent efficace. / The conventional bearings-only target motion analysis methods assume that the source is in constant velocity motion (constant speed and heading) while the observer maneuvers. In this thesis, we reassess this hypothesis and propose another model of the kinematics of the source: the constant turn motion (an arc of circle followed at constant speed). We prove that this kind of trajectory is observable by an observer in constant velocity motion. Then, we study the contribution of the addition of frequency measurements or the feasibility of target motion analysis methods that use range only measurements. The case of a source in constant velocity motion with a maneuvering observer is examined for this last type of measurements. Each case leads to an analysis of the observability of the trajectory of the source and to the development of the associated maximum likelihood estimator. We show that this estimator often appears to be efficient.

In this study, accurate target tracking for bearings-only tracking problem is investigated. A new tracking filter for this nonlinear problem is designed where both range parameterization and Rao-Blackwellized (marginalized) particle filtering techniques are used in a Gaussian mixture formulation to track both constant velocity and maneuvering targets. The idea of using target turn rate in the state equation in such a way that marginalization is possible is elaborated. Addition to nonlinear nature, unobservability is a major problem of bearings-only tracking. Observer trajectory generation to increase the observability of the bearings-only tracking problem is studied. Novel formulation of observability measures based on mutual information between the state and the measurement sequences are derived for the problem. These measures are used as objective functions to improve observability. Based on the results obtained better understanding of the required observer trajectory for accurate bearings-only target tracking is developed.