UGHF for acoustic tracking with state-dependent propagation delay

Acoustic tracking with propagation delay is a challenging problem for the following reasons: It is difficult to perform an accurate state prediction, as the time interval between the current state and the previous state is varying and unknown due to the propagation delay; and the target time (signal emission time) needs to be estimated in addition to the target position and velocity. With the state augmented with the target time, the state transition cannot be described by the commonly used explicit Gauss-Markov model. In this paper, we propose a new approach to solving this difficult problem by using the Gauss-Helmert model for the state transition, which consists of an implicit equation between two consecutive states. An unscented Gauss-Helmert filter is then developed based on this formulation. The new approach is applied to the bearings-only tracking problem with state-dependent propagation delay. Simulation tests are conducted to demonstrate the performance of the unscented Gauss-Helmert filter, which is shown to outperform other approaches in terms of estimation accuracy, especially when a target is moving at high speed.