Due to the existence of signal propagation delay, the time interval between two consecutive signal emission times from the same target is varying and unknown, it will not be equal to the sampling interval of the observer. This phenomenon occurs more apparently in acoustic sensor surveillance system and complicates angle-only target tracking problems. As a result, the current state of the target kinematic information is difficult to estimate. For the double observer systems, even if they are synchronized, there is a time-offset between the observers due to signal propagation delay. So each observer receives signals from the same target at different emission times. In this paper, we propose a new algorithm to deal with this time-offset by building a set of constraints for a centralized double observer system in a three-dimensional environment, and using the Gauss-Helmert model for the state transition of two adjacent consecutive states. Furthermore, we consider the varying underwater sound speed and apply a sound speed profile model. Also, a novel algorithm is developed for the underwater environment, and its convergence condition is mathematically derived. Simulation results clearly validate that our proposed algorithm has better estimation accuracy in the underwater environment with comparison to other existing methods.