State Estimation With Implicit Constraints of Circular Trajectory Using Pseudomeasurements

In some target tracking scenarios, tracking performance can be improved by the incorporation of a constraint imposed by a preset trajectory. When the complete information about the trajectory is known, the constraint can be formulated in an explicit way. However, in practical applications, only partial information about the trajectory may be available. This article deals with the modeling of implicit constraints, imposed by a circular trajectory, along with the constrained state estimation. First, constraint models for two kinds of representative implicit constraints, the destination constraint and the trajectory shape constraint, are proposed for various cases with different conditions of prior information. In the cases with destination constraints, the destination information and the trajectory shape information are assumed to be known a priori. For each case, two forms of constraint models are derived. One is a direct form model where the constraint relationships are used to eliminate the unknowns in the final model, whereas the other is a state augmentation form model, where the unknowns are augmented into the state vector being estimated along with the target state. In the cases with trajectory shape constraints, only the trajectory shape information is available. For each case, the state augmentation form models are formulated. Second, constrained state estimation methods are proposed by utilizing pseudomeasurement constructed based on the constraint models. Furthermore, an extension to the maneuvering target tracking by integrating the proposed constraint filters into an interacting multiple model estimator is also presented. Numerical simulations in two scenarios are provided to show the effectiveness of the proposed constraint models and state estimation methods.