Method for calibrating a vibratory inertial sensor

Abstract

A method (100) for calibrating an inertial angle sensor (10) comprising the following steps: A, for at least two electrical angles (θj) of the vibration wave: A1, applying, via each of the three trim controls CTi, a sinusoidal stiffness perturbation PSi with a perturbation frequency fi, and for each applied perturbation: A11, determining and storing, based on the excitation control determined by the driver, an estimated excitation force Fei that would be applied to the resonator in the presence of the perturbation PSi; B, determining three 2x2 matrices M'i from the three estimated excitation forces Fei i=1,2,3 stored in step A11, the matrices M'i representing the response of the gyro tester to the perturbation PSi; C, determining and storing from the three matrices M'i determined in step B an estimated inverse excitation matrix (formula (A)) and an estimated inverse detection matrix (formula B), the excitation matrix E and the detection matrix D representing respectively the effect of the excitation chain and the effect of the detection chain of the sensor.

Description

Technical Field

[0001] The field of this invention is the field of vibratory inertial sensors in which two masses are vibrated. More specifically, the invention relates to MEMS-type inertial sensors with planar structures, typically fabricated from a support wafer through micromachining. Background Technology

[0002] Tuning fork inertial sensors are known to those skilled in the art. Document EP2960625 describes an inertial sensor fabricated from a thin-plane wafer through micromachining, which allows for the measurement of angular position (gyroscope) or angular velocity (gyroscope meter). Its key features are reviewed below.

[0003] These microfabricated sensors (also known as MEMS (microelectromechanical systems) sensors) are manufactured using collective microfabrication, etching, doping deposition, and other techniques, similar to those used in the manufacture of electronic integrated circuits, thus allowing for low production costs.

[0004] These sensors consist of two vibrating moving masses M1 and M2 (such as... Figure 1 As shown, two vibrating moving masses, M1 and M2, are arranged concentrically around each other and are excited to vibrate in tuning fork mode in the plane of the wafer (plane xy in the figure) via one or more excitation transducers. The two masses are suspended from a fixed anchor point A on the wafer by (orthogonal) suspension springs RS. The two masses are coupled together by stiffness elements RC. The aim is to achieve a stiffness along x equal to the stiffness along y, and a zero-coupling stiffness between x and y. Useful vibration modes correspond to linear vibrations of the two masses in opposite phase.

[0005] This architecture forms a resonant system in which two masses are coupled together via Coriolis acceleration. As the gyroscope rotates about the z-axis (called the sensitive axis) perpendicular to the xy-plane, the combination of the forced vibration and the angular rotation vector generates a force via the Coriolis effect that sets the moving mass into a natural vibration perpendicular to both the excitation vibration and the sensitive axis; the amplitude of the natural vibration is proportional to the rotational speed. Electronics associated with the sensor calculates the vibration amplitude along a direction orthogonal to the excitation direction, regardless of the excitation direction (which is assumed to be known).

[0006] The sensor can operate in gyroscope mode: by modifying the excitation to keep the direction of the natural vibration fixed relative to the sensor housing, the output information is an image of the necessary energy that must be applied to the excitation transducer to maintain the direction of the natural vibration, despite the movement of the housing. The measurement of this reaction force provides the sensor's angular velocity Ω. The sensor can also operate in gyroscope mode: the direction of the natural vibration is free and is detected, thus providing the sensor's angular orientation.

[0007] The overall structure of the resonator is symmetrical about two axes, x and y, which define the sensor reference frame, such as... Figure 2 As shown. Axisymmetry is understood to mean that the structure is symmetric about x and symmetric about y. As described below, these axes constitute the principal directions of the actuator / detector operating along these two axes.

[0008] To excite a useful vibration mode in any given direction in the plane, the excitation signal is decomposed into two components with corresponding adjusted amplitudes, which are applied respectively to an excitation transducer Ex acting in the x-direction and an excitation transducer Ey acting in the y-direction, the transducers being coupled to at least one moving mass ( Figure 2 The internal mass M1 in the medium is associated with this. Therefore, an excitation force is applied to these transducers to generate and sustain vibrational waves: the transducers are able to maintain forced vibrations via amplitude control (to counteract the damping of the MEMS) and via precession control (to rotate the wave) in any direction along the xy plane.

[0009] The motion of the obtained wave is detected by combining information collected by at least one pair of detection transducers Dx and Dy, wherein the at least one pair of detection transducers Dx and Dy are in the mass in the sensor reference frame xy( Figure 2 The position of each of the two (in each) is collected during the movement of the mass block and associated with at least one moving mass block.

[0010] Preferably, such as Figure 3 As shown, the transducer is implemented on two masses, with index 1 corresponding to mass M1 and index 2 corresponding to mass M2. Figure 2 and Figure 3 This constitutes an unrestricted example of the arrangement; many other types of arrangements with constraints on the generation of axisymmetric systems are also possible.

[0011] The transducer is preferably implemented by electrodes in the form of a finger-crossed comb with varying gaps. There are fixed combs (the teeth of the fixed comb are fixed to fixed electrodes on the processed wafer) and movable combs (the teeth of the movable comb intersect the teeth of the fixed comb in a finger-crossing manner and are fixed to a movable mass associated with the transducer under consideration).

[0012] The excitation is achieved by applying an excitation force via an alternating voltage between the moving and stationary combs at a desired vibration frequency (the mechanical resonant frequency of the suspended moving mass, typically on the order of 10 kHz). The resulting motion is perpendicular to the teeth of the combs.

[0013] The detection involves applying a polarization voltage between the fixed comb and the moving comb; and observing the change in charge resulting from the change in capacitance between the fixed and moving combs due to the change in the spacing between the teeth of the fixed and moving combs. The measured motion is perpendicular to the teeth of the comb.

[0014] The vibrating assembly of a mass / spring is characterized by a symmetric 2×2 stiffness matrix, referred to as K. For optimal sensor operation, the goal is to obtain a final stiffness matrix proportional to the identity matrix. However, due to imperfections in production, this is not always the case (see below for details).

[0015] The axis x' is called the vibration axis of the wave. This axis defines the reference frame x'y', where y' is perpendicular to x' in the plane of the MEMS. The axis x' forms an angle with the axis x called the electrical angle θ, and the reference frame x'y' is called the wave reference frame. Now we will assume that the wave vibrates along x (x' = x).

