Abstract
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.
Highlights
Echoes, as measured through the receiver of an active monostatic sensor system, will typically fluctuate from ping to ping as the beam emitted from the system scans across a volume containing scatterers or as the scatterers in that volume move through the beam (Fig. 1)
One convenient approach is to normalize the random variable by its root-mean-square value hx2i1=2 and plot the probability density function (PDF), cumulative distribution function (CDF), and probability of false alarm (PFA) versus the random variable divided by hx2i1=2, where hÁ Á Ái is the average over a statistical ensemble of values
Since ai in this case is observed through the receiver of the sensor system, the exponential PDF includes the effects of both fluctuations from the stochastic nature of the scatterer and the variability due to the scatterer being randomly located in the beam
Summary
As measured through the receiver of an active monostatic sensor system, will typically fluctuate from ping to ping as the beam emitted from the system scans across a volume containing scatterers or as the scatterers in that volume move through the beam (Fig. 1). The formulations are completely limited to (1) first-order statistics as described above, and are mostly limited to (2) narrowband signals that are long enough so that the echoes from the scatterers overlap significantly, (3) direct path geometries where there are no boundaries present, and (4) a homogeneous medium Beyond those limited scenarios, examples are presented of more complex cases involving pulsed signals in which the echoes from the scatterers only partially overlap and the presence of boundaries and/or heterogeneities, including waveguide effects. II–IV in a presentation of echo statistics formulations for a wide range of important physical scenarios These scenarios include beampattern effects associated with main lobes of various width, narrowband and broadband signals, completely overlapping echoes (long signal) and partially overlapping echoes (short signal), single scatterers and mixed assemblages of scatterers, elongated and randomized scatterers, and geometries involving either a direct path and a homogeneous medium or ones involving the presence of boundaries and/or heterogeneities. II–IV are given, as well as references to previously published papers
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
