Technology X-Treme

If three single-axis gyros together with three accelerometers are mounted on X, Y and Z axes (‘orthogonal mounting’), then these six sensors comprise a clockwise rotating, Cartesian, sensor co-ordinate system. In order to read the angles related to the earth’s surface, the sensor data is transformed mathematically from the sensor co-ordinate system so as to relate to the three dimensional reference co-ordinate system of the earth.

It should be emphasized that single-axis measurements from one gyro with accelerometers or inclinometer will also show precise instantaneous values; however applying this approach to two or three independent orthogonal subsystems will result in errors. This is because independent integration of three sensor signals over time will lead to ambiguous states of orientation.

Imagine an aircraft flying horizontally northwards has to execute two manoeuvres; it is to turn 90° around both its Pitch and Roll axes; these movements are to be executed consecutively. First of all it turns around its Roll axis, as a result the aircraft will have its right wing pointing downwards. Then it is to turn around its Pitch axis; that is to say that with the right wing still pointing down, the aircraft will now have changed its heading to the east.

Now change the sequence of manoeuvres from its starting position, i.e. it turns around its Pitch axis, and the aircraft will now climb vertically with its wings pointing east/west. Turning around the Roll axis leaves the plane still climbing vertically but rotated by 90° and with its wings pointing north/south.

Independent integration over time with three gyros will correctly show Pitch and Roll turned by 90 degrees. However two end-states of orientation are possible depending on the order of execution of the manoeuvres. Similarly, if mathematical transformation of the signals is incorrectly executed then errors will also occur.

An appreciation of the nature of these imperfections in Inertial reference systems is of value when the time comes to choose a system for a particular application, and is able to reduce those errors to known and acceptable limits.