GLRT-Based CFAR Detection in the Latent Space for Extended Targets in Gaussian and Non-Gaussian Disturbance

The design of detectors with constant false alarm rate (CFAR) property is a cornerstone challenge in radar signal processing, for both Gaussian and non-Gaussian environments. To this aim, a forward-thinking strategy is to construct decision statistics as functions of suitable maximal invariants associated with invariant tests that guarantee, through a suitable transformation group, the CFAR property by construction. However, the distribution of such maximal invariants is often difficult to handle, especially for complicated non-Gaussian models, making the derivation of the generalized likelihood ratio test (GLRT) challenging. In this work, we introduce a novel learning-based CFAR detection framework, in which a trained probabilistic encoder maps maximal invariant statistics (or functions thereof) to a convenient low-dimensional latent space where a latent GLRT-based detector (L-GLRT) is easy to derive. More specifically, a cross-entropy loss function with Kullback-Leibler (KL) divergence regularization is adopted to encourage the latent distributions under both H0 (target free) and H1 (target present) hypotheses to be as close as possible, in an information-theoretic sense, to Gaussian densities. Mismatched data incorporated under either hypotheses are introduced to promote robustness or selectivity. The approach unifies Gaussian and non-Gaussian settings, spanning from point- like to extended targets under the complex multivariate elliptically contoured matrix (CMECM) family, and is benchmarked against state-of-the-art classical and data-driven detectors. Moreover, since the latent space low dimensional, insightful visualization of the behavior of the designed L-GLRT detectors can be obtained. Numerical results show that the proposed method achieves superior robustness/selectivity trade-offs while preserving CFAR guarantees by design and containing Pd losses under matched conditions.