<title>Detection of small targets in clutter modeled as a Gaussian mixture or a hidden Markov process</title>

Abstract

Sea clutter amplitude is often modeled as a compound random variable Z equals AX, where A is a positive valued random variable and X has a Rayleigh distribution. The K, class A, and discrete Rayleigh mixture distributions can be derived from these assumptions. Moreover, successive values of A may be correlated. If A is modeled as a finite Markov process, Z is described by a hidden Markov model (HMM). The applicability of Rayleigh mixture and hidden Markov models to RADAR sea clutter is demonstrated empirically. Amplitude only and phase coherent detection statistics are derived from these models using locally optimal and likelihood ratio techniques. Robust implementations of the locally optimal processor based on the Rayleigh mixture model have been developed, and empirical ROC curves demonstrate performance improvement of up to 9 dB in comparison with a CFAR detector for small targets in sea clutter. In a test case, the locally optimal hidden Markov detector is then shown to offer an additional 3 dB over the Gaussian mixture detector. Further examples compare the amplitude and phase coherent hidden Markov detectors with CFAR and Doppler processors.