Method for correcting the measurement of a vibrating inertial angle sensor

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The field of the invention is that of vibrating inertial sensors in which at least two masses are vibrated, or even a single mass comprising at least two parts, one mass or one part of a mass being capable of deforming relative to the other. Without this being limiting, the invention relates in particular to MEMs type inertial sensors which may have a planar structure, for example sensors micro-machined in a support plate. The invention relates to a method of angular measurement (angle or angular speed) and in particular a method of correcting such a measurement. STATE OF THE ART

[0002] Vibrating (or tuning fork) inertial sensors are known to those skilled in the art. A vibrating inertial sensor comprises a resonator, which may be axisymmetric, but not necessarily, associated with means for setting the resonator into vibration and with means for detecting an orientation of the vibration (vibration wave) relative to a frame of reference of the sensor. These means generally comprise at least two groups of actuators secured to the sensor housing and / or the resonator and at least two groups of detectors also secured to the housing and / or the resonator.

[0003] For the sake of simplification, an angular inertial sensor may be referred to interchangeably throughout this description as “inertial sensor” or “angular sensor” or even “sensor”.

[0004] Such a sensor is arranged on a carrier in order to measure the angle and / or angular velocity values ​​of said carrier. The carrier may be all or part of an airplane, a boat, a train, a truck, a car, a satellite or any other air, land or sea vehicle.

[0005] In particular, there are inertial sensors micro-machined in a thin flat plate, allowing the measurement of an angular position (gyroscope) or an angular speed (gyrometers), which are described in particular in document EP2960625. Their main characteristics are recalled below.

[0006] The manufacture of these micro-machined sensors, also known as "MEMS" sensors (for "Micro-Electro-Mechanical-Systems" in English), uses collective micro-machining techniques, etching, doping deposition, etc., similar to those used for the manufacture of electronic integrated circuits, allowing low production costs.

[0007] The MEMS sensors described in application EP2960625 consist of two vibrating moving masses M1 and M2 illustrated in Figure 1 arranged around each other concentrically and excited in tuning fork mode vibration in the plane of the plate (xy plane on the Figure 1 ) via one or more excitation transducers. The two masses are suspended from fixed anchor points A of the plate by suspension springs RS (orthotropic). The two masses are coupled together by stiffness elements RC. The aim is generally to obtain by construction a stiffness along x equal to a stiffness along y and a coupling stiffness between x and y zero. The useful vibration mode corresponds to a linear vibration of the two masses in phase opposition.

[0008] More generally, it may involve more than two moving masses, for example four moving masses, or conversely a single mass comprising at least two parts, one being capable of deforming relative to the other, for example on a hemispherical resonant micro gyrometer (µGRH).

[0009] The structure described in application EP2960625 forms a resonant system (called a "resonator") with two masses coupled together by the Coriolis acceleration. When the sensor rotates around the z axis perpendicular to the xy plane, the z axis being called the "sensitive axis", the composition of the forced vibration with the angular rotation vector generates, by the Coriolis effect, forces which put the moving masses into natural vibration perpendicular to the excitation vibration and to the sensitive axis; the amplitude of the natural vibration is proportional to the rotation speed. The electronics associated with the sensor calculates the amplitude of the natural vibration according to the direction orthogonal to the excitation direction, whatever this may be (known by hypothesis).

[0010] The sensor can operate in gyrometer mode: the excitation direction is kept fixed by changing the excitation, and therefore the axis perpendicular to this vibration is kept fixed relative to the sensor housing and the output information is then an image of the necessary energy that must be applied to the excitation transducers to keep the natural vibration direction fixed despite the movements of the housing. The measurement of this energy (or "counter force") gives access to the angular velocity Ω of the sensor.

[0011] The sensor can also operate in gyroscope mode: the direction of the excitation vibration is left free and is detected to give the angular orientation of the sensor compared with to an inertial reference frame, which can also be simply called “angle”. We can also deduce the angular velocity of the sensor by deriving the angle measurement.

[0012] The entire structure of the resonator described in application EP2960625 is axisymmetric around the two axes x and y defining a sensor reference frame as illustrated in Figure 1 . Axisymmetric means that the structure is symmetrical about x and symmetrical about y. But it should be understood that this definition can cover all possible minor asymmetries. As described below, these axes constitute the main directions of actuators and detectors, which operate along these two axes.

[0013] To excite the useful vibration mode in any given direction of the plane, the excitation signal is decomposed into two components of respective adjusted amplitudes. As illustrated in Figure 2, the two amplitude components can be applied respectively to the excitation transducer Ex acting in the x direction and to the excitation transducer Ey acting in the y direction, the two excitation transducers being associated with at least one mobile mass (internal mass M1 on the Figure 2 ). Excitation forces are therefore applied to these transducers to generate and maintain the vibration wave: they are able to maintain the forced vibration via an amplitude control Ca (to combat the sensor damping) and in any direction of the xy plane, via a precession control Cp (to rotate the wave).

