Method and system for determining the attitude of an aircraft by multi-axis accelerometric measurements

• US 8,655,511 B2
• Filed: 02/29/2012
• Issued: 02/18/2014
• Est. Priority Date: 03/03/2011
• Status: Active Grant

• Current Assignee: Thales SA
• Original Assignee: Thales SA
• Inventors: Revol, Marc, Mandle, Jacques, Bibaut, Alain, Coatantiec, Jacques
• Primary Examiner(s): Trammell, James
• Assistant Examiner(s): ALSOMIRI, MAJDI A
• Application Number:
  US13/408,749
• Publication Number:
  US 20120226395A1
• Time in Patent Office: 720 Days
• Field of Search: 701 1- 4, 701500-504, 731/78, 735/05, 735/14, 735/17
• US Class Current: 701/4
• CPC Class Codes: G01C 21/188 for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems

Abstract

An inertial system measures the attitude of an aircraft consisting at least in determining the angle of pitch and/or the angle of heading and/or the angle of roll of the aircraft, each of the said angles of attitude being determined by successive double integration of their second derivative. A pair of accelerometers to determine the angle of pitch being are disposed on either side of the centre of gravity along an axis substantially merged with the longitudinal axis of the aircraft. A pair of accelerometers to determine the angle of heading are disposed on either side of the centre of gravity along an axis substantially merged with the transverse axis of the aircraft. A pair of accelerometers to determine the angle of roll are disposed on either side of the centre of gravity along a vertical axis perpendicular to the plane formed by the other axes.

Claims

1. Method of determination, by an inertial system, of a measurement of the attitude of an aircraft consisting at least in determining the angle of pitch θ

and/or the angle of heading ψ and

/or the angle of roll φ

of the said aircraft, each of the said angles of attitude being determined by successive double integration of their second derivative, the said second derivative being determined as the difference between the acceleration measurements delivered by two matched accelerometers, divided by the sum of the respective distances between the said accelerometers and the centre of gravity G of the said inertial system, the pair of accelerometers used for the determination of the angle of pitch θ

being disposed on either side of the centre of gravity G along an axis x substantially merged with the longitudinal axis of the aircraft, the pair of accelerometers used for the determination of the angle of heading ψ

being disposed on either side of the centre of gravity G along an axis y substantially merged with the transverse axis of the aircraft, the pair of accelerometers used for the determination of the angle of roll φ

being disposed on either side of the centre of gravity G along a vertical axis z perpendicular to the plane formed by the x and y axes.

2. Method according to claim 1 furthermore consisting in compensating for the errors of calibration of the said accelerometers by correcting the second derivative of the angle(s) of attitude θ

, ψ

, φ

, by a differential bias Δ

_x21 divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the said inertial system, the said differential bias Δ

_x21 being determined on the basis of the integration, over a given duration T, of the difference between on the one hand, the difference between the acceleration measurements delivered by the pair of matched accelerometers and on the other hand, an unbiased estimate of the second derivative of the angle of attitude θ

, ψ

, φ

that multiplies the sum of the said distances.

3. Method according to claim 1 wherein the measurement of the attitude of the aircraft is used as an item of backup information in support of a reference navigation system.

4. Method according to claim 3 wherein the said reference navigation system delivers the unbiased estimate of the second derivative of the angle or angles of attitude.

5. Method according to claim 1 furthermore consisting in correcting the long-term drifts impacting the said attitude measurements by determining at least one compensation δ

_θ

of the angle of pitch and/or one compensation δ

_φ

of the angle of roll, the said compensations δ

_θ

,δ

_φ

being determined on the basis of the comparison of the vector {right arrow over (B)}, orthogonal to the plane of the trim as defined by the angles of pitch θ and

of roll φ and

of the acceleration vector {right arrow over (g)} of the aircraft subject to terrestrial gravity, the said vector {right arrow over (g)} being determined as the gravimetric acceleration of the aircraft at its centre of gravity G, on the basis of the average of the acceleration measurements delivered by two matched accelerometers, the respective distances between two accelerometers of one and the same pair and the centre of gravity G of the said inertial system being fixed to be mutually equal.

