• 专利附录
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    • 专利摘要:
    The present invention relates to a device (1) for estimating a speed with respect to the ground and a heading of an aircraft not exploiting the Earth's rotation or the Earth's magnetic field. The device (1) comprises in particular a first linear estimator (13) carrying out the hybridization between a speed measurement with respect to the ground of said aircraft provided by a GNSS receiver (11) and measurements of the acceleration and attitudes of said aircraft coming from an AHRS device (12) without a gyrocompass and without a magnetometer. This first estimator (13) is linear by replacing the single state "estimation of the heading error ΔΨ" of the embodiments of the prior art by two states, namely the sine and cosine estimates of said heading error. .
    公开号:FR3058229A1
    申请号:FR1601555
    申请日:2016-10-27
    公开日:2018-05-04
    发明作者:Jean Paul Petillon；Julien FLORENS
    申请人:Airbus Helicopters SAS；
    IPC主号:
    专利说明:

    © Publication no .: 3,058,229 (to be used only for reproduction orders)
    ©) National registration number: 16 01555 ® FRENCH REPUBLIC
    NATIONAL INSTITUTE OF INDUSTRIAL PROPERTY
    COURBEVOIE © IntCI 8 : G 01 S 19/52 (2017.01), G 01 C 21/20
    A1 PATENT APPLICATION
    ©) Date of filing: 27.10.16.(© Priority: © Applicant (s): AIRBUS HELICOPTERS — RR. ©) Date of availability of the request: 04.05.18 Bulletin 18/18. @ Inventor (s): PETILLON JEAN PAUL and FLORENS JULIEN. ©) List of documents cited in the preliminary search report: See the end of this booklet (© References to other related national documents: ® Holder (s): AIRBUS HELICOPTERS. ©) Extension request (s): (© Agent (s): GPI & ASSOCIES.
    (04 / ESTIMATE, INDEPENDENT OF MAGNETIC MEASUREMENT, SPEED AND CAPE OF AN AIRCRAFT.
    FR 3 058 229 - A1 _ The present invention relates to a device (1) for estimating a speed with respect to the ground and a heading of an aircraft exploiting neither terrestrial rotation nor the terrestrial magnetic field. The device (1) notably comprises a first linear estimator (13) performing the hybridization between a speed measurement with respect to the ground of said aircraft provided by a GNSS receiver (11) and measurements of the acceleration and attitudes of said aircraft originating from an AHRS device (12) without gyrocompass and without magnetometer. This first estimator (13) is linear thanks to the replacement of the single state "estimation of the heading error ΔΨ" of the embodiments of the prior art by two states, namely the estimates of sines and cosines of said heading error .
    Estimation, independent of a magnetic measurement, of the speed and heading of an aircraft.
    The present invention is in the field of pilot assistance systems for aircraft. The present invention is in particular in the field of piloting sensors for aircraft delivering speed information relative to the ground and heading of an aircraft in a reference linked to the aircraft for assistance in piloting the aircraft.
    The present invention relates to a device for estimating the speed with respect to the ground and the heading of an aircraft as well as a method for estimating this speed and this heading of the aircraft. This device and this method are independent of a magnetic heading measurement.
    An integral estimate of the speed relative to the ground of an aircraft is required for certain modes of an autopilot. For the sake of simplification, the expression “ground speeds” will be used hereinafter to denote a speed with respect to the ground of an aircraft.
    An aircraft was historically equipped with a Doppler radar providing a measurement of the aircraft's ground speed. Today, the Doppler radar is disappearing in favor of a satellite navigation receiver which is more precise, but above all less bulky and less expensive. This on-board receiver receives signals from several satellites belonging to one or more satellite constellations and forms with these satellite constellations a satellite navigation system designated by the acronym GNSS meaning in English "Global Navigation Satellite System". Several constellations are currently operational, including the United States’s GPS system.
    A GNSS receiver on board an aircraft can in particular provide a measurement of the aircraft's ground speed in a geographical location as well as the position of the aircraft. A geographic coordinate system, also called a terrestrial coordinate system or navigation coordinate system, is for example formed from the directions of the cardinal points, typically the directions of North and East as well as by a vertical direction, generally that of terrestrial gravity.
    However, the piloting function of the aircraft needs an estimate of the ground speed in a carrier frame, also known as the fuselage frame, linked to the aircraft. This fuselage coordinate system is, for example, defined by particular directions of the aircraft, such as its roll axis, its pitch axis and its yaw axis. It is therefore necessary to have a measurement of the heading of the aircraft as well as of its attitude angles to carry out a projection or a change of reference point between the geographical reference point and the fuselage reference point.
    It will also be noted that for an aircraft, and in particular for a rotary wing aircraft, the heading is different from the course angle, also called the trajectory angle. Indeed, the heading is the angle between on the one hand an orthogonal projection of the longitudinal direction of the aircraft in a horizontal plane defined perpendicular to the direction of the Earth's gravity, and on the other hand the direction of geographic North. The course angle is the angle between an orthogonal projection of the direction of the route followed by the aircraft in such a horizontal plane and the direction of geographic North. This direction of the route can also be defined as the direction of the ground speed vector of the aircraft.
    However, if for a land vehicle, it can be considered that the course angle is generally equal to the heading, this is not the case for an aircraft which can fly with a certain drift corresponding to the difference between the heading and the road angle. In addition, a rotary wing aircraft has the particularity of being able to move laterally as well as rearward, the difference between the course angle and the heading then being respectively ± 90 degrees and 180 degrees (± 90 ° and 180 °).
    Estimates of a magnetic heading and angles of attitude of the aircraft are today available on board an aircraft and supplied for example by a device known as AHRS meaning in English "Attitude and Heading Reference System". An AHRS device also provides measurements of the aircraft's accelerations.
    This AHRS device uses, on the one hand, measurements from gyrometers and accelerometers to estimate the aircraft's attitude, and on the other hand, magnetic measurements specifically to estimate the magnetic heading of the aircraft. This last heading estimate is sometimes called "gyromagnetic" because it is aligned with the measurement of the magnetometer in the long term, but it uses the integral of the measurement of gyrometers in the short term.
    AHRS devices make a command available to the pilot to change the operating mode of their heading estimator and temporarily remove the long-term alignment on the magnetic measurement. This operating mode is qualified as “directional” or “pure gyrometer”. The course is then insensitive to any magnetic disturbances that can corrupt it. This mode is typically used when approaching a boat or an oil platform. However, this operating mode cannot be used for more than a few tens of minutes, failing which Heading terror, caused by gyros and manifesting as drift, would become prohibitive.
