METHOD AND DEVICE FOR COMPENSATING VERTICAL MAGNETIC DEFECTS OF A MAGNETOMETER INSTALLED IN AN AIRCRAFT

Description

[0001] The present invention relates to a method and a device for compensating for vertical magnetic defects of a magnetometer installed in an aircraft.

[0002] The invention lies in the field of aircraft piloting, and more particularly in the field of determining the heading of an aircraft using magnetic measurements.

[0003] In the field of aircraft piloting, as is known, one of the problems that arises is the problem of determining, with good accuracy, the heading of the aircraft relative to the magnetic heading, measured using a measuring instrument, for example a standby magnetometer, installed on or in the aircraft. The orientation of the aircraft in a chosen frame of reference, also called the attitude of the aircraft, is defined by yaw, pitch and roll angles. As is known, the measurements of a magnetometer on board a vehicle are disturbed by magnetic fields induced by the vehicle.In particular, magnetic disturbances are due to the presence of permanently magnetized ferromagnetic materials or electrical conductors carrying established currents (also called "hard irons") and non-magnetized or reversibly magnetized ferromagnetic materials (also called "soft irons") leading to an error depending on the aircraft attitude, fields induced by eddy currents, alignment errors of the magnetometer with respect to the aircraft reference frame (harmonization errors). Compensation for induced magnetic defects and harmonization of geometric alignment defects must be applied to obtain measurements consistent with the expected performance.

[0004] There are known methods in the state of the art that estimate compensation values ​​to be applied, the estimation being based on complete 3-dimensional models of the magnetic disturbances, this type of estimation method being generally complex and sensitive to measurement noise. In addition, methods of this type generally require performing specific, prescribed maneuvers to obtain sufficient measured magnetic field values ​​to perform the calculations of the compensation values, which is expensive and generally undesirable.

[0005] Patent FR 3094082 B1 proposes a method for estimating the harmonization values ​​of a magnetometer, comprising the acquisition of a plurality of magnetic field vector values ​​measured by a magnetometer corresponding to successive positions of the aircraft on the ground on a flat ground inclined by less than 2°, corresponding to various successive headings. This method makes it possible to obtain horizontal geometric harmonization values ​​with good precision. During this ground harmonization step, the magnetic compensation close to the horizontal is also carried out by methods known to those skilled in the art.

[0006] When the aircraft is on the ground, magnetic measurements are very insensitive to vertical magnetic faults. Therefore, working in a horizontal plane does not allow vertical magnetic faults to be identified and compensated for.

[0007] However, in flight conditions, and particularly when the aircraft's attitude (or longitudinal inclination of the aircraft) is not horizontal, the heading error linked to these vertical magnetic defects is significant. If the vertical magnetic defects are not duly identified and compensated for, then the heading accuracy will not reach the expected performance of a standby magnetometer in flight.

[0008] Vertical magnetic defects are geometrically observable in a dish configuration moving away from the horizontal.

[0009] The object of the invention is to remedy the aforementioned drawbacks of the state of the art, by proposing an estimation of vertical magnetic defects in flight, and a compensation for these vertical magnetic defects. To this end, the invention proposes, according to one aspect, a method for compensating for vertical magnetic defects of a magnetometer installed in an aircraft, said magnetometer being associated with its reference frame XM, YM, ZM and the aircraft being associated with its aircraft reference frame XA, YA, ZA. This method, implemented by a processor of a programmable electronic device, comprises: a first step of obtaining first values ​​of compensation coefficients for magnetic defects of the magnetometer, the compensation coefficients corresponding to the Euler angles associated with a rotation to pass from the reference frame of the magnetometer to the aircraft frame, a second refining step comprising the estimation of at least one compensation coefficient for vertical magnetic defects of the magnetometer, implemented in a flight phase when the attitude of the aircraft moves away from the horizontal, the second step comprising: a) an acquisition of a plurality of values ​​of magnetic field vectors measured by the magnetometer in flight and values ​​of attitude angles of the associated aircraft, b) a calculation of a magnetic heading as a function of the first values ​​of compensation coefficients resulting from the first step and the acquired magnetic field vector values, c) a recursive calculation of a coefficient, called the slope coefficient,as a function of a heading deviation between the calculated magnetic heading and a reference magnetic heading, and of attitude angle values ​​of the aircraft, d) a calculation of a vertical magnetic fault compensation coefficient value using a vertical bias estimator, implementing the calculated slope coefficient, the attitude angle values ​​of the aircraft and characterizing values ​​of the local Earth magnetic field.

[0010] Advantageously, the method for compensating for vertical magnetic defects according to the invention makes it possible to refine first magnetic compensation values ​​obtained on the ground, and in particular to obtain and refine a vertical magnetic compensation value.

