Maximum likelihood estimation for compound-gaussian clutter with inverse gamma texture

The inverse gamma distributed texture is important for modeling compound-Gaussian clutter (e.g. for sea reflections), due to the simplicity of estimating its parameters. We develop maximum-likelihood (ML) and method of fractional moments (MoFM) estimates to find the parameters of this distribution. We compute the Cramer-Rao bounds (CRBs) on the estimate variances and present numerical examples. We also show examples demonstrating the applicability of our methods to real lake-clutter data. Our results illustrate that, as expected, the ML estimates are asymptotically efficient, and also that the real lake-clutter data can be very well modeled by the inverse gamma distributed texture compound-Gaussian model.

I. Introduction

Compound-Gaussian models are often used to characterize heavy-tailed clutter distributions in high-resolution radar [1], [2] as well as to model speech waveforms, fast fading channels, and various radio propagation channel disturbances (see [1] and the references therein). The key problems in compound-Gaussian clutter modeling are choosing the texture distribution and estimating its parameters. Many texture distributions have been studied (see [2]–[4] and references therein) and their parameters are typically estimated using the method of moments (MoM). We present maximum-likelihood (ML) and method of fractional moments (MoFM) estimates to find the parameters of a compound-Gaussian clutter with a texture having an inverse gamma probability density function (pdf), which leads to a closed form pdf of the clutter and simplifies the computations. Using numerical examples, we compare the mean-square errors (MSEs) of these estimates with their Cramér-Rao bounds (CRBs). We illustrate the applicability of our results to real lake-clutter data, collected by the IPIX radar of McMaster University, Hamilton, ON, Canada.