    The difficulty with this type of heading estimator is that the pilot is likely to forget to switch to directional mode before approaching a magnetically disturbed area. We can also encounter situations where the pilot approaches the aircraft from the ground without being aware that the area is disturbed, for example by buried metallic infrastructures.
    There is therefore a need to develop a more robust heading, without however using an expensive inertial unit, the alignment time of which at start-up can be prohibitive for certain aircraft missions.
    To completely eliminate corruptible magnetic measurements from the chain of steering sensors, it is possible to calculate another heading estimate, distinct from the gyromagnetic estimate, and operating in directional mode at all times. Such a heading estimate is then effectively independent of any magnetic measurement. On the other hand, such a heading estimate, permanently in directional mode, is affected by an unrestricted error, including at system startup. For example, if the heading estimate is initialized to the North while the aircraft nose is oriented to the South, this error can be as large as 180 ° when the systems have just been powered up.
    The problem is therefore to operate a heading, in directional mode permanently, and which can therefore be affected by an unbounded amplitude error, but slowly variable.
    To solve this problem, for example, document US 8860609 is known which describes the coupling of a GNSS receiver and an inertial navigation system as well as the use of an integration filter. The speed or position of an aircraft, supplied by the GNSS receiver, is combined with the inertial measurements of the inertial navigation system according to a non-linear modeling. The integration filter uses an extended Kalman filter to estimate on the one hand an estimated combined position and combined speed as well as at least one speed bias or heading bias. However, the use of extended Kalman filters is only an approximation of the process to be estimated, and therefore is not applicable to large heading error values.
    Another solution consists in replacing the magnetic measurement of the heading by a pure gyroscopic measurement. For this purpose, the AHRS magnetometer device is replaced by an inertial unit, or by an AHRS device capable of aligning in gyrocompass mode, namely based on the one hand on a detection of the direction of the Earth's rotation during the phase alignment, and on the other hand on gyros sufficiently precise to be able to function then in pure gyroscopic mode. Such a measurement device is much more expensive than an AHRS magnetometer device. In addition, the alignment time in a gyrocompass is much longer than an alignment via a magnetometer, which can be detrimental during missions for which the initialization time is crucial.
    These solutions therefore do not meet the need for the piloting function of an aircraft to have an accurate estimate of its ground speed, independent of magnetic measurements and not requiring the use of expensive inertial units and awkward implementation.
    The present invention therefore aims to overcome the limitations mentioned above and to propose a hybridization of a GNSS receiver and an AHRS device in order to estimate a hybrid ground speed and a heading of the aircraft, independently a magnetic measurement and - therefore - insensitive to magnetic disturbances in the environment of the aircraft. The present invention is capable of correcting, whatever its amplitude, an error affecting a very imprecise gyroscopic estimate of the heading of the aircraft, and thus of estimating precise and integral values of the ground speed and the heading of the aircraft. .
    In this context, the present invention provides a device for estimating a ground speed and a heading of an aircraft as well as a method for estimating this ground speed and this heading.
    According to the invention, a device for estimating a ground speed and a heading of an aircraft, the aircraft comprising three axes forming a fuselage coordinate system (X B , Y B , Z B ) rigidly linked to a structure of the aircraft, includes:
    a GNSS receiver receiving signals from several satellites and configured to provide a measurement v GNSS of a ground speed vector v N of the aircraft in a geographical coordinate system (X N , Y N , Z N ), this geographical coordinate system (X N , Y N , Z N ) comprising in particular a horizontal plane (X N , Y N ) substantially perpendicular to the direction of Earth's gravity,
    - an AHRS device providing a measure γ Β of an aircraft acceleration vector in the fuselage frame (X B , Y B , Z B ) as well as estimates des, θ of attitude angles and an estimate directional i ^ dir from the heading of the aircraft, and
    - a first estimator connected to the GNSS receiver and to the AHRS device.
    The device according to the invention is remarkable in that said first estimator is linear and configured to develop an estimate Δψ of the unbounded error affecting the directional estimate of the heading, determined by the AHRS device, by combining the measurement v GNSS of the ground speed vector with the estimates φ, θ of the attitude angles, with the said directional estimate i / idir of the heading, and with the measure γ Β of the acceleration vector, independently of any magnetic measure.
    The input data of said first estimator are therefore supplied on the one hand by the AHRS device and on the other hand by the GNSS receiver respectively in the fuselage frame (X B , Y B , Z B ) and the geographic frame (X N , Y N , Z N ). In particular, the directional estimation ip D iR of the heading does not come from a magnetic measurement.
    This directional estimate ipDiR of the heading is for example calculated and supplied directly by the AHRS device. This directional estimate ipDiR of the heading can also be calculated by another computer, present in the aircraft, on the basis in particular of the measurements supplied by gyrometers of the AHRS device, and in particular of the estimates φ, θ of attitude angles. This directional estimate i / jdir of the heading is thus determined by the integration of the estimated angular speed ψ of the aircraft.
    The geographic coordinate system (X N , Y N , Z N ) is for example formed from the directions of the cardinal points, preferably by the directions of North and East, as well as by a substantially vertical direction. The substantially horizontal plane (X N , Y N ) belonging to this geographical reference (X N , Y N , Z N ) is thus substantially perpendicular to the direction of the Earth's gravity and then has as axes X N , Y N , respectively the direction North and direction East.
    The fuselage frame (X B , Y B , Z B ) of the aircraft is rigidly linked to the structure of the aircraft. It is for example formed by particular directions of the aircraft, for example its longitudinal, transverse and normal directions, corresponding respectively to the axes of roll, pitch and yaw.
    The attitude angles of the aircraft are, for relatively small values of these attitude angles, the two angles between a horizontal plane, namely perpendicular to the direction of earth's gravity, and respectively the longitudinal direction and the direction cross-section of the aircraft. The directional estimate i / jdir of the heading is the angle between an orthogonal projection of the longitudinal direction of the aircraft in the horizontal plane and any direction, but substantially fixed, that is to say which is slowly variable with the over time, from the horizontal plane (X N , Y N ).
    The objective of the device for estimating a ground speed and a heading of an aircraft according to the invention is to determine, from the information provided by the AHRS device, an estimate v N of the ground speed vector of l aircraft, then compare this estimate with the vGNSS measurement provided by the GNSS receiver of this same ground speed vector, in order to develop an estimate Δψ of the error affecting the directional estimate ipDiR of the heading, and then to deduce therefrom corrections, applied to the inputs of the estimators of the geographic heading error and of the ground speed, so that the estimate v N remains aligned in the long term with the measurement vGNSS.