6. Method according to claim 5 furthermore consisting in compensating the said acceleration vector {right arrow over (g)} by an estimate {right arrow over (γ

)}_d of the dynamic acceleration of the aircraft.

7. An inertial navigation system, on board an aircraft, comprising:

a first pair of matched accelerometers disposed along an axis x substantially merged with the longitudinal axis of the aircraft, on either side of the centre of gravity G of the navigation inertial system and at a respective distance x₁,x₂ from the latter, the sensitive axes of the first pair of accelerometers being disposed substantially mutually parallel and perpendicular to the x axis, the inertial system furthermore comprising calculation means linked to the first pair of accelerometers and configured to determine the angle of pitch θ

of the aircraft by successive double integration of their second derivative, the second derivative being determined as the difference between the acceleration measurements delivered by the first pair of accelerometers, divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system.

8. The inertial navigation system according to claim 7 wherein the calculation means are further configured to compensate for the errors of calibration of the first pair of accelerometers by correcting the second derivative of the angle of pitch θ

by a differential bias Δ

_x21 divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system, the differential bias Δ

_x21 being determined on the basis of the integration, over a given duration T, of the difference between on the one hand, the difference between the acceleration measurements delivered by the first pair of accelerometers and on the other hand, an unbiased estimate of the second derivative of the angle of pitch θ

that multiplies the sum of the distances.

9. The inertial navigation system according to claim 7, further comprising a second pair of matched accelerometers disposed along a vertical axis z perpendicular, at the centre of gravity G, to the x axis, on either side of the centre of gravity G and at a respective distance z₁,z₂ from the latter, the sensitive axes of the second pair of accelerometers being disposed substantially mutually parallel and perpendicular to the z axis wherein the calculation means is linked to the second pair of accelerometers and configured to determine the angle of roll φ

of the aircraft by successive double integration of their second derivative, the second derivative being determined as the difference between the acceleration measurements delivered by the second pair of matched accelerometers, divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system.

10. The inertial navigation system according to claim 9, further comprising a gyrometer disposed substantially at the centre of gravity G and oriented according to a vertical axis z perpendicular, at the centre of gravity G, to the x axis, the said gyrometer being suitable for delivering an estimate of the angle of heading ψ

of the aircraft.

11. The inertial navigation system according to claim 9 wherein the calculation means are further configured to compensate for the errors of calibration of the second pair of accelerometers by correcting the second derivative of the angle of roll φ

by a differential bias Δ

_x21 divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system, the differential bias Δ

_x21 being determined on the basis of the integration, over a given duration T, of the difference between on the one hand, the difference between the acceleration measurements delivered by the second pair of accelerometers and on the other hand, an unbiased estimate of the second derivative of the angle of roll φ

that multiplies the sum of the distances.

12. The inertial navigation system according to claim 9 wherein the calculation means are further configured to correct for long-term drifts impacting the pitch angle measurements by determining at least one compensation δ

_θ

of the angle of pitch and/or one compensation δ

_φ

of the angle of roll, the compensations δ

_θ

,δ

_φ

being determined on the basis of the comparison of the vector {right arrow over (B)}, orthogonal to the plane of the trim as defined by the angles of pitch θ and

of roll φ and

of the acceleration vector {right arrow over (g)} of the aircraft subject to terrestrial gravity, the said vector {right arrow over (g)} being determined as the gravimetric acceleration of the aircraft at its centre of gravity G, on the basis of the average of the acceleration measurements delivered by two matched accelerometers, the respective distances between two accelerometers of one and the same pair and the centre of gravity G of the said inertial system being fixed to be mutually equal.

13. The inertial navigation system according to claim 12 wherein the calculation means are further configured to compensate the acceleration vector {right arrow over (g)} by an estimate {right arrow over (γ

)}_d of the dynamic acceleration of the aircraft.

14. The inertial navigation system according to claim 7, further comprising a third pair of matched accelerometers disposed along an axis y substantially merged with the transverse axis of the aircraft and perpendicular at the centre of gravity G, to the x axis, on either side of the centre of gravity G and at a respective distance y₁,y₂ from the latter, the sensitive axes of the accelerometers being disposed substantially mutually parallel and perpendicular to the y axis wherein the calculation means are linked to the third pair of accelerometers and configured to determine the angle of heading ψ

of the aircraft by successive double integration of their second derivative, the second derivative being determined as the difference between the acceleration measurements delivered by the third pair of accelerometers, divided by the sum of the respective distances between the third pair of accelerometers and the centre of gravity G of the inertial system.

