As an effective clutter suppression method for airborne radar, the atomic norm minimization (ANM)-based space-time adaptive processing (STAP) method suffers from high computational complexity and parameter setting difficulty. To solve these problems, a deep unfolded (DU) ANM algorithm is proposed for STAP in this study. First, the clutter estimation problem based on ANM is established. Then, the problem is solved via the alternating direction method of multipliers (ADMMs) and a deep neural network (DNN), which is trained by designing an appropriate loss function and constructing a complete dataset. At last, the clutter-plus-noise covariance matrix (CNCM) and the STAP weighting vector are obtained by processing the training range cell data via the trained network. Simulation results show that the proposed DU-ANM-STAP method can achieve higher clutter and noise suppression performance with lower computational cost than the existing ANM-STAP methods.

In this paper, 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 spectrums 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.

Moving targets in a heterogeneous environment can be extracted through traditional robust principal component analysis (RPCA). Competitive RPCA algorithms address a nonconvex constraint by relaxing it to a fixed rank. However, the solution does not necessarily reach a global optimum. To address this problem, a moving target detection method by RPCA in the topological space of low-rank matrices is proposed to obtain superior target detection performance. First, RPCA is considered in the topological space of low-rank matrices, which is the closure of the fixed-rank manifold. Then, combined with manifold optimization and the proximal gradient, the RPCA-PGTSLr algorithm is applied to solve the problem caused by a non-differentiable sparsity term, so that the target can be precisely extracted. Experiments performed on measured data demonstrate that the proposed method exhibits advantages in detection performance over competitive methods in a heterogeneous environment.

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.

Recently, the matrix information geometry (MIG) detector, which characterizes sample data as a Hermitian positive definite (HPD) matrix located on the HPD manifold, was rapidly developed and demonstrated extraordinary performance in numerous applications, especially in heterogeneous clutter backgrounds. In this paper, the geodesic normal coordinate (GNC)-based manifold filter is proposed to improve the detection performance of the MIG detector in strong clutter backgrounds. Using the GNC system, the distribution of target echoes and clutter on the high-dimensional manifold can be visualized and analyzed. Moreover, by exploiting the information concerning the distribution of matrices, the manifold filter is proposed to enhance target echoes and suppress strong clutter. Then, the manifold-filter-based MIG detector is designed, and its superiority is theoretically analyzed. The actual clutter data is utilized to verify the effectiveness of the proposed method. The results show that the proposed manifold filter achieves a signal-to-clutter ratio improvement of more than 5 dB over the existing MIG detectors.

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.