Radar detection using Siegel distance between autoregressive processes, application to HF and X-band radar

In this paper, we present an original generalization of the CFAR technique . The technique of CFAR consists in testing two alternative assumptions ldquopresence of targetrdquo versus ldquoabsence of targetrdquo in a distance-azimuth cell called ldquocell under testrdquo. In the case where the noise is Gaussian and additive, one can show that the CFAR is equivalent to withdraw from the signal under test the average of the surrounding signal and to divide the whole by the standard deviation of the surrounding signal. The presence of a target is then decided if the resulting quantity is higher than a given threshold determinated in order to maintain false alarm ratio constant. In our article, the treated data are the In Phase-Quadrature data obtained in each distance-azimuth cell. Those are interesting because their Fourier transform makes one possible to acquire the Doppler spectrum. These data are vectorial and more exactly are regarded as the realization of circular and centered complex Gaussian vectors. In order to generalize the technique of the CFAR, we take into account the works of C. R. Rao in information geometry and the works of T. Ando and D. Petz in order to define the distance between distributions as well as the concept of average. We will decide the presence of a target if the distance from the sample under test to the mean of the surrounding samples is higher than a certain threshold.