H(infinity)/H(2)/Kalman filtering of linear dynamical systems via variational techniques with applications to target tracking .

摘要

In this thesis, the similarities between the structure of the H _∞, H₂, and Kalman filters are examined. The filters used in this examination have been derived through duality to the full information controller. In addition, a direct variation of parameters derivation of the H_∞ filter is presented for both continuous and discrete time (staler case). Direct and controller dual derivations using differential games exist in the literature and also employ variational techniques. Using a variational, rather than a differential games, viewpoint has resulted in a simple relationship between the Riccati equations that arise from the derivation and the results of the Bounded Real Lemma. This same relation has previously been found in the literature and used to relate the Riccati inequality for linear systems to the Hamilton Jacobi inequality for nonlinear systems when implementing the H_∞ controller.; The H_∞, H₂, and Kalman filters are applied to the two-state target tracking problem. In continuous time, closed form analytic expressions for the trackers and their performance are determined. To evaluate the trackers using a neutral, realistic, criterion, the probability of target escape is developed. That is, the probability that the target position error will be such that the target is outside the radar beam width resulting in a loss of measurement. In discrete time, a numerical example, using the probability of target escape, is presented to illustrate the differences in tracker performance.