[0016] The dynamic equations describing the vibrating gyroscope tester can be simplified to a single-mass model of mass M, whose displacements X and Y are modeled as follows:

[0017]

[0018] M is the mass matrix; for simplicity, it will be treated as a scalar in the following text.

[0019] A is the damping matrix, K is the stiffness matrix, and C is the Coriolis matrix with values: Where M is mass and Ω is angular velocity.

[0020] FX and FY are excitation forces applied along the x and y axes of the gyroscope. These forces originate from the demodulation of the displacement of the detected signal relative to the vibration, and are calculated in the wave reference frame by servo control known to those skilled in the art (and not described herein). Based on measurements of the motion of waves X and Y performed in reference frame xy, a rotation is applied to transmit to the wave reference frame x'y', then (via demodulation of the detected signal) the control is determined, and a reverse rotation is applied to transmit back to reference frame xy, where the excitation forces are applied. The control is determined such that the displacement of the mass (i.e., the vibration wave of the gyroscope) takes a desired form. Generally, the desired form is a linear displacement oscillating in a given direction with respect to the gyroscope's reference frame xy.

[0021] The control force Cr corresponds to the stiffness force used to control the natural frequency of the resonator; since phase is the integral of frequency, Cr controls the phase of the wave. Cr is the external force (estimated displacement) applied to the resonator, which modifies the frequency of vibration by slowing down or speeding up the vibration, but does not modify the inherent stiffness of the resonator.

[0022] Control Ca corresponds to the amplitude force used to control the amplitude of the wave, and control Cp corresponds to the precession force that enables control of the angular velocity of the wave.

[0023] The control Cq corresponds to the orthogonal force used to control the wave (that is, to ensure the linearity of the wave, or in the case that the desired wave is not linear, it is generally elliptical, and Cq makes it possible to control the minor axis of the ellipse).

[0024] It is well known to those skilled in the art that imperfections in the manufacturing of sensors result in errors in the information transmitted as their output. Most of these imperfections need to be compensated for by balancing the gyroscope tester.

[0025] It is known that this compensation is performed by locally removing material (e.g., by laser ablation), thereby modifying the distribution of mass or stiffness. This process is expensive, or even impossible, to implement on a gyroscope fabricated from a thin silicon wafer micromachining, where the detection and excitation of motion are located in the plane of the substrate.

[0026] The first type of imperfection that forms the basis of the nonidentity of the stiffness matrix K is the frequency difference between the principal axes of vibration in the plane of a MEMS and the axes perpendicular to the vibration, corresponding to the stiffness matrix of a system in which the stiffness along the x-axis differs from the stiffness along the y-axis. The goal is to achieve equal resonant frequencies along the two axes mentioned above by means of adjustable electrostatic stiffness. This is achieved by adjusting the frequencies acting along the directions x and y using transducers Tx and Ty (at least one pair of Tx and Ty on at least one mass, see...). Figure 2 This provides electrostatic stiffness (called equalization stiffness). The purpose of applying this equalization stiffness is to equalize the stiffness along the two axes of vibration by reducing the value of the highest stiffness, thereby equalizing the frequencies. Frequency correction is called "fine-tuning".

[0027] The second type of imperfection stems from the mechanical coupling between the vibrating axis and the vertical axis, forming the basis of so-called orthogonal bias. It involves an anisotropic defect in the dynamic stiffness of the two vibrating masses, resulting in elliptical vibrations that are no longer linear, and corresponding to the presence of non-zero coupling stiffness. A known solution from the prior art is to cancel this by applying a (sinusoidal) force F to the system via an excitation transducer. The problem is that this force is not applied correctly at the correct time (phase error) and in the correct axis (gain error), leading to a drift in the application. To avoid applying force F, instead of applying a force directly, it is necessary to... Figure 2 At least one pair of transducers Q+ and Q- (shown) Figure 2The two Q+ / Q- pairs directly alter the stiffness of the resonator to physically cancel the coupling terms. To comply with symmetry and "geometric" anisotropy, and for volume reasons, these operations place the transducers on the X and Y axes diagonally. Correction of the orthogonal bias is called orthogonal "fine-tuning." Preferably, the transducers Tx, Ty, Q+, and Q- are also finger-shaped cross-combs (such as...). Figure 2 and Figure 3 As shown, this finger-shaped cross comb is controlled by DC voltage and is called a fine-tuning comb.

[0028] Therefore, transducers used for orthogonal "fine-tuning" modify the characteristics of the MEMS to eliminate coupling between the two axes of the wave reference system, and transducers used for frequency "fine-tuning" modify the characteristics of the MEMS sensor to eliminate frequency differences between the two axes of the wave reference system. They modify the intrinsic characteristics of the resonator. In other words, if a fine-tuning voltage is applied, even when the resonator is not vibrating, its stiffness is changed, which is the opposite of the control Cr described above (which is the force that slows down or speeds up the vibration when the resonator is vibrating). Fine-tuning is performed with the help of a DC or low-frequency voltage that modifies the electrostatic stiffness of the sensor, without needing to evaluate the phase of the vibration, and is implemented by sending a sinusoidal voltage (at the resonant frequency of the sensor) after the phase of the vibration has already been estimated. Therefore, the frequency change achieved by fine-tuning has a completely different nature from the frequency change achieved by controlling Cr.

[0029] They are controlled by a fine-tuning servo control (known to those skilled in the art), which generates an orthogonal fine-tuning control CTxy, a frequency fine-tuning control CTx along X, and a frequency fine-tuning control CTy along Y. The fine-tuning control is a DC voltage.

[0030] Therefore, using a fine-tuning comb, the stiffness matrix K is directly modified with the help of matrix Kt, and the dynamic equation of the gyroscope tester is:

[0031]

[0032] The comb used to fine-tune the frequency along x modifies the stiffness of the resonator by generating a matrix Kt:

[0033]

[0034] The comb used to fine-tune the frequency along y modifies the stiffness of the resonator by generating a matrix Kt:

[0035]

[0036] Orthogonal fine-tuning combs modify the stiffness of the resonator by generating a matrix Kt:

[0037]

[0038] Stiffnesses Kx, Ky, and Kxy correspond to control values ​​CTx, CTY, and CTxy (DC voltages) within the gain coefficients. Control values ​​CTx, CTY, and CTxy are obtained by modifying the voltages of stiffnesses Kx, Ky, and Kxy through a comb. Applying fine-tuning control by converting K to K-Kt is equivalent to modifying matrix K in differential equation (2).

