Model and Algorithm Improvement on Single Beacon Underwater Tracking

In range-based underwater tracking, the accuracy of the calculated slant range depends largely on the accuracy of the effective sound velocity (ESV). The ESV between a pinger and a receiver certainly is location dependent, and is very difficult to determine accurately. However, a common assumption adopted by many published papers related to single beacon underwater tracking is that the ESV is not only a known quantity, but also location independent. This paper proposes a novel Kalman-based single beacon tracking model that treats the ESV as a state variable. For applying this novel model, a solution method by treating transit time directly as measurement is developed. Traditional Kalman filters for single beacon underwater tracking often update state variables at a uniform rate. However, because the time of arrival measurement arrives at irregular time intervals, implementing a Kalman-based filter for updating state variables should carry out at nonuniform sampling rates. In addition to the realtime filter tracking, this paper also implements the Rauch–Tung–Striebel (RTS) smoother for postprocessing (reconstruction). This paper proposes a hybrid timing algorithm that can achieve both accuracy in filtering and efficiency in smoothing. Through numerical examples of using simulated and field data, both the extended Kalman filter and RTS smoother results show that while implementing the proposed model and algorithm, the tracking accuracy can be significantly improved and the estimated ESV agrees well with its true value.