A fall detector for use in detecting falls by a user, the fall detector comprising: 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 vertical displacement of the fall detector from the measurement samples and using the estimated vertical velocity and/or vertical displacement to determine whether the user has suffered a fall; wherein the processor is configured to estimate a vertical velocity and/or vertical displacement of the fall detector from the measurement samples 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; refine the series of estimates to correct for excess acceleration due to sampling errors and/or clipping in the measurement samples; and integrating the refined series of estimates for the vertical acceleration over a time period to give a time series of values for the vertical velocity and/or vertical displacement of the fall detector (109, 111). 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 vertical displacement of the fall detector from the measurement samples and using the estimated vertical velocity and/or vertical displacement to determine whether the user has suffered a fall; wherein the processor is configured to estimate a vertical velocity and/or vertical displacement of the fall detector from the measurement samples 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; refine the series of estimates to correct for excess acceleration due to sampling errors and/or clipping in the measurement samples; and integrating the refined series of estimates for the vertical acceleration over a time period to give a time series of values for the vertical velocity and/or vertical displacement of the fall detector (109, 111). 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; refine the series of estimates to correct for excess acceleration due to sampling errors and/or clipping in the measurement samples; and integrating the refined series of estimates for the vertical acceleration over a time period to give a time series of values for the vertical velocity and/or vertical displacement of the fall detector (109, 111).