Estimating the speed and the heading of an aircraft, independently of a magnetic measurement

Abstract

A device for estimating an aircraft's speed relative to the ground and heading, while making no use of the rotation of the Earth or of the Earth's magnetic field. The device comprises in particular a first linear estimator that hybridizes a measurement of the speed of the aircraft relative to the ground as provided by a global navigation satellite system (GNSS) receiver with measurements of the acceleration and the attitudes of the aircraft coming from an attitude and heading reference system (AHRS) device without a gyrocompass and without a magnetometer. The first estimator is made linear by replacing the single heading error estimate state of prior art embodiments with two states, namely estimates of the sine and of the cosine of the heading error.

Claims

1. A device for estimating ground speed and heading of an aircraft, the aircraft having three axes forming a fuselage reference frame rigidly associated with a structure of the aircraft, the device comprising: a global navigation satellite system (GNSS) receiver receiving signals from a plurality of satellites and configured to provide a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, the geographical reference frame including a horizontal plane; an attitude and heading reference system (AHRS) device providing a measurement of an acceleration vector of the aircraft in the fuselage reference frame together with estimates of the attitude angles, and a directional estimate of the heading of the aircraft; and a first estimator connected to the GNSS receiver and to the AHRS; wherein the first estimator is linear and configured to prepare an estimate of an unbounded error affecting the directional estimate of the heading determined by the AHRS device by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector, independently of any magnetic measurement.

2. The device according to claim 1, wherein the first estimator is a linear estimator having at least four states, which are estimated values for horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame, and estimated values for the values of cosine and of sine of the estimate of the unbounded error affecting the directional estimate of the heading.

3. The device according to claim 2, wherein the first estimator performs trigonomic calculations to determine the estimate of the unbounded error from the estimated values and for the cosine and for the sine, and performs a difference operation to subtract the estimate of the unbounded error from the directional estimate of the heading determined by the AHRS device in order to generate an estimated value for a geographical heading of the aircraft that is unaffected by potential magnetic disturbances of the environment of the aircraft.

4. The device according to claim 2, wherein the device includes two outputs constituted by the estimated values for the horizontal components of the speed vector relative to the ground, which values take account of the estimate of the unbounded error.

5. The device according to claim 2, wherein the first estimator applies the equations of a Kalman filter based on a model of a process, in continuous time, such that: $\frac{d}{\mathrm{dt}}x\left(t\right)=F\left(t\right).Math.x\left(t\right)+w_c\left(t\right),\mathrm{and}z\left(t\right)=H\left(t\right).Math.x\left(t\right)+w_m\left(t\right);$ with: $x\left(t\right)=\left(\begin{array}{c}C\\ S\\ v_x^N\\ v_y^N\\ \mathrm{.Math.}\end{array}\right)$ being a state vector comprising at least the four states, namely the estimated values for the cosine and for the sine of the estimate of the unbounded error and the estimated values for the horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame; w.sub.c(t) being a control noise vector; w.sub.m(t) being a measurement noise vector; $z\left(t\right)=\left(\begin{array}{c}{v}_x^N\\ v_y^N\\ \mathrm{.Math.}\end{array}\right)$ being an estimation vector of the measurement comprising at least the two estimated values for the horizontal components of the speed vector relative to the ground of the aircraft in the geographical reference frame; $F\left(t\right)=\left(\begin{array}{ccccc}-\frac{1}{}& 0& 0& 0& \mathrm{.Math.}\\ 0& -\frac{1}{}& 0& 0& \mathrm{.Math.}\\ {}_x^{N*}& -{}_y^{N*}& 0& 0& \mathrm{.Math.}\\ {}_y^{N*}& {}_x^{N*}& 0& 0& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\end{array}\right)$ being a sub-matrix of a matrix relating the derivative of the state vector to the state vector; and $H\left(t\right)=\left(\begin{array}{ccccc}0& 0& 1& 0& \mathrm{.Math.}\\ 0& 0& 0& 1& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\end{array}\right)$ being a sub-matrix of a measurement matrix relating the estimation vector of the measurement to the state vector.