    For this comparison to be possible, the estimate v N of the ground speed vector must be expressed in the same frame of reference as the measurement vcwss of the ground speed vector carried out by the GNSS receiver. For this purpose, the measurement γ Β of the acceleration vector of the aircraft carried out by the AHRS device must first of all be projected into a local horizontal coordinate system (X H , Y H ) using the estimates φ, θ of the angles of plates, also from the AHRS device, in order to develop an estimate ÿHor of the horizontal component of the acceleration vector.
    Then, this estimate y Hor of the horizontal component of the acceleration must be transferred to the estimate of the horizontal plane (X N , Y N ). This transfer between the local horizontal coordinate system (X H , Y H ) and the estimation of the horizontal plane (X N , Y N ) is broken down into two stages: a first transfer by the directional estimation of the heading, resulting from the AHRS device, then a second transfer by the current estimate of the error Δψ. The acceleration vector thus obtained is based on the estimation of the error Δψ. It is therefore also an estimate rather than a measure.
    Said estimate of the acceleration vector in the horizontal plane (X N , Y N ) is then integrated to obtain an estimate v N of the ground speed vector, expressed in the horizontal plane (X N , Y N ) as well.
    The estimate v N of the ground speed vector thus obtained is then subtracted from the measurement v GNSS of the ground speed vector carried out by the GNSS receiver to determine speed differences, themselves used to develop corrections applied to the inputs of three estimator integrators , the heading error on the one hand, and the two horizontal components the ground speed of the aircraft on the other hand.
    As described above, this system constitutes a three-state estimator, these three states being the estimates v N of the two horizontal components of the ground speed vector, and the estimate Δψ of the error affecting the directional estimate ψΰΐϋ of the heading . The main difficulty in producing this estimator lies in the highly non-linear nature of the propagation of the heading error.
    The resolution of such a nonlinear formulation can be obtained by the use of a local linearization method, such as an extended Kalman filter, designated by the acronym “EKF” meaning in English “Extended Kalman Filter” , or else the use of a higher order approximation method of non-linearity, such as for example "UKF" and "CKF" meaning respectively in English "Unscented Kalman Filter" and " Cubature Kalman Filter ”.
    However, each of these methods is only an approximation of the reality of the process, with varying degrees of precision. But none of these methods is capable of modeling with sufficient precision a non-linearity such as those presented by sines and cosines of an unbounded angle, for example likely to evolve on a complete revolution.
    The device for estimating a ground speed and a heading of an aircraft according to the invention comprises a first estimator characterized in that it is of the linear type. The device according to the invention thus avoids a non-linear formulation and, therefore, the use of a local linearization method or else an approximation method of the non-linearity. This first linear estimator is configured to develop an estimate Δψ of the error affecting the directional estimate of the heading by combining the measurement Vgnss of the ground speed vector with the estimates φ and Θ of the angles of attitude, with the directional estimate 0d / / heading, and with the measure γ Β of the acceleration vector.
    Said first estimator is a linear estimator comprising at least four states which are the estimated values vfi and Vy of the horizontal components of the ground speed vector in the horizontal plane of the horizontal frame of reference (X N , Y N ), as well as the estimated values Câip and ΞΔψ values of the cosine and sine of the error affecting the directional estimate ipDiit of the heading.
    This first estimator constitutes a hybridization filter and comprises several calculation blocks in order to allow, after several transformations, to determine from the information provided by the AHRS device estimated values vfl and Vy of the horizontal components of the ground speed vector v N in the frame of reference. horizontal (X N , Y N ), compare them with the GNSS measurement v of the ground speed vector carried out by the GNSS receiver and develop an estimate Δψ of the error affecting the directional estimate of the heading from the AHRS device. The device according to the invention can then calculate an estimated value φ of the geographic heading and an estimate v N of the horizontal component of the ground speed vector of the aircraft.
    The first estimator notably includes:
    - a first operator for projecting the fuselage frame (X B , Y B , Z B ) to a local horizontal frame (X H , Y H ), the local horizontal frame (X H , Y H ) being formed on the one hand by a projection X H of the direction X B of the fuselage frame (X B , Y B , Z B ) in a horizontal plane and on the other hand by a direction Y H perpendicular to the projection X H and also located in this horizontal plane,
    - a second operator for projecting from the local horizontal coordinate system (X H , Y H ) to a horizontal pseudo-geographic coordinate system (X N *, Y N '), | e horizontal pseudo-geographic coordinate system (X N ', Y N *) being defined from the local horizontal coordinate system (X H , Y H ) and the directional estimate ψο / R of the heading, the directions X N * and Y N * of the horizontal pseudo-geographic coordinate system (X N *, Y N ') respectively forming an angle equal to the directional estimate ψο / R of the heading with the directions X H and Y H of the local horizontal coordinate system (X H , Y H ) ,
    - an operator for linear transformation of said horizontal pseudogeographic coordinate system (X N *, Y N ) to an estimate (X N , Y N ) of the horizontal geographic coordinate system, the angle between said estimate of the horizontal geographic coordinate system and the horizontal pseudo-geographic coordinate system (X N *, Y N *) being the current estimate Δψ of the error affecting the directional estimate of the heading, and
    - a feedback loop whose gains are calculated for example according to the equations of the Kalman filter.
    Recall that a linear estimator is based on a linear model of the process, which can for example be formulated as follows in continuous time:
    £ x (t) = F (t) .x (t) + w c (t) and z (t) = H (t) .x (t) +
    In a device according to the invention, the state vector x (t) notably comprises the estimated values ΞΔψ and εΔψ of the sines and cosines of the error affecting the directional estimation ipow of the heading, as well as the two estimated values v x and Vy of the horizontal components of the ground speed vector in the geographic coordinate system (X N , Y N , Z N ) such that:
    / O x (t) =
    In a device according to the invention, the measurement estimation vector comprises at least the two estimated values v x , Vy of the horizontal components of the ground speed vector in the geographic frame (X N , Y N , Z N ), such as :
    z (t) =
    In a device according to the invention, the matrix relating the derivative of the state vector x (t) to the state vector x (t] comprises at least the following sub-matrix where τ is an equal time constant for example at 600 seconds (600s):
    F (t) = i
    T
    In a device according to the invention, the measurement matrix, also called “observation”, which relates the estimation vector z (t) of the measurement to the state vector x (t), comprises at least the following sub-matrix:
    / 0010 ...
