Geometric nonlinear filtering theory with application to the maneuvering aircraft tracking problem
Bishop, Robert H.
Antoulas, Athanasios C.
Doctor of Philosophy
A geometric nonlinear filter (GNF) is designed for application to the problem of tracking a maneuvering aircraft. The aircraft tracking problem is a state estimation problem and a state prediction problem. A nonlinear aircraft maneuver model is proposed for use in the state estimation as well as the state prediction. This nonlinear model is based on the so-called coordinated turn and describes planar trajectories. The GNF design approach involves state transformations with output injection to transform the nonlinear system model to a linear form, known as the observer canonical form. For many nonlinear systems, such as the proposed aircraft maneuver model, this linearizing transformation does not exist. Therefore, for the maneuvering aircraft model, a transformation to an approximate observer canonical form is given. Utilizing a Lyapunov stability approach, sufficient conditions for stability of the GNF estimation error are derived. No such conditions exist for the extended Kalman filter (EKF). The GNF was found to be stable in cases where the EKF was not stable. The tracking performance of the GNF compares favorably with the EKF for various levels of measurement noise. However, the GNF offers a substantial savings in computational time making it more attractive than the EKF for use in a fire control computer.