Signal Processing for Non-Gaussian Statistics: Clutter Distribution Identification and Adaptive Threshold Estimation

Abstract

We examine the problem of determining a decision threshold for the binary hypothesis test that naturally arises when a radar system must decide if there is a target present in a range cell under test. Modern radar systems require predictable, low, constant rates of false alarm (i.e. when unwanted noise and clutter returns are mistaken for a target). Measured clutter returns have often been fitted to heavy tailed, non-Gaussian distributions. The heavy tails on these distributions cause an unacceptable rise in the number of false alarms. We use the class of spherically invariant random vectors (SIRVs) to model clutter returns. SIRVs arise from a phenomenological consideration of the radar sensing problem, and include both the Gaussian distribution and most commonly reported non-Gaussian clutter distributions (e.g. K distribution, Weibull distribution). We propose an extension of a prior technique called the Ozturk algorithm. The Ozturk algorithm generates a graphical library of points corresponding to known SIRV distributions. These points are generated from linked vectors whose magnitude is derived from the order statistics of the SIRV distributions. Measured data is then compared to the library and a distribution is chosen that best approximates the measured data. Our extension introduces a framework of weighting functions and examines both a distribution classification technique as well as a method of determining an adaptive threshold in data that may or may not belong to a known distribution. The extensions are then compared to neural networking techniques. Special attention is paid to producing a robust, adaptive estimation of the detection threshold. Finally, divergence measures of SIRVs are examined.