Modeling and State Estimation of Destination-Constrained Dynamic Systems Part II: Uncertain Arrival Time

Numerous human activities and object motions are intrinsically motivated by a goal or guided towards a destination. Exploring and exploiting such valuable intent information is expected to lead to considerably improved modeling and inference. This paper delves into a class of more practical destination-constrained (DC) systems, where the arrival time is unavailable in advance, and addresses two critical issues: DC dynamics modeling and estimation of DC state and arrival time. First, a generalized DC dynamic model is constructed by conforming a relaxed dynamics to the destination constraint. This modeling is not only easy to implement in practice but also produces a congruous DC dynamic model that has superior properties, e.g., applicable to various arrival time, whether known or uncertain. Second, a connection between the proposed DC dynamic model and the pseudo-observation-based bridge distribution model is established. For a linear Gaussian system with a linear destination constraint, these two models are mathematically equivalent despite their different modeling strategies and resultant model forms. Third, two DC state estimation algorithms are developed by incorporating the spatial information of the destination into state prediction. The two algorithms differ in computational efficiency and estimation capability. In particular, one of them can estimate more accurately the state and the arrival time simultaneously. Finally, for tracking of adversarial destination-guided targets, numerical simulations are provided to validate the effectiveness of the proposed modeling and estimation algorithms.