Robust Recursive Widely Linear Diffusion Adaptive Filtering With Linear Constraint

Modern distributed estimation systems, particularly in distributed sensor networks including those for radar and navigation, frequently involve processing complex-valued signals corrupted by intricate noise within linear constraint. Conventional diffusion adaptive filters often lack robustness in such challenging environments and fail to incorporate structural constraints, limiting their practical effectiveness. This paper proposes a widely-linear diffusion constrained complex Gaussian mixture model (WL-DCGMM) algorithm. The parameters of the proposed algorithm are optimized by a dedicated expectation- maximization (EM) approach derived for the complex Gaussian mixture model (CGMM). Theoretical analysis establishes the convergence and steady-state performance of the designed algorithm under linear constraint. Extensive simulations across diverse noise distributions with linear constraint demonstrate the superior estimation accuracy of the designed method, particularly in scenarios where traditional approaches falter, and confirm the validity of the theoretical performance evaluation.