METHOD FOR CALIBRINGING A VIBRANT INERTIAL SENSOR

Description

DOMAINE DE L'INVENTION

[0001] The field of the invention is that of vibrating inertial sensors in which two masses are set in vibration. More particularly, the invention relates to MEMS-type inertial sensors having a planar structure, typically micro-machined from a support plate. ETAT DE LA TECHNIQUE

[0002] Tuning fork inertial sensors are well known to those skilled in the art. Micro-machined inertial sensors in a thin flat plate, allowing the measurement of angular position (gyroscope) or angular velocity (gyrometers), are described in document EP2960625. Their main characteristics are summarized below.

[0003] The manufacture of these micro-machined sensors, also known as MEMS (Micro-Electro-Mechanical-Systems) sensors, uses collective micro-machining techniques, etching, doping deposition, etc., similar to those used for the manufacture of electronic integrated circuits, allowing for low production costs.

[0004] These sensors consist of two vibrating moving masses M1 and M2, as illustrated. figure 1 The two masses are arranged concentrically around each other and excited to a tuning fork vibration in the plane of the plate (xy plane in the figure) via one or more excitation transducers. They are suspended from fixed anchor points A on the plate by orthotropic suspension springs RS. The two masses are coupled together by stiffness elements RC. The design aims to achieve a stiffness along x equal to a stiffness along y and a zero coupling stiffness between x and y. The desired vibration mode corresponds to a linear vibration of the two masses in opposite phase.

[0005] This architecture forms a resonant system with two masses coupled by the Coriolis acceleration. When the gyroscope rotates around the z-axis, perpendicular to the xy-plane (called the sensitive axis), the combination of the forced vibration with the angular rotation vector generates, through the Coriolis effect, forces that set the moving masses into natural vibration perpendicular to the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotation speed. The electronics associated with the sensor calculate the amplitude of the vibration along the direction orthogonal to the excitation direction, whatever that direction may be (which is known by assumption).

[0006] The sensor can operate in gyroscope mode: the natural vibration direction is kept fixed relative to the sensor housing by varying the excitation, and the output information then represents the energy required to maintain the natural vibration direction despite housing movements. Measuring this counterforce provides the sensor's angular velocity Ω. The sensor can also operate in gyroscope mode: the natural vibration direction is left free and is detected to determine the sensor's angular orientation.

[0007] The entire resonator structure is axisymmetric around two axes x and y, defining a sensor frame as illustrated. figure 2 Axisymmetric means that the structure is symmetric with respect to x and symmetric with respect to y. As described below, these axes constitute the principal directions of the actuators / detectors, which operate along these two axes.

[0008] To excite the desired vibration mode in any given direction of the plane, the excitation signal is decomposed into two components of adjusted respective amplitudes, applied respectively to the excitation transducer Ex acting along the x direction and to the excitation transducer Ey acting along the y direction, each associated with at least one moving mass (internal mass M1 on the figure 2 ). Excitation forces are therefore applied to these transducers to generate and maintain the vibrating wave: they are capable of maintaining the forced vibration via an amplitude control (to counteract the damping of the MEMS) and in any direction of the xy plane, via a precession control (to rotate the wave).

[0009] The movements of the resulting wave are detected by combining the information gathered by at least one pair of detection transducers Dx, Dy, which recover the position of the mass in its path in the xy sensor frame (two of each on the figure 2 ) and associated with at least one moving mass.

[0010] Preferably, transducers are made on both grounds, as illustrated. figure 3 The index 1 corresponds to mass M1 and the index 2 to mass M2. figures 2 And 3 These are non-limiting examples of arrangement; many other types of arrangement are possible, with the constraint of creating an axisymmetric system.

[0011] Transducers are preferably made using interdigitated comb electrodes with variable air gaps. There is a fixed comb whose teeth are fixed to a fixed electrode on the machined plate and a movable comb whose teeth, interdigitated with the teeth of the fixed comb, are fixed to the movable mass associated with the transducer in question.

[0012] Excitation involves applying an excitation force via an alternating voltage between the moving comb and the fixed comb, at the desired vibration frequency (the mechanical resonance frequency of the suspended moving mass, typically around 10 kHz). The resulting movement is perpendicular to the teeth of the comb.

[0013] The detection method involves applying a bias voltage between the fixed and moving combs and observing the resulting charge variations due to capacitance differences between the fixed and moving combs caused by variations in the spacing between their teeth. The measured movement is the movement perpendicular to the comb teeth.

[0014] The vibrating mass / spring assembly is characterized by a symmetrical 2x2 stiffness matrix denoted K. For optimal sensor operation, the aim is to obtain a final stiffness matrix proportional to the identity. Due to manufacturing imperfections, this is not the case (see below).

[0015] The x' axis is the axis of vibration of the wave. This axis defines a coordinate system x'y', with y' perpendicular to x' in the plane of the MEMS. The x' axis makes an angle with the x-axis called the electric angle θ, and the x'y' coordinate system is called the wave coordinate system. For now, we will assume that the wave vibrates along x (x'=x).

[0016] The dynamic equation describing a vibrating gyroscope can be reduced to a single-mass model of mass M, whose displacement X, Y is modeled as follows: M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ = FX FY M is the mass matrix; for simplicity, we will consider it to be a scalar. A is the damping matrix, K is the stiffness matrix, and C is the Coriolis matrix and is equal to: 0 − M Ω M Ω 0 where M is the mass and Ω is the angular velocity,

[0017] FX and FY are the excitation forces applied along the x and y axes of the gyroscope. These forces are derived from commands Cr, Ca, Cq, and Cp calculated in the wave frame using control systems known to those skilled in the art (and not described here), based on the demodulation of detected signals related to the vibration displacement. From measurements of the X and Y wave motion in the xy frame, a rotation is applied to transition to the x'y' wave frame. The commands are then determined (via demodulation of detected signals), and a reverse rotation is applied to return to the xy frame, in which the excitation forces are applied. The commands are determined so that the displacement of the mass, i.e., the vibration wave of the gyroscope, takes on a desired shape. Generally, the desired shape is a linear oscillating displacement in a given direction relative to the gyroscope's xy frame.

[0018] The Cr control force corresponds to the stiffness forces used to control the resonator's natural frequency; since phase is the integral of frequency, Cr therefore controls the phase of the wave. Cr is an external force applied to the resonator (by estimating the displacement) that modifies the vibration frequency, slowing down or speeding up the vibration as it vibrates, but does not change the intrinsic stiffness of the resonator.

[0019] The Ca control corresponds to the amplitude forces to control the amplitude of the wave and the Cp control corresponds to the precession forces which allow control of the angular velocity of the wave.