    H (t) = I 0 0 0 1 ... I.
    The linear model of a process involved in the formulation of an estimator further comprises two noise vectors, added respectively to the command (w c (t)) and to the measurement.
    Furthermore, the device for estimating a ground speed and a heading of an aircraft according to the invention may include a trigonometric calculation and a difference operator. Said trigonometric calculation makes it possible to determine an estimate of the angle of error affecting the directional estimate x [) dir of the heading from the estimated values εΔψ and ΞΔψ of the values of its cosines and sines. This trigonometric calculation uses for example the trigonometric function with two arguments "atan2", which is the reciprocal function of the tangent trigonometric function. It allows to find the angle in its full range [-π ... π [when it is applied to the two estimated values SA-ψ and CAip in order to determine an estimate Δψ of the error affecting the directional estimate xpDiR of the heading .
    The difference operator then makes it possible to subtract said estimate Δψ from the directional estimate t / z D / R of the heading in order to generate an estimated value ψ of the geographical heading. This estimated value ψ of the geographic heading is thus corrected for the error affecting the directional estimation of the heading provided by the device of the AHRS type.
    Thus, a device in accordance with the invention makes it possible, without using magnetic measurements, to combine inertial measurements provided by an AHRS device, expressed in fuselage benchmark, with speed measurements provided by a GNSS receiver, expressed in geographic benchmark . In addition, the heading estimation provided by a device in accordance with the invention also makes it possible, without using magnetic measurements, to express the ground speed vector in a robust manner and integrates into the local horizontal frame, which is required by pilotage laws.
    According to a variant of the invention, the device for estimating a ground speed and a heading of an aircraft may include a second estimator operating according to an approximation known to the skilled person and called "small angles" . The first estimator then operates during an initial phase of convergence and is then replaced, when convergence on the estimate Δψ of the error is reached, by the second estimator to continue the estimate Δψ of the error and, consequently , improve the accuracy of the estimated values of the aircraft ground speed and the geographic heading. For this variant, the device for estimating a ground speed and a heading of an aircraft comprises a switch so that the estimate Δψ of the error is provided by the first estimator or else the second estimator.
    The second estimator then replaces the first estimator as a function of operating conditions of the device for estimating a ground speed and a heading of an aircraft according to the invention and in particular of one or more internal values of the first estimator .
    For example, the second estimator replaces the first estimator from the moment when the covariance associated with the estimate Δψ of the error becomes less than a first predetermined threshold.
    Advantageously, the second estimator is thus used from the moment when there is a sufficiently precise estimate Δψ of the error. The first estimator first performs a first estimate Δψ of the error by estimating its sines and cosines, so as to circumvent the difficulty of the non-linearity of the model, then the second estimator can refine and maintain, in a second phase , the estimate Δψ of the error.
    In another embodiment of the invention, the second estimator replaces the first estimator from the moment when the modulus of the vector formed by the estimated values ΞΔψ, CA-ψ of the sines and cosines of the angular error becomes close unity, to within a margin, such as:
    <margin.
    The device for estimating a ground speed and a heading of an aircraft according to the invention can also combine these two conditions. In this embodiment, the second estimator replaces the first estimator, for example from the moment when at least one of these two conditions set out above is met.
    This first threshold applied to the covariance associated with the estimate Δψ of the angular error is for example of the order of (10 °) 2 , and the deviation of the modulus of the vector formed by the estimated values ΞΔψ, CAip with respect the unit module is around 10%, that is; margin = 0.7.
    It should be noted that the replacement of the first estimator by the second estimator is generally final during the flight of an aircraft equipped with the device for estimating a ground speed and a heading according to the invention. In this way, the first estimator operates during an initial phase of convergence and the second estimator is then used until the device stops, generally corresponding to the end of the flight of the aircraft.
    However, if the covariance associated with the estimate Δψ of the error affecting the heading estimate provided by the AHRS type device increases sharply following a very long flight phase during which no turn or speed change n 'is performed, it can be provided in certain embodiments of the invention that the first estimator can again be used to replace the second estimator. Indeed, the good functioning of the second estimator could then be compromised, the hypothesis of “small angles” being able to be faulted. This is for example the case when the covariance associated with the error Δψ becomes greater than (30 °) 2 .
    The second estimator allows, thanks to the approximation of small angles, to directly use the estimate Δψ as a state, without using the trigonometric sine and cosine functions. In this way, the second estimator satisfies the requirement of minimality of the state representation, and thus uses a linearized modeling by the "small angles" hypothesis. Said second estimator may furthermore comprise more than three states and thus allow a more faithful modeling than that of the first estimator of the errors affecting the AHRS device, and in particular of the directional estimation i / jdir of the heading. This reconfiguration advantageously makes it possible to improve the accuracy of the estimated values of the ground speed and the geographic heading of the aircraft of the device according to the invention.
    The second estimator can for example adopt an estimator structure with at least seven states:
    - the estimate & ψ of the error affecting the directional estimate of the heading, an error which is assumed to have a low value,
    - the estimates of the two errors affecting the estimates φ, θ of the attitude angles delivered by the AHRS device (we also assume that these errors are small angles),
    - the estimated values vf and Vy of the horizontal components of the ground speed vector of the aircraft, and
    - the estimation of the horizontal part (two components Ay / and Ay) of the bias vector affecting the measurement of the acceleration vector of the aircraft from the AHRS device.
    The present invention also relates to a method of estimating a ground speed and a heading of an aircraft. This process includes the following steps:
    a first step of supplying a measurement v GNSS of a ground speed vector of the aircraft in the geographical coordinate system (X N , Y N , Z N ), this geographical coordinate system (X N , Y N , Z N ) comprising in particular a horizontal plane (X N , Y N ) substantially perpendicular to the direction of Earth's gravity,
    a second step of providing a measurement y s of an acceleration vector of the aircraft in a fuselage reference frame (X B , Y B , Z B ) rigidly linked to the aircraft as well as estimates φ, θ d ' angles of attitude and a directional estimate $ dir of the heading of the aircraft, and
    a third step of developing an estimate Δψ of the error affecting the directional estimate i / jdir of the heading of the aircraft, carried out in a linear fashion and making it possible to estimate an unbounded error affecting the directional estimate ipDiR of the heading by combining the measure GNSS of the ground speed vector with the estimates φ, θ of the angles of attitude, the directional estimate i / jdir of the heading, and the measure γ Β of the acceleration vector.