[0011] The method for compensating for vertical magnetic defects according to the invention may also have one or more of the characteristics below, taken independently or in any technically conceivable combination.

[0012] The first step involves a ground estimation of initial values ​​of horizontal magnetic defect compensation coefficients of the magnetometer.

[0013] The first step involves an estimation of the first values ​​of magnetic defect compensation coefficients by generic compensation coefficients from a predefined model of magnetic defects based on an aircraft type.

[0014] The recursive calculation of a slope coefficient is a recursive least squares calculation.

[0015] The method further comprises a calculation of compensated magnetic field components from a measured magnetic field vector and the first values ​​of the magnetic defect compensation coefficients, prior to the magnetic heading calculation.

[0016] The method further comprises a step of updating the compensated vertical magnetic field component, based on the calculated vertical magnetic defect compensation coefficient value.

[0017] Steps a) to d) of the second refining step are iterated, and the compensated vertical magnetic field component value is injected into a subsequent iteration of the method in the compensated magnetic field component calculation step.

[0018] The slope coefficient is related to the heading deviation and the attitude angle values ​​of the aircraft by the formula: δψ _ i = α _ i ⋅ sin ψ _ i sin θ _ i cos φ _ i − cos ψ i sin φ _ i

[0019] Where i is an iteration index, α_i is the slope coefficient, δ Ψ_i is the heading deviation, ϕ_i, θ_i, ψ_i, are the attitude angles of the aircraft, respectively roll, pitch and yaw.

[0020] A vertical bias estimator is calculated, for the iteration of index i, according to the formula: Δ H ^ Z _ i = − H 0 m i ⋅ cos I _ i ⋅ α _ i 1 − α _ i ⋅ sin ψ i ⋅ sin φ i + cos ψ _ i ⋅ sin θ _ i ⋅ cos φ _ i

[0021] Where Δ Ĥ Z _i is the said vertical bias estimator, H 0m_i is the norm of the measured local Earth magnetic field, I_i is the inclination of the Earth's magnetic field in radians, α_i is the slope coefficient and ϕ_i, θ_i, ψ_i, are the attitude angles of the aircraft, respectively roll, pitch and yaw.

[0022] The aircraft following a trajectory in the flight phase, the method implements a geometric observability criterion combining a cumulative deviation of a solid angle in pitch and roll and a variation of heading in the trajectory, the satisfaction of the geometric observability criterion making it possible to define a condition for implementing in flight the estimation of at least one coefficient of compensation of vertical magnetic defects in an appropriate observability phase.

[0023] According to another aspect, the invention relates to a device for compensating for vertical magnetic defects of a magnetometer installed in an aircraft, said magnetometer being associated with its reference frame XM, YM, ZM and the aircraft being associated with its aircraft frame XA, YA, ZA,. the device comprises a processor configured to implement: a module for obtaining first values ​​of compensation coefficients for magnetic defects of the magnetometer, the compensation coefficients corresponding to the Euler angles associated with a rotation to move from the reference frame of the magnetometer to the aircraft frame, a set of modules, implemented in a flight phase when the attitude of the aircraft moves away from the horizontal, configured to implement a refinement comprising the estimation of at least one compensation coefficient for vertical magnetic defects of the magnetometer, comprising: a module for acquiring a plurality of values ​​of magnetic field vectors measured by the magnetometer in flight and values ​​of associated attitude angles of the aircraft, a module for calculating a magnetic heading as a function of the first values ​​of compensation coefficients resulting from the first step and acquired magnetic field vector values, a module for recursively calculating a coefficient,said slope coefficient, as a function of a heading deviation between the calculated magnetic heading and a reference magnetic heading, and of attitude angle values ​​of the aircraft, a module for calculating a vertical magnetic fault compensation coefficient value using a vertical bias estimator, implementing the calculated slope coefficient, the attitude angle values ​​of the aircraft and characterizing values ​​of the local Earth magnetic field.

[0024] According to another aspect, the invention relates to a computer program comprising software instructions which, when executed by a programmable electronic device, implement a method of compensating for vertical magnetic defects of a magnetometer as briefly described above.

[0025] Other characteristics and advantages of the invention will emerge from the description given below, for information purposes only and in no way limiting, with reference to the appended figures, among which: [ Fig 1 ] there figure 1 schematically represented an aircraft equipped with a magnetometer and the respective associated reference frames; [ Fig 2 ] there figure 2 schematically represents a system for determining the heading of an aircraft comprising a device for compensating for vertical magnetic defects according to one embodiment; [ Fig 3 ] there figure 3 is a flowchart of the main steps of a method for compensating for vertical magnetic defects of a magnetometer according to one embodiment of the invention; [ Fig 4 ] there figure 4 is a flowchart of the main steps of a method for refining field components by recursive in-flight estimation.

[0026] There figure 1 schematically illustrates an aircraft 10 equipped with a heading determination system 12, schematically represented in figure 2 .