[0020] The Cq command corresponds to the quadrature forces to control the quadrature of the wave (that is, to guarantee the linearity of the wave or, when the desired wave is not linear, it is generally elliptical, and Cq allows control of the minor axis of the ellipse).

[0021] It is well known to those skilled in the art that imperfections in the sensor's manufacturing lead to errors in the information it outputs. Most of these imperfections must be compensated for by balancing the gyroscope.

[0022] It is known to achieve this compensation by locally removing material, for example by laser ablation to modify the mass or stiffness distribution. This method is costly or even impossible to implement on a micro-machined gyroscope in a thin silicon wafer, whose detection and excitation movements are located in the plane of the substrate.

[0023] A first type of imperfection leading to the non-identity of the stiffness matrix K is the frequency difference between the principal axis of vibration and the axis perpendicular to the vibration in the plane of the MEMS, corresponding to a system stiffness matrix in which the stiffness along the x-axis differs from the stiffness along the y-axis. The aim is to equalize the resonance frequencies along the two aforementioned axes using an adjustable electrostatic stiffness. This electrostatic stiffness, called the equalization stiffness, is provided by frequency-tuning transducers Tx, Ty (at least one Tx Ty pair on at least one ground). figure 2 acting along the x and y directions. Its purpose is to equalize the stiffness along the two axes of vibration by reducing the value of the highest stiffness, thus making the frequencies equal. Frequency correction is called "frequency trimming" in English.

[0024] A second type of imperfection arises from the mechanical coupling between the vibration axis and the perpendicular axis, which is the origin of the so-called quadrature bias. This involves anisotropy defects in the dynamic stiffness of the two vibrating masses, resulting in a vibration that is no longer linear but elliptical, and corresponding to the existence of a non-zero coupling stiffness. A known solution in the prior art is to cancel this term by applying a sinusoidal force F to the system via the excitation transducers. The problem is that the application of this force is not exerted at exactly the right time (phase errors) and along the correct axis (gain error), causing drift. To avoid applying a force F, the coupling term is physically canceled not by applying a force, but by directly changing the stiffness of the resonator via at least one pair of transducers Q+ and Q-, as illustrated. figure 2 (2 Q+ / Q- pairs on the figure 2 These transducers, operating on the X and Y axes, are arranged on the diagonals to maintain symmetry and geometric anisotropy, and for space-saving reasons. Quadrature bias correction is called quadrature trimming. The Tx, Ty, Q+, and Q- transducers are preferably also interdigitated combs, as illustrated. figures 2 And 3 controlled by direct current voltages and called trimming combs.

[0025] Thus, quadrature trim transducers modify the characteristics of the MEMS sensor to eliminate coupling between the two axes of the wave coordinate system, and frequency trim transducers modify the characteristics of the MEMS sensor to eliminate frequency differences between the two axes of the wave coordinate system. They modify the intrinsic characteristics of the resonator. In other words, if the trimming voltage is adjusted even when the resonator is not vibrating, its stiffness is changed, unlike the Cr control described above, which is a force that slows down or accelerates the vibration when it is vibrating. Trimming is performed using a DC or low-frequency voltage that modifies the electrostatic stiffness of the sensor without needing to evaluate the phase of the vibration, whereas the Cr control is achieved by sending a sinusoidal voltage (at the sensor's resonant frequency) after estimating the phase of the vibration.The frequency change achieved by trimming is therefore completely different in nature from a frequency change achieved by a Cr command.

[0026] They are controlled by trim servos (known to those skilled in the art) which generate a quadrature trim control CTxy, a frequency trim control along X CTx, and a frequency trim control along Y CTy. The trim controls are DC voltages.

[0027] Thus, via the trimming combs, the stiffness matrix K is directly modified using a matrix Kt, and the dynamic equation of the gyroscope is: M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ − Kt X Y = FX FY

[0028] The frequency trimming comb along x modifies the stiffness of the resonator by generating a Kt matrix: Kt = Kx 0 0 0

[0029] The frequency trimming comb along y modifies the resonator's stiffness by generating a Kt matrix: Kt = 0 0 0 Ky

[0030] The quadrature trimming comb modifies the resonator's stiffness by generating a Kt matrix: Kt = 0 Kxy Kxy 0

[0031] The stiffnesses Kx, Ky, and Kxy correspond to the CTx, CTy, and CTxy commands (DC voltages) up to a gain factor. The CTx, CTy, and CTxy commands are voltages that, when applied through the combs, modify the stiffnesses Kx, Ky, and Kxy. Applying trimming commands is equivalent to modifying the matrix K in the differential equation (2), transforming K into K-Kt.

[0032] There figure 4 This illustrates the operation of an inertial sensor according to the state of the art. The resonator Res comprises the various transducers described above and symbolized by Et (excitation), Dt (detection), TQ (quadrature trim), and TF (frequency trim). The vibration wave OV vibrates along X' with an electrical angle θ. A processing unit UT performs the various calculations for the control systems and generates, for the corrections, all the aforementioned commands / forces to the different transducers. The excitation and trim commands are determined by separate control systems.

[0033] In the processing unit, the detected X and Y movements are first transformed into the wave frame x'y' by a rotation around θ, then the excitation commands are determined in the wave frame by servo systems in the form of electrical voltages Ux' and Uy': Ux ′ = iCa + Cr Uy ′ = iCp + Cq

[0034] Trim commands are also determined by dedicated servo systems.

[0035] The commands are then switched back to the xy coordinate system by an inverse rotation and then applied (with a gain factor) to the different transducers.

[0036] The excitation chain consists of the electronics and actuators that apply the forces calculated by the control systems to the excitation transducers. It takes as input forces estimated by the control systems FXe and FYe and outputs the forces actually applied to the FX and FY resonators. An excitation matrix E is defined to represent the effect of the excitation chain (see also figure 5 ) : FX FY = E FXe FYe = E 11 E 12 E 21 E 22 FXe FYe where E is the excitation matrix.

[0037] There are actually two types of problems: (1) the fact that a force applied along x appears along the y axis and vice versa: these are the non-diagonal terms E12 and E21. (2) The fact that the forces applied along x and y do not have the same gains: this is the fact that E11 is generally different from E22.

[0038] A perfect excitation matrix E has the following form: E 11 0 0 E 11 where E11 is a real gain.

[0039] The detection chain consists of the electronics and sensors used to detect the X and Y displacements of the vibration wave. It takes the actual X and Y displacements as input and outputs the estimated Xe and Ye displacements. A detection matrix D is defined to represent the effect of the detection chain (see also figure 5 ): Xe Ye = D X Y = D 11 D 12 D 21 D 22 X Y where D is the detection matrix.

[0040] A perfect detection matrix D has the following form: D 11 0 0 D 11 where D11 is a real gain.