[0014] The x' axis is called the vibration axis of the wave. This axis defines an x'y' coordinate system, with y' perpendicular to x' in the plane of the sensor (as a reminder, the main axes of the sensor are x and y). The x' axis makes an angle Θ with the x axis called the "electric angle" and the x'y' coordinate system is called the "wave coordinate system". This is illustrated in Figure 3 .

[0015] The excitation forces FX and FY applied along the x axis and the y axis of the sensor come from commands Cr, Ca, Cq and Cp calculated in the wave frame by servocontrols known to those skilled in the art, from the demodulation of the detected signals relating to the displacement of the vibration. From the measurements of the movement of the X and Y waves made in the xy frame, a rotation is applied to pass into the x'y' wave frame, then the commands are determined (via a demodulation of detected signals) and a reverse rotation is reapplied to pass back into the xy sensor 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 sensor, takes a desired shape. Generally the desired shape of the wave is an oscillating linear displacement in the x' direction relative to the xy frame of the sensor.But the wave is generally elliptical in shape, substantially flat in the direction perpendicular to the x' direction (in other words the minor axis of the ellipse is very small relative to the major axis, which major axis corresponds to the given direction).

[0016] The Cr control corresponds to the stiffness forces to control the natural frequency of the resonator. Since the phase is related to the integral of the frequency, Cr therefore controls the phase of the wave.

[0017] The Ca command corresponds to the amplitude forces to compensate for the effect of the sensor damping forces and keep the vibration amplitude constant: it therefore allows the amplitude of the wave to be controlled.

[0018] The Cp command corresponds to the precession forces which control the angular velocity of the wave.

[0019] In the case of a sensor operating in gyrometer mode, a precession command Cp is applied so as to control the orientation of the vibration (or electrical angle) to a constant setpoint value.

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

[0021] The movements of the resulting wave are detected by combining the information collected by at least one pair of detection transducers Dx, Dy recovering the position of the mass in its travel in the sensor frame xy and associated with at least one mobile mass (M1 on the Figure 2 ). In the Figure 2 , two pairs of detection transducers Dx, Dy are shown.

[0022] According to a known and advantageous variant, transducers can be produced on the two masses M1 and M2 (not shown). Figure 2 and this variant constitute non-limiting examples of arrangement, many other types of arrangement are possible, with the constraint of producing an axisymmetric system.

[0023] The sensor thus formed from a resonator Res associated with the excitation transducers E and detection transducers D is connected to a processing unit UT, as illustrated in Figure 3. FX and FY are the excitation forces applied along the x-axis and the y-axis of the sensor, X and Y are the measurements of the wave motion in the sensor frame xy. The vibration wave OV vibrates along x' with an electrical angle θ. The processing unit UT performs the various calculations for the servocontrols and generates, for the corrections, all the aforementioned commands / forces Cr, Ca, Cq and Cp to the different transducers. In the processing unit UT, the detected movements X and Y are first transformed into the wave frame x'y' by a rotation along θ then the excitation commands are determined in the wave frame by servocontrols in the form of electrical voltages U'x and U'y with, for example: U x ′ = iC a + C r U y ′ = iC p + C q

[0024] The transducers are preferably made of interdigitated comb electrodes with air gap variation. There is a fixed comb whose teeth are secured to a fixed mass of the machined plate and a mobile comb whose teeth, interdigitated with the teeth of the fixed comb, are secured to the mobile mass associated with the transducer considered.

[0025] Excitation consists of applying an excitation force via an alternating voltage between the moving comb and the fixed comb, at the desired vibration frequency (mechanical resonance frequency of the suspended moving mass, typically of the order of a few KHz). The movement generated is perpendicular to the teeth of the comb.

[0026] Detection involves applying a bias voltage between the fixed comb and the moving comb and observing the charge variations that result from the capacitance variations between the fixed comb and the moving comb due to the spacing variations between the teeth of the fixed comb and the moving comb. The movement measured is the movement perpendicular to the comb teeth. Alternatively, in another configuration, the longitudinal movement to the comb teeth can be measured.

[0027] Due to manufacturing defects, the measurements provided by these axisymmetric vibrating inertial sensors exhibit measurement defects or “drifts” (defect in estimating the angular speed in gyrometer mode or the angle in gyroscope mode), and have the effect of degrading the level of precision of the values ​​thus measured, whether they are used in gyroscope mode or in gyrometer mode.

