A fall detector includes an accelerometer for producing a time series of measurement samples representing the acceleration acting on the fall detector a processor for estimating a vertical velocity and/or displacement of the fall detector from the measurement samples and using the estimated vertical velocity and/or displacement to determine whether the user has suffered a fall. The processor is configured to estimate a vertical velocity and/or displacement of the fall detector by estimating a corresponding time series of unit vectors representing acceleration due to gravity in the reference frame of the accelerometer from the time series of measurement samples projecting each measurement sample onto the corresponding unit vector and subtracting acceleration due to gravity to give a series of estimates for the vertical acceleration of the fall detector and integrating the series of estimates to give a time series of values for the vertical velocity and/or displacement of the fall detector.
