Geometric Adaptive Matched Filtering on HPD Manifolds for Radar Target Detection

Matrix information geometry (MIG) has recently demonstrated distinct advantages in detecting radar targets in heterogeneous clutter backgrounds. However, existing MIG detectors still adopt a single geometric distance to quantify the dissimilarity between target signals and clutter, overlooking the availability of target prior information. This paper proposes a geometric adaptive matched filter (GAMF) for target detection on the Hermitian positive definite (HPD) manifolds. By exploiting target prior information, a steering-vector-guided trajectory is constructed, imposing an additional geometric constraint on the cell under test (CUT). The detection decision is then made by jointly measuring the deviation of the CUT from the clutter centroid and its proximity to the steering-vector-guided trajectory. GAMF realizes a dual mechanism of adaptive clutter characterization and steering-vector-guided target matching on the HPD manifold. Experimental results on simulated and measured data demonstrate that GAMF achieves superior detection performance and robustness, with an average detection performance gain of 4.6 dB compared with conventional methods, while exhibiting improved tolerance to steering-vector mismatch.