[0027] The aircraft 10 has an aircraft reference frame TA, of origin G, which is a reference point, for example its center of gravity or any other reference point of its structure. The aircraft reference frame has three axes XA, Y A, ZA which are perpendicular to each other, the XA axis being the longitudinal axis of the aircraft, oriented towards the nose of the aircraft. This longitudinal axis of the aircraft is also called the aircraft's heading line. The Y A axis is perpendicular to XA, in the horizontal plane when the aircraft is on the ground, it is the axis which connects the wings, oriented towards the right wing. The ZA axis is the vertical axis when the aircraft is on the ground, directed downwards. The aircraft reference frame TA is linked to the aircraft.

[0028] The attitude of the aircraft when in motion is defined relative to a geographical reference point TGL (Local Geographic Trihedron also called NorthEastDown), which is represented at figure 1 with the same center as the center G of the aircraft reference frame. This TGL reference frame includes 3 axes X, Y, Z perpendicular two by two, the X axis pointing towards Geographic North ("North" in English), the Y axis pointing towards Geographic East ("East" in English), and the Z axis defining the vertical direction, pointing towards the center of the Earth ("Down" in English).

[0029] The attitude of the aircraft relative to the geographical reference point TGL is defined, in a known manner, by three Euler angles allowing the transition from the TGL reference point to the TA reference point of the aircraft, which are respectively the yaw ψ (in English "yaw"), the pitch θ (in English "pitch") and the roll ϕ (in English "roll"). These angles are represented in figure 1 .

[0030] The yaw ψ corresponds to a rotation of the aircraft around ZA.

[0031] The yaw Ψ T , also called geographic heading, shown on the figure 1 , is the angle between the XA axis and the X axis, corresponding to a rotation of the aircraft around ZA . The pitch represents the rotation around the Y axis A , and the roll the rotation around the longitudinal axis XA . These angles define the reference frame change matrix, from the reference frame TGL to the aircraft frame TA.

[0032] The angles ϕ and ψ are defined in ]-π,+π], and θ is defined in ]-π / 2,π / 2].

[0033] The attitude of the aircraft 10 is obtained by changing the reference frame from the TGL reference frame to the TA reference frame, using the matrix B(ψ,θ,ϕ), called the direction cosine matrix: B ψ θ φ = cos ψ cos θ − sin ψ cos φ + cos ψ sin θ sin φ sin ψ sin φ + cos ψ sin θ cos φ sin ψ sin θ cos ψ cos φ + sin ψ sin θ sin φ − cos ψ sin φ + sin ψ sin θ cos φ − sin θ cos θ sin φ cos θ cos φ

[0034] The heading determination system 12, shown schematically in figure 2 , comprises a magnetometer 14, an inertial measurement unit 16, a processing device 18 and a human-machine interface 20.

[0035] This heading determination system 12 also includes an instrument 22 called “stand-by attitude” (unit providing emergency attitudes), adapted to obtain and display to the pilot the attitudes of the aircraft.

[0036] The magnetometer 14 is an instrument suitable for providing values ​​of a measured magnetic field, in particular to indicate the direction of magnetic North. A magnetometer has its own reference frame TMAG, shown schematically in figure 1 , having an origin OM and axes XM , YM , ZM perpendicular to each other. The magnetometer provides, at each measurement, components H xm , H ym , H zm forming a three-dimensional vector [H m ].

[0037] The yaw angle Ψ mag between the XA axis (longitudinal axis of the aircraft) and the X m axis is the magnetic heading according to the magnetometer measurement. As mentioned in the introduction, magnetometer measurements are disturbed by local magnetic defects, for example, magnetic fields induced by the aircraft.

[0038] The inertial measurement unit (IMU) 16 usually comprises three accelerometers and three gyrometers, and determines the attitude angles of the aircraft 10 in the TGL reference frame.

[0039] Alternatively, the heading determination system 12 includes another position and orientation determination device, such as a primary navigation unit or a dual-antenna GPS heading, which provides aircraft attitude angles in real time to the processing unit 18.

[0040] Subsequently, the aircraft's "attitude angles" will be referred to as the yaw, pitch and roll angles provided by the inertial measurement unit 16 or any other similar device, designated by the term "primary inertial unit".

[0041] According to another variant, called “autonomous” configuration mode, the heading determination system 12 is only equipped with a magnetometer, without including a primary inertial unit.

[0042] The processing device 18 is a programmable electronic device, and comprises a central processing unit (CPU) 24, e.g. a processor, capable of executing computer program instructions when the device 18 is powered on, and an electronic memory unit 25, for example registers, the electronic memory unit 25 being adapted to store executable code instructions allowing the implementation of programs comprising code instructions capable of implementing the method according to the invention. Thus, the processing device 18 is a device for compensating for vertical magnetic defects of a magnetometer according to the invention.