[0041] There figure 6 The diagram illustrates the effect of the excitation and detection chains with the dashed and solid lines, respectively. At the excitation level, the values ​​of the forces to be applied, FXe and FYe, are calculated by the Ass servocontrols of the processing unit. Due to the excitation chain, the values ​​actually applied to the resonator are FX and FY. Similarly, the true displacement values ​​X and Y undergo a transformation by the detection chain, and it is Xe and Ye that are fed into the input of the Ass servocontrols. The detection and excitation errors generate drift errors, and in particular average drift errors that cannot be compensated by electrical rotation methods.

[0042] To correct these errors, i.e., to calibrate the sensor, one solution is to determine the inverses inv(E) and inv(D) (or E - 1 < and or D - < 1) of these matrices E and D, so that the corresponding inverse matrix can be applied to each chain. For perfect correction, we then obtain the correct values ​​to apply to the resonators and the correct detected values, as illustrated. figure 7 A perfectly corrected sensor operation is illustrated. figure 8 We apply inv(E) to the output of the Ass control system and inv(D) to the measurements at the detection output, before their injection into the control system. Then, for perfect correction, we have FXe=FX and FYe = FY and Xe=X and Ye=Y.

[0043] The document US9927256 describes a calibration method for determining the correction of at least one excitation command applied to a gyroscope: a amplitude (Ca command), φ phase (Cr command), θ angle (Cp command), b quadrature (Cq command).

[0044] The method involves applying a sinusoidal force at a frequency close to the resonant frequency of the vibration sensor disturbing the gyroscope, and then using the detected outputs to extract excitation and detection errors. This is based on the assumption that, under forced conditions, the detection signals have sinusoidal components identical to those of the disturbances. The detection signals are then used to extract matrices A and B, taking advantage of the fact that the detected signals have a frequency signature identical to the inserted disturbance because the system is linear. These matrices A and B are then fed into the control system, and the process is iterated until a predefined criterion is met. However, beyond the general principle, the method for determining the coefficients of matrices A and B is not described, nor is their role in correction explained.The idea behind this method is to send specific excitation commands and observe what happens at the detection signal level. Applying forces to the excitation commands alters the waveform. Not all coefficients of matrices A and B are observable (determinable) from the set of observations provided by the excitation commands because the observations made at the detection signal level are highly redundant, rendering some coefficients of A and B unobservable even though the number of equations appears sufficient relative to the number of unknowns in the system.

[0045] One object of the present invention is to remedy the aforementioned drawbacks by proposing an alternative calibration method enabling the simultaneous determination of the inverse detection matrix and the inverse excitation matrix by a direct matrix calculation where all matrix terms are observable. DESCRIPTION DE L'INVENTION

[0046] The present invention relates to a method for calibrating an angular inertial sensor, the inertial sensor comprising: a resonator having a planar and axisymmetric structure around two perpendicular axes x and y defining a sensor frame xy and comprising two vibrating mobile masses arranged around each other configured to vibrate in opposite phase at a vibration frequency (ω) and along a direction x' defining a wave frame x'y', the vibration wave along x' making an electrical angle with respect to the x axis, the resonator further comprising a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, of which at least, on at least one of the two masses, a pair of detection transducers configured to detect the movements of the vibration wave along x and y and a pair of excitation transducers to which excitation forces are applied respectively along x and y,via a plurality of excitation commands determined by servosystems from the detected movements, and to maintain the vibration wave in a desired shape and vibrating along x', and a pair of quadrature bias compensation transducers, controlled via a quadrature CTxy command, and a pair of frequency adjustment transducers, controlled respectively via a CTx frequency command along x and a CTy frequency command along y, the three CTx, CTy and CTxy commands being called CTi trim commands indexed i with i=1,2, 3, , the procedure applicable when the sensor is operating in gyroscope mode, and comprising the steps of: A for at least two electrical angles of the vibration wave: A1apply sequentially via each of the three CTi trim commands a sinusoidal disturbance of stiffness PSi having a disturbance frequency fi, and for each applied disturbance: A11 determine and store an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi, based on the excitation commands determined by the servo systems, B determine, from the said three estimated excitation forces Fei i=1,2,3 stored at the step A11, as a function of said electrical angles and applied perturbations, three 2x2 matrices M'i, one matrix M'i being representative of the gyroscope's response to the perturbation PSi, C determine and store an estimated inverse excitation matrix ιnv E ^ and an estimated inverse detection matrix ιnv D ^ from the three matrices M'i determined in the step B,an excitation matrix E and a detection matrix D being respectively representative of the effects of the excitation chain and the effect of the detection chain of the sensor.

[0047] According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to a standard sensor control and an estimated disturbance compensation excitation force Fepi, and wherein the step B includes the sub-steps consisting of: B1 demodulate each estimated excitation force Fei by the vibration frequency and then by the associated perturbation frequency fi to obtain an amplitude of said excitation force compensating for the perturbation Fepi, B2 determine the matrix M'i from the amplitude of said force Fepi;

[0048] According to one embodiment, the step Ais implemented with a plurality of electrical angles, the said matrices M'i then being determined at the step B by statistical filtering minimizing the contribution of sensor noise.

[0049] According to one embodiment, each representative matrix M'i determined at the step B is of the form: M ′ i = ιnv E ^ . Mi . ιnv D ^ Mi defined by: M 1 = 1 0 0 0 ; M 2 = 0 0 0 1 ; And M 3 = 0 1 1 0

[0050] According to one embodiment, matrices are considered ιnv E ^ And ιnv D ^ close to unitary matrices and expressed as: ιnv E ^ = 1 + A ιnv D ^ = 1 + B the three representative matrices M'i determined at the stage B expressing itself then, neglecting second-order terms: M ' i = AMi + MiB and in which the step C includes a substep consisting of determining said matrices A and B from said matrices M'i.

[0051] Preferably the disturbance frequencies fi i=1,2,3 are between 1000 times less and 100000 times less than the vibration frequency of the wave.

[0052] Preferably the fi frequencies are less than 10Hz.

[0053] According to one embodiment, each disturbance PSi has an identical amplitude for all electrical angles.

[0054] According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to a standard sensor control and an estimated disturbance compensation excitation force Fepi, and in which an amplitude of the disturbance is chosen such that an amplitude of the force Fepi is at least 10 times greater than an amplitude of the force Fec.