15. The inertial navigation system according to claim 14 wherein the calculation means are further configured to compensate for the errors of calibration of the third pair of accelerometers by correcting the second derivative of the angle of heading ψ

of the aircraft by a differential bias Δ

_x21 divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system, the differential bias Δ

_x21 being determined on the basis of the integration, over a given duration T, of the difference between on the one hand, the difference between the acceleration measurements delivered by the third pair of accelerometers and on the other hand, an unbiased estimate of the second derivative of the angle of heading ψ

that multiplies the sum of the distances.

16. The inertial navigation system according to claim 7 wherein it constitutes a backup navigation system in support of a primary navigation system on board the aircraft.

17. An inertial navigation system, on board an aircraft, comprising:

a first pair of matched accelerometers disposed along an axis x substantially merged with the longitudinal axis of the aircraft, on either side of the centre of gravity G of the navigation inertial system and at a respective distance x₁,x₂ from the latter, the sensitive axes of the first pair of accelerometers being disposed substantially mutually parallel and perpendicular to the x axis to provide a measure for determining the angle of pitch θ

;

a second pair of matched accelerometers disposed along a vertical axis z perpendicular, at the centre of gravity G, to the x axis, on either side of the centre of gravity G and at a respective distance z₁,z₂ from the latter, the sensitive axes of the second pair of accelerometers being disposed substantially mutually parallel and perpendicular to the z axis to provide a measure for determining the angle of roll φ

;

a third pair of matched accelerometers disposed along an axis y substantially merged with the transverse axis of the aircraft and perpendicular at the centre of gravity G, to the x axis, on either side of the centre of gravity G and at a respective distance y₁,y₂ from the latter, the sensitive axes of the accelerometers being disposed substantially mutually parallel and perpendicular to the y axis to provide a measure for determining the angle of heading ψ

; and

calculation means linked to the first, second, and third pairs of accelerometers and configured to determine the angle of pitch θ

, the angle of roll φ

, and the angle of heading ψ

based on the measures from the first, second, and third pairs of accelerometers, respectively, by successive double integration of their second derivatives, the second derivatives being determined as the difference between the acceleration measurements delivered by the respective pairs of accelerometers, divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system.

18. The inertial navigation system according to claim 17 wherein the calculation means is further configured to compensate for the errors of calibration of the first, second, and third pairs of accelerometers by correcting the second derivative of the angle(s) of attitude θ

, ψ

, φ

, by a differential bias Δ

_x21 divided by the sum of the respective distances between the accelerometers and the centre of gravity G of the inertial system, the differential bias Δ

_x21 being determined on the basis of the integration, over a given duration T, of the difference between on the one hand, the difference between the acceleration measurements delivered by a respective pair of matched accelerometers and on the other hand, an unbiased estimate of the second derivative of the angle of attitude θ

, ψ

, φ

that multiplies the sum of the distances.

19. The inertial navigation system according to claim 17 wherein the calculation means is further configured to correct the long-term drifts impacting the attitude measurements by determining at least one compensation δ

_θ

of the angle of pitch and/or one compensation δ

_φ

of the angle of roll, the said compensations δ

_θ

,δ

_φ

being determined on the basis of the comparison of the vector {right arrow over (B)}, orthogonal to the plane of the trim as defined by the angles of pitch θ and

of roll φ and

of the acceleration vector {right arrow over (g)} of the aircraft subject to terrestrial gravity, the vector {right arrow over (g)} being determined as the gravimetric acceleration of the aircraft at its centre of gravity G, on the basis of the average of the acceleration measurements delivered by two matched accelerometers, the respective distances between two accelerometers of one and the same pair and the centre of gravity G of the inertial system being fixed to be mutually equal.

20. The inertial navigation system according to claim 19 wherein the calculation means are further configured to compensate the acceleration vector {right arrow over (g)} by an estimate {right arrow over (γ

)}_d of the dynamic acceleration of the aircraft.