[0043] The processing device 18 is adapted to communicate with the human-machine interface 20, to receive commands and display results, for example by means of a communication bus (not shown).

[0044] The electronic memory unit 25 is configured to store: a module 26 for obtaining first values ​​of magnetic defect compensation coefficients; a set of modules, implemented in a flight phase, configured to implement a refinement comprising the estimation of at least one compensation coefficient for vertical magnetic defects of the magnetometer, comprising: a module 28 for acquiring a plurality of magnetic field vector values ​​measured by the magnetometer 14 in flight and associated attitude angle values ​​of the aircraft provided; a module 30 for calculating a magnetic heading as a function of the first values ​​of the compensation coefficients and acquired magnetic field vector values;a module 32 for recursive calculation of a coefficient, called slope coefficient, as a function of a difference between the magnetic heading and a reference magnetic heading and values ​​of attitude angles of the aircraft; a module 34 for calculating a value of compensation coefficient for vertical magnetic defects, implementing the calculated slope coefficient, values ​​of attitude angles of the aircraft and values ​​characterizing the local Earth magnetic field.;

[0045] The modules are implemented in the flight phase, when the aircraft attitude moves away from the horizontal, for example when the longitudinal inclination of the aircraft with respect to the horizontal plane is greater, in absolute value, than 10°, in particular greater than 25°.

[0046] In one embodiment, the modules 26, 28, 30, 32, 34 are produced in the form of software instructions forming a computer program 36, which, when executed by a programmable electronic device, implements a method for compensating for vertical magnetic defects of a magnetometer according to the invention.

[0047] In a variant not shown, the modules 26, 28, 30, 32, 34 are each produced (or part of them) in the form of a programmable logic component, such as an FPGA (from the English Field Programmable Gate Array ), a GPU (graphics processing unit) or a GPGPU (from the English General-purpose processing on graphics processing ), or in the form of a dedicated integrated circuit, such as an ASIC (from the English Application Specific Integrated Circuit).

[0048] The computer program 36 comprising software instructions is further capable of being recorded on a computer-readable medium, not shown. The computer-readable medium is, for example, a medium capable of storing the electronic instructions and of being coupled to a bus of a computer system. For example, this medium is an optical disk, a magneto-optical disk, a ROM memory, a RAM memory, any type of non-volatile memory (for example EPROM, EEPROM, FLASH, NVRAM), a magnetic card or an optical card.

[0049] There figure 3 is a synopsis of the main steps of a method for compensating for vertical magnetic defects of a magnetometer, implemented by a processing device 18, according to one embodiment.

[0050] The process performs in-flight estimation and refinement of vertical magnetic defect compensation coefficients, using pre-established data, on the ground or in the factory.

[0051] The method comprises a step 41 of obtaining the first values ​​of magnetic defect compensation coefficients.

[0052] A general model of magnetic field compensation measured in the TMAG frame is written: H xt H yt H zt = K cxx K cxy K cxz K cyx K cyy K cyz K czx K czy K czz H xm + B cx H ym + B cy H zm + B cz

[0053] With Bc → = B cx B cy B cz the compensation vector of hard irons and K c = K cxx K cxy K cxz K cyx K cyy K cyz K czx K czy K czz the soft iron compensation matrix.

[0054] The vector H t is the vector of the theoretical magnetic field expressed in the TA frame, and H m is the magnetic field vector measured by the magnetometer, expressed in the TMAG frame.

[0055] The first values ​​of magnetic defect compensation coefficients are first values ​​respectively of [ K c ] and of B c .

[0056] According to a first embodiment, these are values ​​of horizontal magnetic defect compensation coefficients, preferably obtained by a method implemented on maneuvers carried out on the ground as described in patent FR3094082 B1.

[0057] In this first embodiment, the vertical components are zero: Bc → = B cx B cy 0 K c = K cxx K cxy 0 K cyx K cyy 0 0 0 1

[0058] According to a second embodiment, the first values ​​of horizontal and vertical magnetic defect coefficients are first generic approximations, obtained from a predefined model of magnetic defects in the factory, by type of aircraft.

[0059] In this case, first values ​​of three-dimensional compensation coefficients are obtained, respectively for the matrix [ K c ] and the vector B c .

[0060] In addition, first harmonization values ​​of the alignment defects of the magnetometer with the axes of the aircraft, also called geometric defects, are obtained in step 41, either by a method implemented on maneuvers carried out on the ground, or from a factory model.

