Robust RLS via the nonconvex sparsity prompting penalties of outlier components

Recursive least square (RLS) is a ubiquitous adaptive filtering algorithm used in general adaptive signal processing applications. However, it is well known that RLS is sensitive to outlier contaminated in measurements. Traditional robust RLS has difficulties to cope with correlated ambient noise. To provide robustness in such cases, a robust RLS via outlier pursuit (RRLSvOP) framework is proposed with outlier´s sparsity control via possibly nonconvex penalties, such as the minimax concave penalty (MCP). Because of the nonconvexity of the proposed model, more advanced numerical procedures with convergence guarantees, such as multi-stage convex relaxation (MSCR), coordinate descent (CD), proximal gradient (PG) and PG with homotopy (PGH), are adapted in the online update stage, while the initialization stage is solved via MSCR strategy. Simulations demonstrate improved robustness of the model using nonconvex penalties via these procedures in comparison with that using ℓ₁ penalty.