Maximum likelihood localization of sources propagating in a random media using intensity measurements

A statistical signal processing solution is proposed for locating a monochromatic source propagating in a random media. The media is fully parametrized by the normalized scattering strength γ and scaled range X, which depend upon the physics of the media. M independent intensity measurements are observed, each drawn from the generalized gamma distribution. This has been shown by Ewart [J. Acoust. Soc. Am. 86, 1490–1498 (1989)] to describe sources propagating through internal waves in ocean environments. The parameters of the distribution are related to the scattering parameters, γ and X. Maximum likelihood estimation is used to infer X, given the observations and our knowledge of γ. The estimation performance is well-characterized by the Cramer–Rao lower bound (CRLB). The results show that we can estimate range to a precision of about 20%, for ranges up to half the distance to the focus of the medium. Simulation results verify both the normality of the estimates and the validity of the CRLB as a predictor of the estimator precision at these ranges. The practical value of this method will depend on our ability to gather enough independent measurements, and on the accuracy of the statistical models we assume, including prior knowledge of γ. It can be expected to augment other methods such as matched field processing.