[0061] Preferably, for geometric defects, the method for estimating harmonization values ​​described in patent FR3094082B1. This method allows an estimation on the ground of horizontal harmonization values ​​hx, hy, where hx corresponds to the Euler angle associated with the rotation around XA, and hy corresponds to the Euler angle associated with the rotation around Y A to pass from the reference frame XM, YM, ZM of the magnetometer to the aircraft frame XA, Y A, ZA. This method for estimating harmonization values ​​makes it possible to obtain, for the horizontal harmonization values, an accuracy of the order of 0.5° with regard to small soft iron defects on the aircraft. In addition, an estimation by calculation of the vertical harmonization value hz is described, this estimated hz value nevertheless being affected by errors.

[0062] Preferably, the method for compensating for vertical magnetic defects comprises a second refining step comprising the estimation of at least one compensation coefficient for vertical magnetic defects of the magnetometer, implemented in a flight phase, the second step comprising the sub-steps 42 to 58 described below. Steps 42 to 58 are implemented iteratively, each iteration having an associated index i, i being equal to 1 during the first iteration, and being incremented by 1 at each iteration.

[0063] The method comprises a step 42 of acquiring the components H mx_i, H my_i; H mz_i, forming a three-dimensional vector H m_i , representing the values ​​of the magnetic field measured by the magnetometer attached to the aircraft, during the flight phase.

[0064] For example, the magnetic field values ​​are measured at a given rate, for example 60 Hz, so as to obtain in-flight measurements at several time steps and several attitude values. These magnetic field measurements (three-dimensional vectors, measured in the magnetometer frame of reference) are each recorded in correspondence with the corresponding attitude of the aircraft 10 as delivered by the Inertial Measurement Unit 16.

[0065] A compensation 46 makes it possible to obtain a vector [H comp_i ] of components H Xcomp_i , H Ycomp_i , H Zcomp_i compensated from a measured magnetic field vector H m_i , of the first values ​​of the magnetic defect compensation coefficients, [ K c ], B c . and the first harmonization values ​​hx, hy, hz, by a calculation method known to those skilled in the art.

[0066] Compensated component vectors H Xcomp_i , H Ycomp_i , H Zcomp_i are calculated and stored for each vector of measured magnetic field values.

[0067] The method then comprises a projection step 48 of the vector H comp_i to obtain a horizontal projection vector noted [H HORZ_i ], having components H XH_i , H YH_i , H ZH_i by applying a projection matrix B HORZ , corresponding to B(0,θ,ϕ) defined by the equation [MATH 1]. The projection matrix is ​​defined by: B HORZ = cos θ sin θ sin φ sin θ cos φ 0 cos φ − sin φ − sin θ cos θ sin φ cos θ cos φ

[0068] Analogously to what was described above, the angles θ,ϕ also evolve with the index i of the iteration, which makes it possible to obtain a matrix B HORZ_i at the ith iteration.

[0069] Thus, the components H XH_i , X YH_i , H ZH_i are obtained, at the ith iteration, by: H XH _ i H YH _ i H ZH _ i = B HORZ _ i ⋅ H Xcomp _ i H Ycomp _ i H Zcomp _ i

[0070] The angular values ​​of pitch θ and roll ϕ used in the matrix B HORZ are provided for example by the inertial unit UMI, and more generally by a primary inertial unit.

[0071] The method subsequently comprises an operation 50 of calculating the estimated magnetic heading. ψ mag_i , calculated at the ith iteration by the following formula: ψ mag _ i = − atan H XH _ i H YH _ i

[0072] A reference magnetic heading ψ ref is provided at step 51, either by a primary navigation center or by calculation in autonomous configuration.

[0073] For example, the primary navigation unit uses a precision gyrometer that senses the Earth's rotation and determines the geographic heading, then calculates the reference magnetic heading by compensating for magnetic declination and an Earth map model.

[0074] In a stand-alone configuration, the calculation of the reference magnetic heading uses compensation coefficient values ​​calculated in step 41 and measurements obtained in step 42. The measurements obtained in step 42, at several time steps and several attitude values, will be used to calculate vertical magnetic compensation coefficients, for better overall compensation of the measured fields and thus obtain better accuracy of the calculated magnetic heading, even for non-horizontal attitudes.

[0075] The course deviation δψ_i between the estimated magnetic heading ψ mag_i and the reference magnetic heading ψ ref_i is calculated in step 52 of magnetic heading deviation estimation. The angles ψ mag_i , ψ ref_i are expressed in radians.

[0076] The heading deviation is calculated by: δψ _ i = ψ mag _ i − ψ ref _ i

[0077] The calculated deviation δΨ_i, as well as the attitude angle values ​​of the aircraft are implemented in a recursive calculation 54 of a slope coefficient, noted α_i.

[0078] The following formula is applied, this formula explaining the law between the magnetic heading deviation and the aircraft attitude angles: δψ _ i = α _ i ⋅ sin ψ _ i sin θ _ i cos φ _ i − cos ψ i sin φ _ i

[0079] In one embodiment, the slope coefficient α_i is estimated by applying a recursive least squares method. Alternatively, Kalman filtering is used for estimating the slope coefficient.

