An inertial measurement apparatus comprising: first and second inertial instruments (2, 3) oriented to have parallel sense axes and produce respective first and second sensed output signals representative of an inertial attribute to be measured, the first and second inertial instruments using respective first and second scale factors (SFA, SFB) which are reversible in sign in producing the first and second sensed output signals; and means for receiving said first and second sensed output signals and for accessing the first and second scale factors, the inertial measurement apparatus being characterised through further comprising: means for determining a substitute scale factor as an equivalent of the second scale factor based on the first scale factor and a difference between the first and second scale factors; means for calculating differences in the first and second scale factors based on the first scale factor and the substitute scale factor during first and second time intervals where a sign of one of first and second scale factors changes from one state during the first time interval to the other state during the second time interval; means for sequencing the reversal of the signs of the first and second scale factors and for combining the corresponding outputs from the first and second inertial instruments to measure the bias errors of the first and second inertial instruments and to measure the difference between the scale factors of the first and second inertial instruments based on the combined outputs; and means for generating first and second corrected output signals based on arithmetically combining the respective first and second sensed output signals over at least the first and second time intervals so that certain components that make up the first and second sensed output signals cancel each other. first and second inertial instruments (2, 3) oriented to have parallel sense axes and produce respective first and second sensed output signals representative of an inertial attribute to be measured, the first and second inertial instruments using respective first and second scale factors (SFA, SFB) which are reversible in sign in producing the first and second sensed output signals; and means for receiving said first and second sensed output signals and for accessing the first and second scale factors, the inertial measurement apparatus being characterised through further comprising: means for determining a substitute scale factor as an equivalent of the second scale factor based on the first scale factor and a difference between the first and second scale factors; means for calculating differences in the first and second scale factors based on the first scale factor and the substitute scale factor during first and second time intervals where a sign of one of first and second scale factors changes from one state during the first time interval to the other state during the second time interval; means for sequencing the reversal of the signs of the first and second scale factors and for combining the corresponding outputs from the first and second inertial instruments to measure the bias errors of the first and second inertial instruments and to measure the difference between the scale factors of the first and second inertial instruments based on the combined outputs; and means for generating first and second corrected output signals based on arithmetically combining the respective first and second sensed output signals over at least the first and second time intervals so that certain components that make up the first and second sensed output signals cancel each other. means for determining a substitute scale factor as an equivalent of the second scale factor based on the first scale factor and a difference between the first and second scale factors; means for calculating differences in the first and second scale factors based on the first scale factor and the substitute scale factor during first and second time intervals where a sign of one of first and second scale factors changes from one state during the first time interval to the other state during the second time interval; means for sequencing the reversal of the signs of the first and second scale factors and for combining the corresponding outputs from the first and second inertial instruments to measure the bias errors of the first and second inertial instruments and to measure the difference between the scale factors of the first and second inertial instruments based on the combined outputs; and means for generating first and second corrected output signals based on arithmetically combining the respective first and second sensed output signals over at least the first and second time intervals so that certain components that make up the first and second sensed output signals cancel each other.