[0039] Figure 4 The operation of an inertial sensor according to the prior art is illustrated. The resonator Res comprises various transducers described above and symbolized by Et (excitation), Dt (detection), TQ (orthogonal fine-tuning), and TF (frequency fine-tuning). The vibration wave OV vibrates along X' with an electrical angle θ. The processing unit UT performs various calculations for servo control and generates a set of control / forces mentioned above for the various transducers for correction. The excitation and fine-tuning control are determined by different servo controls.

[0040] In the processing unit, the detected motions X and Y are first converted into a wave reference system x'y' by rotation via θ, and then the excitation control is determined in the wave reference system in the form of voltages Ux' and Uy' by servo control.

[0041] Ux'=iCa+Cr

[0042] Uy'=iCp+Cq

[0043] It also uses dedicated servo control to determine fine-tuning control.

[0044] The control is then switched back to the reference frame xy by a reverse rotation, and then applied (within the gain coefficient) to the various transducers.

[0045] The excitation chain corresponds to the electronics and actuators, enabling the application of forces calculated by servo control to the excitation transducer. It takes the forces FXe and FYe estimated by the servo control as inputs and provides the actual forces FX and FY applied to the resonator as outputs. The excitation matrix E, representing the effect of the excitation chain, is defined as (see also...) Figure 5 ):

[0046]

[0047] Where E is the activation matrix.

[0048] In fact, there are two types of problems: (1) the fact that the force applied along x appears to be along the y-axis (and vice versa): this involves the off-diagonal terms E12 and E21. (2) the fact that the forces applied along x and y do not have the same gain: this is related to the fact that E11 is generally different from E22.

[0049] The ideal excitation matrix E has the following form:

[0050] E11 is the actual gain.

[0051] The detection chain corresponds to electronic devices and sensors that enable the detection of displacements X and Y of a vibration wave. It takes the actual displacements X and Y as input and provides estimated displacements Xe and Ye as output. The detection matrix D, representing the effect of the detection chain, is defined as (see also...) Figure 5 ):

[0052]

[0053] Where D is the detection matrix.

[0054] An ideal detection matrix D has the following form:

[0055] D11 is the actual gain.

[0056] Figure 6 The effects of the excitation chain and the detection chain are illustrated using dashed and solid lines, respectively. Regarding excitation, the values ​​of the applied forces FXe and FYe are calculated by the servo control Ass in the processing unit. Due to the excitation chain, the actual values ​​applied to the resonator are FX and FY. Similarly, the true values ​​of displacements X and Y are transformed by the detection chain, and Xe and Ye are injected at the input of the servo control Ass. Errors in detection and excitation produce drift errors, and in particular, an average drift error that cannot be compensated for by electro-rotation.

[0057] To correct these errors, i.e., to calibrate the sensor, the solution is to determine the inverse matrices inv(E) and inv(D) (or E) of these matrices E and D. -1 and D -1 This allows the corresponding inverse matrix to be applied to each chain. For ideal correction, the correct values ​​to be applied to the resonator and the correct detection values ​​are obtained, such as... Figure 7 As shown. Figure 8 The ideal calibration operation of the sensor is illustrated. Before inv(E) and inv(D) are injected into the servo control, inv(E) is applied to the output of the servo control Ass, and inv(D) is applied to the measurement at the output of the detection. Then, for the ideal calibration, we have FXe = FX and FYe = FY, and Xe = X and Ye = Y.

[0058] Document US9927256 describes a calibration method that enables the determination of corrections for at least one excitation control applied to a gyroscope tester: amplitude (control Ca). Phase (controls Cr), angle θ (controls Cp), orthogonality b (controls Cq).

[0059] The method involves sending a sinusoidal force (from a perturbation gyroscope tester) at a frequency close to the resonant frequency of a vibration sensor, and utilizing the detected output to extract the excitation error and detection error by assuming that the detected signal in the forced method has the same sinusoidal component as the perturbation. Because the system is linear, the detected signal is used to extract matrices A and B by using the fact that it has the same frequency characteristics as the inserted perturbation. These matrices A and B are then inserted into servo control, and the method is iterated to reach a predefined standard. However, apart from the general principles, no method is described for determining the coefficients of matrices A and B, and their role in the correction is not explained. The spirit of the method is to send specific excitation control and observe what happens in the detected signal. The sending of force on the excitation control causes waveform changes. Not all coefficients of matrices A and B can be observed (determined) through a set of observations provided by the excitation control, because the observations made in the detected signal exhibit much redundancy about each other, making some coefficients of A and B unobservable even if the number of equations seems sufficient relative to the number of unknowns in the system.

[0060] The purpose of this invention is to correct the shortcomings by proposing an alternative calibration method that allows the simultaneous determination of the inverse detection matrix and the inverse excitation matrix through direct matrix computation (where all terms of the matrix are observable). Summary of the Invention

[0061] The subject of this invention is a method for calibrating an inertial angle sensor, the inertial sensor comprising:

[0062] A resonator has a planar structure symmetrical about two vertical axes x and y, defining a sensor reference frame xy between the two vertical axes x and y. The resonator includes two vibrating moving masses arranged around each other and configured to vibrate out of phase at a vibrational frequency (ω) along a direction x' that defines the wave reference frame x'y'. The vibrational waves along x' form an electrical angle relative to the axis x.

[0063] The resonator also includes multiple electrostatic transducers, which are voltage-controlled and operate along at least one of two axes (x or y) on at least one of the two masses.

[0064] A pair of detection transducers and a pair of excitation transducers are provided. The detection transducers are configured to detect the motion of a vibration wave along x and y. Based on the detected motion, excitation forces are applied to the pair of excitation transducers along x and y respectively via multiple excitation controls determined by servo control. The pair of excitation transducers are used to maintain the vibration wave in a desired form and to vibrate along x'.

[0065] A pair of transducers for compensating for quadrature bias and a pair of frequency-adjusting transducers are provided. The pair of transducers for compensating for quadrature bias is controlled by quadrature control CTxy. The pair of frequency-adjusting transducers is controlled by frequency control CTx along x and frequency control CTY along y, respectively. The three controls CTx, CTY and CTxy are referred to as the i-indexed fine-tuning control CTi, where i = 1, 2, 3.

[0066] The method is applied while the sensor is operating according to the gyroscope tester mode, and the method includes the following steps:

[0067] A, for at least two electrical angles of the vibration wave:

[0068] A1, a sinusoidal stiffness perturbation PSi with a perturbation frequency fi is sequentially applied via each of the three fine-tuning controls CTi, and for each applied perturbation:

[0069] A11, based on the excitation control determined by the servo control, determines and stores the estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi.

