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Adaptive Radar Detectors Based on the Observed FIM

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 also known as Adaptive Normalized Matched Filter (ANMF) [2], 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.


The application of this new approach to the design of adaptive detectors for range-spread targets would be of great interest, since it would allow to synthesize new decision rules due to the absence of the UMP detector for the specific problem, they could possibly ensure different performance tradeoffs than already existing architectures, and/or possibly share some improved robustness and/or a smaller computational complexity


This approach is dictated by several motivations. First, for a general detection problem, the computation of the exact FIM may be difficult and, hence, it would be reasonable replacing the exact FIM with a suitable (and possibly more tractable) estimator; second, the resulting performance and ranking of detectors using a FIM estimator are not a-priori predictable and, hence, would deserve investigation.

In our specific case, the OFIM has been selected among the FIM estimators due to the fact that, under some technical conditions, it is a well-behaved estimator and may lead to the asymptotic equivalence between a specific test using FIM and the counterpart coupled with the OFIM.


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