Direction of Arrival Estimation in Elliptical Models via Sparse Penalized Likelihood Approach.

Area of Science:

• Signal Processing
• Array Signal Processing
• Statistical Inference

Background:

• Direction of Arrival (DOA) estimation is crucial for source localization.
• Existing methods can be sensitive to array output distribution uncertainty and noise.
• Exploiting signal sparsity is key for improved DOA accuracy.

Purpose of the Study:

• To develop a robust and accurate DOA estimation method using l1-penalized maximum likelihood (ML).
• To leverage the sparsity of gridded directions and the robustness of Complex Elliptically Symmetric (CES) distributions.
• To address non-convex optimization challenges in the presence of uniform or non-uniform sensor noise.

Main Methods:

• An l1-penalized maximum likelihood (ML) approach is proposed.
• Two majorization-minimization (MM) algorithms are developed to solve the non-convex optimization problem.
• A modified Bayesian Information Criterion (BIC) is introduced for penalty parameter selection.

Main Results:

• The proposed methods demonstrate high DOA estimation accuracy.
• The l1-norm penalty effectively exploits gridded direction sparsity.
• The CES distribution provides robustness against array output distribution uncertainty.
• Computational complexities of the MM algorithms are analyzed.

Conclusions:

• The developed l1-penalized ML approach offers superior DOA estimation accuracy.
• The MM algorithms provide efficient solutions for the optimization problem.
• The modified BIC effectively selects the appropriate penalty parameter, enhancing method performance.