Nonlinear transformations for spatial matched filtering (detect‐on‐track)

Abstract

A detect‐on‐track algorithm based on the Hough transform has been applied to acoustic broadband correlograms for passive detection and localization. The Hough transform integrates (sums) the amplitudes along a set of delay curves of interest. The delay curves are calculated over a range of closest point of approach (CPA), speed, and heading of the targets. When normalized by the number of points, the Hough transform computes the arithmetic‐mean along the track. This process is referred to as an arithmetic‐sum (AS) transform. This AS transform optimally reduces the variance of the noise, but can also generate significant ambiguous sidelobes. To reduce the sidelobe, two nonlinear transforms are proposed: The logarithmic‐sum (LS) transform and the harmonic‐sum (HS) transform. The LS‐transform sums dB’s while the HS‐transform sums the reciprocal of the amplitudes along the track. When normalized by the number of points, the LS transform computes the geometric‐mean and the HS transform computes the harmonic‐mean along the track. Simulations show that the nonlinear transforms perform the same as the AS transform in noise‐limited environments but outperform the AS transform in sidelobe‐limited environments.