Clutter background suppression and velocity estimation for moving targets are two critical problems in synthetic aperture radar-ground moving target indication (SAR-GMTI). A robust principal component analysis (RPCA) method is used to separate the sparse matrix of moving targets from the low-rank matrix of static backgrounds by using amplitude information in the image domain. However, the nonsparsity of the moving target echoes limits the performance of the RPCA in SAR-GMTI, and the velocity of the moving target cannot be estimated since the phase information is destroyed by the soft-thresholding operator in the RPCA process. To solve these problems, a novel moving target detection method based on RPCA (NRPCA) for SAR systems is proposed in this article. An atomic norm-based optimization program is first constructed to transform the data sparsity requirement into a moving target sparsity requirement. Although this optimization program is NP-hard, it is transformed to semidefinite programming by relaxation. Furthermore, accurate velocity estimation is performed using dual function theory and the alternating direction method of multipliers (ADMM) algorithm while the selection of the sparsity order k is avoided. Simulations and analyses based on experimental data illustrate the effectiveness of the proposed method.

Due to a serious shortage of training data, the performance of adaptive clutter suppression suffers remarkable degradation in heterogeneous environments. To address this problem, a novel clutter suppression method via affine transformation on manifolds is proposed. First, training samples in heterogeneous environments are characterized on an established manifold in which the distribution properties are analyzed. Then, a clutter classification scheme is proposed, whereby the KL divergence decision rule is derived to identify the training data as either homogenous or heterogeneous samples. Afterward, based on the distribution properties of samples and the clutter classification scheme, an affine transformation on manifolds is proposed for sample augmentation by transporting heterogeneous samples into the region of homogeneous samples. Finally, the clutter in the area of interest is suppressed on the manifold, which combines the transformed samples with the homogeneous samples, such that superior performance is obtained. Experiments on both simulated and real data validate the superiority of the proposed method in highly heterogeneous environments.

To treat the slow-moving fluctuating target detection issues, the information geometry-based track-before-detect algorithms, which combines the performance advantages of information geometry detectors and the multi-frame information integration ability of dynamic programming algorithm, are proposed in this paper. The proposed methods are based on the Hermitian positive definite (HPD) manifold and power spectrum (PS) manifold, that the geometric properties of the target feature track and clutter track on the HPD or PS manifold are exploited for the integration of inter-frame target information. Specifically, the IG-based scoring function is designed to evaluate the candidate trajectories, and a general IG-based DP algorithm is deduced to obtain the trajectories with the maximum integration of scoring functions. Moreover, to avoid the performance degradation resulting from the illegal candidate trajectories, a stricter constraint for the trajectories of slow-moving target is established, and a corresponding efficient IG-based DP algorithm is deduced by utilizing the skipping transition. Experimentally, the superiority of the proposed methods have been validated with the real-recorded ship target echo data and sea clutter data. The experimental results show that the proposed methods can provide a signal-to-clutter ratio improvement of approximately 5.5 dB.

Recently, the matrix information geometry (MIG) detectors have been speedily developed and demonstrated satisfactory performance in numerous applications. However, the MIG detector with a specific geometric measure is not always satisfactory under changing environments. This paper proposes the adaptive MIG detector with local metric tensor to match the detection environment for improving the adaptability of MIG detectors. The determination of the adaptive local metric tensor is formulated as an optimization problem based on the Neyman-Pearson criterion. Although this optimization is non-convex and constrained, this paper shows the equivalence between it and its Lagrange dual, and then a two-stage gradient descent method is designed to solve it. Moreover, the performance guarantee of the proposed method is provided, which reveals that it achieves asymptotically optimal detection performance among all MIG detectors. Experimentally, the adaptability and the effectiveness of the adaptive MIG detector are validated in three detection scenarios.

In this article, the power spectrum information geometry (PSIG) detector, which inherits the performance advantages of matrix information geometry (MIG) detectors in heterogeneous clutter backgrounds, is proposed. The PSIG detector can address two urgent problems in applications of MIG detectors, which are the expensive computation expense and unavailable acquisition ability of target velocity. Specifically, the PSIG detector utilizes power spectra (PSs) instead of high-dimensional covariance matrices to characterize sample data and employs subband filter bank to extend the detection from range cells to range-Doppler cells; thus, it requires less computation expense and can obtain the target velocity information according to the Doppler cell. Experiments based on the real data show the advantages of the proposed PSIG detectors in comparison with competitive methods. Especially, in the experiments with the real-recorded airborne radar data, the proposed method can effectively suppress the heterogeneous main-lobe clutter without any prior knowledge and provides detection probability improvement of more than 30% to the competitive methods with low false-alarm ratios.

To improve target detection performance in non-Gaussian backgrounds, the joint design of transmit sequence and receive filter for multiple-input-multiple-output (MIMO) radar is studied. By approximating the probability density function of observed non-Gaussian data with the Gaussian mixture model, a Riemannian manifold of Gaussian mixture distribution is developed to depict the complicated background first. Then, maximizing the geometric distance on manifolds, which is converted by maximizing the discrimination between the target and clutter, is proposed as the criterion for the joint design of transmit sequence and receive filter. Thereby, under the constant-modulus constraint, the joint design problem can be transformed into an optimization problem. However, the proposed optimization problem is non-convex and constrained. To solve this problem, a Riemannian optimization framework is provided. By taking the advantage of the underlying geometric and algebraic structure of the constraint space, the original constrained optimization problem in Euclidean space can be transformed into the unconstraint optimization problem over Riemannian product manifolds. Moreover, to obtain the global optimal solution, the Riemannian gradient of the geometric distance cost is derived for the conjugate gradient algorithm. Experiments demonstrate that the proposed method shows advantages in detection performance compared with competitive methods.