[0080] More generally, the slope coefficient is estimated by a recursive estimation method, any known recursive estimation method being applicable.

[0081] This recursive estimation method is applied iteratively to a plurality of measured values ​​of attitude angles of the aircraft in a flight phase, preferably in the takeoff phase, which makes it possible to obtain a variety of positions / orientations of the aircraft. Indeed, in the takeoff phase, the aircraft is piloted to climb and make at least one turn.

[0082] For example, attitude measurements are performed with a frequency of 60 Hz, and for each aircraft attitude angle measurement, the corresponding magnetic heading deviation δΨ_i is estimated.

[0083] For example, the slope coefficient α_i is estimated over 180° heading, 30° roll and 15° pitch.

[0084] The slope coefficient α_i is used in the estimation 56 of a vertical magnetic defect compensation coefficient value, Δ Ĥ Z_i , also called vertical bias, by applying the estimator given by the following formula, developed by the inventors: Δ H ^ Z _ i = − H 0 m _ i ⋅ cos I _ i ⋅ α _ i 1 − α _ i ⋅ sin ψ i ⋅ sin φ i + cos ψ _ i ⋅ sin θ _ i ⋅ cos φ _ i

[0085] Where H 0m_i is the norm of the measured local Earth magnetic field, whose formula is, as is known: H 0 m _ i = H xm _ i 2 + H ym _ i 2 + H zm _ i 2

[0086] The components [H xm_i , H ym_i , H zm_i ] are provided by the magnetometer, and I_i is the inclination of the Earth's magnetic field in radians, estimated by the formula: I _ i = − atan H ZH _ i H XH _ i 2 + H YH _ i 2

[0087] In the formula [MATH 8], the magnetic field values ​​H 0m_i , Δ Ĥ Z_i are expressed in nT (nano Tesla), and the angular values ​​in radians.

[0088] Advantageously, the formula [MATH 8] allows to calculate a compensation coefficient value without requiring knowledge of the theoretical Earth's magnetic field, but only the measured local Earth's magnetic field values, attitude angles, heading and slope coefficient α_i.

[0089] Advantageously, the slope coefficient α_i is estimated by a computational method, and refined recursively in real time.

[0090] In one embodiment, step 56 of estimating a compensation coefficient value is followed by a step 58 of updating or refining the refined vertical magnetic field component, making it possible to obtain a compensated vertical magnetic field component at the current iteration: H Zcomp _ i = H Zcomp i − 1 + Δ H ^ Z − i

[0091] Where i is an integer indicating a current iteration index, (i-1) indicating the previous iteration.

[0092] The method makes it possible to obtain second values ​​of compensation coefficients for magnetometer defects, including in particular the value Δ Ĥ Z of compensation coefficient of vertical magnetic defects, in particular of vertical hard iron.

[0093] Steps 42 to 58 are iterated by replacing the vertical component of the vector [Hcomp] by the value H Zcomp_i of the vertical component of the compensated magnetic field at the current iteration calculated by the formula [MATH 11], for a chosen number of iterations or until a criterion for stopping the iterations is verified.

[0094] For example, a stopping criterion is verified if the variation of the coefficient Δ Ĥ Z_i between two successive iterations is less than a predetermined threshold, for example the variation between the (i-1)th iteration and the i-th iteration is expressed by: |Δ Ĥ Zi - Δ Ĥ Z ( i -1) |..

[0095] For example, the predetermined threshold is between 30 and 70 nT. In a simplified alternative, the number of iterations is predetermined.

[0096] In one embodiment, the stopping criterion also verifies a criterion called the geometric observability criterion, which makes it possible to ensure that sufficient distinct maneuvers are carried out, then, once the observability criterion has been validated, the criterion of variation of the coefficient Δ Ĥ Z_i explained above is implemented.

[0097] In one embodiment, the aircraft following a trajectory in the flight phase, the geometric observability criterion combining an accumulation of deviation of a solid angle in pitch and / or roll and a variation of heading in the trajectory, the satisfaction of the geometric observability criterion making it possible to define a condition for implementing in flight the estimation of at least one coefficient of compensation for vertical magnetic defects in an appropriate observability phase.

[0098] For example, the geometric criterion of observability is calculated iteratively by integration (or accumulation of the attitude) indicating the solid angle traveled in the dimensions ϕ and θ, and the variation of heading Ψ. The condition consists, for example, in comparing the value of the accumulation with a first low threshold and a second high threshold, the implementation of the estimation being stopped if the value of the accumulation is lower than the first low threshold or higher than the second high threshold.

[0099] Advantageously, the invention proposes incremental refinement in flight, by a simplified method, more robust than a complete three-dimensional model for estimating the harmonization components.

[0100] Advantageously, the proposed method makes it possible to obtain compensation for vertical magnetic defects with good precision and with a low computational load.