[0055] The invention also relates to a method for measuring the angular velocity of a carrier on which said inertial sensor is disposed, comprising: a calibration phase of said inertial sensor implementing the calibration method according to any one of claims 1 to 9, carried out at the start-up of the inertial sensor, a step D of the operation of said inertial sensor in which said matrices ιnv E ^ And ιnv D ^ stored values ​​are applied, and the estimated inverse excitation matrix ιnv E ^ being applied to the excitation forces determined by said servo systems, prior to being sent to the excitation transducers, so as to pre-compensate said excitation forces, and said estimated inverse detection matrix ιnv D ^ being applied to the detected motion values ​​in order to correct said detected motion values.

[0056] According to one variant, the method for measuring the angular velocity of a carrier on which said inertial sensor is placed comprises: a calibration phase of said inertial sensor implementing the calibration method according to any one of claims 1 to 9, carried out while the sensor is in operation, the measurement of the angular velocity being interrupted, a step D' angular velocity measurement, implemented during the calibration phase, performed by an additional inertial sensor also located on the carrier, a step D of the operation of said inertial sensor in which said matrices ιnv E ^ And ιnv D ^ stored values ​​are applied, and the estimated inverse excitation matrix ιnv E ^ being applied to the excitation forces determined by said servo systems, prior to being sent to the excitation transducers, so as to pre-compensate said excitation forces, and said estimated inverse detection matrix ιnv D ^ being applied to the detected motion values ​​in order to correct said detected motion values.

[0057] The invention also relates to an inertial angular sensor comprising: a resonator having a planar and axisymmetric structure around two perpendicular axes x and y defining a sensor frame xy and comprising two vibrating mobile masses arranged around each other configured to vibrate in opposite phase at a vibration frequency and along a direction x' defining a wave frame x'y', the vibration wave (OV) along x' making an electrical angle (θ) with respect to the x axis, the resonator further comprising a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, of which at least, on at least one of the two masses: a pair of excitation transducers to which excitation forces are applied respectively along x and y, via a plurality of excitation controls, to maintain the vibration wave in a desired shape and vibrating along x',and a pair of detection transducers configured to detect the movements of the vibration wave along x and y, a pair of quadrature bias compensation transducers, controlled via a quadrature control CTxy, and a pair of frequency adjustment transducers, controlled respectively via a frequency control CTx along x and a frequency control CTy along y, the three controls CTx, CTy and CTxy being called indexed trim controls CTi with i=1,2, 3, , said excitation commands being determined by servo systems from the detected movements, the sensor being in operation in gyroscope mode, the three trim commands CTi being configured to sequentially apply a sinusoidal disturbance of stiffness PSi having a disturbance frequency fi, for at least two electrical angles (θj) of the vibration wave, a processing unit configured to: determine and store, for each applied disturbance, an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi, from the excitation commands determined by the servo systems, determine, from said three estimated excitation forces Fei i=1,2,3 stored in the previous step, as a function of said electrical angles and the applied disturbances, three 2x2 matrices M'i, one matrix M'i being representative of the gyroscope's response to the disturbance PSi,determine and store an estimated inverse excitation matrix, ιnv E ^ and an estimated inverse detection matrix ιnv D ^ From the three matrices M'i determined in the previous step, an excitation matrix E and a detection matrix D being respectively representative of the effects of the excitation chain and the effect of the sensor's detection chain, said estimated inverse excitation matrix ιnv E ^ being intended to be applied to the excitation forces determined by said servo systems, prior to being sent to the excitation transducers, so as to pre-compensate said excitation forces, and said estimated inverse detection matrix ιnv D ^ being intended to be applied to the detected motion values ​​in order to correct said detected motion values, when the sensor is in operation.

[0058] The following description presents several embodiments of the device of the invention; these examples are not limiting to the scope of the invention. These embodiments illustrate both the essential features of the invention and additional features related to the embodiments considered.

[0059] The invention will be better understood, and other features, purposes, and advantages thereof will become apparent from the detailed description that follows and with reference to the accompanying drawings, which are given by way of non-limiting examples and on which: [ Fig 1 ] There figure 1 The already cited illustration depicts a MEMS sensor consisting of two vibrating moving masses arranged one around the other. Fig 2 ] There figure 2 already cited illustrates the structure of a MEMS sensor with an axisymmetric resonator around two axes x and y defining a sensor frame [ Fig 3 ] There figure 3 The already cited illustration shows a MEMS sensor with transducers on both grounds. Fig 4 ] There figure 4 The already cited example illustrates the operation of an inertial sensor according to the state of the art. Fig 5 ] There figure 5 The already cited example illustrates the effect of the excitation matrix on the values ​​estimated by the control systems, and the effect of the detection matrix on the movements of the vibration wave. Fig 6 ] There figure 6 The diagram already cited illustrates the effect of the excitation and detection chains respectively with the dotted and solid lines. Fig 7 ] There figure 7 The already cited example illustrates perfect correction in excitation and detection. Fig 8 ] There figure 8 The already cited example illustrates a perfectly corrected operation of the sensor [ Fig 9 ] There figure 9 illustrates the application of an estimated, and therefore imperfect, inverse excitation matrix ιnv E ^ as determined by the method according to the invention. Fig 10 ] There figure 10 illustrates the application of an estimated, and therefore imperfect, inverse detection matrix ιnv D ^ as determined by the method according to the invention. Fig 11 ] There figure 11 illustrates the calibration method for a sensor according to the invention. Fig 12 ] There figure 12 illustrates the angular inertial sensor 10 implementing the calibration method according to the invention. Fig 13 ] There figure 13 illustrates a sensor in operation implementing the calibration according to the invention. DESCRIPTION DETAILLEE DE L'INVENTION

[0060] The calibration method according to the invention applies to an angular inertial sensor comprising a resonator Res and transducers Et, Dt, TF, and TQ controlled by excitation (Et) and trim (TF, TQ) controls as described above. The vibration wave OV vibrates at a vibration frequency ω. The method according to the invention applies to an inertial sensor operating in gyroscope mode, with the excitation control systems active.

[0061] One object of the invention is a calibration method for determining an estimated inverse excitation matrix ιnv E ^ and an estimated inverse detection matrix ιnv D ^ , in order to improve the operation of the sensor by minimizing excitation and detection errors.

[0062] To this end, disturbances are sent not to the excitation commands as in document US9927256, but via the trim commands. In the classic operation of a gyroscope including these additional transducers (which is not covered in the document cited above), these commands have a completely different role from that of the excitation commands, as explained above.

[0063] In the following, the trim commands CTx, CTy and CTxy are respectively named CTi, i=1,2, 3, i.e. CT1 for CTx, CT2 for CTY and CT3 for CTxy.

[0064] By sending sinusoidal disturbances via these CTi trim commands, the aim is to directly modify the coefficients of the differential equation (2) by inserting a new stiffness matrix Ktp, and not to modify the right-hand side (i.e., the excitation forces applied as described in the cited document). Note that the trimming combs modify the resonator, while the excitation commands constrain its displacement.