    In addition, the third step in developing the Δψ estimate of the error affecting the directional estimate x / jdir of the heading can be broken down into several sub-steps:
    - a first substep of projection of the measure γ Β of the acceleration vector in a local horizontal coordinate system (X H , Y H ) using the estimates φ and Θ of the angles of the bases in order to obtain an estimate y H of the horizontal component of the acceleration vector, the local horizontal frame (X H , Y H ) being formed on the one hand by a projection X H of the direction X B of the fuselage frame (X B , Y B , Z B ) in a horizontal plane and on the other hand by a direction Y H perpendicular to the projection X H and located in this horizontal plane,
    a second substep of projection of the estimate y H of the horizontal component of the acceleration vector in a horizontal pseudo-geographic coordinate system (X N *, Y N *) in order to obtain an estimate y w *, called pseudo- horizontal geographic, of the horizontal component of the acceleration vector, the horizontal pseudo-geographic coordinate system (X N *, Y N ) being defined starting from the local horizontal coordinate system (X H , Y H ) and the directional estimate x [) dir from the course, the directions X
    NOT*
    N * and Y, N of the horizontal pseudo-geographic coordinate system (X N *, Y N ) respectively forming an angle equal to the directional estimate iJjdir of the heading with the directions X H and Y H of the local horizontal coordinate system (X H , Y H ), a third linear transformation sub-step - defined by the matrix cyO “ , horizontal estimate γ Ν * of the horizontal component of the acceleration vector in the pseudo-geographic coordinate system to obtain an estimate γ Ν of the horizontal component of the acceleration vector in geographic benchmark, this estimate γ Ν of the acceleration in geographic benchmark thus being corrected with the estimate of the error affecting the directional estimate i / jdir of the heading, via the use of the estimated values CAip and SAip of its cosine and its sine,
    a fourth sub-step of integration of this estimate γ Ν of the acceleration vector in geographic reference frame in order to obtain an estimate v N of the ground speed vector in the horizontal geographic reference frame (X N , Y N ) taking into account an estimate Δψ the error affecting the directional estimation iPdir of the heading,
    a fifth substep for comparing this estimate v N of the ground speed vector in the horizontal geographic coordinate system (X N , Y N ) with the measurement v GNSS of this same ground speed vector to obtain two components of speed difference, and
    - a sixth sub-stage of development, by applying a matrix gain (4x2 matrix) to the two speed difference components, of four corrections acting on the inputs of four integrators, carrying respectively the four states of the estimator of the invention.
    In the sixth sub-step, the matrix gain (4x2 matrix) is for example calculated according to the equations of the Kalman filter.
    This sixth sub-step thus makes it possible to close the loop of the linear estimator according to the invention and to ensure that the four states of the state vector x (t) are optimal estimates.
    In addition, the third, fourth and fifth substeps can alternatively apply the so-called "small angles" approximation when the operating conditions allow it. In this way, the linear estimator previously described, not based on the so-called “small angles” approximation, is used during an initial phase of convergence, then another estimator, based on the so-called “small angles” approximation, is then used, as soon as a convergence on the estimate Δψ of the error affecting the directional estimate of the heading is reached.
    These operating conditions can be characterized for example by the covariance associated with the estimate Δψ of the error affecting the directional estimate iJjdir of the heading and / or the modulus of the sub state vector formed by the estimated values ΞΔψ, ΘΔψ of the sine and cosine of the estimate Δψ of the error affecting the directional estimate of the heading.
    In addition, the third stage of development may include a seventh and final substep for calculating the estimated value ψ of the geographic heading of the aircraft.
    The invention and its advantages will appear in more detail in the context of the description which follows with examples of embodiment given by way of illustration with reference to the appended figures which represent:
    FIG. 1, a rotary wing aircraft,
    FIG. 2, a device for estimating a ground speed and a heading of an aircraft according to the invention,
    - Figure 3, a variant of such a device,
    FIG. 4, a representation of the various references used by the device, and
    - Figure 5, a block diagram of a method for estimating a ground speed and a heading of an aircraft.
    The elements present in several separate figures are assigned a single reference.
    In FIG. 1, an aircraft 20 with rotary wing is shown. A fuselage mark (X B , Y B , Z B ) is rigidly linked to the aircraft 20, attached for example to the average center of gravity of the aircraft 20. This fuselage mark (X B , Y B , Z B ) is defined by particular directions of the aircraft 20 which are respectively the longitudinal direction X 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 aft towards the front of the aircraft 20, the normal direction Z B extending from top to bottom perpendicular to the longitudinal direction X B and the transverse direction Y B extending from the left to the right perpendicular to the longitudinal directions X B and normal Z B. The longitudinal direction X B is the roll axis of the aircraft 20, the transverse direction Y B is its pitch axis and the normal direction Z B is its yaw axis.
    A geographic coordinate system (X N , Y N , Z N ) is also shown in FIG. 1. This geographic coordinate system (X N , Y N , Z N ) is formed from the directions of the cardinal points, for example by the directions of the North and East respectively constituting the directions X N , Y N as well as by a direction Z N substantially parallel to the Earth's gravity. The directions X N , Y N thus form a substantially horizontal plane (X N , Y N ).
    The aircraft 20 comprises a device 1 for estimating a ground speed and a heading of the aircraft 20, a detailed view of which is shown in FIG. 2. A variant of this device 1 is also shown in FIG. 3 This device 1 and its variant can implement a method for estimating a ground speed and a heading of an aircraft, a block diagram of which is shown in FIG. 5. This method comprises three main steps 101 to 103 , the third step 103 comprising seven sub-steps 111 to 117.
    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 measure GNSS of a ground speed vector of l aircraft 20 in the geographic coordinate system (X N , Y N , Z N ) while the AHRS device 12 provides the first estimator 13 with a measurement γ Β of an acceleration vector of the aircraft 20 in the fuselage coordinate system (Χ θ , Υ θ , Ζ Β ), as well as estimates φ and Θ of attitude angles, and a directional estimate if) Dw of the heading of the aircraft 20. The directional estimation ipDiR of the heading is notably determined without using a magnetic measurement .
    The first estimator 13 comprises, as shown in FIG. 2, two projection operators 15,16 and a linear estimator 17.