[0101] Advantageously, the method of compensating for vertical magnetic defects of a magnetometer is implemented in a flight phase, for example at the start of flight after takeoff and first turns, without requiring the implementation of imposed maneuvers and a wide airspace.

[0102] In one configuration, the method does not require a precise magnetic heading reference, allowing application to aircraft not having a precise magnetic heading reference (provided by a primary unit or a magnetic model), or allowing the autonomy of a backup magnetometer to be increased.

[0103] In another configuration, the vertical magnetic defect compensation method uses initial compensation values ​​from generic compensation coefficients derived from a predefined model, for example in the factory, for each type of aircraft. This makes prior compensation on the ground on a dedicated compensation area unnecessary for each aircraft of the same type, thus providing economic savings in maintenance.

[0104] The iterative estimation principle explained above applies to the refinement of field components by recursive (or incremental) estimation in flight.

[0105] An embodiment of a method for refining field components by recursive estimation is described below with reference to the figure 4 .

[0106] The method comprises a step 60 of acquiring a plurality of magnetic field vector values ​​measured by the magnetometer in flight and associated aircraft attitude angle values, similar to step 42 previously described.

[0107] This allows the acquisition of the components H mx_i , H my_i ; H mz_i , forming a three-dimensional vector H m_i representing the values ​​of the magnetic field measured by the magnetometer attached to the aircraft, during the flight phase.

[0108] The method comprises a step 62 of obtaining first values ​​of magnetic defect compensation coefficients of the magnetometer, these first values ​​being obtained on the ground, as explained above with reference to step 41 or being predefined according to the type of aircraft (factory model).

[0109] During a step 64, the calculation of a field component deviation is carried out, taking into account angular values ​​of pitch θ and roll ϕ, and optionally yaw ψ, provided (step 66) for example by the inertial unit UMI, and more generally by a primary inertial unit.

[0110] Field component deviations δH xm_i , δH yxm_i , δH zm_i are obtained, i being an iteration index.

[0111] Then a vector Hcomp_i comprising compensated components H Xcomp_i , H Ycomp_i , H Zcomp_i is calculated and stored in step 68.

[0112] The calculation of step 68 implements an estimated vertical bias value ΔHz as well as estimated components Kcxz, Kcyz of the soft iron compensation matrix Kc, these components being estimated in step 70, following the implementation of a recursive estimation step 72.

[0113] The recursive estimate 72 is a ground model estimate reinjected into a difference equation between the two measured field components (horizontal and vertical) and those compensated for by the model identified on the ground, so as to identify in flight the complementary parameters of vertical defects, including the predominant vertical hard iron bias ΔHz.

[0114] The recursive estimation 72 takes as input the component deviations calculated in step 64, as well as an observability criterion, for example of the FOP type (for “Field of Precision”).

[0115] The recursive estimation 72 takes as input the component deviations calculated in step 64, as well as an observability criterion, for example of the iterative geometric calculation type combining the accumulation of a solid angle deviation in pitch / roll and a heading angle deviation, thus proposing a concept of “Field Of Precision” in the domain of the magnetic field in a single integrated criterion.

[0116] For example, a recursive least squares estimation algorithm is implemented.

[0117] The method then comprises steps of horizontal projection 74 (analogous to step 48 previously described) and of calculation of compensated magnetic heading (analogous to step 76 previously described).

[0118] This refinement method has a good estimation signal-to-noise ratio in the domain of field components, the numerical difference equations being without quadratic terms or higher power and benefits from further feeding of the algorithm only when the combined observability criterion detects sufficient observability by predefined threshold justifiable by the conjunction of sufficient variation of pitch, roll and heading.

[0119] Advantageously, the implementation of an observability criterion according to the invention makes it possible to feed the bias estimation only during an appropriate observability phase, thus optimizing a rapid estimation at the start of flight with better estimation quality.

Claims

1. A method for compensating vertical magnetic anomalies of a magnetometer (14) installed in an aircraft (10), said magnetometer being associated with the coordinate frame XM, YM, ZM thereof and the aircraft being associated with the aircraft coordinate frame XA, YA, ZA thereof, said method, as implemented by a processor of a programmable electronic device, being characterized in that the method includes: - a first step (41) of obtaining first values of compensation coefficients for magnetic anomalies on the magnetometer, the compensation coefficients corresponding to the Euler angles associated with a rotation which changes from the reference coordinate frame of the magnetometer to the aircraft coordinate frame, - a second refining step including the estimation of at least one compensation coefficient for the magnetometer's vertical magnetic anomalies, implemented in a flight phase when the aircraft's attitude departs from the horizontal, the second step comprising: - a) an acquisition (42) of a plurality of values for the magnetic field vectors, as measured by the in-flight magnetometer and of values for associated aircraft attitude angles, - b) a calculation (50) of a magnetic heading as a function the first values for compensation coefficients from the first step and the acquired values for magnetic field vector, - c) a recursive calculation (54) of a coefficient, called the slope coefficient, as a function of a difference in heading between the calculated magnetic heading and a reference magnetic heading, and of values for aircraft attitude angles, - d) a calculation (56) of a value of a compensation coefficient for vertical magnetic anomalies, using a vertical bias estimator, using the calculated slope coefficient, aircraft attitude angle values and characterizing values of the local terrestrial magnetic field.

