This paper introduces an innovative adaptive control approach utilizing a nonlinear filter for a specific subset of nonlinear discrete-time systems, considering the presence of both input and output noise. The system can be transformed into a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. The concept of discrete Nussbaum gain is introduced to address the theoretical constraint associated with unknown directions of feed-forward or control gains, and the extended adaptive tuning sequence is introduced to facilitate the acceleration of parameter updating. In the case of no noise, asymptotical output tracking and global stability are achieved with the adaptive control. Further, in the presence of input noise and output noise, a novel nonlinear filter is designed to generate a more accurate filtered output, which improves the control system’s ability to adapt and track accurately. Finally, examples are provided to showcase the effectiveness and precision of the method.