    The first projection operator 15 makes it possible to transfer the fuselage coordinate system (X B , Y B , Z B ) to a local horizontal coordinate system (X H , Y H ) formed by a projection X H of the direction X B in a plane horizontal, therefore parallel to the plane (X N , Y N ), even confused with it, and by a direction Y H perpendicular to the projection X H and located in this horizontal plane. This first projection operator 15 thus makes it possible to project the measurement y s of the acceleration vector into this local horizontal coordinate system (X H , Y H ) in order to determine an estimate γ Η of the horizontal component of the acceleration vector of the aircraft 20 .
    The second projection operator 16 makes it possible to transfer the local horizontal frame (X H , Y H ) to a horizontal pseudogeographic frame (X N *, Y N *) defined from the local horizontal frame (X H , Y H ) and the directional estimate ψΰΐϋ of the heading. The directions X N * and Y N * are located in a horizontal plane and respectively form an angle equal to the directional estimate iJjdir of the heading with the directions X H and Y H. This second projection operator 16 thus makes it possible to transfer the estimate γ Η of the horizontal component of the acceleration vector into this horizontal pseudo-geographical coordinate system (X N *, Y N *) in order to determine a pseudo-geographical estimate γ Ν * of the acceleration vector of the aircraft 20.
    Figure 4 is a representation of these different benchmarks and the relationships between them.
    The linear estimator 17 includes integrators 21 and 22 intended to estimate values CAÿ and ΞΔψ of the sines and cosines of the angular difference between the pseudo-geographic coordinate system and the geographical coordinate system.
    The linear estimator 17 includes a linear transformation operator 40 from the horizontal pseudo-geographic coordinate system (X N *, Y N ') to an estimate of the horizontal geographic coordinate system (X N , Y N ). This linear transformation operator 40 consists of the gain operators 31-34 as well as the difference operators 27 and sum 28. The matrix operation performed by these six scalar operators is as follows:
    (y » _ (Cup Yy / [Sai /> C ^) [y ^)
    Those skilled in the art will recognize in this matrix operator an operator of rotation in the horizontal plane (X N , Y N ), of an angle Aip = tan- 1 (Càip, Sàip), once we have C & ^ 2 + S ^ 2 = 1.
    Said linear transformation operator 40 elaborates, from the estimate y N * of the acceleration vector in the pseudogeographic frame of reference, an estimate y N of the acceleration vector in the geographic frame of reference taking into account the estimate Δψ of the error affecting the directional estimate iJjdir from the cape.
    The linear estimator 17 includes integrators 23, 24 intended to integrate the estimate y N of said acceleration vector in geographic coordinate system in order to obtain the estimate v N of the ground speed vector in geographic coordinate system taking into account the estimate Δψ of the error affecting the directional estimate ψοΐϋ of the heading. The linear estimator 17 also includes difference operators 29, 30 calculating the difference between, on the one hand, each of the components of said estimate v N of the ground speed vector in geographic frame taking into account the estimate Δψ of the error affecting the directional estimation ψΰΐϋ of the heading and, on the other hand, each of the components (v ^ GNSS , Vy GNSS ) of the measurement v GNSS of the ground speed vector v N in the geographic frame (X N , Y N , Z N ).
    The linear estimator 17 comprises a matrix gain operator K of dimensions (4x2), marked 35 in FIG. 2, which propagates the components of a speed difference vector on each of the inputs of the integrators 21, 22, 23 and 24, such as:
    with
    / 'kex k C y IfH'SX k S y IfH'XX L · n xy kyx kyy /
    CorCRate CorSRate | CorVxRate I CorVyRate /
    (k cx k C y ksx b l , S y kxx b^ xy kyx kyy / K.
    The elements of the matrix K are for example the "Kalman gains" calculated from the Riccati differential equation.
    In this linear estimator 17, the state vector x (t) comprises four states, which are the estimated values v x , Vy of the horizontal components of the ground speed vector of the aircraft 20 in the horizontal plane of the geographic frame (X N , Y N , Z N ) as well as the estimated values ΘΔψ and ΞΔψ of the cosine and sine of an estimate Δψ of the error affecting the directional estimate i / jdir of the heading.
    The four states of the linear estimator 17 converge as soon as the aircraft 20 experiences an acceleration phase. In particular, the states ΘΔψ and ΞΔψ carried by the integrators 21 and 22 then constitute precise estimates of the sines and cosines of the angular error Δψ affecting the directional estimation i / jdir of the heading produced by the AHRS device 12.
    The calculation of the gain matrix K is for example based on the known equations of the Kalman filter, itself based on the linear model of the process previously described.
    Finally, the first estimator 13 includes a “ATAN2” trigonometric calculation block 18 and a difference operator 36. The “ATAN2” trigonometric calculation block 18 makes it possible to determine an estimate Δψ of the error affecting the directional estimate of the heading to starting from the estimated values CAtp and ΞΔψ of the cosine and the sine of this estimate Δψ by applying the trigonometric function with two arguments "atan2" to the two estimated values SAi /> and The difference operator 36 then makes it possible to subtract this estimate Δψ from l directional estimate 0 D / R of the heading developed by the AHRS device 12 in order to generate an estimated value ψ of the geographical heading, corrected for inaccuracies in the gyroscopic measurement of the heading and which, moreover, is not affected by any disturbances magnetic of the environment of the aircraft 20. This estimated value ψ of the geographic heading of the aircraft 20 constitutes an output 53 of the device 1.
    In addition, the device 1 includes two other outputs 51, 52 made up of the estimated values vf, v $ of the horizontal components of the ground speed vector which take into account the estimate Δψ of the error.
    Furthermore, according to the variant shown in FIG. 3, the device 1 comprises a second estimator 14 operating according to an approximation known as "small angles" as well as a switch 5. This switch 5 is arranged between the first estimator 13 and the second estimator 14. In this way, the outputs 51, 52, 53 of the device 1 are constituted by the outputs of the switch 5. This switch 5 then makes it possible to switch between the first estimator 13 and the second estimator 14. The first and the second estimator 13, 14 as well as the switch 5 can form an integral part of a computer present in the aircraft 20.
    The first estimator 13 operates during an initial phase of convergence and is then replaced by the second estimator 14, when convergence on the estimate Δψ of the error affecting the directional estimate of the Δψ heading is reached. This second estimator 14 then only has to process a residual angular error of small amplitude, and can thus be based on the so-called “small angle” approximation in its own structure for estimating the angular error. residual. The decrease in the number of states (one estimator, directly estimating Δψ, rather than two, estimating the sines and cosines of the error angle) improves the precision of the estimate Δψ and, consequently, that of the estimated values v x , Vy and ψ of the ground speed of the aircraft 20 and of the geographic heading.
