Acoustic tracking with propagation delay is a challenging problem due to the following reasons: 1) 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; 2) 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 (GMM). We have presented recently a new approach to solve this difficult problem by using the Gauss-Helmert model (GHM) for the state transition, which consists of an implicit equation between two consecutive states. An interacting multiple model unscented Gauss-Helmert filter (IMM-UGHF) is presented here based on this formulation, and is applied to the bearings-only tracking (BOT) with state-dependent propagation delay. Two GHMs, the nearly constant velocity (CV) model and coordinated turn (CT) model, are developed to cope with different target motions in the IMM-UGHF. Simulation tests are conducted to demonstrate the performance of the IMM-UGHF, which is shown to outperform other approaches in terms of estimation accuracy.