Performance Bounds for Waveguide-invariant-based Receiver Localization

Abstract

This paper examines performance bounds for the 2-D spatial localization (i.e., latitude and longitude) of a receiver in a shallow water environment using waveguide invariant (WI)-based estimates of the time-varying range to a source of opportunity (SOO). The time-varying position, or track, of the SOO is assumed known, and the source range estimates, which can be obtained from processing striations in the time-frequency spectrum of the measured acoustic pressure, are modeled as Gaussian random variables. Two nonlinear least squares (NLLS)-based localization methods are compared: the first method, based on prior work by the authors, applies uniform weighting to each of the range estimates and is shown to be sub-optimal, while the second method incorporates inverse-covariance weighting and achieves the Cramer-Rao lower bound (CRLB). A specific application for autonomous underwater vehicles (AUVs) is presented in which a submerged AUV operating near a coastal shipping lane attempts to localize itself using the acoustic emissions from nearby, transiting surface vessels that broadcast their position in real time via the automatic identification system (AIS). Sensitivity of the CRLB to source and receiver motion is investigated. Simulation results indicate the potential for WI-based localization methods to achieve errors of less than 100 m for AUVs operating in proximity to shipping lanes.