[0028] It is known that the sensor drift varies as a function of the electrical angle θ. It is also known that an axisymmetric vibrating inertial sensor has, after calibration of electronic and balancing defects, a very low average drift (which is defined as the drift obtained by averaging the drifts obtained for different uniformly distributed electrical angles), typically between ten and one hundred times lower than the maximum drift of said sensor for a given electrical angle.

[0029] To measure an angular velocity or an angle whose default is the average drift, one solution is to rotate the vibration wave. To be able to rotate the vibration wave, a rotation command must be sent, which will be found in the output signal. Removing this rotation command (although known) from the sensor output is not simple because the said command is distorted by the sensor's transfer function between the injected command and the command found on the signal of the said sensor, and it is therefore not enough to simply remove the rotation command to find the useful signal.

[0030] By sensor transfer function we mean the function which has as input an injected angular velocity and as output the measured angular velocity.

[0031] Many patents exploit the rotational wave control and its correction, for example in US patent 6,598,455 B1 which relates to a method for calibrating a vibrating MEMS gyroscope comprising introducing a simulated rotational signal into the gyroscope, detecting the motion created by the simulated rotational signal and combining a correction signal for the detected motion with the simulated rotational signal. Specifically, electrostatic elements already present in the vibrating MEMS gyroscope are used to simulate Coriolis forces, and the simulated rotational signal is added to the closed-loop excitation force rebalancing system to perform inertial testing on vibrating MEMS gyroscopes, without the use of a rotation table.However, sending such a signal disrupts the sensor measurement and generates errors due to the scale factor, and the aforementioned patent does not provide any means to eliminate these generated errors if we want to use the method in real time and not only during a calibration.

[0032] By scale factor, we mean the ratio between the angular speed (or more broadly angular value) measured at the output, at which the measurement bias has been removed and the angular speed (or more broadly angular value) commanded at the input (injected electrically for an electrical scale factor or by rotation of the sensor for a mechanical scale factor).

[0033] Solutions are known to cancel the scale factor error, and reduce the errors generated by the previously described solution. Patent application EP0392104 A1 for example describes a sensor in which the sensitive axis is rotated by 180° to cancel the scale factor error. In other patent applications FR 2 937 414, FR 2 959 009 and FR 2 958 029, the solutions for canceling the scale factor error which correspond to a combination of the patents US 6,598,455 B1 and EP0392104 A1 previously described and consist of sending a command to rotate the wave on a setpoint value adapted to rotate the wave in one direction then in the opposite direction, with a zero-average control signal over a given period of time (FR 2 937 414 and FR 2 958 029), and possibly by adding a step where the time derivative of the setpoint is deduced from the command (FR 2 958 029).In these two patents FR 2 937 414 and FR 2 958 029, the problem is that it is not enough to remove the introduced command to cancel the errors induced by said command on the sensor, because said rotation command is distorted by the transfer function of the sensor, as explained further. Thus, these solutions induce new errors in the measurement. Furthermore, in patent application FR 2 959 009, it is planned to eliminate these new errors induced by the rotation command of the wave, by using an external reference sensor. Thus, the error introduced by the command is compensated using an additional external sensor.

[0034] Other methods and devices for calibrating the scale factor of a vibrating gyroscope with an axisymmetric resonator are also described in documents WO 2010 / 072922 A1, WO 2016 / 189078 A1 and FR 2 939 192 A1.

[0035] Thus, the proposed solutions are based on rotation commands that generate new errors. We note that rotating the wave in one direction permanently allows us to benefit from the average drift but a new drift generated by the scale factor appears, and that rotating the wave in one direction then in the opposite direction induces errors that cannot be easily removed due to the sensor transfer function. In addition, the use of an external measurement providing a reference output value generates a larger, more expensive system that consumes more power.

[0036] The invention aims to overcome the aforementioned drawbacks of the prior art.

[0037] More specifically, it aims to provide a method for correcting the measurement of an inertial sensor, which allows measurement errors to be reduced and which does not require an additional reference sensor. STATEMENT OF THE INVENTION