6. The device according to claim 1, wherein the device includes a second estimator operating with a model that is linearized by the small angles assumption, the first estimator operating during an initial convergence stage and subsequently being replaced by the second estimator for continuing to prepare the estimate of the unbounded error affecting the directional estimate of the heading, and consequently to refine the estimated values and for the horizontal components of the vector of the speed relative to the ground and for a geographical heading of the aircraft.

7. The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold.

8. The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the modulus of the vector formed by the estimated values for sine and cosine of the estimate of the unbounded error become close to unity, to within a margin, such that:
|1{square root over ((S).sup.2+(C).sup.2)}|<margin.

9. The device according to claim 6, wherein the second estimator replaces the first estimator from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold, or else from the instant at which the modulus of the vector formed by the estimated values for sine and cosine of the unbounded error become close to unity, to within a margin, such that:
|1{square root over ((S).sup.2+(C).sup.2)}|<margin.

10. The device according to claim 1, wherein the first estimator: performs a first projection operation for projecting the fuselage reference frame onto a local horizontal reference frame, the local horizontal reference frame being formed firstly by a projection onto a horizontal plane of the direction of the fuselage reference frame, and secondly by a direction perpendicular to the projection and situated in the horizontal plane; performs a second projection operation for projecting the local horizontal reference frame onto a horizontal pseudo-geographical reference frame, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame; and performs a linear transformation operation for transforming the horizontal pseudo-geographical reference frame into an estimate of the horizontal plane, with the angle between the estimate of the horizontal plane and the horizontal pseudo-geographical reference frame being the estimate of the unbounded error affecting the directional estimate of the heading; and the first estimator comprising a feedback loop having its gains calculated using the equations of a Kalman filter.

11. The device according to claim 1, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

12. A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises: providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane; providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft; and preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector.

13. The method according to claim 12, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading comprises the following sub-steps: projecting the measurement of the acceleration vector onto a local horizontal reference frame while using the estimates of the attitude angles in order to obtain an estimate of a horizontal component of the acceleration vector, the local horizontal reference frame being formed firstly by a projection of the direction of the fuselage reference frame onto a horizontal plane, and secondly by a direction perpendicular to the projection and situated in the horizontal plane; projecting the estimate of the horizontal component of the acceleration vector onto a horizontal pseudo-geographical reference frame in order to obtain a pseudo-geographical estimate of a horizontal component of the acceleration vector, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame; linearly transforming the pseudo-geographical estimate of the horizontal component in the pseudo-geographical reference frame of the acceleration vector into an estimate of a horizontal component in a geographical reference frame of the acceleration vector, the estimate being corrected with the estimate of the unbounded error affecting the directional estimate of the heading, by means of the estimated values; integrating the estimate of the horizontal component of the acceleration vector in the pseudo-geographical reference frame in order to obtain an estimate of the speed vector relative to the ground in the horizontal geographical reference frame, taking account of the estimate of the unbounded error affecting the directional estimate of the heading; comparing the estimate of the speed vector relative to the ground in the horizontal geographical reference frame with the measurement of the speed vector relative to the ground; and preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground.

14. The method according to claim 13, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading includes calculating the estimated value of the geographical heading.

15. The method according to claim 13, wherein the preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground applies a Kalman filter having at least four states, which are the estimated values for the horizontal component of the speed vector relative to the ground in the geographical reference frame, and also the estimated values and for cosine and sine of the estimate of the unbounded error affecting the directional estimate of the heading.

16. The method according to claim 13, wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading applies a model that is linearized by the small angles assumption as from the instant at which the covariance associated with the estimate of the unbounded error becomes less than a first predetermined threshold, or else the modulus of the vector formed by the estimated values for sine and cosine of the estimate of the unbounded error come close to unity, to within a margin, such that:
|1{square root over ((S).sup.2+(C).sup.2)}|<margin.

