Integrated redundant reference system for the flight control and for generating heading and attitude informations

• US 4,914,598 A
• Filed: 10/06/1987
• Issued: 04/03/1990
• Est. Priority Date: 10/07/1986
• Status: Expired due to Fees

• Current Assignee: Bodenseewerk Gerätetechnik Gmbh
• Original Assignee: Bodenseewerk Gerätetechnik Gmbh
• Inventors: Bessel, Jurgen, Krogmann, Uwe
• Primary Examiner(s): Laroche, Eugene R.
• Assistant Examiner(s): LEE, BENNY T
• Application Number:
  US07/106,380
• Time in Patent Office: 910 Days
• Field of Search: 364/453, 364/443, 364/566, 364/559, 73/504, 33/321-324, 244/177, 244/194, 244/76 R
• US Class Current: 701/11
• CPC Class Codes: G01C 21/183 Compensation of inertial measurements, e.g. for temperature effects

Abstract

A plurality of two-axis rate gyros are arranged in relation to an aircraft-fixed coordinate system such that they redundantly supply angular rate information. A plurality of accelerometers supply correspondingly redundant acceleration information. First signal processing means comprise means for failure detection and elimination, such that angular rate and acceleration information subjected to error are eliminated. The angular rate and acceleration information thus cleared from errors supply stabilization signals for the autopilot. Second signal processing means obtain the angular rate and acceleration information cleared from errors and integrated if required, and therefrom supply heading and attitude reference signals.

Claims

1. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals referenced to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft, and

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals.

2. Reference system as set forth in claim 1, wherein the axis of the cone extends parallel to a pitch axis (y) of the aircraft which is horizontal and perpendicular to the longitudinal axis of the aircraft.

3. Reference system as set forth in claim 1, wherein the means for failure detection of the sensors comprise

(a) linear combination and comparison means for

forming, for each of said passed signals, a comparison value by linear combination of signals from other ones of said gyros,

forming the differences of said signals and said comparison values and

comparing said differences with second threshold values, and

(b) locating means for determining a deficient sensor, if a signal is deficient, from the subset of the sensors, for which said linear combination and comparison means indicate exceeding of said threshold value, signals from said deficient sensor being excluded from further signal processing.

4. Reference system as set forth in claim 1, wherein the input axes of the four dynamically tuned gyros are orientated in pairs symmetrically with reference to the axis of the cone.

16. The integrated, redundant reference system as claimed in claim 1 and further comprising

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals being also applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft.

17. Reference system as set forth in claim 16, wherein the first signal processing means comprise

(a) coordinate transformation means for transformation of the signals obtained from the means for failure detection and elimination into

transformed angular rate signals, which are referred to a vehicle-fixed coordinate system, and

transformed acceleration signals, which are referred to a vehicle-fixed coordinate system, respectively, and

(b) means for calculation and output of output signals for the autopilot, to which means these angular rate and acceleration signals are applied.

18. Reference system as set forth in claim 16, characterized in that the first signal processing means (120) have first integrating means (140) for integrating the transformed angular rate signals and second integrating means (142) for integrating the transformed acceleration signals.

19. Refence system as set forth in claim 16, wherein

(a) the first signal processing means supply transformation parameters for the transformation of vectors from an aircraft-fixed coordinate system into an earth-fixed coordinate system to attitude outputs, which transformation parameters result from integration of angular rate information,

(b) the second signal processing means comprise

initial aligning means for determination of initial values of the transformation parameters,

means for determination of correcting values for taking earth rotation and transport rate into consideration,

correcting means for correction of the transformation parameters with respect to initial values, earth rotation and transport rate, and

means for calculation and output of the heading and attitude angles from the thus corrected transformation parameters.

20. Reference system as set forth in claim 19, wherein

(a) the first signal processing means supply velocity values to velocity outputs which velocity values result from integration of acceleration informations in a vehicle-fixed coordinate system,

(b) the second signal processing means comprise a coordinate transformation circuit,

which operates with the corrected transformation parameters from said correcting means and

which is arranged to transform said velocity values into an earth-fixed coordinate system,

(c) the velocity components measured with the vehicle at rest by integration of acceleration components are applied to the initial aligning means, which velocity components form a measure of the initial inclination of the vehicle.

