An inertial measurement system comprising: an accelerometer processing unit, including an accelerometer sensor responsive to acceleration, the accelerometer processing unit also including a calibration and gravity extraction block responsive to the accelerometer sensor output, configured to generate calibrated accelerometer data, and a first comparator arranged to compare the calibrated accelerometer data with a predefined reference in world coordinates and output first comparator output data; a magnetometer processing unit, including a magnetometer sensor responsive to magnetic field, the magnetometer processing unit also including a magnetometer calibration unit, responsive to the magnetometer sensor output, configured to calibrate the magnetometer sensor output to generate calibrated magnetometer data in world coordinates, and a second comparator arranged to compare the calibrated magnetometer data with the predefined reference in world coordinates and output second comparator output data; and a gyroscope processing unit configured to generate calibrated gyroscope data and output gyroscope quaternion data; wherein the magnetometer output and/or the accelerometer output include a heading error, the heading error being primarily generated from imperfections of one or both of the accelerometer and magnetometer sensors (308, 310); the inertial measurement system also including: a summer, responsive to the first and second comparator output data (342, 344), configured to perform an operation on the first and second comparator output data (342, 344) to generate a summation, the summation representing a header uncertainty estimate based on the heading error; a converter arranged to convert the summation to generate a heading confidence interval; and a sensor fusion arranged to combine the summation and the gyroscope quaternion data to generate a quaternion output. an accelerometer processing unit, including an accelerometer sensor responsive to acceleration, the accelerometer processing unit also including a calibration and gravity extraction block responsive to the accelerometer sensor output, configured to generate calibrated accelerometer data, and a first comparator arranged to compare the calibrated accelerometer data with a predefined reference in world coordinates and output first comparator output data; a magnetometer processing unit, including a magnetometer sensor responsive to magnetic field, the magnetometer processing unit also including a magnetometer calibration unit, responsive to the magnetometer sensor output, configured to calibrate the magnetometer sensor output to generate calibrated magnetometer data in world coordinates, and a second comparator arranged to compare the calibrated magnetometer data with the predefined reference in world coordinates and output second comparator output data; and a gyroscope processing unit configured to generate calibrated gyroscope data and output gyroscope quaternion data; wherein the magnetometer output and/or the accelerometer output include a heading error, the heading error being primarily generated from imperfections of one or both of the accelerometer and magnetometer sensors (308, 310); the inertial measurement system also including: a summer, responsive to the first and second comparator output data (342, 344), configured to perform an operation on the first and second comparator output data (342, 344) to generate a summation, the summation representing a header uncertainty estimate based on the heading error; a converter arranged to convert the summation to generate a heading confidence interval; and a sensor fusion arranged to combine the summation and the gyroscope quaternion data to generate a quaternion output. a summer, responsive to the first and second comparator output data (342, 344), configured to perform an operation on the first and second comparator output data (342, 344) to generate a summation, the summation representing a header uncertainty estimate based on the heading error; a converter arranged to convert the summation to generate a heading confidence interval; and a sensor fusion arranged to combine the summation and the gyroscope quaternion data to generate a quaternion output.