[0065] The estimated matrices ιnv E ^ And ιnv D ^ determined by the method according to the invention are not perfect, as illustrated figure 9 for the excitement and figure 10 for detection, that is to say that they are not strictly equal respectively to the inverse of matrix E and to the inverse of matrix D: the D products. inv D ^ And ιnv E ^ .E are not equal to the identity matrix, but are close to it.

[0066] The method 100 according to the invention, as illustrated figure 11 includes a first step A consisting of, for at least two electric angles θj of the vibration wave, carrying out a sub-step A1 consisting of sequentially applying, via each of the three CTi trim commands, a sinusoidal disturbance of stiffness PSi of disturbance frequency fi.

[0067] To do this, a sinusoidal electrical voltage of frequency fi is applied to the CTi control.

[0068] For each applied perturbation PSi, we determine and store it in the substep A11 An estimated excitation force Fei is applied to the resonator in the presence of the disturbance PSi to maintain linear vibration, based on excitation commands determined by the control systems. The resonator's characteristics are changed to sinusoidal, and the forces required to obtain a linear wave are determined.

[0069] A sinusoidal disturbance of stiffness PS1 applied via the CT1 command produces a sinusoidal stiffness variation of Kx corresponding to a stiffness matrix Ktp1: Ktp 1 = A 1 cos 2 πf 1 t 0 0 0

[0070] A sinusoidal perturbation of stiffness PS2 applied via the CT2 command produces a sinusoidal stiffness variation of Ky corresponding to a stiffness matrix Ktp2: Ktp 2 = 0 0 0 A 2 cos 2 πf 2 t

[0071] A sinusoidal perturbation of stiffness PS3 applied via the CT3 command produces a sinusoidal stiffness variation of Kxy corresponding to a stiffness matrix Ktp3: Ktp 3 = 0 A 3 cos 2 πf 3 t A 3 cos 2 πf 3 t 0

[0072] Then during a stage B From the three estimated excitation forces Fei, we determine i=1,2,3 stored at the stage A11,As a function of the electric angles θj and the applied perturbations PSi, three 2x2 matrices M'i represent the gyroscope's response to the perturbation PSi. A preferred method for calculating the matrices M'i is described later.

[0073] Finally, in step C, an estimated inverse excitation matrix is ​​determined and stored. ιnv E ^ and an estimated inverse detection matrix ιnv D ^ from the three matrices M'i determined in the step B. an excitation matrix E and a detection matrix D being respectively representative of the effect of the excitation chain and the effect of the detection chain of the sensor.

[0074] Once these estimated matrices have been determined and stored, they are intended to be implemented during the operation of the sensor, that is, when it performs a measurement: ιnv E ^ is intended to be applied to the excitation forces determined by the servo systems, prior to being sent to the excitation transducers, so as to pre-compensate for these excitation forces; ιnv D ^ is intended to be applied to the detected motion values ​​in order to correct these values. This minimizes excitation and measurement detection errors by applying the estimated inverse matrices.

[0075] In other words, the advantage of the method according to the invention is to trace back to the detection and excitation defects "easily" by calculation, by exploiting an additional actuator, the trimming one included in certain MEMS gyroscopes, which gives additional observability.

[0076] In practice, according to one embodiment, the method according to the invention is iterative, which improves its accuracy. Typically, there are no more than two iterations.

[0077] When a perturbative Ktpi matrix as described above is applied to a TQ or TF transducer, equation (2) becomes, for a first variant in which only PSi disturbances are applied and not the classic trim commands (the trim servos are cut off here). M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ − Ktpi X Y = FXc FYc + FXpi FYpi

[0078] For simplicity, we denote the applied excitation force as Fi, expressed in two components (FX, FY). Fi is decomposed into a standard excitation force Fc (FXc, FYc) to achieve the current control of the sensor in the absence of disturbance, and a compensating excitation force Fpi (FXpi, FYpi) to compensate for the application of the disturbance PSi:

[0079] We observe that the application of a perturbation induces a modification of certain coefficients in the differential equation (5) compared to the classical equation (2): Fi = Fc + Fpi ; FXi = FXc + FXpi ; FYi = FYc + FYpi FXi FYi = FXc FYc + FXpi FYpi

[0080] The amplitude of the applied disturbances PSi is chosen so that the amplitudes of (FXpi, FYpi) are at least 10 times greater than the amplitudes of (FXc, FYc). This choice is made to ensure that the phenomena to be observed stand out from the noise and are more easily observable. However, the amplitude cannot be increased too much because the controls practically do not allow it.

[0081] The force Fc is responsible for controlling the resonator in a classical way so that the wave is, for example, linear and of a given amplitude, and we have (similarly to equation (1): M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ = FXc FYc

[0082] Due to the difference in frequency between Fc and Fp and the linearity of the system, we can isolate: − Ktpi X Y = FXpi FYpi

[0083] According to a second variant, the PSi disturbances are applied in superposition to the conventional trim commands (Kt matrix) (the trim servos are then in operation). Equation (2) then becomes: M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ − Kt X Y − Ktpi X Y = FXc FYc + FXpi FYpi

[0084] Similarly, the classic resonator control can be expressed as follows: M X ¨ Y ¨ + A X ˙ Y ˙ + K X Y + C X ˙ Y ˙ − Kt X Y = FXc FYc and formula (7) remains verified.

[0085] From formula (7), and (3) and (4) we introduce the excitation and detection matrices E and D (also called the excitation and detection error matrix): inv D X ¨ e Y ¨ e + Ainv D X ˙ e Y ˙ e + Kinv D Xe Ye + Cinv D X ˙ e Y ˙ e − Ktpi . inv D Xe Ye = E FXec FYec + E FXepi FYepi

[0086] With Fe (FXe,FYe) the estimated force to control the oscillator, which is decomposed into a force Fec (FXec, FYec) and a force Fepi (FXepi, FYepi) according to the same logic as before: Fec is the estimated standard excitation force to achieve classical sensor control in the absence of disturbance, Fepi is the estimated compensation excitation force to compensate for the application of the disturbance. FXeiFYei=FXecFYec+FXepiFYepi

[0087] Let FXei = FXec + FXepi and FYei = FYec + FYepi

[0088] The forces actually applied are: FXi FYi = FXc FYc + FXpi FYpi = E FXei FYei = E FXec FYec + FXepi FYepi

[0089] Starting with Fei FXei FYei we will extract the amplitudes of FXepi FYepi .

[0090] FXec and FYec are sinusoidal functions of frequency ω.

[0091] FXepi And FYepi are sinusoidal functions in ω modulated by the perturbations introduced in Ktpi, i.e. at the frequency fi.

