Track Parameter Estimation from Multipath Delay Information

It is desired to track the location of an underwater acoustic source with range difference measurements from a stationary passive array. Many times, the array has only one or two sensors, and the multipath and intersensor range difference measurements are insufficient to localize and track a source moving along an arbitrary path 1]. Here, we propose to track sources with one- or two-sensur stationary passive arrays by making the simplifying assumption that the source's path can be described by a small set of so-called track parameters. Range difference information can then be used to estimate the track parameter set rather than the source location as a function of time. In this paper, we choose the track parameters to specify a straight-line constant-velocity constant-depth path. Cramer-Rao bounds are presented for estimating these track parameters from the time history of multipath and intersensor range difference measurements. It is shown that this track parameter set cannot be accurately estimated from the time history of a single multipath range difference without side information (an independent velocity estimate, for instance), although multipath and intersensor range difference measurements from a two-sensor array are generally sufficient to estimate the track parameter set. Computationally efficient techniques are presented which estimate track parameters from range difference measurements taken from one- and two-sensor arrays. Monte-Carlo simulations are presented which show that these techniques have sample mean-square error approximately equal to the Cramer-Rao bound when a single multipath range difference and an independent velocity estimate are available. The sample mean-square error is shown to be in the range of two to ten times the corresponding Cramer-Rao bounds when these techniques are applied to two-sensor range difference data.