An exemplary inertial measurement apparatus has first and second inertial instruments that are oriented to have parallel sense axes and that produce respective first and second sensed output signals representative of an inertial attribute to be measured. Respective first and second scale factors are used in producing the first and second sensed output signals. Bias errors in the first and second instruments are estimated using the change in state of sign of the first and second scale factors during the first and succeeding time intervals. To facilitate measurement of bias errors in the first and second instruments, a substitute scale factor is determined to be an equivalent of the second scale factor and is based on the first scale factor and a difference between the first and second scale factors. Errors in the second scale factor are calculated based on the first scale factor and the substitute scale factor during first and succeeding 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 succeeding time intervals. First and second corrected output signals are generated based on the respective first and second sensed output signals and correction of said second scale factor error.