17. The method according to claim 12, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

18. A device for estimating ground speed and heading of an aircraft, the aircraft having three axes forming a fuselage reference frame rigidly associated with a structure of the aircraft, the device comprising: a global navigation satellite system (GNSS) receiver receiving signals from a plurality of satellites and configured to provide a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, the geographical reference frame including a horizontal plane; an attitude and heading reference system (AHRS) device providing a measurement of an acceleration vector of the aircraft in the fuselage reference frame together with estimates of the attitude angles, and a directional estimate of the heading of the aircraft; and a first estimator connected to the GNSS receiver and to the AHRS; wherein the first estimator is linear and configured to prepare an estimate of an unbounded error affecting the directional estimate of the heading determined by the AHRS device by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector, independently of any magnetic measurement; and wherein the device includes a second estimator operating with a model that is linearized by the small angles assumption, the first estimator operating during an initial convergence stage and subsequently being replaced by the second estimator for continuing to prepare the estimate of the unbounded error affecting the directional estimate of the heading, and consequently to refine the estimated values and for the horizontal components of the vector of the speed relative to the ground and for a geographical heading of the aircraft.

19. The device according to claim 18, wherein the horizontal plane of the geographical reference frame is substantially perpendicular to the Earth's gravity direction.

20. A method of estimating speed relative to the ground and heading of an aircraft, wherein the method comprises: providing a measurement of a speed vector relative to the ground of the aircraft in a geographical reference frame, by receiving signals from a plurality of satellites, the geographical reference frame including a horizontal plane; providing a measurement of an acceleration vector of the aircraft in a fuselage reference frame rigidly associated with the aircraft, together with estimates of attitude angles and a directional estimate of the heading of the aircraft; and preparing an estimate of an unbounded error affecting the directional estimate of the heading, which preparation is performed in a manner that is linear by combining the measurement of the speed vector relative to the ground with the estimates of the attitude angles, with the directional estimate of the heading, and with the measurement of the acceleration vector; wherein the preparing the estimate of the unbounded error affecting the directional estimate of the heading comprises the following sub-steps: projecting the measurement of the acceleration vector onto a local horizontal reference frame while using the estimates of the attitude angles in order to obtain an estimate of a horizontal component of the acceleration vector, the local horizontal reference frame being formed firstly by a projection of the direction of the fuselage reference frame onto a horizontal plane, and secondly by a direction perpendicular to the projection and situated in the horizontal plane; projecting the estimate of the horizontal component of the acceleration vector onto a horizontal pseudo-geographical reference frame in order to obtain a pseudo-geographical estimate of a horizontal component of the acceleration vector, the horizontal pseudo-geographical reference frame being defined from the local horizontal reference frame and from the directional estimate of the heading, the directions of the horizontal pseudo-geographical reference frame each forming an angle equal to the directional estimate of the heading with a respective one of the directions of the local horizontal reference frame; linearly transforming the pseudo-geographical estimate of the horizontal component in the pseudo-geographical reference frame of the acceleration vector into an estimate of a horizontal component in the geographical reference frame of the acceleration vector, the estimate being corrected with the estimate of the unbounded error affecting the directional estimate of the heading, by means of the estimated values; integrating the estimate of the horizontal component of the acceleration vector in the pseudo-geographical reference frame in order to obtain an estimate of the speed vector relative to the ground in the horizontal geographical reference frame, taking account of the estimate of the unbounded error affecting the directional estimate of the heading; comparing the estimate of the speed vector relative to the ground in the horizontal geographical reference frame with the measurement of the speed vector relative to the ground; and preparing corrections acting on the estimate of the unbounded error and on the estimate of the speed vector relative to the ground; and wherein, during certain stages, preparing the estimate of the unbounded error affecting the directional estimate of the heading applies a model that is linearized by the small angles assumption.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention and its advantages appear in greater detail in the context of the following description of embodiments given by way of illustration and with reference to the accompanying figures, in which:

(2) FIG. 1 shows a rotary wing aircraft;

(3) FIG. 2 shows a device of the invention for estimating the ground speed and the heading of an aircraft;

(4) FIG. 3 shows a variant of such a device;

(5) FIG. 4 shows the various reference frames used by the device; and

(6) FIG. 5 is a diagram summarizing a method of estimating the ground speed and the heading of an aircraft.