21. The integrated, redundant reference system as claimed in claim 16 additionally including acceleration failure detecting and eliminating means, wherein

(a) said acceleration sensor means comprise means for sensing acceleration along more than three input axes, said input axes being oriented to provide redundant acceleration information,

(b) all of said acceleration signals from said acceleration sensor means providing redundant acceleration information being applied to acceleration failure detecting and eliminating means eliminating deficient accelerating signals and for selecting from said applied acceleration signals, in normal operation, a set of acceleration signals from operative acceleration sensors, and

(c) said selected set of acceleration signals from operative acceleration sensors being applied to said first and second signal processing means.

5. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft,

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals, and

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals

(1) said acceleration sensor means comprise means for sensing acceleration along more than three input axes, said input axes being oriented to provide redundant acceleration information,

(2) plurality of said acceleration signals from said acceleration sensor means providing redundant acceleration information being applied to acceleration failure detecting and eliminating means eliminating deficient accelerating signals and for selecting from said plurality of acceleration signals, in normal operation, a selected set of acceleration signals from operative acceleration sensors,

(3) said selected set of acceleration signals being applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft, and

(4) said acceleration sensor means comprising a respective pair of accelerometers associated with each two-axis gyro, the input axes of which accelerometers are parallel to one of the input axes of the gyro.

6. Reference system as set forth in claim 5, wherein

(a) a separate power supply unit, a separate motor power supply, and a separate signal processing unit to which the measuring signals of the angular rate sensors are applied, are provided for each of the gyros,

(b) acceleration signals from at least one associated acceleration sensor means are additionally applied to each signal processing unit,

(c) the acceleration sensor means are also supplied by power supply units of the gyros, and

(d) each signal processing unit supplies two angular rate signals and at least one acceleration signal.

7. Reference system as set forth in claim 6, wherein

(a) each gyro comprises

a first and a second position pick-off, which are supplied with alternating current from the motor power supply, and

a first and a second torquer,

(b) demodulators arranged to demodulate the alternating current pick-off signals generated by the first and second position pick-offs to form demodulated pick-off signals,

(c) a multiplexer arranged to apply the demodulated pick-off signals to an analog-to-digital converter to form digitized pick-off signals,

(d) the digitized pick-off signals are applied to a digital signal processing circuit, which supplies digital restraining signals for the gyro,

(e) the digital restraining signals are adapted to be applied to a digital-to-analog converter for generating analog restraining signals,

(f) analog value storing means for the analog restraining signals are connected to the digital-to-analog converter, and

(g) the analog value storing means are connected to the torquers of the gyro.

8. Reference system as set forth in claim 5, wherein

(a) the axis of the notional cone extends parallel to the longitudinal axis of the aircraft, the surface of which cone determines the input axes of the angular rate sensors,

(b) said acceleration sensor means comprise five acceleration sensors,

(c) the input axes of the acceleration sensors extend parallel to different generatrices of the surface of an imaginary second cone, and

(d) the axis of the notional second cone extends parallel to a vertical craft axis of the aircraft which is vertical and perpendicular to the longitudinal axis of the aircraft.

9. Reference system as set forth in claim 8, wherein

(a) the gyros are arranged in a sensor block semicircularly in space about the longitudinal axis of the vehicle and

(b) the acceleration sensors are arranged in the sensor block substantially within this semicircular arrangement of the gyros.

10. Reference system as set forth in claim 8, wherein

(a) the cone angle of the notional second cone is 54.73°

, and

(b) the input axes of the five acceleration sensors are determined by six generatrices equally distributed about the axis of the cone in that each of these input axes extends parallel to one of five of these six generatrices.

11. An integrated, redundant reference system providing angular rate and heading and attitude information for the fight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft,

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals,

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals being also applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft,

(g) first means for the transformation of the true airspeed, which is the aerodynamically measured aircraft velocity relative to the surrounding air, into the aircraft-fixed coordinate system, on the basis of the angle of attack and angle of side-slip likewise measured by aerodynamical sensors,

(h) second means for determination of the aircraft velocity over ground in an aircraft-fixed coordinate system,

(i) difference forming means for determination of the wind velocity in the aircraft-fixed coordinate system as difference between the aircraft velocity relative to the surrounding air determined by the first means and the aircraft velocity over ground determined by the second means,

(j) memory means for memorizing the thus determined wind velocity,

(k) third means for forming estimated values of the angle of attack and the angle of side-slip from the wind velocity memorized in the memory means and the aircraft velocity over ground supplied from the second means, and

(l) conversion means, which, in case of failure of the aerodynamical sensors for angle of attack and angle of side-slip, is adapted to

separate the memory means from the difference forming means and

apply the estimated values of angle of attack and angle of side-slip formed by the third means, instead of the sensor signals, to the autopilot computer.

12. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft, and

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals,

wherein

(f) a first set of gyros is used for measuring the three components of the angular rate while they are operating properly, and

(g) when a failure appears a change-over is caused to a second set of gyros from a sequence of alternative sets with different combinations of gyros, none of which have failed.

13. The integrated, redundant reference system as claimed in claim 12, wherein said deficiency detecting and eliminating means comprise:

(a) voter means to which reference axis angular rate signals are applied, each of these applied reference axis angular rate signals being indicative of angular rate about said reference axis and proportional to the sum of the angular rates sensed about the input axes of one of said dynamically tuned gyros, said voter means being arranged to form a reference value for each of said reference axis angular rate signals from all the other reference axis angular rate signals and to determine reference axis angular rate signals which exceed a first threshold value, the associated gyros being regarded as inoperative,

(b) means for eliminating signals from such inoperative gyros and for passing signals from operative gyros,

(c) sensor error compensation means for compensating sensor errors of said passed signals to an accuracy required for providing the attitude and heading information for the flight control,

(d) linear combination and comparison means for

forming, for each of said passed signals, a comparison value by linear combination of signals from other ones of said gyros,

forming the differences of said signals and said comparison values and

comparing said differences with second threshold values, and

(e) locating means for determining a deficient sensor, if a signal is deficient, from the subset of the sensors, for which said linear combination and comparison means indicate exceeding of said threshold value, signals from said deficient sensor being excluded from further signal processing.

14. Reference system as set forth in claim 13, wherein self-test of the gyros is connected to the input of the means for failure detection according to the principle of majority monitoring.

15. Reference system as set forth in claim 13 wherein the threshold values are automatically variable as a function of the measuring values.

22. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft,

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals,

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals being also applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft,

wherein

(g) the first signal processing means supply

transformation parameters for the transformation of vectors from an aircraft-fixed coordinate system into an earth-fixed coordinate system to attitude outputs, which transformation parameters result from integration of angular rate information,

velocity values to velocity outputs, which velocity values result from integration of acceleration information in a vehicle-fixed coordinate system,

(h) the second signal processing means comprise

initial aligning means for determination of initial values of the transformation parameters,

means for determination of correcting values for taking earth rotation and transport rate into consideration,

correcting means for correction of the transformation parameters with respect to initial values, earth rotation and transport rate, and

means for calculation and output of the heading and attitude angles from the thus corrected transformation parameters,

a coordinate transformation circuit which operates with the corrected transformation parameters from said correcting means, and which is arranged to transform said velocity values into an earth-fixed coordinate system, and

(i) the velocity components measured with the vehicle at rest by integration of acceleration componenets are applied to the initial aligning means, which velocity components form a measure of the initial inclination of the vehicle, and velocity computer means

to which the velocity values transformed by the coordinate transformation circuit and

flying speed as well as angle of attack and angle of side-slip are supplied, and

which apply velocity components to the means for determination of correcting values for taking the earth rotation and transport rate into consideration, and

which apply velocity components to a vertical channel aided by the pressure altitude, which vertical channel supplies flight altitude and vertical velocity.

23. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft,

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals,

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals being also applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft,

wherein

(g) the first signal processing meaNs supply

transformation parameters for the tranrformation of vectors from an aircraft-fixed coordinate system into an earth-fixed coordinate system to attitude outputs, which transformation parametars result from integration of angular rate information,

velocity vlues to velocity outputs, which velocity values result from integration of acceleration information In a vehicle-fixed coordinate system,

(h) the second signal processing means comprise

initial aligning means for determination of initial values of the transformation parameters,

means for determination of correcting values for taking earth rotation and transport rate into consideration,

correcting means for correction of the transformation parameters with respect to initial values, earth rotation and transport rate, and

means for calculation and output of the heading and attitude angles from the thus corrected transformation parameters,

coordinate transformation circuit which operates with the corrected transformation parameters from said correcting means, which is arranged to transform said velocity values into an earth-fixed coordinate system, and

(i) the velocity components measured with the vehicle at rest by integration of acceleration components are applied to the initial aligning means, which velocity components form a measure of the initial inclination of the vehicle, furthermore an external initial heading information is applied to the initial aligning means.

