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This paper first reviews least mean modulus-Newton (LMM-Newton) algorithm that combines LMM algorithm for complex-domain adaptive filters with simple recurrent calculation of the inverse covariance matrix of the filter reference input process. The LMM-Newton algorithm is effective in improving the convergence of an adaptive filter with a strongly correlated input, while preserving the robustness of the LMM algorithm against impulsive observation noise. For identification of random walk modeled non-stationary systems, it is known that there exists a step-size value that gives the minimum steady-state error. The paper proposes a new adaptive step-size control algorithm to be combined with the LMM-Newton algorithm that yields adaptive step-size least mean modulus-Newton (ASS-LMM-Newton) algorithm to realize the optimum tracking performance. Through performance analysis and experiment with simulations and theoretical calculations of filter convergence, we demonstrate effectiveness of the proposed ASS-LMM-Newton algorithm in identification of non-stationary systems in the presence of impulse noise.