(7) Elements that are present in more than one of the figures are given the same references in each of them.

DETAILED DESCRIPTION OF THE INVENTION

(8) In FIG. 1, there can be seen a rotary wing aircraft 20. A fuselage reference frame (X.sup.B, Y.sup.B, Z.sup.B) is rigidly associated with the aircraft 20, e.g. being attached to the mean center of gravity of the aircraft 20. The fuselage reference frame (X.sup.B, Y.sup.B, Z.sup.B) is defined by particular directions of the aircraft 20, which are respectively the longitudinal direction X.sup.B contained in the plane of symmetry of the aircraft 20, parallel to the floor of the passenger cabin of the aircraft 20, and extending from the rear to the front of the aircraft 20, the normal direction Z.sup.B extending downwards perpendicularly to the longitudinal direction X.sup.B, and the transverse direction Y.sup.B extending from left to right perpendicularly to the longitudinal direction X.sup.B and to the normal direction Z.sup.B. The longitudinal direction X.sup.B is the roll axis of the aircraft 20, the transverse direction Y.sup.B is its pitching axis, and the normal direction Z.sup.B is its yaw axis.

(9) A geographical reference frame (X.sup.N, Y.sup.N, Z.sup.N) is also shown in FIG. 1. This geographical reference frame (X.sup.N, Y.sup.N, Z.sup.N) is formed on the basis of the directions of cardinal points, e.g. by the directions North and East respectively constituting the directions X.sup.N, Y.sup.N, and by a direction Z.sup.N substantially parallel to the Earth's gravity. The directions X.sup.N, Y.sup.N thus form a substantially horizontal plane (X.sup.N, Y.sup.N).

(10) The aircraft 20 includes a device 1 for estimating the ground speed and the heading of the aircraft 20, which device is shown in detail in FIG. 2. A variant of this device 1 is also shown in FIG. 3. This device 1 and its variant are suitable for implementing a method of estimating the ground speed and the heading of an aircraft, which method is summarized diagrammatically in FIG. 5. The method comprises three main steps 101 to 103, the third step 103 comprising seven sub-steps 111 to 117.

(11) The device 1 comprises a GNSS receiver 11, an AHRS device 12, and a first estimator 13 connected to the GNSS receiver 11 and to the AHRS device 12. The GNSS receiver 11 provides the first estimator 13 with a measurement {right arrow over ()}.sub.GNSS of a first ground speed vector of the aircraft 20 in the geographical reference frame (X.sup.N, Y.sup.N, Z.sup.N), while the AHRS device 12 provides the first estimator 13 with a measurement {right arrow over ()}.sup.B of an acceleration vector of the aircraft 20 in the fuselage reference frame (X.sup.B, Y.sup.B, Z.sup.B), together with estimates and of the attitude angles, and a directional estimate .sub.DIR of the heading of the aircraft 20. The directional estimate .sub.DIR of the heading is determined in particular without using any magnetic measurement.

(12) As shown in FIG. 2, the first estimator 13 comprises two projection operators 15, 16 and a linear estimator 17.

(13) The first projection operator 15 serves to perform a transfer from the fuselage reference frame (X.sup.B, Y.sup.B, Z.sup.B) to a local reference frame (X.sup.H, Y.sup.H) formed by a projection X.sup.H of the direction X.sup.B onto a plane that is horizontal, and thus parallel to the plane (X.sup.N, Y.sup.N), possibly coinciding therewith, and by a direction Y.sup.H perpendicular to the projection X.sup.H and situated in the same horizontal plane.

(14) This first projection operator 15 thus enables the measurement {right arrow over ()}.sup.B of the acceleration vector to be projected onto this local horizontal reference frame (X.sup.H, Y.sup.H) in order to determine an estimate {right arrow over ()}.sup.H of the horizontal component of the acceleration vector of the aircraft 20.