[0092] Theoretically, we have: − Ktpi . inv D Xe Ye = E FXepi FYepi because E FXepi FYepi is the force that, by definition, counteracts the disturbance.

[0093] For each trimming comb, and therefore for each applied perturbation PSi, and for a wave vibration angle θ, we theoretically have: inv E A 1 cos 2 πf 1 t 0 0 0 inv D X 0 cos θ cos ωt X 0 sin θ cos ωt = FXep 1 θ FYep 1 θ inv E 0 0 0 A 2 cos 2 πf 1 t inv D X 0 cos θ cos ωt X 0 sin θ cos ωt = FXep 2 θ FYep 2 θ inv E 0 A 3 cos 2 πf 1 t A 3 cos 2 πf 1 t 0 inv D X 0 cos θ cos ωt X 0 sin θ cos ωt = FXep 3 θ FYep 3 θ

[0094] Or : X0 is the known amplitude of the controlled vibration, ω is the known angular frequency of the resonator, Ai are the known amplitudes of the disturbances PSi, fi are the known frequencies of the disturbances PSi, and θ is the known angle at which the gyroscope is controlled.

[0095] The calculations are carried out for i=1 and the reasoning is the same for i=2 and 3.

[0096] The magnitudes of the terms on the right and left sides of equation (9) are the same, so theoretically we have: A 1 . inv E 1 0 0 0 inv D X 0 cos θ X 0 sin θ = AFXep 1 θ AFYep 1 θ Or AFXep 1( θ ) denotes the amplitude of FXep 1( θ ).

[0097] We want to determine AFXep 1 θ AFYep 1 θ to deduce the matrix M'1 defined by: M ′ 1 = inv E 1 0 0 0 inv D = inv E . M 1 . inv D with M 1 = 1 0 0 0

[0098] We have access to the Fei forces (FXei, FYei) that were memorized in step A11, i.e. here: FXe 1 θ FYe 1 θ = FXec θ FYec θ + FXep 1 θ FYep 1 θ FXec θ FYec θ are sinusoids at the resonator's angular frequency ω, FXep 1 θ FYep 1 θ are sinusoids at the resonator pulsation ω modulated by a sinusoidal function at the pulsation 2πf1.

[0099] We demodulate in ω and then in 2πf1 to get back to the amplitudes of FXep 1 θ FYep 1 θ which provides AFXep 1 θ AFYep 1 θ (Demodulation is an operation well known to those skilled in the art in various fields).

[0100] Thus, according to one embodiment of the invention, step B comprises: a sub-step B1 consisting of demodulating each estimated excitation force Fei by the vibration frequency ω and then by the associated perturbation frequency fi, to obtain an amplitude AFpei (AFXepi, AFYepi) of the excitation force compensating the perturbation Fepi (FXepi, FYepi). a substep B2consisting of determining the matrix M'i from the amplitude of the force Fepi determined in B1.

[0101] According to one embodiment of the invention, each matrix M'i represents the response of the gyroscope to the perturbation M'i determined at the step B is of the form: M ′ i = ιnv E ^ . Mi . ιnv D ^

[0102] With Mi i=1, 2 3 defined by: M 1 = 1 0 0 0 ; M 2 = 0 0 0 1 ; And M 3 = 0 1 1 0

[0103] We will now explain how M'i is determined from AFpei.

[0104] We start from equation (12): A 1 . inv E 1 0 0 0 inv D X 0 cos θ X 0 sin θ = AFXep 1 θ AFYep 1 θ which can be in the form of: M ′ 1 . A 1 . X 0 cos θ A 1 . X 0 sin θ = AFXep 1 θ AFYep 1 θ

[0105] A1, X0, θ, AFXep 1( θ ) And AFYep 1( θ ) are known.

[0106] M'1 has 4 unknowns (4 coefficients). Therefore, at least two angles are needed to access the four coefficients of M'1.

[0107] In practice, this is done for more than two angles, and a statistical filtering, typically of the least squares type, is performed to best estimate the coefficients of M'1. Thus, according to one embodiment, the step A is implemented with a plurality of electrical angles, the matrices M'i then being determined at the step B by statistical filtering (of the least squares type for example) minimizing the contribution of sensor noise.

[0108] Thus, from equation (14) and the various known quantities, we have access to the estimated M'1 of inv E 1 0 0 0 inv D either : M ′ 1 = ιnv E ^ 1 0 0 0 ιnv D ^

[0109] We do the same for M'2 and M'3. M ′ 2 = ιnv E ^ 0 0 0 1 ιnv D ^ M ′ 3 = ιnv E ^ 0 1 1 0 ιnv D ^

[0110] We will now show that we go back to ιnv E ^ And ιnv D ^ from the matrices M'i determined in step B (with equation (14) and its equivalents for i=2 and 3) using equations (15) to (17).

[0111] This is a non-linear problem, but ιnv E ^ And ιnv D ^ are matrices close to the identity because the electronic errors are small.

[0112] They can therefore be broken down as follows: ιnv E ^ = 1 + e 11 e 12 e 21 1 + e 22 = I + A ιnv D ^ = 1 + d 11 d 12 d 21 1 + d 22 = I + B

[0113] Where I denotes identity and eij, dij are small values ​​(typically less than 0.01)

[0114] SO : ιnv E ^ . Mi . ιnv D ^ = AMi + MiB neglecting orders 2.

[0115] Starting from AMi+MiB = M'i known we will go back to A and B.

[0116] With M1: AM 1 + M 1 B = e 11 e 12 e 21 e 22 1 0 0 0 + 1 0 0 0 d 11 d 12 d 21 d 22 = e 11 + d 11 d 12 e 21 0 We can therefore identify d12 and e21, as well as e11+d11

[0117] With M2: AM 2 + M 2 B = e 11 e 12 e 21 e 22 0 0 0 1 + 0 0 0 1 d 11 d 12 d 21 d 22 = 0 e 12 d 21 e 22 + d 22 We obtain d21, e12 and e22+d22

[0118] With M3: AM 3 + M 3 B = e 11 e 12 e 21 e 22 0 1 1 0 + 0 1 1 0 d 11 d 12 d 21 d 22 = e 12 + d 21 e 11 + d 22 e 22 + d 11 e 21 + d 12

[0119] Therefore, we obtain e 22+ d 11 and e11+d22, which allows in combination with e11+d11 ​​from (20) and e22+d22 from (21).

[0120] Note that the equations e22 + d11, e11+d22, e11+d11 ​​and e22+d22 are not independent; the system is of rank 3: for example, (e22+d22)+( e11+d11)-( e11+d22)= e 22+ d 11. Therefore, the four coefficients cannot be determined from the four equations. However, equation (8) can be multiplied arbitrarily on both sides by any value. For example, we can arbitrarily decide to divide everything by (1 + d11), such that d11 would be equal to 0 in this new system, thus eliminating this unknown and allowing us to work our way back to the unknowns e22, then d22, and then e11.

