Use of the Kullback-Leibler divergence in estimating clutter distributions

This paper investigates the application of the Kullback-Leibler divergence (KLD) to quantify the loss in detection performance associated with misestimating clutter distributions. The problem of detecting targets in long-tailed clutter is presented. The significance of the KLD as an information theoretic measure to enhance the accuracy of threshold setting is discussed. The behaviour of the KLD is shown by comparing K-distributions with different shape parameters, since this distribution is known to be a good fit to clutter, particularly to sea clutter. The KLD is compared with the difference in Probability of False Alarm, threshold and other ad hoc measures of the accuracy of the fit. The KLD is then used to analyse the quality of the fit to the K-distribution of the statistics in different Doppler bins of a coherent sea clutter spectrum. The paper concludes that the KLD is better than the ad-hoc measures for determining the cost of misestimating the distributions, although some ad-hoc measures can give results that are close to it.