This study aims to recover transient, trial-varying evoked potentials (EPs), in particular the movement-related potentials (MRPs), embedded within the background cerebral activity at very low signal-to-noise ratios (SNRs). A new adaptive neuro-fuzzy technique will attempt to estimate movement-related potentials within multi-channel EEG recordings, enabling this method to completely adapt to each input sweep without system training procedures. We assume that one of the sensors is corrupted by noise deriving from other sensors via an unknown function that will be estimated. We will approach this problem by: (1) spatially decorrelating the sensors in the preprocessing phase, (2) choosing the most informative of the filtered channels that will permit the best MRP estimation (input-selection phase) and (3) training the neuro-fuzzy model to fit the noise over the chosen sensor and therefore estimating the buried MRP. We tested this framework with simulations to validate the analytical results before applying them to the real biological data. Whenever it is applied to biological data, this method improves the SNR by more than 12 dB, even to very low SNRs. The processing method proposed here is likely to complement other estimation techniques and can be useful to process, enhance and analyse single-trial MRPs.