[0070] B, based on the three estimated excitation forces Fei i = 1, 2, 3 stored in step A11, three 2×2 matrices M'i are determined according to the electrical angle and the applied perturbation. Matrix M'i represents the response of the gyroscope to the perturbation PSi.

[0071] C, Based on the three matrices M'i determined in step B, determine and store the estimated inverse excitation matrix. and the estimated inverse detection matrix The excitation matrix E and the detection matrix D represent the effects of the sensor's excitation chain and detection chain, respectively.

[0072] According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to the standard servo control of the sensor and an estimated disturbance compensation excitation force Fepi.

[0073] Furthermore, step B includes the following sub-steps:

[0074] B1, using the vibration frequency and then the associated perturbation frequency fi, demodulates each estimated excitation force Fei to obtain the amplitude of the perturbation-compensated excitation force Fepi.

[0075] B2, determine matrix M'i based on the magnitude of the force Fepi.

[0076] According to one embodiment, step A is performed using multiple electrical angles, and then the matrix M'i is determined in step B by statistically filtering to minimize the contribution of sensor noise.

[0077] According to one embodiment, each representative matrix M'i determined in step B has the following form:

[0078]

[0079] Mi is defined as follows: as well as

[0080] According to one embodiment, the matrix and It is considered to be close to a unitary matrix and is represented as:

[0081]

[0082]

[0083] Then, ignoring the second-order terms, the three representative matrices M'i determined in step B are represented as:

[0084] M'i=AMi+MiB

[0085] Furthermore, step C includes a sub-step of determining matrices A and B based on the matrix M'i.

[0086] Preferably, the disturbance frequencies fi i = 1, 2, 3 are between 1000 times and 100000 times less than the vibration frequency of the wave.

[0087] Preferably, the frequency fi is below 10Hz.

[0088] According to one embodiment, for all electrical angles, each perturbation PSi has the same magnitude.

[0089] According to one embodiment, each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to the standard servo control of the sensor and an estimated disturbance compensation excitation force Fepi, wherein the amplitude of the disturbance is selected such that the amplitude of force Fepi is at least 10 times the amplitude of force Fec.

[0090] The present invention also relates to a method for measuring the angular velocity of a carrier on which the inertial sensor is mounted, the method comprising:

[0091] A calibration phase for the inertial sensor implementing the calibration method claimed in any one of claims 1 to 9, said calibration phase being performed when the inertial sensor is started.

[0092] Step D of operating the inertial sensor, wherein the stored matrix is ​​applied. and The estimated inverse excitation matrix is ​​transmitted to the excitation transducer before being sent. An excitation force determined by the servo control is applied to pre-compensate the excitation force, and the estimated inverse detection matrix is ​​then applied. The detected motion value is applied to correct the detected motion value.

[0093] According to one variant, a method for measuring the angular velocity of a carrier on which the inertial sensor is mounted includes:

[0094] A calibration phase is performed on the inertial sensor implementing the calibration method claimed in any one of claims 1 to 9, said calibration phase being performed while the sensor is operating, after which the measurement of angular velocity is interrupted.

[0095] Step D', which measures the angular velocity, is performed during the calibration phase and is accomplished by an additional inertial sensor also mounted on the carrier.

[0096] Step D of operating the inertial sensor, wherein the stored matrix is ​​applied. and The estimated inverse excitation matrix is ​​transmitted to the excitation transducer before being sent. An excitation force determined by the servo control is applied to pre-compensate the excitation force, and the estimated inverse detection matrix is ​​then applied. The detected motion value is applied to correct the detected motion value.

[0097] The present invention also relates to an inertial angle sensor, comprising:

[0098] A resonator has a planar structure symmetrical about two vertical axes x and y, defining a sensor reference frame xy between the two vertical axes x and y. The resonator includes two vibrating moving masses arranged around each other and configured to vibrate out of phase at a vibrational frequency and along a direction x' of the defined wave reference frame x'y'. The vibrational wave (OV) along x' forms an electrical angle (θ) relative to the axis x.

[0099] The resonator also includes multiple electrostatic transducers, which are voltage-controlled and operate along at least one of two axes (x or y) on at least one of the two masses.

[0100] A pair of excitation transducers, to which excitation forces are applied along x and y respectively via multiple excitation controls to maintain the vibration wave in a desired form and vibrate along x'; and a pair of detection transducers configured to detect the motion of the vibration wave along x and y.

[0101] A pair of transducers for compensating for quadrature bias, controlled by a quadrature control CTxy; and a pair of frequency-adjustable transducers, controlled by a frequency control CTx along x and a frequency control CTy along y, respectively. The three controls CTx, CTY, and CTxy are referred to as the indexed fine-tuning control CTi, where i = 1, 2, 3.

[0102] The excitation control is determined by servo control based on the detected motion, and the sensor operates according to the gyroscope tester mode.

[0103] For at least two electrical angles (θj) of the vibration wave, three fine-tuning controls CTi are configured to sequentially apply sinusoidal stiffness perturbations PSi with perturbation frequencies fi.

[0104] The processing unit is configured as follows:

[0105] Based on the excitation control determined by the servo control, the estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi is determined and stored.

[0106] Based on the three estimated excitation forces Fei i = 1, 2, 3 stored in the previous step, as a function of the electrical angle and the applied perturbation, three 2×2 matrices M'i are determined, whereby matrix M'i represents the gyroscope's response to the perturbation PSi.

[0107] The estimated inverse excitation matrix is ​​determined and stored based on the three matrices M'i determined in the previous step. and the estimated inverse detection matrix The excitation matrix E and the detection matrix D represent the effects of the sensor's excitation chain and detection chain, respectively.

[0108] The estimated inverse excitation matrix is ​​transmitted before being sent to the excitation transducer. The estimated inverse detection matrix is ​​intended to be applied to an excitation force determined by the servo control, thereby pre-compensating for the excitation force, and when the sensor is in operation. The purpose is to be applied to the detected motion value to correct the detected motion value.

[0109] The following description presents several examples of embodiments of the apparatus of the present invention: these examples do not limit the scope of the invention. These examples of embodiments not only contain the essential features of the invention, but also contain additional features relevant to the embodiments discussed. Attached Figure Description

[0110] The invention will be better understood from the following detailed description, which is given with reference to the accompanying drawings, in which:

[0111] [ Figure 1 As already mentioned Figure 1 A MEMS sensor consisting of two vibrating moving masses arranged around each other is shown.

