Optimal Transmission Theory-Based Covariance Matrix Estimation for Low-Altitude Target Detection

‍ ‍Against the backdrop of rapid development in the low-altitude economy， typical application scenarios， such as drone logistics and offshore monitoring， face significant challenges in target detection due to complex electromagnetic interference， non-stationary target scattering characteristics， and limited sample data. Traditional covariance matrix estimation methods suffer severe performance degradation under strong non-Gaussian clutter and constrained reference cell conditions， leading to reduced detection probabilities and increased false alarm rates. To address these challenges， this study proposes a covariance matrix estimation framework based on optimal transport theory. By introducing the Bures-Wasserstein （BW） distance， an adaptive metric criterion is established in a multidimensional geometric space， effectively capturing the manifold structure and spatial correlations of clutter covariance matrices while enhancing adaptability to complex multidimensional scenarios. Two efficient covariance matrix estimation algorithms are subsequently presented. The Riemannian gradient descent （RGD）-based algorithm， BWRGD， performs iterative optimization on the positive-definite matrix manifold to converge to local optima under suitable step sizes. In contrast， the semi-definite programming （SDP）-based algorithm， BWSDP， ensures global optimality using the Schur complement theorem and linear matrix inequality constraints， thereby guaranteeing the tightness of the relaxation. Building on this， the estimated covariance matrices are embedded into an adaptive normalized matched filter （ANMF） to construct the BWRGD-ANMF and BWSDP-ANMF detectors. Their test statistics， expressed as functions of the covariance matrix， significantly enhance clutter suppression capabilities. Finally， simulated and measured clutter environments are used to evaluate the impact of factors such as the number of reference cells and radar pulse counts on detector performance. The results demonstrate that the proposed detectors outperform existing methods under constrained reference cell conditions， effectively improving target detection capability and robustness. Moreover， while the BWSDP-ANMF detector entails higher computational complexity， it delivers superior detection performance compared to the BWRGD-ANMF detector.