Sparse recovery algorithms have been applied to the Space-time adaptive processing for reducing the requirement of samples over the past 15 years. However, many Sparse recovery algorithms are not robust and need accurate user parameters. Conventional sparse Bayesian learning (SBL) algorithms are insensitivity to user parameters but converge slowly. To remedy the limitation, two iterative reweighted algorithms are proposed based on SBL. In order to minimise the SBL penalty function, we construct its upper-bounding surrogate function via the concave conjugate function and apply iterative reweighted algorithms to minimise the surrogate function. Theoretical analysis and numerical experiments all exhibit great performance of the proposed algorithms.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Space-time adaptive processing (STAP) plays an essential role in clutter suppression and moving target detection in airborne radar systems. The main difficulty is that independent and identically distributed (i.i.d) training samples may not be sufficient to guarantee the performance in the heterogeneous clutter environment. Currently, most sparse recovery/representation (SR) techniques to reduce the requirement of training samples still suffer from high computational complexities. To remedy this problem, a fast group sparse Bayesian learning approach is proposed. Instead of employing all the dictionary atoms, the proposed algorithm identifies the support space of the data and then employs the support space in the sparse Bayesian learning (SBL) algorithm. Moreover, to extend the modified hierarchical model, which can only apply to real-valued signals, the real and imaginary components of the complex-valued signals are treated as two independent real-valued variables. The efficiency of the proposed algorithm is demonstrated both with the simulated and measured data.

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Space-time adaptive processing (STAP) algorithms based on sparse recovery (SR) have been researched because of their low requirement of training snapshots. However, once some portion of clutter is not located on the grids, i.e., off-grid problems, the performances of most SR-STAP algorithms degrade significantly. Reducing the grid interval can mitigate off-grid effects, but brings strong column coherence of the dictionary, heavy computational load, and heavy storage load. A sparse Bayesian learning approach is proposed to mitigate the off-grid effects in the paper. The algorithm employs an efficient sequential addition and deletion of dictionary atoms to estimate the clutter subspace, which means that strong column coherence has no effect on the performance of the proposed algorithm. Besides, the proposed algorithm does not require much computational load and storage load. Off-grid effects can be mitigated with the proposed algorithm when the grid-interval is sufficiently small. The excellent performance of the novel algorithm is demonstrated on the simulated data.

To enhance the system performance of airborne radar in a limited‐sample environment, a robust sparsity‐based tri‐iterative space‐time adaptive processing (RSBTI‐STAP) method is proposed here. First, the proposed RSBTI‐STAP method constructs the clutter dictionary matrix by exploiting the a priori knowledge of radar platform. Next, the clutter representation coefficient, array error and weighted vectors are iteratively updated until convergence so as to obtain the estimated values of these three parameters. Finally, combined with the estimated clutter representation coefficient and array error vectors, the STAP weight vector is calculated for the purpose of clutter suppression. The proposed method can be robust to the array amplitude/phase error and can be free of the hyperparameters. Additionally, it does not need the training samples and has the global convergent properties. Numerical experiments based on the simulated data demonstrate the effectiveness of the proposed RSBTI‐STAP method.