Adaptive Radar Detectors Based on the Observed FIM

Modified versions of Rao, Wald, and Durbin tests are considered exploiting an estimator of the Fisher Information Matrix (FIM) in place of the exact one. They are asymptotically equivalent (under some technical conditions) to the standard counterparts and rely on the use of the Observed FIM (OFIM), which is proportional to the negative Hessian of the log-likelihood. The developed framework is applied to the problem of adaptive radar detection of a point-like target in homogeneous or partially-homogeneous interference. Remarkably, for both the scenarios, it is shown that Rao, Wald, and Durbin tests with OFIM are statistically equivalent to the Generalized Likelihood Ratio Test (GLRT) for the specific detection problem (namely Kelly's detector for the homogeneous environment and the Adaptive Coherence Estimator (ACE) [S. Kraut and L. L. Scharf, "The CFAR adaptive subspace detector is a scale-invariant GLRT," IEEE Trans. Signal Process., vol. 47, no. 9, pp. 2538-2541, Sep. 1999.], also known as Adaptive Normalized Matched Filter (ANMF) [E. Conte, M. Lops, and G. Ricci, "Asymptotically optimum radar detection in compound-gaussian clutter," IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 617-625, Apr. 19951, for the partially-homogeneous scenario). This provides a new interpretation of the mentioned GLRTs laying the foundations for a better understanding of their theoretical validity.