[0112] [ Figure 2 As already mentioned Figure 2 The structure of a MEMS sensor with resonators that are symmetric about two axes, x and y, that define the sensor reference frame is shown.

[0113] [ Figure 3 As already mentioned Figure 3 A MEMS sensor with transducers on two mass blocks is shown.

[0114] [ Figure 4 As already mentioned Figure 4 The operation of an inertial sensor according to the prior art is shown.

[0115] [ Figure 5 As already mentioned Figure 5 The effect of the excitation matrix on the value estimated by the servo control is shown, as well as the effect of the detection matrix on the motion of the vibration wave.

[0116] [ Figure 6 As already mentioned Figure 6 The effects of the excitation chain and the detection chain are shown using dashed and solid lines, respectively.

[0117] [ Figure 7 As already mentioned Figure 7 The ideal correction in excitation and detection is shown.

[0118] [ Figure 8 As already mentioned Figure 8 The ideal calibration procedure for the sensor is shown.

[0119] [ Figure 9 ] Figure 9 The estimated, and therefore imperfect, inverse excitation matrix determined by the method according to the invention is shown. The application of.

[0120] [ Figure 10 ] Figure 10 The estimated, and therefore imperfect, inverse detection matrix determined by the method according to the invention is shown. The application of.

[0121] [ Figure 11 ] Figure 11 A method for calibrating a sensor according to the present invention is shown.

[0122] [ Figure 12 ] Figure 12 An inertial angle sensor 10 implementing the calibration method according to the present invention is shown.

[0123] [ Figure 13 ] Figure 13 The sensor is shown in the operation of performing calibration according to the invention. Detailed Implementation

[0124] The calibration method according to the invention is applied to an inertial angle sensor comprising a resonator Res and transducers Et, Dt, TF, and TQ controlled by excitation control (Et) and fine-tuning control (TF, TQ) as described above. The vibration wave OV vibrates at a vibration frequency ω. When the inertial sensor is operated in gyroscope tester mode, the servo control of the excitation control is in operation.

[0125] The object of this invention is a calibration method that allows for the determination of the estimated inverse excitation matrix. and the estimated inverse detection matrix In order to improve sensor operation by minimizing excitation and detection errors.

[0126] Therefore, the disturbance is transmitted not through excitation control (as described in document US9927256), but through fine-tuning control. In the normal operation of a gyroscope that includes three additional transducers (which are not discussed in the documents cited above), these controls play a completely different role from the excitation control explained above.

[0127] In the following text, the fine-tuning controls CTx, CTy, and CTxy are referred to as CTi, i = 1, 2, 3, that is, CT1 for CTx, CT2 for CTY, and CT3 for CTxy.

[0128] This involves directly modifying the coefficients of differential equation (2) by inserting a new stiffness matrix Ktp through sinusoidal perturbations sent via these fine-tuning controls CTi, without modifying its right-hand side (i.e., the applied excitation force as described in the cited document). It should be noted that fine-tuning combs are used to modify the resonator, while excitation control is used to constrain its displacement.

[0129] like Figure 9 The incentives shown in the middle and Figure 10 The estimated matrix determined by the method according to the invention is shown in the figure for the detection. and It is not ideal, that is, they are not strictly equal to the inverses of matrix E and matrix D respectively: although they are closer to them, the product... and It is not equal to the identity matrix.

[0130] like Figure 11 As shown, the method 100 according to the present invention includes: a first step A: for at least two electrical angles θj of the vibration wave, performing a sub-step A1 in which a sinusoidal hardness perturbation PSi with perturbation frequency fi is sequentially applied via each of three fine-tuning controls CTi.

[0131] Therefore, a sinusoidal voltage of frequency fi is applied to the control CTi.

[0132] For each applied disturbance PSi, based on the excitation control determined by the servo control, during sub-step A11, an estimated excitation force Fei to be applied to the resonator to maintain linear vibration in the presence of the disturbance PSi is determined and stored. The characteristics of the resonator are altered by making its characteristics sinusoidal, and it is observed that a force with a linear wave needs to be applied.

[0133] The sinusoidal stiffness change corresponding to Kx in the stiffness matrix Ktp1 is generated by the sinusoidal stiffness perturbation PS1 applied by CT1:

[0134]

[0135] The sinusoidal stiffness change corresponding to the stiffness matrix Ktp2 is generated by the sinusoidal stiffness perturbation PS2 applied by CT2:

[0136]

[0137] The sinusoidal stiffness change corresponding to the Kxy of the stiffness matrix Ktp3 is generated by the sinusoidal stiffness perturbation PS3 applied by CT3:

[0138]

[0139] Then, during step B, based on the three estimated excitation forces Fei i = 1, 2, 3 stored in step A11, as a function of the electrical angle θj and the applied perturbation Psi, three 2×2 matrices M'i representing the gyroscope's response to the perturbation Psi are determined. A preferred calculation mode for matrix M'i is further described below.

[0140] Finally, in step C, the estimated inverse excitation matrix is ​​determined and stored based on the three matrices M'i determined in step B. and the estimated inverse detection matrix The excitation matrix E and the detection matrix D represent the effects of the sensor's excitation chain and detection chain, respectively.

[0141] Once these estimated matrices have been determined and stored, they are intended to be implemented during sensor operation, that is, when the sensor performs measurements: before being transmitted to the excitation transducer. The purpose is to apply excitation forces determined by servo control, thereby pre-compensating for these excitation forces; The aim is to apply the estimated inverse matrix to the detected motion values ​​to correct them. Therefore, the measured excitation and detection errors are minimized by applying the estimated inverse matrix.

[0142] In other words, by utilizing supplementary actuators that provide additional observability, included in certain MEMS gyroscope testers, the method according to the invention has the advantage of "easily" determining the detection and excitation faults through computation.

[0143] In fact, according to one embodiment, the method according to the invention is iterative, thus allowing for improved accuracy. Typically, no more than two iterations are required.

