On Pseudorange Estimation in a Quadratic Sound Speed Profile

A common assumption on a time-of-flight (ToF) measurement is that the transmitted wave propagates in a line-of-sight (LoS), i.e in a straight line. Nonetheless, there are occurrences when this premise does not hold, i.e. when the wave propagates in multipath or travels in a bending path. The latter is mostly the case for underwater acoustic waves when its speed varies w.r.t. depth in accordance with the medium's sound-speed-profile (SSP). In such case, the wave's traveled distance would not equal to its displacement. Therefore, calculating range based on ToFs becomes a less trivial task. In this paper, we address pseudorange estimation between an acoustic transponder and an autonomous underwater vehicle (AUV) when the wave travels in a non constant speed. Here, our main take is to consider a certain interval of depth where the SSP is not isogradient, i.e. change of the wave speed w.r.t. depth is not linear. Specifically, we deploy a quadratic function as an approximation for an actual SSP. This results in 2.5 • 10
^-2
% error. For a given ToF and depth measurement, we estimate the Snell parameter of the wave in question through root finding algorithm. Subsequently, we use the estimated parameter to calculate the pseudorange measurement in horizontal axis. Once the required measurements are available, we apply a standard discrete Kalman filter to estimate the kinematics of the AUV, i.e. its position and velocity. Through simulation, we demonstrate that the estimator is able to provide navigation with less than 1 m accuracy.