Estimating numerical density of scatterers in monotype aggregations using the statistics of broadband echoes: Applications to fish echoes

Abstract

The statistics of echoes from active sonar systems can yield important information on aggregations of scatterers. This study explores the use of echo statistics for estimating the numerical density of scatterers in monotype aggregations. Here, “monotype” refers to scatterers with the same scattering amplitude distribution in the considered frequency range. The signals are broadband, and the geometry involves direct paths between the sonar and the scatterers without interference from boundaries. Model probability density functions (pdf's) of envelope amplitudes of matched-filter outputs are numerically generated by varying the number of Rayleigh scatterers randomly-distributed in a half-space shell while accounting for the frequency-dependent system response, scatterer response, and beampattern effects. The shape of the echo pdf as observed by the sonar receiver is highly non-Rayleigh when there are few scatterers in the beam, and gradually approaches the Rayleigh distribution when the number of scatterers increases. This model is applied to broadband fish echoes (30-70 kHz) collected in the ocean through a best-fit procedure. The inferred numerical density of fish is comparable to the density estimated using corresponding measurements of volume backscattering strength and modeled target strengths.