(15) The second projection operator 16 serves to perform a transfer from the local horizontal reference frame (X.sup.H, Y.sup.H) to a horizontal pseudo-geographical reference frame (X.sup.N*, Y.sup.N*) defined on the basis of the local horizontal reference frame (X.sup.H, Y.sup.H) and of the directional estimate .sub.DIR of the heading. The directions X.sup.N* and Y.sup.N* are situated in a horizontal plane, and each of them forms an angle equal to the directional estimate .sub.DIR of the heading with a respective one of the directions X.sup.H and Y.sup.H. The second projection operator 16 thus serves to transfer the estimate {right arrow over ()}.sup.H of the horizontal component of the acceleration vector into this horizontal pseudo-geographical reference frame (X.sup.N*, Y.sup.N*) so as to determine a pseudo-geographical estimate {right arrow over ()}.sup.N* of the acceleration vector of the aircraft 20.

(16) FIG. 4 shows these various reference frames and the relationships between them.

(17) The linear estimator 17 comprises integrators 21 and 22 for estimating values C and S for the sine and the cosine of the angular difference between the pseudo-geographical reference frame and the geographical reference frame

(18) The linear estimator 17 has a linear transformation operator 40 for transforming the horizontal pseudo-geographical reference frame (X.sup.N*, Y.sup.N*) to an estimate of the horizontal geographical reference frame (X.sup.N, Y.sup.N). This linear transformation operator 40 is constituted by gain operators 31-34 together with a difference operator 27 and a sum operator 28. The matrix operation performed by these six scalar operators is the following:

(19) $\left(\begin{array}{c}{}_x^N\\ {}_y^N\end{array}\right)=\left(\begin{array}{cc}C& -S\\ S& C\end{array}\right)\left(\begin{array}{c}{}_x^{N*}\\ {}_y^{N*}\end{array}\right).$

(20) The person skilled in the art will recognize in the matrix operator an operator for turning through an angle =tan.sup.1(C, S) in the horizontal plane (X.sup.N, Y.sup.N), since C.sub..sup.2+S.sub..sup.2=1.

(21) Starting from the estimate {right arrow over ()}.sub.N* of the acceleration vector in the pseudo-geographical reference frame, said linear transformation operator 40 prepares an estimate {right arrow over ()}.sup.N of the acceleration vector in the geographical reference frame, taking account of the estimate of the error that affects the directional estimate .sub.DIR of the heading.

(22) The linear estimator 17 has integrators 23, 24 for integrating the estimate {right arrow over ()}.sup.N of said acceleration vector in the geographical reference frame in order to obtain the estimate {right arrow over ()}.sup.N of the ground speed vector in the geographical reference frame, taking account of the estimate of the error affecting the directional estimate .sub.DIR of the heading. The linear estimator 17 also has difference operators 29, 30 calculating the difference between firstly each of the components (.sub.x.sup.N, .sub.y.sup.N) of said estimate {right arrow over ()}.sup.N of the ground speed vector in the geographical reference frame, taking account of the estimate of the error affecting the directional estimate .sub.DIR of the heading, and secondly each of the components (.sub.x.sub.GNSS.sup.N, .sub.y.sub.GNSS.sup.N) of the measurement {right arrow over ()}.sub.GNSS.sup.N of the ground speed vector {right arrow over ()}.sup.N in the geographical reference frame (X.sup.N, Y.sup.N, Z.sup.N).

(23) The linear estimator 17 comprises a matrix gain operator K of dimensions (42), referenced 35 in FIG. 2, which propagates the components of a speed difference vector on each of the inputs of integrators 21, 22, 23, and 24, such that:

