An expectation maximization and smoothing approach for indirect acoustic estimation of fish size and density

The smoothed expectation and maximization (EMS) method is shown to be superior to deconvolution, the most commonly used indirect method for estimating fish acoustic size. This is primarily because EMS avoids artifactual modes in estimates of acoustic size. The expectation, maximization and smoothing method starts with the iterative statistical technique called expectation and maximization and adds smoothing between iterations. Application of the EMS method assumes that the acoustic observations in the voltage domain are realizations of a non-homogeneous Poisson process of rate λi. The E-step estimates expected values ofλiusing the conditional distribution of the “complete” data, which is binomial, given the Poisson distributed acoustic observations. The M-step uses the log likelihood function of the Poisson distributed “complete” data to find maximum likelihood estimates of λi. The S-step smoothes theλiestimates, with a Gaussian convolution filter. The method is demonstrated using a simulated data set of known statistical properties and a data set from the acoustics literature.