A method for detecting an erroneous velocity data using a controller in communication with a velocity sensor onboard a vehicle includes receiving a time-series velocity data from the velocity sensor, calculating a time-series acceleration data using the time-series velocity data, calculating a time-series jerk data using the time-series acceleration data, calculating a saturated (numerically bounded) jerk data using the time-series jerk data, calculating an estimated acceleration data using the saturated jerk data, calculating a difference between the estimated acceleration data and the time-series acceleration data, and determining whether the difference is greater than a threshold value. The erroneous velocity data is detected in response to the difference being greater than the threshold value.