2. The method according to claim 1, wherein the first step includes an estimation on the ground of first values of compensations coefficients for horizontal magnetic anomalies of the magnetometer.

3. The method according to claim 1, wherein the first step includes an estimation of the first values of compensation coefficients for magnetic anomalies by generic compensation coefficients coming from a predefined model of magnetic anomalies depending on the type of aircraft.

4. The method according to one of claims 1 to 3, wherein the recursive calculation of a slope coefficient is a calculation using recursive least squares.

5. The method according to any of claims 1 to 4, further including a calculation (46) of compensated magnetic field components from a measured magnetic field vector and the first values of the compensation coefficients for magnetic anomalies prior to the calculation of the magnetic heading.

6. The method according to one of claims 1 to 5, further including a step of updating (58) the vertical component of the compensated magnetic field, as a function of the calculated value of compensation coefficient for vertical magnetic anomalies.

7. The method according to claim 6, wherein steps a) to d) of the second refining step, are iterated, and wherein the value of compensated magnetic field vertical component is fed into a subsequent iteration of the method in the calculation step (46) for the compensated magnetic field component.

8. The method according to claim 7, wherein the slope coefficient is related to the heading deviation and to the attitude angle values of the aircraft, by the formula: δψ _ i = α _ i ⋅ sin ψ _ i sin θ _ i cos φ _ i − cos ψ i sin φ _ i where i is an iteration index, α_i is the slope coefficient, δψ_i is the heading deviation, ϕ_I, θ_i, ψ_i, are the aircraft attitude angles of roll, pitch and yaw, respectively.

9. The method according to claim 8, wherein a vertical bias estimator is calculated, for the iteration of index i, according to the formula: Δ H ^ Z _ i = − H 0 m i ⋅ cos I _ i ⋅ α _ i 1 − α _ i ⋅ sin ψ i ⋅ sin φ i + cos ψ _ i ⋅ sin θ _ i ⋅ cos φ _ i where ΔĤZ_i is said vertical bias estimator, H0m_i is the norm of the measured local terrestrial magnetic field, I_i is the inclination of the terrestrial magnetic field in radians, α_i is the slope coefficient and ϕ_i, θ_I, ψ_I, are the aircraft attitude angles of roll, pitch and yaw, respectively.

10. The method according to any of claims 1 to 9, the aircraft following a trajectory in the flight phase, the method implementing a geometric observability criterion combining a cumulative deviation of a solid pitch and roll angle and a heading change in the trajectory, satisfying said geometric observability criterion making it possible to define a condition of implementation in-flight of the estimation of at least one compensation coefficient for vertical magnetic anomalies in an appropriate observability phase.

11. A computer program including software instructions which, when executed by a programmable electronic system, implement a method for compensating vertical magnetic anomalies of a magnetometer according to claims 1 to 10.

12. A device for compensating vertical magnetic anomalies of a magnetometer (14) installed in an aircraft (10), said magnetometer being associated with the reference coordinate frame XM, YM, ZM thereof and the aircraft being associated with the aircraft coordinate frame XA, YA, ZA thereof, the device comprising a processor (24) characterized in that same is configured for implementing: - a module (26) for obtaining first values of compensation coefficients for magnetometer magnetic anomalies, the compensation coefficients corresponding to the Euler angles associated with a rotation for changing from the reference coordinate frame of the magnetometer to the aircraft coordinate frame, - a set of modules, implemented in a flight phase when the aircraft's attitude departs from the horizontal, configured for implementing a refinement which includes the estimation of at least one compensation coefficient for the magnetometer's vertical magnetic anomalies, comprising: a module (28) for acquiring a plurality of magnetic field vector values measured by the magnetometer in-flight and associated aircraft attitude angle values, a module (30) for calculating a magnetic heading as a function of the first values of compensation coefficients from the first step and acquired magnetic field vector values, a module (32) for the recursive calculation of a coefficient, called the slope coefficient, as a function of a difference in heading between the calculated magnetic heading and a reference magnetic heading, and of values for aircraft attitude angles, a module (34) for calculating a value of compensation coefficient for vertical magnetic anomalies using a vertical bias estimator, using the calculated slope coefficient, aircraft attitude angle values and characterizing values of the local terrestrial magnetic field.