Statistical sampling and Bayesian illumination waveform design for multiple-hypothesis target classification in cognitive signal processing

Abstract

Statistical sampling algorithms are widely used in Bayesian signal processing for drawing real-valued independent, identically distributed (i.i.d.) samples from a desired distribution. This paper focuses on the more difficult problem of how to draw complex correlated samples from a distribution specified by both an arbitrary desired probability density function and a desired power spectral density. This problem arises in cognitive signal processing. A cognitive signal processing system (for example, in radar or sonar) is one that observes and learns from the environment; then uses a dynamic closed-loop feedback mechanism to adapt the illumination waveform so as to provide system performance improvements over traditional systems. Current cognitive radar algorithms focus only on target impulse responses that are Gaussian distributed to achieve mathematical tractability. This research generalizes the cognitive radar target classifier to deal effectively with arbitrary non-Gaussian distributed target responses. The key contribution lies in the use of a kernel density estimator and an extension of a new algorithm by Nichols et al. for drawing complex correlated samples from target distributions specified by both an arbitrary desired probability density function and a desired power spectral density. Simulations using non-Gaussian target impulse response waveforms demonstrate very effective classification performance.