[0144] When the disturbance matrix Ktpi described above is applied to transducers TQ and TF, for the first variant in which only the disturbance PSi is applied without the application of conventional fine-tuning control (in which case fine-tuning servo control is not feasible), equation (2) becomes:

[0145]

[0146] For simplicity, Fi, represented as two components (FX, FY), is called the applied excitation force. Fi is decomposed into a standard excitation force Fc (FXc, FYc) for performing the current servo control of the sensor in the absence of disturbance, and a compensating excitation force Fpi (FXpi, FYpi) for compensating for the application of disturbance PSi:

[0147] It can be seen that the application of the perturbation results in modifications to some coefficients in differential equation (5) relative to the conventional equation (2):

[0148] Fi=Fc+Fpi; FXi=FXc+FXpi; FYi=FYc+FYpi

[0149]

[0150] The amplitude of the applied perturbation PSi is chosen such that the amplitude of (FXpi, FYpi) is at least 10 times the amplitude of (FXc, FYc). This choice makes the observed phenomenon more easily distinguishable from noise and easier to observe. However, the amplitude should not be increased excessively, as the control practically does not allow this to happen.

[0151] The force Fc controls the resonator in a conventional manner, such that the wave (e.g.) is linear and has a given amplitude, and obtains (in a manner similar to equation (1)):

[0152]

[0153] Due to the frequency difference between Fc and Fp, and due to the linearity of the system, it is possible to separate:

[0154]

[0155] According to the second variant, a perturbation PSi is applied in addition to the conventional fine-tuning control (matrix Kt) (fine-tuning servo control is then in operation). Equation (2) then becomes:

[0156]

[0157] Similarly, the conventional servo control of the resonator is represented as:

[0158]

[0159] And formula (7) is still proven to be correct.

[0160] Based on formulas (7) and (3) and (4), the excitation matrix E and the detection matrix D (also known as the excitation error matrix and the detection error matrix) are introduced:

[0161]

[0162] Where Fe(FXe, FYe): the estimated force used to control the oscillator, which is decomposed into force Fec(FXec, FYec) and force Fepi(FXepi, FYepi) according to the same logic as above:

[0163] Fec: The estimated standard excitation force used to perform routine servo control of the sensor in the absence of disturbances.

[0164] Fepi: The estimated compensating excitation force used to compensate for the application of disturbances.

[0165]

[0166] That is, FXei = FXec + FXepi and FYei = FYec + FYepi

[0167] The actual applied force has the following values:

[0168]

[0169] based on Extract The range.

[0170] FXec and FYec are sine functions of frequency ω.

[0171] FXepi and FYepi are sinusoidal functions of ω, which are modulated by a perturbation introduced in Ktpi (i.e. at frequency fi).

[0172] Theoretically, we get:

[0173] Because according to the definition, It is the force that counteracts disturbances.

[0174] For each fine-tuning comb and therefore for each applied perturbation PSi, and for the wave's vibration angle θ, theoretically we obtain:

[0175]

[0176]

[0177]

[0178] in:

[0179] X0 is the known amplitude of the vibration controlled by the servo controller.

[0180] ω is the known angular frequency of the resonator.

[0181] Ai is the known magnitude of the perturbation PSi.

[0182] fi is the known frequency of the perturbation PSi.

[0183] θ is the known angle to which the gyroscope is controlled.

[0184] For i=1, perform the calculation, and for i=2 and 3, the reasoning is the same.

[0185] The terms on the right and left sides of equation (9) have the same magnitude, therefore theoretically we have:

[0186]

[0187] Where AFXep1(θ) represents the magnitude of FXep1(θ).

[0188] The expectation is certainty. In order to derive from it the matrix M'1 defined as follows:

[0189]

[0190] in

[0191] Provide the force Fei (FXei, FYei) stored in step A11, that is, in this case:

[0192]

[0193] It is a sine wave at the angular frequency ω of the resonator.

[0194] It is a sine wave modulated by a sine function at an angular frequency of 2πf1 at the angular frequency ω of the resonator.

[0195] Demodulation is performed in the ω direction and then in the 2πf1 direction to determine The amplitude, to obtain (Demodulation is a well-known operation among technicians in various fields.)

[0196] Therefore, according to one embodiment of the present invention, step B includes:

[0197] Sub-step B1 involves demodulating each estimated excitation force Fei using the vibration frequency ω and then the associated perturbation frequency fi to obtain the amplitude AFpei (AFXpei, AFYpei) of the perturbation compensation excitation force Fepi (FXepi, FYepi).

[0198] Sub-step B2 determines matrix M'i based on the magnitude of force Fepi determined in B1.

[0199] According to one embodiment of the invention, each matrix M'i representing the response of the gyroscope tester to the disturbance M'i and determined in step B has the following form:

[0200]

[0201] Where Mi i = 1, 2, 3 is defined as follows: and

[0202] The method for determining M'i based on AFpei will now be explained.

[0203] We begin with equation (12):

[0204]

[0205] It can be in the following forms:

[0206]

[0207] A1, X0, θ, AFXep1(θ), and AFYep1(θ) are known.

[0208] M'1 has 4 unknowns (4 coefficients). Therefore, at least two angles are needed to obtain the four coefficients of M'1.

[0209] In fact, the process is performed for more than two angles, and typically least-squares type statistical filtering is performed to optimally estimate the coefficients of M'1. Therefore, according to one embodiment, step A is performed using multiple electrical angles, and then matrix M'i is determined in step B by minimizing the contribution of sensor noise through statistical filtering (e.g., least-squares type).

[0210] Therefore, based on equation (14) and the various known quantities, we provide a basis for... The estimated M'1 is:

[0211]

[0212] Perform the same procedure on M'2 and M'3.

[0213]

[0214]

[0215] It will now be shown that it is possible to determine the matrix M'i based on equations (15) to (17) in step B (using equation (14) and its equivalent equation for i = 2 and 3). and

[0216] This is a nonlinear problem, but because the electronic error is small, therefore and It is a matrix that is close to the identity matrix.

[0217] Therefore, they can be decomposed:

[0218]

[0219]

[0220] Where I represents the identity matrix, and eij and dij are small values ​​(typically less than 0.01).

[0221] therefore:

[0222] Ignore the second-order terms.

[0223] Based on the known M'i, A and B can be determined.

[0224] For M1:

[0225]

[0226] Therefore, d12 and e21, as well as e11+d11, were identified.

[0227] For M2:

[0228]

[0229] We obtained d21, e12, and e22+d22.

[0230] For M3:

[0231]

[0232] Thus, e22+d11 and e11+d22 are obtained, which allows for combination with e11+d11 ​​from (20) and e22+d22 from (21).

