Adaptive array invariant

Abstract

The array invariant (χ) developed for robust source-range estimation in shallow water is based on the broadband dispersion characteristics in ideal waveguides that can be summarized by the waveguide invariant, β=cos²θ, with propagation angle θ. The standard array invariant relies on the waveguide invariant being constant, e.g., β = 1, valid for small propagation angles (θ<20°). In this paper, the array invariant is extended to fully incorporate the angle dependence of the waveguide invariant (β=cos²θ), referred to as adaptive array invariant and denoted by χ_β=χ/β, which, in theory, provides a perfect range estimate without constraining the propagation angle. The superior performance of the adaptive array invariant is illustrated via numerical simulations in an ideal waveguide, and then demonstrated using experimental data from a ship of opportunity radiating broadband noise (200-900 Hz) and a vertical array in a shallow-water environment.