Generalized Taylor expansion of the waveguide invariant for a homogenous waveguide with variable bathymetry (L)

In a weakly range-dependent waveguide with variable bathymetry, range estimation using the adaptive array invariant incorporated the waveguide invariant β via an eighth-order Taylor expansion [Byun, Song, and Cho, J. Acoust. Soc. Am. 149, 1363-1370 (2021)]. This letter extends the method by introducing a generalized Taylor expansion for β, enabling flexible order selection for convergence to the analytic expression and providing new insights into convergence rates. Validation with experimental data shows reduced angular dependency at longer ranges and highlights the effectiveness of low-order approximations due to the smaller maximum angle of arrival.