When a beam emitted from an active monostatic sensor system sweeps across a volume, the echoes from scatterers present will fluctuate from ping to ping due to various interference phenomena and statistical processes. Observations of these fluctuations can be used, in combination with models, to infer properties of the scatterers such as numerical density. Modeling the fluctuations can also help predict system performance and associated uncertainties in expected echoes. This tutorial focuses on "physics-based statistics," which is a predictive form of modeling the fluctuations. The modeling is based principally on the physics of the scattering by individual scatterers, addition of echoes from randomized multiple scatterers, system effects involving the beampattern and signal type, and signal theory including matched filter processing. Some consideration is also given to environment-specific effects such as the presence of boundaries and heterogeneities in the medium. Although the modeling was inspired by applications of sonar in the field of underwater acoustics, the material is presented in a general form, and involving only scalar fields. Therefore, it is broadly applicable to other areas such as medical ultrasound, non-destructive acoustic testing, in-air acoustics, as well as radar and lasers.

The twilight feeding migration of fish around a shallow water artificial reef (a shipwreck) was observed by a horizontal-looking, mid-frequency sonar. The sonar operated at frequencies between 1.8 and 3.6 kHz and consisted of a co-located source and horizontal line array deployed at 4 km from the reef. The experiment was conducted in a well-mixed shallow water waveguide which is conducive to characterizing fish aggregations at these distances. Large aggregations of fish were repeatedly seen to emerge rapidly from the shipwreck at dusk, disperse into the surrounding area during the night, and quickly converge back to the shipwreck at dawn. This is a rare, macroscopic observation of an ecologically-important reef fish behavior, delivered at the level of aggregations, instead of individual fish tracks that have been documented previously. The significance of this observation on sonar performance associated with target detection in the presence of fish clutter is discussed based on analyses of echo intensity and statistics. Building on previous studies of long-range fish echoes, this study further substantiates the unique utility of such sonar systems as an ecosystem monitoring tool, and illustrates the importance of considering the impact of the presence of fish on sonar applications.

Animals enhance sensory acquisition from a specific direction by movements of head, ears or eyes. As active sensing animals, echolocating bats also aim their directional sonar beam to selectively "illuminate" a confined volume of space, facilitating efficient information processing by reducing echo interference and clutter. Such sonar beam control is generally achieved by head movements or shape changes of the sound-emitting mouth or nose. However, lingual-echolocating Egyptian fruit bats, Rousettus aegyptiacus, which produce sound by clicking their tongue, can dramatically change beam direction at very short temporal intervals without visible morphological changes. The mechanism supporting this capability has remained a mystery.

Here we measured signals from free-flying Egyptian fruit bats and discovered a systematic angular sweep of beam focus across increasing frequency. This unusual signal structure has not been observed in other animals, and cannot be explained by the conventional and widely used "piston model" that describes the emission pattern of other bat species. Through modeling we show that the observed beam features can be captured by an array of tongue-driven sound sources located along the side of the mouth, and that the sonar beam direction can be steered parsimoniously by inducing changes to the pattern of phase differences through moving tongue location. The effects are broadly similar to those found in a phased array–an engineering design widely found in human-made sonar systems that enables beam direction changes without changes in the physical transducer assembly. Our study reveals an intriguing parallel between biology and human engineering in solving problems in fundamentally similar ways.