Target Localization and Tracking for an Isogradient Sound Speed Profile

In an underwater medium the sound speed is not constant, but varies with depth. This phenomenon upsets the linear dependency of the distance traveled by an acoustic wave to the time it takes for the wave to travel that distance, and therefore makes existing distance-based localization algorithms less effective in an underwater environment. This paper addresses the problems of localizing a fixed node and tracking a mobile target from acoustic time-of-flight (ToF) measurements in a three-dimensional underwater environment with an isogradient sound speed profile. To solve these problems we first analytically relate the acoustic wave ToF between two nodes to their positions. After obtaining sufficient ToF measurements, we then adopt the Gauss-Newton algorithm to localize the fixed node in an iterative manner, and we utilize the extended Kalman filter for tracking the mobile target in a recursive manner. Through several simulations, we will illustrate that the proposed algorithms perform superb since they meet the Cramér-Rao bound (CRB) for localization and posterior CRB for tracking.