Estimating the degrees of freedom for a common CFAR detector

摘要

The heavy tailed false alarm density function of a common CFAR detector was previously derived. That density function was shown to be well approximated by a t-distribution with a reduced number of degrees of freedom. The number of degrees of freedom used in the approximate probability density function must be estimated form the data at the output of the clutter filter. Three estimators for the number of degrees of freedom have been developed. Their relative advantages and disadvantages are discussed. The most practical one is presented and its performance is analyzed. Experimental results on synthetic and real data are provided. The synthetic data is used to empirically test the bias of the estimator and to qualitatively evaluate its efficiency. The effectiveness of this estimator has been quantitatively demonstrated on ocean scenes with glint. The interest in knowing the false alarm density goes beyond just setting a CFAR threshold. This estimator is incorporated into an IRST signal processing and tracking algorithm suite containing a constant threshold. This density function together with the estimated number of degrees of freedom is used to adaptively estimate the probability of false alarm. Regions with a small number of degrees of freedom have a higher false alarm probability and consequently the tracker is more conservative in initiating tracks. The tracker uses the adaptive P$-FA$/ to improve the logic which initiates, confirms and deletes tracks.