An Efficient Sparse Bayesian Learning STAP Algorithm with Adaptive Laplace Prior

Abstract

Space-time adaptive processing (STAP) encounters severe performance degradation with insufficient training samples in inhomogeneous environments. Sparse Bayesian learning (SBL) algorithms have attracted extensive attention because of their robust and self-regularizing nature. In this study, a computationally efficient SBL STAP algorithm with adaptive Laplace prior is developed. Firstly, a hierarchical Bayesian model with adaptive Laplace prior for complex-value space-time snapshots (CALM-SBL) is formulated. Laplace prior enforces the sparsity more heavily than Gaussian, which achieves a better reconstruction of the clutter plus noise covariance matrix (CNCM). However, similar to other SBL-based algorithms, a large degree of freedom will bring a heavy burden to the real-time processing system. To overcome this drawback, an efficient localized reduced-dimension sparse recovery-based space-time adaptive processing (LRDSR-STAP) framework is proposed in this paper. By using a set of deeply weighted Doppler filters and exploiting prior knowledge of the clutter ridge, a novel localized reduced-dimension dictionary is constructed, and the computational load can be considerably reduced. Numerical experiments validate that the proposed method achieves better performance with significantly reduced computational complexity in limited snapshots scenarios. It can be found that the proposed LRDSR-CALM-STAP algorithm has the potential to be implemented in practical real-time processing systems.

A novel sparse recovery‐based space‐time adaptive processing algorithm based on gridless sparse Bayesian learning for non‐sidelooking airborne radar

“…where η > 0 is the regularisation parameter balancing the datafitting term kX − ΦAk 2 F versus the sparse penalty term kAk 2;0 . Nevertheless, solving the above optimisation problem is NP-hard [36], so many recently proposed algorithms have been developed to efficiently find sparse solutions [24][25][26][27].…”

“…The canonical $${\mathscr{l}}_{2,0}$$ MNM cost function of SR‐STAP is formulated by $$$\underset{\mathbf{A}}{\min }\ {\Vert \boldsymbol{X}-\boldsymbol{\Phi }\boldsymbol{A}\Vert }_{\mathrm{F}}^{2}+\eta {\Vert \boldsymbol{A}\Vert }_{2,0}$$$ where $$\eta > 0$$ is the regularisation parameter balancing the data‐fitting term $${\Vert \boldsymbol{X}-\boldsymbol{\Phi }\boldsymbol{A}\Vert }_{\mathrm{F}}^{2}$$ versus the sparse penalty term $${\Vert \boldsymbol{A}\Vert }_{2,0}$$. Nevertheless, solving the above optimisation problem is NP‐hard [36], so many recently proposed algorithms have been developed to efficiently find sparse solutions [24–27].…”

“…Motived by the burgeoning development of compressed sensing techniques, sparse recovery theory was first applied to estimate a high-resolution clutter spectrum by Maria in 2006 [16], demonstrating great potential for tackling the sample shortage problem. Since then, numerous sparse recovery-based STAP (SR-STAP) algorithms have been developed [17][18][19][20][21][22][23][24][25][26][27][28][29], exploiting the intrinsic sparsity of the clutter spectrum. Studies have shown that SR-STAP algorithms can outperform traditional statistical STAP methods with limited training samples (even with a single sample) in ideal cases [26,27].…”

“…Since then, numerous sparse recovery-based STAP (SR-STAP) algorithms have been developed [17][18][19][20][21][22][23][24][25][26][27][28][29], exploiting the intrinsic sparsity of the clutter spectrum. Studies have shown that SR-STAP algorithms can outperform traditional statistical STAP methods with limited training samples (even with a single sample) in ideal cases [26,27]. Depending on the adopted sparse signal model, SR-STAP can be further classified into two categories, namely, grid-based methods [17][18][19][20][21][22][23][24][25][26][27] and gridless methods [28,29].…”

“…Studies have shown that SR-STAP algorithms can outperform traditional statistical STAP methods with limited training samples (even with a single sample) in ideal cases [26,27]. Depending on the adopted sparse signal model, SR-STAP can be further classified into two categories, namely, grid-based methods [17][18][19][20][21][22][23][24][25][26][27] and gridless methods [28,29].…”