[0233] It should be noted that the equations e22+d11, e11+d22, e11+d11, and e22+d22 are not independent, and the system has rank 3: for example, (e22+d22)+(e11+d11)-(e11+d22)=e22+d11. Therefore, it is impossible to determine the four coefficients from the four equations. However, the right and left sides of equation (8) can be arbitrarily multiplied by any value. For example, it is possible to arbitrarily decide to divide all values ​​by (1+d11) such that d11 will be equal to 0 in the new system, thus eliminating the unknown and making it possible to determine the unknown e22, then d22, and then e11.

[0234] Therefore, according to one embodiment of the method according to the invention, the three representative matrices M'i (ignoring second-order terms) determined in step B are represented in the form M'i = AMi + MiB, and step C includes a sub-step of determining matrices A and B (eight coefficients) based on said matrix M'i. Thus, using the claimed method, all eight coefficients are observable. Then, the matrices are determined based on A and B (equations (18) and (19)). and

[0235] By simulating the actual behavior of the gyroscope in detail, it is possible to determine the simulated coefficients of matrices E and D. When using these simulated coefficients and those determined by the method according to the invention... and The computational complexity of the coefficient values and At that time, an identity matrix with an error between 10 ppm and 200 ppm was obtained, which constitutes the... and A very high degree of accuracy in estimation.

[0236] To ensure that the stiffness changes slowly enough in equation (8) to be considered constant, it is preferable to choose frequencies f1, f2, and f3 of the disturbances PS1, PS2, and PS3 that are much lower than the vibration frequency ω, typically between a factor of less than 1000 and less than 100000. Since the vibration frequency of the wave is typically on the order of approximately ten kHz, frequencies f1, f2, and f3 are typically below 10 Hz or even below one Hz.

[0237] Furthermore, the frequencies f1, f2, and f3 of the disturbances to PS1, PS2, and PS3 are preferably selected to be greater than the frequencies of the physical phenomena responsible for sensor drift or, more specifically, those related to changes in sensor temperature. These phenomena typically have frequencies much lower than one Hz or even less than one-tenth of a Hz.

[0238] Therefore, preferably, the frequencies f1, f2 and f3 are greater than 0.1 Hz.

[0239] Preferably, frequencies f1, f2, and f3 are injected separately; therefore, these frequencies can be equal. However, this is not important for the implementation of the method.

[0240] Figure 12 An inertial angle sensor 10 implementing the calibration method 100 according to the present invention is shown. A disturbance PSi is sequentially applied to transducers TQ or TF. The processing unit UT performs a reference frame change on the estimated motion (Xe, Ye) of the obtained vibration, and then calculates the estimated excitation control for the sensor's servo control (servo 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). Based on these forces, the processing unit determines the matrix. and The coefficients are calculated and stored.

[0241] Figure 13 The sensor in operation is shown, meaning that calibration has been completed during the angular velocity measurement process, and the matrix... and It will be stored. The processing unit will... Applying motion measured by a sensor, and An excitation force estimated by the servo control is applied. The servo control (not shown) is then fine-tuned to operate in the normal manner.

[0242] Calibration methods can be implemented according to multiple usage modes.

[0243] For all modes, once calibration has been performed and the estimated inverse excitation matrix is ​​sent to the excitation transducer while the sensor is in operation. An excitation force determined by servo control is applied, thereby pre-compensating the excitation force, and the estimated inverse detection matrix is ​​then applied. It is applied to the detected motion value to correct the detected motion value.

[0244] In the first mode of use, a calibration phase for the inertial sensor implementing the method 100 according to the invention is typically performed at the output of the manufacturing chain (factory calibration) before the sensor is put into operation. The inverse excitation and detection matrix is ​​stored in the processing unit. Then, while the sensor is in operation and performing a measurement, the inverse excitation and detection matrix is ​​applied.

[0245] According to a second mode of use, the present invention relates to a method for measuring the angular velocity of a carrier on which an inertial sensor 10 is mounted, comprising implementing a calibration method 100 according to the invention and a calibration phase performed upon sensor startup. Once calibration is complete, step D involves applying a stored matrix. and Measurement.

[0246] According to a third mode of use, the present invention relates to a method for measuring the angular velocity of a carrier on which an inertial sensor 10 is mounted, comprising implementing a calibration method 100 according to the invention and a calibration phase implemented during operation. During the calibration phase, the inertial sensor cannot perform measurements, and therefore, the measurement of angular velocity by the sensor 10 is interrupted during the calibration phase.

[0247] While the sensor 10 is being calibrated, the method performs step D' of measuring angular velocity, which is performed by an additional inertial sensor also mounted on the carrier, and this step is performed to ensure the continuity of the measurement.

[0248] Once calibration is complete, sensor 10 applies the stored matrix in step D. and The measurement is used to re-establish control over the measurement.

[0249] For example, switching from one sensor to another can be implemented periodically over time, thereby allowing calibration to be performed throughout the entire duration of operation of sensor 10.

[0250] By simulating the actual behavior of the gyroscope in detail, it is possible to determine the simulation coefficients of matrices E and D.

[0251] When determined using the method according to the invention and The computational complexity of the coefficient values and An identity matrix with an error between 10 ppm and 200 ppm was obtained, which is very high precision.

Claims

1. A method (100) for calibrating an inertial angle sensor (10), the sensor comprising: A resonator (Res) has a planar structure symmetrical about two vertical axes x and y, defining a sensor reference frame xy between the two vertical axes x and y, and the resonator includes two vibrating moving masses (M1 and M2) arranged around each other and configured to vibrate out of phase at a vibrational frequency (ω) along a direction x' defining the wave reference frame x'y', the vibrational wave (OV) along x' forming an electrical angle (θ) relative to the axis x. The resonator also includes a plurality of electrostatic transducers, which are voltage-controlled and operate along at least one of the two axes x or y on at least one of the two masses. A pair of detection transducers (Dt) configured to detect the motion of the vibration wave along x and y; and a pair of excitation transducers (Et) that apply excitation forces along x and y respectively via multiple excitation controls determined by servo control based on the detected motion, and the pair of excitation transducers are used to maintain the vibration wave in a desired form and vibrate along x'. A pair of transducers (TQ) for compensating for quadrature bias, controlled via quadrature control CTxy, and a pair of frequency-adjusting transducers (TF), controlled via frequency control CTx along x and frequency control CTy along y, respectively. These three controls CTx, CTY, and CTxy are referred to as i-indexed fine-tuning controls CTi, where i = 1, 2, 3. The method is applied while the sensor is operating according to a gyroscope tester mode, and the method includes the following steps: A, for at least two electrical angles (θj) of the vibration wave: A1, a sinusoidal stiffness perturbation PSi with a perturbation frequency fi is sequentially applied via each of the three fine-tuning controls CTi, and for each applied perturbation: A11, based on the excitation control determined by the servo control, determines and stores the estimated excitation force Fei to be applied to the resonator in the presence of the disturbance PSi. B. Based on the three estimated excitation forces Fei stored in step A11, where i = 1, 2, 3, as a function of the electrical angle and the applied perturbation, determine three 2×2 matrices M'i, where matrix M'i represents the response of the gyroscope to the perturbation PSi. C, Based on the three matrices M'i determined in step B, determine and store the estimated inverse excitation matrix. and the estimated inverse detection matrix The excitation matrix E and the detection matrix D represent the effects of the excitation chain and the detection chain of the sensor, respectively.