[0121] Thus, according to one embodiment of the process according to the invention, the three representative matrices M'i determined at the stage B are expressed, neglecting second-order terms, in the form M'i = AMi+MiB and the step Cincludes a substep consisting of determining matrices A and B (8 coefficients) from said matrices M'i. Thus, with the method as claimed, these 8 coefficients are all observable. The matrices ιnv E ^ And ιnv D ^ are then determined from A and B (equations (18) and (19)).

[0122] By accurately simulating the practical behavior of the gyroscope, we can determine simulated coefficients of the E and D matrices. When calculating the quantities ιnv E ^ . E And D . ιnv D ^ using these simulated coefficients and the values ​​of the coefficients of ιnv E ^ And ιnv D ^ determined by the method according to the invention, the identity matrix is ​​obtained with an error between 10 ppm and 200 ppm, which constitutes a very good estimation accuracy for ιnv E ^ . E And D . ιnv D ^ .

[0123] In order for the stiffnesses in equation (8) to change sufficiently slowly to be considered constants, the frequencies f1, f2, and f3 of the disturbances PS1, PS2, and PS3 are preferably chosen to be much lower than the vibration frequency ω, typically between 1000 and 100,000 times lower. Since the wave vibration frequency is typically on the order of tens of kHz, the frequencies f1, f2, and f3 are typically less than 10 Hz or even 1 Hz.

[0124] Furthermore, the frequencies f1, f2, and f3 of the disturbances PS1, PS2, and PS3 are preferentially chosen to be higher than the frequencies of the physical phenomena responsible for sensor drift, and more specifically, the physical phenomena related to variations in sensor temperature. These phenomena typically have frequencies much lower than 1 Hz, or even a tenth of a Hz.

[0125] Thus, preferentially the frequencies f1, f2 and f3 are greater than 0.1 Hz.

[0126] Preferably, the frequencies f1, f2, and f3 are injected separately, so these frequencies can be equal. However, this is irrelevant for the implementation of the method.

[0127] There figure 12 Figure 10 illustrates the angular inertial sensor implementing the calibration method 100 according to the invention. The disturbances PSi are sequentially applied to the transducers TQ or TF. The processing unit UT performs a change of reference frame on the estimated movements (Xe, Ye) of the resulting vibration and then calculates the estimated excitation commands enabling the control of the sensor (control module Ass) in the presence of the disturbance. Then, after returning to the sensor reference frame, the estimated excitation forces FXei, FYei are determined and stored (MEM). From these forces, the processing unit determines the coefficients of the matrices. ιnv E ^ And ιnv D ^ and memorizes them.

[0128] There figure 13illustrates a sensor in operation, that is to say, performing an angular velocity measurement, with calibration complete and matrices ιnv E ^ And ιnv D ^ stored. The processing unit applies ιnv D ^ to the movements measured by the sensor and ιnv E ^ to the excitation forces estimated by the control systems. The trimming control systems (not shown) then operate in a conventional manner.

[0129] The calibration process can be implemented in several modes of use.

[0130] For all modes, once calibration is complete and the sensor is operating, the estimated inverse excitation matrix ιnv E ^ is applied to the excitation forces determined by the servo systems, prior to being sent to the excitation transducers, so as to pre-compensate for said excitation forces, and the estimated inverse detection matrix ιnv D ^ is applied to the detected motion values ​​in order to correct the detected motion values.

[0131] In a first operating mode, a calibration phase of the inertial sensor, implementing method 100 according to the invention, is carried out prior to the sensor's operation, typically at the end of the manufacturing line (factory calibration). The inverse excitation and detection matrices are stored in the processing unit. They are then applied when the sensor is operating and performing a measurement.

[0132] According to a second embodiment, the invention relates to a method for measuring the angular velocity of a carrier on which the inertial sensor 10 is placed, comprising a calibration phase implementing the calibration method 100 according to the invention, carried out when the sensor is switched on. Once the calibration is complete, a measurement applying the matrices is performed in a step D. ιnv E ^ And ιnv D ^ memorized.

[0133] According to a third embodiment, the invention relates to a method for measuring the angular velocity of a carrier on which an inertial sensor 10 is placed, comprising a calibration phase implementing the calibration method 100 according to the invention, carried out during operation. During the calibration phase, the inertial sensor cannot perform any measurements, and therefore the measurement of the angular velocity by the sensor 10 is interrupted during the calibration phase.

[0134] While sensor 10 is being calibrated, the process implements a step D' angular velocity measurement is carried out by an additional inertial sensor also placed on the carrier, in order to guarantee continuity of measurement.

[0135] Once the calibration is complete, sensor 10 resumes control of the measurement by performing the following steps D a measure applying matrices ιnv E ^ And ιnv D ^ memorized.

[0136] The switching from one sensor to another occurs, for example, periodically over time, allowing calibration throughout the operating time of sensor 10.

[0137] By accurately simulating the practical behavior of the gyroscope, we can determine simulated coefficients of the matrices E and D.

[0138] When calculating quantities ιnv E ^ . E And D . ιnv D ^ using the values ​​of the coefficients of ιnv E ^ And ιnv D ^ determined by the method according to the invention, we obtain the identity matrix with an error between 10 ppm and 200 ppm, which gives very good precision.

Claims

1. Method (100) for calibrating an inertial angular sensor (10), the inertial sensor comprising: - a resonator (Res) having a flat and axisymmetrical structure about two axes x and y, perpendicular to one another, defining a sensor system xy and comprising two vibrating movable masses (M1, M2) disposed around one another, configured to vibrate in phase opposition at a vibration frequency (ω) and along a direction x' defining a wave system x'y', the vibration wave (OV) along x' forming an electrical angle (θ) with respect to the axis x, - the resonator further comprising a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x and y, of which at least one, on at least one of the two masses, - a pair of detection transducers (Dt) configured to detect the movements of the vibration wave along x and y, and a pair of excitation transducers (Et) to which excitation forces are applied respectively along x and y, via a plurality of excitation commands determined by drives from detected movements, and to maintain the vibration wave in a desired form and vibrating along x', and - a pair of transducers for compensating a quadrature bias (TQ), controlled via a quadrature command CTxy, and a pair of frequency adjustment transducers (TF), controlled via respectively a frequency command CTx along x and a frequency command CTy along y, the three commands CTx, CTy and CTxy being called trim commands CTi indexed i with i=1,2,3, the method being applied when the sensor is in operation according to a gyrometer mode, and characterised in that it comprises the steps comprising of: A for at least two electrical angles (θj) of the vibration wave: A1 sequentially applying, via each of the three trim commands CTi, a sinusoidal stiffness disturbance PSi having a disturbance frequency fi, and for each disturbance applied: A11 determining and storing an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi, from the excitation commands determined by the drives, B determining from the three estimated excitation forces Fei i=1,2,3 stored in step A11, as a function of said electrical angles and disturbances applied, three matrices 2×2 M'i, a matrix M'i being representative of the gyrometer response to the disturbance PSi, C determining and storing an estimated inverse excitation matrix inv E ^ and an estimated inverse detection matrix inv D ^ from the three matrices M'i determined in step B, an excitation matrix E and a detection matrix D being representative of the effects of the excitation chain and the effect of the detection chain of the sensor.

