Modeling and analyzing the statistics of sonar echoes from marine organisms

The statistics of echoes from active sonar systems can yield information on aggregations of scatterers. Of particular importance is the shape of the probability density function of echo magnitude (echo pdf), which can become strongly non-Rayleigh with heavy tails under important scenarios in the observation of marine organisms. The statistical methods utilize features in the echo fluctuation for inference, which differs significantly from conventional echo energy methods such as echo integration. Based on the physics of scattering from individual and aggregations of scatterers, as well as sonar system characteristics, we derive echo statistics models for direct inference of the composition and numerical density of marine organisms based on the shape of echo pdfs. These models are predictive and generally applicable to data collected from different systems in a variety of environments. The utility of echo statistics methods is demonstrated in a study where the numerical density of fish is estimated using the pdf of broadband echoes (30-70 kHz) collected in the ocean. Such application is enabled by the significantly improved temporal resolution of pulse-compressed broadband echoes, which reduces echo overlap and results in non-Rayleigh discriminative echo features for real-world data analysis. We also show by modeling that the statistics could offer information for interpreting echoes from mixed biological assemblages that are ubiquitous in the marine trophic cascade. We propose that echo statistics provide an additional dimension of information complementary to conventional spectral and temporal features, and can be applied without the need for absolute calibration of the system.