Truncated Nuclear Norm Regularization Based Covariance Estimation for Airborne STAP

The low-rank feature of clutter covariance matrix (CCM) can reduce the number of training samples required for space-time adaptive processing (STAP). Therefore, this paper proposes a novel covariance estimation method based on truncated nuclear norm regularization (TNNR) for airborne STAP in heterogeneous environment. Specifically, TNNR is introduced to ensure the low rank estimation of CCM and transform the NP-hard problem to be convex. Different from the conventional rank minimization algorithm, such as the nuclear norm relaxation approach, the proposed TNNR based approach only minimizes portion of the smallest singular values, which are unrelated to the focused subspace, deriving a more accurate approximation to the rank function. Moreover, we combine the low rank property with the block-Toeplitz structure to estimate the CCM. The block-Toeplitz structure constrain can ensure the model established in continuous domain without off-grid problem. The simulation results indicate that the proposed CCM estimation algorithm based on TNNR outperforms several other methods.