Recursive adaptive filtering algorithms are widely employed for parameter estimation and tracking in nonstationary environments. The extended recursive least-squares (EX-RLS) algorithm incorporates an explicit state-space model into the recursive estimation procedure, providing enhanced tracking capability for time-varying systems. However, its estimation mechanism is fundamentally based on a quadratic criterion and may therefore exhibit significant performance degradation in the presence of impulsive disturbances and heavy-tailed noise. This paper proposes a robust tanh-based extended recursive least-squares (Tanh-EX-RLS) algorithm for tracking time-varying systems under non-Gaussian noise. The proposed approach introduces a bounded hyperbolic-tangent influence function into the innovation mechanism of the EX-RLS framework while preserving its state-space structure. In addition, an innovation-dependent weighting mechanism is incorporated into the effective observation uncertainty, reducing the influence of large and potentially impulsive prediction errors on both the gain vector and the state estimate. The resulting algorithm behaves approximately as the conventional EX-RLS for small innovations while limiting the influence of large errors. The robustness of the proposed method is investigated under symmetric α-stable noise, which provides a general model for impulsive environments. Theoretical properties of the proposed recursion are analyzed, including its bounded-influence behavior and its relationship with the conventional EX-RLS algorithm.
