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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 less then 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
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