Multiscale Log-Euclidean Filtering on Matrix Manifolds for Enhanced Target Detection

In complex maritime environments, heavy-tailed non-Gaussian sea clutter presents a significant challenge for radar target detection, especially at low signal-to-clutter ratios (SCR) where target echoes are easily masked. To overcome this, we propose a multiscale CFAR detector operating on the Hermitian Positive-Definite (HPD) matrix manifold, introducing a multiscale Gaussian-weighted fusion mechanism in the Log-Euclidean domain to enhance target responses and suppress clutter while preserving HPD geometry. Covariance matrices are mapped to Log-Euclidean space, enabling multiscale weighted fusion across selected scales for improved target-background separation. Monte Carlo simulations on both synthetic and real sea-clutter data across various SCRs verify the effectiveness of the method. Experimental results show that, at a false alarm probability of $\mathbf {10^{-3}}$ and an SCR of 5 dB in real sea clutter, the proposed detector achieves a 28.2% increase in detection probability over the Log-Euclidean mean, outperforming conventional CFAR and LE-CFAR methods.