24. An integrated, redundant reference system providing angular rate and heading and attitude information for the flight control of aircraft by means of an autopilot, comprising

(a) at least four strap-down, dynamically tuned gyros, each of said gyros having a spin axis and two mutually orthogonal input axes normal to said spin axis, the directions of said axes being defined by respective direction vectors, each of said dynamically tuned gyros providing two angular rate signals indicative of angular rates about said two input axes,

(b) said gyros being oriented with the direction vectors of their spin axes extending radially with respect to a common reference axis, the direction vectors of said input axes of all gyros being different and located on a notional cone having a cone angle of 90°

, the axis of said cone coinciding with said reference axis,

(c) means equally operatively connected to all gyros for detecting deficiencies of said gyros and for eliminating signals from deficient gyros, the angular rate signals from all said gyros being supplied to said deficiency detecting and eliminating means, said deficiency detecting and eliminating means, in normal operation, providing a set of selected angular rate signals from operative gyros,

(d) first signal processing means to which said set of selected angular rate signals is applied for providing a set of corrected angular rate signals reference to a vehicle-fixed coordinate system, said corrected angular rate signals being applied to said autopilot for stabilizing said aircraft,

(e) second signal processing means to which said corrected angular rate signals are applied for providing heading and attitude reference signals,

(f) strap-down acceleration sensor means for providing a plurality of acceleration signals being also applied to said first signal processing means for providing a set of corrected acceleration signals referenced to said vehicle fixed coordinate system, also said corrected acceleration signals being applied to said autopilot for stabilizing said aircraft,

wherein

(g) the first signal processing means supply

transformation parameters for the transformation of vectors from an aircraft-fixed coordinate system into an earth-fixed coordinate system to attitude outputs, which transformation parameters result from integration of angular rate information,

velocity values to velocity outputs, which velocity values result from integration of acceleration information in a vehicle-fixed coordinate system,

(h) the second signal processing means comprise

initial aligning means for determination of initial values of the transformation parameters,

means for determination of correcting values for taking earth rotation and transport rate into consideration,

correcting means for correction of the transformation parameters with respect to initial values, earth rotation and transport rate,

means for calculation and output of the heading and attitude angles from the thus corrected transformation parameters, and

a coordinate transformation circuit which operates with the corrected transformation parameters from said correcting means, and which is arranged to transform said velocity values into an earth-fixed coordinate system, and

(i) the velocity components measured with the vehicle at rest by integration of acceleration components are applied to the initial aligning means, which velocity components form a measure of the initial inclination of the vehicle, wherein the initial aligning means comprise

(1) fast responding coarse leveling means, to which velocity increment signals from the acceleration sensor means are applied and which supply an initial direction cosine matrix for transformation from an aircraft-fixed system into an earth-fixed system,

(2) means for updating the direction cosine matrix, to which angular increment signals from the angular rate sensor means are applied,

(3) velocity transformation means, to which the velocity increment signals are applied and which supply a velocity vector transformed with the direction cosine matrix in an earth-fixed coordinate system,

(4) fine leveling means, to which the transformed velocity vector and the geographical latitude are applied, and which apply attitude correction signals to the means for updating the direction cosine matrix and which supply signals, which are determined by the influence of the earth rotation on the angular rate sensors, and

(5) means for determining the heading from said signals determined by the earth rotation.

25. Reference system as set forth in claim 24, wherein

(a) for initial fine alignment of the system the angular increment signals from the gyros are converted into a quaternion through conversion means, said quaternion starting from an initial value and being updated by said angular increment signals

(b) conversion means for conversion of the quaternion into the direction cosine matrix, by means of which a transformation of the velocity increment signals from the acceleration sensor means is effected from a system-fixed coordinate system into an earth-fixed coordinate system,

(c) the thus transformed velocity increment signals are applied to a Kalman filter, which simulates the influence of the earth rotation on the gyros and generates actuating signals depending on the earth rotation for the heading and attitude correction, when the coordinate system defined by the direction cosine matrix differs from the earth-fixed coordinate system, and

(d) the actuating signals effect a correction of the quaterion through conversion means.