An optimal attitude estimator is presented for a human body-mounted inertial measurement unit employing orthogonal triads of gyroscopes, accelerometers and magnetometers. The estimator continuously fuses gyroscope and accelerometer measurements together in a manner that minimizes the mean square error in the estimate of the gravity vector, based on known spectral characteristics for the gyroscope noise and the linear acceleration of points on the human body. The gyroscope noise is modelled as a white noise process of power spectral density δn2/2 while the linear acceleration is modelled as the derivative of a band-limited white noise process of power spectral density δv2/2. The estimator is robust to centripetal acceleration and guaranteed to have zero mean error regardless of the motion of the sensor. The mean square angular error in attitude is shown to be independent of the module's angular velocity and equal to 21/2g−1/2δn3/2δv1/2.