10.5 Sensor Errors

All gyroscopic sensors are subject to errors which limit the accuracy to which the angle of rotation or applied turn rate can be measured. Spurious and undesired torques (caused by design limitations and constructional deficiencies) act on the rotors of all mechanical gyroscopes. These imperfections give rise to precession of the rotor, which manifests itself as a ‘drift’ in the reference direction defined by the spin axis of the rotor. For a restrained gyroscope, i.e. one operating in a nulling or rebalance loop mode to provide a measure of angular rate, any unwanted torques act to produce a ‘bias’ on the measurement of angular rate.

Major sources of error which arise in mechanical gyroscopes include the following:

1. Fixed bias – a sensor output which is present even in the absence of an applied input rotation;
2. Acceleration-dependent (g-dependent) bias – biases in the sensor outputs proportional to the magnitude of the applied acceleration. In this context, mass-unbalance effects are of particular concern, and are discussed further below
3. Anisoelastic (g2-dependent) bias – bias proportional to the product of accelerations applied along orthogonal axes of the sensor;
4. Scale factor errors – errors in the ratio relating the change in the output signal to a change in the input rate which is to be measured;
5. Cross-coupling/misalignment errors – errors arising because of gyroscope sensitivity to turn rates about axes perpendicular to the input axes, or is mounted in a position that is physically misaligned with respect to the required measurement axis.

Each of these errors will, in general, include some or all of the following components:

• fixed or repeatable terms
• temperature induced variations
• switch-on to switch-on variations
• in-run variations

For instance, the measurement of angular rate provided by a gyroscope will include:

• a bias component which is predictable and is present each time the sensor is switched on and can therefore be corrected following calibration
• a temperature dependent bias component which can be corrected with suitable calibration
• a random bias which varies from gyroscope switch-on to switch-on but is constant for any one run
• an in-run random bias which varies throughout a run; the precise form of this error varies from one type of sensor to another.
  

The fixed components of error, and to a large extent the temperature induced variations, can be corrected to leave residual errors attributable to switch-on to switch-on variation and in-run effects, i.e. the random effects caused by instabilities within the gyroscope. It is mainly the switch-on to switch-on and in-run variations which influence the performance of the survey system in which the sensors are installed.

Gyro mass unbalance
The performance of a mechanical gyroscope is extremely sensitive to mass unbalance in the rotor suspension, i.e. non-coincidence of the rotor centre of gravity and the centre of the suspension mechanism. Minute mechanical changes sufficient to affect gyro performance can arise as a result of shock and vibration to which the survey tool may be subjected; either down-hole or at surface as a result of knocks sustained during transport and surface handling. Movements of the rotor centre of gravity with respect to the suspension mechanism of a few nano-metres will produce changes is mass unbalance that are sufficient to give rise to significant changes in measurement accuracy.

Summary: Variations in the residual systematic bias components and the g-dependent bias caused by changes in mass-unbalance present the major concern in survey systems incorporating mechanical gyroscopes. Survey correction techniques are implemented, either during or after a survey operation, in order to compensate for survey inaccuracies resulting from the effects of these particular gyro errors.