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The recursive least squares (RLS) adaptive algorithm is combined with the "adaptive threshold nonlinear algorithm" (ATNA) proposed by the author (Koike, S., IEEE Trans. Sig. Processing, vol.45, p.2391-5, 1997), to derive RLS-ATNA, resulting in improvement of the convergence rate of the ATNA that offers robust adaptive filters in impulse noise environments. For application of the RLS-ATNA to identification of random-walk modeled nonstationary systems, an adaptive forgetting factor (AFF) control algorithm is proposed that further improves the tracking performance in the steady state. Through analysis and experiments, the effectiveness of the AFF-RLS-ATNA is demonstrated. Fairly good agreement between the simulation and the theoretically calculated convergence validates the analysis.