2. The method according to claim 1, wherein, Each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to the standard servo control of the sensor and an estimated disturbance compensation excitation force Fepi. Furthermore, step B includes the following sub-steps: B1, using the vibration frequency (ω) and then the associated perturbation frequency fi, demodulate each estimated excitation force Fei to obtain the amplitude (AFpei) of the perturbation compensation excitation force Fepi. B2, the matrix M'i is determined based on the magnitude of the force Fepi.

3. The method according to claim 1 or 2, wherein, Step A is performed using multiple electrical angles, and then the matrix M'i is determined in step B by statistically filtering to minimize the contribution of the sensor's noise.

4. The method according to claim 1 or 2, wherein, Each representative matrix M'i determined in step B has the following form: Mi is defined as follows: as well as 5. The method according to claim 4, wherein, The matrix and It is represented as: Where I is the identity matrix, and then, ignoring second-order terms, the three representative matrices M'i determined in step B are represented as: M'i=AMi+MiB Furthermore, step C includes a sub-step of determining matrices A and B based on the matrix M'i.

6. The method according to claim 1 or 2, wherein, The disturbance frequency fi, where i = 1, 2, 3, is between 1000 times less than the vibration frequency (ω) of the wave and 100000 times less than the vibration frequency (ω) of the wave.

7. The method according to claim 1 or 2, wherein, The frequency fi is below 10Hz.

8. The method according to claim 1 or 2, wherein, For all the electrical angles, each perturbation PSi has the same magnitude.

9. The method according to claim 1 or 2, wherein, Each estimated excitation force Fei is decomposed into an estimated standard excitation force Fec corresponding to the standard servo control of the sensor and an estimated disturbance compensation excitation force Fepi, wherein the amplitude of the disturbance is selected such that the amplitude of the force Fepi is at least 10 times the amplitude of the force Fec.

10. A method for measuring the angular velocity of a carrier, wherein an inertial sensor (10) is disposed on the carrier, the method comprising: A stage for calibrating the inertial sensor according to the calibration method (100) of any one of claims 1 to 9, the calibration stage being implemented when the inertial sensor is started. Step D of operating the inertial sensor, wherein the stored matrix is ​​applied. and The estimated inverse excitation matrix is ​​transmitted to the excitation transducer before being sent. The excitation force determined by the servo control is applied to pre-compensate the excitation force, and the estimated inverse detection matrix is ​​then applied. The detected motion value is applied to correct the detected motion value.

11. A method for measuring the angular velocity of a carrier, wherein an inertial sensor (10) is disposed on the carrier, the method comprising: A calibration phase is performed on the inertial sensor implementing the calibration method (100) according to any one of claims 1 to 9, the calibration phase is performed while the sensor is operating, and then the measurement of the angular velocity is interrupted. Step D', which measures the angular velocity, is performed during the calibration phase and is implemented by an additional inertial sensor also mounted on the carrier. Step D of operating the inertial sensor, wherein the stored matrix is ​​applied. and The estimated inverse excitation matrix is ​​transmitted to the excitation transducer before being sent. The excitation force determined by the servo control is applied to pre-compensate the excitation force, and the estimated inverse detection matrix is ​​then applied. The detected motion value is applied to correct the detected motion value.

12. An inertial angle sensor (10), comprising: A resonator (Res) has a planar structure symmetrical about two vertical axes x and y, defining a sensor reference frame xy between the two vertical axes x and y, and the resonator includes two vibrating moving masses (M1 and M2) arranged around each other and configured to vibrate out of phase at a vibrational frequency (ω) along a direction x' defining the wave reference frame x'y', the vibrational wave (OV) along x' forming an electrical angle (θ) relative to the axis x. The resonator also includes a plurality of electrostatic transducers, which are voltage-controlled and operate along at least one of the two axes x or y on at least one of the two masses. A pair of excitation transducers (Et) are provided with excitation forces applied along x and y respectively via multiple excitation controls to maintain the vibration wave in a desired form and to vibrate along x'; and a pair of detection transducers (Dt) are configured to detect the motion of the vibration wave along x and y. A pair of transducers (TQ) for compensating for quadrature bias, controlled via quadrature control CTxy; and a pair of frequency-adjusting transducers (TF), controlled via frequency control CTx along x and frequency control CTy along y, respectively. These three controls CTx, CTY, and CTxy are referred to as indexed fine-tuning controls CTi, where i = 1, 2, 3. The excitation control is determined by servo control based on the detected motion, and the sensor operates according to the gyroscope tester mode. For at least two electrical angles (θj) of the vibration wave, the three fine-tuning controls CTi are configured to sequentially apply sinusoidal stiffness perturbations PSi with perturbation frequencies fi. Processing unit (UT), the processing unit being configured to: For each applied perturbation, based on the excitation control determined by the servo control, an estimated excitation force Fei to be applied to the resonator in the presence of the perturbation PSi is determined and stored. Based on the three estimated excitation forces Fei stored in the previous step, where i = 1, 2, 3, as a function of the electrical angle and the applied perturbation, three 2×2 matrices M'i are determined, representing the response of the gyroscope to the perturbation PSi. The estimated inverse excitation matrix is ​​determined and stored based on the three matrices M'i determined in the previous step. and the estimated inverse detection matrix The excitation matrix E and the detection matrix D represent the effects of the excitation chain and the detection chain of the sensor, respectively. The estimated inverse excitation matrix is ​​transmitted before being sent to the excitation transducer. The excitation force is intended to be applied to the servo control, thereby pre-compensating the excitation force, and the estimated inverse detection matrix is ​​used when the sensor is in operation. The purpose is to be applied to the detected motion value to correct the detected motion value.

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