Robust State Estimation with Trajectory Shape Constraints

In some tracking applications, target states are subjected to a trajectory shape constraint, where only the trajectory shape is known a priori. By incorporating the trajectory shape constraint, the tracking performance can be improved. However, the existing state estimation methods with trajectory shape constraints are either of high computational load or of poor robustness due to the nature of the existing constraint models. In this study, in order to improve the robustness of the state estimation method with trajectory shape constraints, a generalised model for the trajectory shape constraint imposed by a straight trajectory is proposed. Three unknown general trajectory parameters of the trajectory are treated as states to be estimated along with the target state. Then, pseudo-measurements are constructed to incorporate the constraint information into estimators. For non-manoeuvring targets, a robust trajectory shape constraint filter is developed. The sequential measurement processing scheme is employed to reduce the computational load. A corresponding filter initialisation method is derived. While for manoeuvring targets, the proposed constraint filters are embedded into a conventional interacting multiple model estimator as sub-filters to handle the manoeuvring target tracking problem with a trajectory shape constraint. Monte-Carlo simulation results illustrate the effectiveness and robustness of the proposed algorithms.