    Naturally, the present invention is subject to numerous variations as to its implementation. Although several embodiments have been described, it is understood that it is not conceivable to identify exhaustively all the possible modes. It is of course conceivable to replace a means described by an equivalent means without departing from the scope of the present invention.
    权利要求:
    Claims (16)
    [1" id="c-fr-0001]
    1. Device (1) for estimating a speed relative to the ground and a heading of an aircraft (20), said aircraft (20) comprising three axes forming a fuselage mark (Χ Β , Υ θ , Ζ θ ) rigidly linked to a structure of said aircraft (20), said device (1) comprising:
    a GNSS receiver (11) receiving signals from several satellites and configured to provide a GNSS v measurement of a speed vector with respect to the ground of said aircraft (20) in a geographical reference (X N , Y N , Z N ), said geographic reference point (X N , Y N , Z N ) comprising a horizontal plane (X N , Y N ),
    - an AHRS device (12) providing a measurement γ Β of an acceleration vector of said aircraft (20) in said fuselage frame (X B , Y B , Z B ) as well as estimates φ, θ of attitude angles, and a directional estimate ip D iR of the heading of said aircraft (20), and
    - a first estimator (13) connected to said GNSS receiver (11) and to said AHRS device (12), characterized in that said first estimator (13) is linear and configured to produce an estimate Δψ of the unbounded error affecting said estimate directional ipDiR of said heading determined by said AHRS device (12) by combining said measurement v GNSS of said speed vector with respect to the ground with said estimates φ, θ of said attitude angles, of said directional estimation ipDiR of said heading and said measurement γ Β of said acceleration vector, independently of any magnetic measurement.
    [2" id="c-fr-0002]
    2. Device (1) according to claim 1, characterized in that said first estimator (13) is a linear estimator comprising at least four states that are estimated values v *, vÿ of the horizontal components of said speed vector with respect to the ground of said aircraft (20) in said geographic coordinate system (X N , Y N , Z N ), as well as estimated values CJ0 and ΞΔψ of the cosine and sine of said estimate Δψ of said error affecting said directional estimate iJjdir of said heading.
    [3" id="c-fr-0003]
    3. Device (1) according to claim 2, characterized in that said first estimator (13) comprises a trigonometric calculation block (18) and a difference operator (36), said trigonometric calculation block (18) making it possible to determine said estimate Δψ of said error from said estimated values βΔψ and 5Δψ of the cosine and sine and said difference operator (36) making it possible to subtract said estimate Δψ of said error from said directional estimate of said heading determined by said AHRS device (12) in order to generate an estimated value ψ of the geographic heading of said aircraft (20) which is not affected by any magnetic disturbances in the environment of said aircraft (20).
    [4" id="c-fr-0004]
    4. Device (1) according to any one of claims 2 to 3, characterized in that said device (1) has two outputs (51,52) made up of said estimated values v x , Vy of said horizontal components of said speed vector with respect to on the ground which take into account said estimate Δψ of said error.
    [5" id="c-fr-0005]
    5. Device (1) according to any one of claims 2 to 4, characterized in that said first estimator (13) applies the equations of the Kalman filter based on a linear model of the process, in continuous time, such as:
    ^ x (t) = F (t) .x (t) + w c (t), and z (t) = H (t) .x (t) + w m (t), with a state vector comprising at least said four states, namely said estimated values € Δψ and Sùtp of the cosine and sine of said estimate Δψ of said error and said estimated values vfvj of said horizontal components of said speed vector relative to the ground of said aircraft (20) in said geographic coordinate system (X N , Y N , Z N ), w c [t), a control noise vector, a measurement noise vector, z (t) = I Vy I, a measurement estimation vector comprising at least said two estimated values of said horizontal components of said speed vector relative to the ground of said aircraft (20) in said geographic reference
    (X N , Y N F (t) = , Z N ), zi 0 Yn * Ye * 01τ~ Ye *Yn * 0000 0 ..ή0 ...0 ...:) , a sub-matrix of a matrix reporting derivative of said state vector x (t) audit vector state x (t), and
    / 0 0 H (t) = 10 0 a sub-matrix of a measurement matrix relating said estimation vector z (t) of the measurement to said state vector x (t).
    [6" id="c-fr-0006]
    6. Device (1) according to any one of claims 1 to 5, characterized in that said device (1) comprises a second estimator (14) operating according to the “small angles” approximation, said first estimator (13) operating during an initial phase of convergence and then being replaced by said second estimator (14) to continue the development of said estimate Δψ of said error affecting said directional estimate i / jdir of said heading and, consequently, refine estimated values v% , vÿ and φ of the horizontal components of a vector of said speed relative to the ground and of the geographic heading of said aircraft (20).
    [7" id="c-fr-0007]
    7. Device (1) according to claim 6, characterized in that said second estimator (14) replaces said first estimator (13) from the moment when the covariance associated with said estimate Δψ of said error becomes less than a first predetermined threshold.
    [8" id="c-fr-0008]
    8. Device (1) according to claim 6, characterized in that said second estimator (14) replaces said first estimator (13) from the moment when the modulus of the vector formed by said estimated values ΞΔψ, ΘΔψ of the sines and cosine of said estimate Δψ of said error becomes close to unity, to within a margin, such that:
    | l - V (SA ^) 2 + (CAi /;) 2 | <margin.
    [9" id="c-fr-0009]
    9. Device (1) according to claim 6, characterized in that said second estimator (14) replaces said first estimator (13) from the moment when the covariance associated with said estimate Δψ of said error becomes less than a first predetermined threshold or from the moment when the modulus of the vector formed by said estimated values ΞΔψ, CAip of the sines and cosines of said heading error Δψ becomes close to unity, to within a margin, such as:
    | l - ^ / (SAi / z) 2 + (CAi />) 2 | <margin.
