Objective. Accurate implementation of real-time non-invasive brain-machine/computer interfaces (BMI/BCI) requires handling physiological and nonphysiological artifacts associated with the measurement modalities. For example, scalp electroencephalographic (EEG) measurements are often considered prone to excessive motion artifacts and other types of artifacts that contaminate the EEG recordings. Although the magnitude of such artifacts heavily depends on the task and the setup, complete minimization or isolation of such artifacts is generally not possible. Approach. We present an adaptive de-noising framework with robustness properties, using a Volterra based non-linear mapping to characterize and handle the motion artifact contamination in EEG measurements. We asked healthy able-bodied subjects to walk on a treadmill at gait speeds of 1-to-4 mph, while we tracked the motion of select EEG electrodes with an infrared video-based motion tracking system. We also placed inertial measurement unit (IMU) sensors on the forehead and feet of the subjects for assessing the overall head movement and segmenting the gait. Main results. We discuss in detail the characteristics of the motion artifacts and propose a real-time compatible solution to filter them. We report the effective handling of both the fundamental frequency of contamination (synchronized to the walking speed) and its harmonics. Event-related spectral perturbation (ERSP) analysis for walking shows that the gait dependency of artifact contamination is also eliminated on all target frequencies. Significance. The real-time compatibility and generalizability of our adaptive filtering framework allows for the effective use of non-invasive BMI/BCI systems and greatly expands the implementation type and application domains to other types of problems where signal denoising is desirable. Combined with our previous efforts of filtering ocular artifacts, the presented technique allows for a comprehensive adaptive filtering framework to increase the EEG signal to noise ratio (SNR). We believe the implementation will benefit all non-invasive neural measurement modalities, including studies discussing neural correlates of movement and other internal states, not necessarily of BMI focus.