(24) $\left(\begin{array}{c}\mathrm{CorCRate}\\ \mathrm{CorSRate}\\ \mathrm{CorVxRate}\\ \mathrm{CorVyRate}\end{array}\right)=\left(\begin{array}{cc}{k}_{\mathrm{cx}}& k_{\mathrm{cy}}\\ k_{\mathrm{sx}}& k_{\mathrm{sy}}\\ k_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{yx}}& k_{\mathrm{yy}}\end{array}\right)\left(\begin{array}{c}{v}_x^N\\ v_y^N\end{array}\right);$$\mathrm{with}\left(\begin{array}{cc}{k}_{\mathrm{cx}}& k_{\mathrm{cy}}\\ k_{\mathrm{sx}}& k_{\mathrm{sy}}\\ k_{\mathrm{xx}}& k_{\mathrm{xy}}\\ k_{\mathrm{yx}}& k_{\mathrm{yy}}\end{array}\right)=K.$

(25) The elements of the matrix K may for example be Kalman gains calculated from the Riccati differential equation.

(26) In this linear estimator 17, the state vector x(t) has four states, which are the estimated values .sub.x.sup.N, .sub.y.sup.N of the horizontal components of the ground speed vector of the aircraft 20 in the horizontal plane of the geographical reference frame (X.sup.N, Y.sup.N, Z.sup.N) and the estimated values C and S of the cosine and of the sine of an estimate of the error affecting the directional estimate .sub.DIR of the heading.

(27) The four states of the linear estimator 17 converge as soon as the aircraft 20 undergoes a stage of acceleration. In particular, the states C and S carried by the integrators 21 and 22 then constitute accurate estimates of the sine and the cosine of the angular error affecting the directional estimate .sub.DIR of the heading prepared by the AHRS device 12.

(28) By way of example, the calculation of the gain matrix K is based on the known equations of the Kalman filter, itself based on the above described linear model of the process.

(29) Finally, the first estimator 13 has an A TAN 2 trigonometrical calculation block 18 and a difference operator 36. The A TAN 2 trigonometrical calculation block 18 serves to determine an estimate of the error affecting the directional estimate .sub.DIR of the heading on the basis of the estimated values C and S for the cosine and the sine of this estimate by applying the two-argument trigonometrical function A TAN 2 to the two estimated values S and C. The difference operator 36 then enables this estimate to be subtracted from the directional estimate .sub.DIR of the heading as prepared by the AHRS device 12 in order to generate an estimated value for the geographical heading, in which the gyro measurement inaccuracies of the heading are corrected, and which, furthermore, is unaffected by potential magnetic disturbances in the environment of the aircraft 20. This estimated value of the geographical heading of the aircraft 20 constitutes an output 53 of the device 1.

(30) In addition, the device 1 has two other outputs 51, 52 constituted by the estimated values .sub.x.sup.N, .sub.y.sup.N for the horizontal components of the ground speed vector that take account of the estimate of the error.

(31) Furthermore, in the variant shown in FIG. 3, the device 1 has a switch 5 and a second estimator 14 operating using the so-called small angles approximation, and thus applying a model that relies on the small angles assumption. The switch 5 is arranged between the first estimator 13 and the second estimator 14. As a result, the outputs 51, 52, and 53 of the device 1 are constituted by the outputs of the switch 5. The switch 5 thus makes it possible to switch between the first estimator 13 and the second estimator 14. The first and second estimators 13, 14 and the switch 5 may form integral portions of a computer present in the aircraft 20.

(32) The first estimator 13 operates during an initial convergence stage, and thereafter it is replaced by the second estimator 14, once convergence has been achieved on the estimate of the error affecting the directional estimate of the heading. The second estimator 14 then needs to process only a residual angular error that is of small amplitude, and it can therefore rely on the small angles approximation in its own structure for estimating the residual angular error. The reduction in the number of states (a single estimator, directly estimating , instead of two, estimating the sine and the cosine of the error angle) improves the accuracy of the estimate and consequently the accuracy of the estimated values .sub.x.sup.N, .sub.y.sup.N and for the ground speed of the aircraft 20 and for the geographical heading.

(33) Naturally, the present invention may be subjected to numerous variations as to its implementation. Although several embodiments are described, it should readily be understood that it is not conceivable to identify exhaustively all possible embodiments. It is naturally possible to envisage replacing any of the means described by equivalent means without going beyond the ambit of the present invention.