    [10" id="c-fr-0010]
    10. Device (1) according to any one of claims 1 to 9, characterized in that said first estimator (13) comprises:
    a first projection operator (15) of said fuselage coordinate system (X B , Y B , Z B ) towards a local horizontal coordinate system (X H , Y H ), said local horizontal coordinate system (X H , Y H ) being formed of on the one hand by a projection X H in a horizontal plane of said direction X B of said fuselage frame (X B , Y B , Z B ) and on the other hand by a direction Y H perpendicular to said projection X H and located in said plane horizontal,
    - a second projection operator (16) from said local horizontal marker (X H , Y H ) to a horizontal pseudo-geographic marker (X N *, Y N *), said horizontal pseudo-geographic marker (X N *, Y N ') being defined from said local horizontal coordinate system (X H , Y H ) and from said directional estimate of said heading, said directions X N * and Y N * of said horizontal pseudo-geographic coordinate system (X N *, Y N *) forming respectively an angle equal to said directional estimate 0o / s of said heading with said directions X H and Y H of said local horizontal coordinate system (X H , Y H ), and
    - a linear transformation operator (40) of said horizontal pseudo-geographic coordinate system (X N *, Y N *) to an estimate of said horizontal plane (X N , Y N ), the angle between said estimate of said horizontal plane (X N , Y N ) and said horizontal pseudo-geographic coordinate system (X N *, Y N *) being said estimate Δψ of said error affecting said directional estimate i / idir of said heading, and
    - a feedback loop whose gains are calculated according to the equations of the Kalman filter.
    [11" id="c-fr-0011]
    11. Method for estimating a speed relative to the ground and a heading of an aircraft (20), characterized in that it comprises:
    a first step of supplying (101) a v GNSS measurement of a speed vector with respect to the ground of said aircraft (20) in a geographical reference (X N , Y N , Z N ), by virtue of the reception of signals of several satellites, said geographic coordinate system (X N , Y N , Z N ) comprising a horizontal plane (X N , Y N ),
    a second step of supplying (102) a measurement γ Β of an acceleration vector of said aircraft (20) in a fuselage coordinate system (Χ θ , Υ θ , Ζ Β ) rigidly linked to said aircraft (20) as well as estimates φ, θ of attitude angles and of a directional estimate i / jdir of the heading of said aircraft (20), and
    a third step of developing (103) an estimate Δψ of the unbounded error affecting said directional estimate ipoiR of said heading carried out in a linear fashion by combining said measurement v GNS s of said speed vector relative to the ground with said estimates φ , θ of said attitude angles, with said directional estimate i / jdir of said heading, and with said measurement γ Β of said acceleration vector.
    [12" id="c-fr-0012]
    12. Method according to claim 11, characterized in that said third development step (103) comprises the following substeps:
    a first projection sub-step (111) of said measurement y B of said acceleration vector in a local horizontal coordinate system (X H , Y H ) using said estimates φ, θ of said angles of bases in order to obtain an estimate y H of a horizontal component of said acceleration vector, said local horizontal frame (X H , Y H ) being formed on the one hand by a projection X H of said direction X B of said fuselage frame (X B , Y B , Z B ) in a horizontal plane and on the other hand by a direction Y H perpendicular to said projection X H and located in said horizontal plane,
    a second projection sub-step (112) of said estimate y H of said horizontal component of said acceleration vector in a horizontal pseudo-geographical coordinate system (X N *, Y N ') in order to obtain a pseudo-geographical estimate y N * of a horizontal component of said acceleration vector, said horizontal pseudo-geographic coordinate system (X N *, Y N *) being defined from said local horizontal coordinate system (X H , Y H ) and from said directional estimate i / jdir of said heading , the directions X N γΝ * of said horizontal pseudo-geographic coordinate system (Χ Ν *, γ Ν *) respectively forming an angle equal to said directional estimate x / jdir of said heading with the directions X H and Y H of said local horizontal coordinate system (X H , Y H ),
    a third sub-step of linear transformation (113) of said pseudo-geographic estimate y N * of said horizontal component in said pseudogeographic coordinate system of said acceleration vector into an estimate y N of a horizontal component in a geographic coordinate system of said acceleration vector, said estimate y N being corrected with said estimate Δψ of said error affecting said directional estimate i / jdir of said heading, via with said estimated values ΘΔψ and ΞΔψ,
    a fourth integration sub-step (114) of said estimate γ Ν of said horizontal component of said acceleration vector in pseudo-geographic coordinate system in order to obtain an estimate v N of said speed vector relative to the ground in said horizontal geographic coordinate system ( X N , Y N ) taking into account said estimate Δψ of said error affecting the directional estimate of the heading,
    a fifth sub-step of comparison (115) of said estimate v N of said speed vector relative to the ground in said horizontal geographic coordinate system (X N , Y N ) and of said measurement v GNS s of said speed vector relative to the ground, and a sixth sub-step for developing (116) corrections acting on said estimate Δψ of said error and on said estimate v N of said speed vector with respect to the ground.
    [13" id="c-fr-0013]
    13. Method according to claim 12, characterized in that said third development step (103) comprises a seventh calculation sub-step (117) of said estimated value ψ of the geographic heading.
    [14" id="c-fr-0014]
    14. Method according to any one of claims 12 to 13, characterized in that said sixth processing sub-step (116) apply a Kalman filter comprising at least four states which are said estimated values vjfvÿ of the horizontal components of said vector speed relative to the ground in said geographic coordinate system (X N , Y N , Z N ), as well as said estimated values εΔψ and ΞΔψ of the cosine and sine of said estimate Δψ of said error affecting said directional estimate ψβίκ of said heading.
    [15" id="c-fr-0015]
    15. Method according to any one of claims 12 to 14, characterized in that said third, fourth and fifth substeps apply during certain phases a
    5 so-called “small angles” approximation.
    [16" id="c-fr-0016]
    16. Method according to any one of claims 12 to 14, characterized in that said third, fourth and fifth substeps apply an approximation called "small
    10 angles ”from the moment when the covariance associated with said estimate Δψ of said error becomes less than a first predetermined threshold or else the modulus of the vector formed by said estimated values ΞΔψ, CAip of the sines and cosines of said estimate Δψ of said error becomes close to unity, at a
    15 near margin, such as:
    1-V (SAi />) 2 + (CAt />) 2 | <margin.
    1/2
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    优先权:
    申请号 | 申请日 | 专利标题
    FR1601555|2016-10-27|
    FR1601555A|FR3058229B1|2016-10-27|2016-10-27|INDEPENDENT ESTIMATE OF A MAGNETIC MEASUREMENT, SPEED AND CAPE OF AN AIRCRAFT|FR1601555A| FR3058229B1|2016-10-27|2016-10-27|INDEPENDENT ESTIMATE OF A MAGNETIC MEASUREMENT, SPEED AND CAPE OF AN AIRCRAFT|
    US15/794,021| US10871374B2|2016-10-27|2017-10-26|Estimating the speed and the heading of an aircraft, independently of a magnetic measurement|
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