Current estimators for single-trial evoked potentials (EP's) require a signal-to-noise ratio (SNR) of 0 dB or better to obtain high quality estimations, yet many types of EP's suffer from substantially lower SNR's. This paper presents a robust-evoked-potential-estimator (REPE) facilitating high quality estimations of single movement related EP's with a relatively low SNR. The estimator is based on a standard ARX model, enhanced to support estimation under poor SNR conditions. The REPE was tested successfully on a computer simulated data set giving reliable single-trial estimations for the low SNR range of around -20 dB. THe REPE was also applied to experimental data, producing clear single-trial estimations of movement related brain signals recorded in a classic scenario of self-paced finger tapping experiment.