2. Method according to claim 1, wherein each estimated excitation force Fei is broken down into an estimated standard excitation force Fec corresponding to a standard drive of the sensor and an estimated disturbance compensation excitation force Fepi, and wherein step B comprises the substeps comprising of: - B1 demodulating each estimated excitation force Fei by the vibration frequency (ω), then by the associated disturbance frequency fi to obtain an amplitude (AFpei) of said disturbance compensation excitation force Fepi, - B2 determining said matrix M'i from said amplitude of said force Fepi.

3. Method according to any one of the preceding claims, wherein step A is implemented with a plurality of electrical angles, said matrices M'i thus being determined in step B by a statistical filtering minimising the contribution of the noise of the sensor.

4. Method according to any one of the preceding claims, wherein each representative matrix M'i determined in step B is of the form: M ′ i = inv E ^ . Mi . inv d ^ Mi defined by: M 1 = 1 0 0 0 ; M 2 = 0 0 0 1 ; and M 3 = 0 1 1 0 5. Method according to the preceding claim, wherein the matrices inv E ^ and inv D ^ close to unit matrices are considered, and being expressed: inv E ^ = 1 + A inv D ^ = 1 + B the three representative matrices M'i determined in step B thus being expressed, by disregarding the second order term: M ′ i = AMi + MiB and in which step C comprises a substep comprising of determining said matrices A and B from said matrices M'i.

6. Method according to any one of the preceding claims, wherein said disturbance frequencies fi i=1,2,3 are between 1,000 times and 100,000 times less than the vibration frequency of the wave (ω).

7. Method according to any one of the preceding claims, wherein said frequencies fi are less than 10Hz.

8. Method according to any one of the preceding claims, wherein each disturbance PSi has an identical amplitude for all the electrical angles.

9. Method according to any one of the preceding claims, wherein each estimated excitation force Fei is broken down into an estimated standard excitation force Fec corresponding to a standard drive of the sensor and an estimated disturbance compensation excitation force Fepi, and wherein an amplitude of the disturbance is chosen, such that an amplitude of the force Fepi is at least 10 times greater than an amplitude of the force Fec.

10. Method for measuring an angular speed of a carrier on which said inertial sensor (10) is disposed, comprising: - a phase of calibrating said inertial sensor implementing the calibration method (100) according to any one of claims 1 to 9, carried out upon starting up the inertial sensor, - a step D of operating said inertial sensor, in which said stored matrices inv E ^ and inv D ^ are applied, said estimated inverse excitation matrix inv E ^ being applied to the excitation forces determined by said drives, prior to the sending over the excitation transducers, so as to pre-compensate for said excitation forces, and said estimated inverse detection matrix inv D ^ being applied to the detected movement values, so as to correct said detected movement values.

11. Method for measuring an angular speed of a carrier on which said inertial sensor (10) is disposed, comprising: - a phase of calibrating said inertial sensor implementing the calibration method (100) according to any one of claims 1 to 9, carried out when the sensor is being operated, the measuring of the angular speed thus being interrupted, - a step D' of measuring the angular speed, implemented during the calibration phase, carried out by an additional inertial sensor, also disposed on the carrier, - a step D of operating said inertial sensor, in which said stored matrices inv E ^ and inv D ^ are applied, said estimated inverse excitation matrix inv E ^ being applied to the excitation forces determined by said drives, prior to the sending over the excitation transducers, so as to pre-compensate for said excitation forces, and said estimated inverse detection matrix inv D ^ being applied to the detected movement values, so as to correct said detected movement values.

12. Inertial angular sensor (10), comprising: - a resonator (Res) having a flat and axisymmetrical structure about two axes x and y, perpendicular to one another, defining a sensor system xy and comprising two vibrating movable masses (M1, M2) disposed around one another, configured to vibrate in phase opposition at a vibration frequency (ω) and along a direction x' defining a wave system x'y', the vibration wave (OV) along x' forming an electrical angle (θ) with respect to the axis x, - the resonator further comprising a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x and y, of which at least one, on at least one of the two masses, - a pair of detection transducers (Et) to which excitation forces are applied respectively along x and y, via a plurality of excitation commands, to maintain the vibration wave in a desired form and vibrating along x', and a pair of detection transducers (Dt) configured to detect the movements of the vibration wave along x and y, - a pair of transducers for compensating a quadrature bias (TQ), controlled via a quadrature command CTxy, and a pair of frequency adjustment transducers (TF), controlled via respectively a frequency command CTx along x and a frequency command CTy along y, the three commands CTx, CTy and CTxy being called trim commands CTi indexed i with i=1,2,3, said excitation commands being determined by drives from the detected movements, the sensor operating according to a gyrometer mode, characterised in that the three trim commands CTi are configured to sequentially apply a sinusoidal stiffness disturbance PSi having a disturbance frequency fi, for at least two electrical angles (θj) of the vibration wave, and in that it comprises a processing unit (UT), configured for: - determining and storing, for each applied disturbance, an estimated excitation force Fei to be applied to the resonator in the presence of said disturbance PSi, from the excitation commands determined by the drives, - determining from said three estimated excitation forces Fei i=1,2,3 stored in the preceding step, as a function of said electrical angles and disturbances applied, three matrices 2×2 M'i, a matrix M'i being representative of the gyrometer response to the disturbance PSi, - determining and storing an estimated inverse excitation matrix inv E ^ and an estimated inverse detection matrix inv D ^ from the three matrices M'i determined in the preceding step, an excitation matrix E and a detection matrix D being representative of the effects of the excitation chain and the effect of the detection chain of the sensor, said estimated inverse excitation matrix inv E ^ being intended to be applied to the excitation forces determined by said drives, prior to the sending over the excitation transducers, so as to pre-compensate for said excitation forces, and said estimated inverse detection matrix inv D ^ being intended to be applied to the detected movement values, so as to correct said detected movement values, when the sensor is operating.