Estimating instantaneous false alarm rate in a CFAR system by Bayesian and empirical Bayesian methods

In this paper it is shown that the instantaneous false alarm rate in a constant false alarm Rate (CFAR) system fluctuates from scan to scan and that Bayesian and Empirical Bayesian estimators can be applied to decrease the error between the actual and the assumed false alarm rate. The instantaneous false alarm rate is a random variable and its probability density function is derived for different system configurations. Bayesian estimators are applied in cases where analytical expressions of the mean and variance of the instantaneous false alarm rate can be derived. The mean square error in the estimated false alarm rate is shown to be less than the mean square variations of the instantaneous false alarm rate. Empirical Bayesian estimators are introduced and applied to cases where statistical properties of the false alarm rate are unknown. Empirical Bayesian estimators rely on past data to estimate the current false alarm rate and it is shown that they will converge asymptotically to the equivalent Bayesian estimators as the amount of past data gets large.