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Oxford Technical Solutions
Some other rotations are also missed in the diagram. The RT does not use a wander angle,
so it will not operate correctly on the North and South poles.
The angular rates have their bias and scale factor corrections (from the Kalman filter)
applied. Earth rotation rate is also subtracted to avoid the 0.25° per minute rotation of the
earth. The transport rate is also corrected; this is the rate that gravity rotates by due to the
vehicle moving across the earth’s surface and it is proportional to horizontal speed.
Finally the angular rates are integrated to give heading, pitch and roll angles. These are
represented internally using a quaternion (so the RT can work at any angle and does not
have any singularities).
The accelerations have their bias corrections (from the Kalman filter) applied. Then they
are rotated to give accelerations in the earth’s co-ordinate frame (north, east down).
Gravity is subtracted and Coriolis acceleration effects removed. The accelerations are
integrated to give velocity. This is integrated to give position.
The strapdown navigator uses a WGS 84 model of the earth, the same as GPS uses. This
is an elliptical model of the earth rather than a spherical one. The position outputs are in
degrees latitude, degrees longitude and altitude. The altitude is the distance from the
model’s earth sea level.
The Kalman filter used in the RT is able to apply corrections to several places in the
strapdown navigator, including position, velocity, heading, pitch, roll, angular rate bias
and scale factor and acceleration bias.
Kalman filter
Kalman filters can be used to merge several measurements of a quantity and therefore
give a better overall measurement. This is the case with position and velocity in the RT;
the Kalman filter is used to improve the position measurement made from two sources,
inertial sensors and GNSS.
Using a model of how one measurement affects another, the Kalman filter is able to
estimate states where it has no direct measurement.
Consider a lift (or elevator) in a building. We might make measurements of acceleration
and we might know what our position is when we pass a floor; these are the two
measurements our system makes. A Kalman filter could be used to measure velocity in
this situation even though no sensor measures velocity directly. The Kalman filter could
also be used to measure the bias (or offset) of the accelerometer, thereby improving the
system by providing on-line calibration. The bias of the accelerometer might mean the
system always believes the lift arrives early at each floor; by changing the bias on the
accelerometer the measurement of lift position can be made to correlate with the floor
sensor more accurately.
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