Methods and systems for detecting and correcting for undesirable vibrations impacting the servo systems in data storage devices. A detection technique is provided wherein a detection filter is configured to scan a position signal of the servo system across a range of frequencies, and, at each respective scanned frequency, record an amplitude associated therewith. The recorded amplitudes are examined to determine whether any exceed a threshold, thereby locating a peak frequency of the vibration. Using the detected peak frequency of the vibration, a corrective filter is configured to operate about the peak frequency of vibration, thereby reducing its impact on the position signal in the servo system. Optimum detection and correction filter structures are disclosed, as are techniques for addressing filter state vectors as initial conditions as the corrective filters are repeatedly engaged during successive settle-out and track follow cycles (between seeks), as are continuous adaptation techniques for changing vibration environments.