TRAJECTORY ESTIMATION UNDER OCCLUSION USING VARIANTS OF STATE-SPACE RECURSIVE LEAST SQUARES

Abstract

Tracking and trajectory determination are important estimation problems that are involved in several applications including surveillance, navigation, autonomous robot and control systems. Trajectory estimation involves accurate estimation of the path of an object based on remote measurement. Trajectory estimation is just not a special case of state estimation but is wider in scope and demands extensive use of statistical decision theory. In practical trajectory estimation problem several aspects should be considered e.g. trajectory dynamics, noise statistics, model uncertainties, external disturbances, missing observations, and dataassociation etc. This thesis is aimed to address practical impediments in trajectory estimation scenario and present algorithms for trajectory estimation under occlusion using variants of state-space recursive least squares (SSRLS). At first, a new approach for estimation of nonlinear systems, named Extended SSRLS (ESSRLS) is developed and its utility in the context of trajectory estimation is explored using nonlinear trajectory example of coordinated turn model. The performance of ESSRLS is contrasted against Extended Kalman filter (EKF) with exact trajectory dynamics, initial condition deviation, model uncertainty and occlusion. With its more sophisticated design vii approach, model independent nature, and the availability of useful tool in the form of forgetting factor ESSRLS exhibits far better performance as compared to EKF. Another major contribution of this thesis is to fulfill the need of an appropriate algorithm for occlusion handling. With the development of reduced-order SSRLS where SSRLS variants are operated in dual – mode form, the estimator performs well under both normal and occluded conditions. A performance comparison of SSRLS variants and other popular standards is made for straight-line, maneuvering and coordinated turn trajectory examples. Using proposed reduced-order approach, SSRLS variants outperforms other estimators under both normal and occluded conditions. In the last, we carry out Monte Carlo simulations to validate upper bounds on steady-state mean square estimation errors earlier developed by Malik in [1]. To study the performance of SSRLS in the presence of external disturbances, we consider straight-line trajectory in the presence of sinusoidal disturbance. The theoretical upper bound on MSE and estimated MSE are plotted for different forgetting factor values and validity of upper bounds is established with simulation results. To study the behavior of SSRLS to reject the effect of model uncertainty bearing estimation example is considered. SSRLS is implemented using constant velocity model and robustness and optimality of SSRLS is investigated through simulations.