[0038] A first object of the invention making it possible to overcome these drawbacks is a method for correcting the measurement of an inertial sensor, said inertial sensor being arranged on a carrier and comprising a resonator extending around two axes x and y perpendicular to each other defining a sensor reference frame xy and comprising: at least one vibrating mobile mass, said at least one mobile mass comprising at least two parts configured to vibrate in phase opposition to a vibration pulse and in a direction x' defining a wave reference frame x'y', the vibration wave along x' making an electrical angle θ relative to the x axis; a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, said transducers comprising at least: -- 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 servocontrols from the detected movements, configured to maintain the wave at a constant amplitude via an amplitude command and, optionally, to rotate said vibration wave via a precession command; the correction method being applied when the sensor is in operation with a vibration wave vibrating along the x' axis; said method comprising the steps consisting, when the wearer is substantially stationary, in: ; Acontrolling an electrical rotation of the vibration wave according to a controlled angular value Ωc, such that the electrical angle θ sweeps at least an angular range of kπ radians, k being an integer greater than or equal to 1, according to which the angular value is included in the set comprising an angular speed and an angle; then B recovering the angular values ​​measured Ωe by the inertial sensor over the angular range of kπ radians of the electrical angle θ for the commanded angular value Ωc, and determining the average Ωem of said angular values ​​measured over said angular range; then C subtract the commanded angular value Ωc from the average Ωem of the measured angular values; the steps A has C being carried out for at least two different commanded angular values ​​so as to determine at least two averages of the measured angular values; then Ddetermine: the average electrical scale factor error FEem, the electrical scale factor corresponding to the ratio between the measured angular value due to the electrical rotation command and la commanded angular value Ωc, and the actual angular value Ωv of the wearer added to a drift value Dm of the sensor, said determination being carried out from the commanded angular values ​​Ωc and the averages Ωem of the measured angular values, according to the formula: Ω em − Ω c = Ω v + Dm + FEem . Ω c .

[0039] The angular value measured by the sensor is defined as either an angular velocity (in gyrometer mode) or an angle (in gyroscope mode) of the wearer. It can be referred to as the "estimated" angular value. Similarly, the actual angular value of the wearer is defined as either the actual angular velocity or the actual angle of said wearer.

[0040] By "average" is meant an average over different electrical angles distributed, preferably uniformly, over the angular range of kπ radians.

[0041] By "substantially stationary" carrier, we mean that the carrier has zero dynamics (e.g., the carrier is a stationary aircraft with no passengers or crew on board) or low dynamics (e.g., the carrier is a stationary aircraft with passengers and / or crew on board). In other words, low dynamics corresponds to rolling and pitching movements of the order of a few degrees and translational movements along the vertical axis so that the horizontal accelerometers detect the rotation, with a heading considered constant. Alternatively to an aircraft, it can be a boat, a train, a truck, a car, a satellite or any air, land or sea vehicle.

[0042] The present invention consists of controlling a rotation of the vibration wave when the dynamics of the carrier are zero or at least low, so as to be able to eliminate the defects generated on the measurement signal by the rotation control.

[0043] With an alternating rotation command (rotation in one direction and another) and at zero mean, the error generated by the change of rotation is high and comes from the fact that the bandwidth of the sensor is not infinite. At the time of the change of direction of rotation, the sensor sees a step at the input and the error on the measurement will be the high frequency part of the step not taken into account in the transfer function of the sensor. In other words, the commanded rotation has a limited spectrum (like any physical signal that does not have infinite energy). If part of the spectrum is outside the bandwidth of the sensor, it will not be detected by the sensor and therefore if we subtract the injected rotation command at the output (we must remove it because it is not a physical rotation of the carrier), there will remain an error linked to the fact that the sensor has only detected part of the commanded rotation.According to the invention, an alternating rotation with zero mean is not commanded.

[0044] With a non-alternative command sent, corresponding to the preferred embodiment of the invention, there will be an error when the rotation command is stopped or if different rotation speeds are commanded. The origin of the error is the same as for an alternative rotation command with zero mean, as described above. It is possible to introduce the command into a known transfer function model of the gyrometer, however this mathematical representation may not be sufficiently precise (in any case not sufficiently to obtain the desired orders of magnitude of precision of the order of a few tens of µrad), so the invention consists in evaluating the consequences of this transfer function through a known type of command during a navigation phase where the movements of the wearer are known so as to remove this error during navigation.

[0045] The correction method according to the invention may further comprise one or more of the following characteristics taken in isolation or in any possible technical combination.

[0046] According to one embodiment, the correction method comprises an additional step consisting, when the wearer is substantially stationary, in: E determining the periodic drift D(θ) of the sensor as a function of the electrical angle θ and the periodic electrical scale factor error FEe(θ) as a function of the electrical angle θ, from measured angular values ​​Ωe during at least one revolution or a fraction of a revolution during an electrical rotation at a commanded angular speed Ωc, according to the formula: Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c

[0047] According to one embodiment, the correction method comprises a complementary step consisting, the wearer not necessarily being stationary, in: F determining the real angular value Ωv of the wearer added to a drift value Dm of the sensor, by removing the periodic drift D(θ) and the periodic electrical scale factor error FEe(θ) determined in step E.

[0048] According to one embodiment, in which the wearer has zero dynamics, the real angular value Ωv is equal to a projection Ωtp in the xy frame of reference of the Earth's rotation sensor, considered constant.

[0049] According to one embodiment, in which the carrier has a low but non-zero dynamic, said real angular value Ωv is equal to a projection Ωtp in the xy frame of reference of the sensor of the earth's rotation considered constant, the variations in angular speed determined by at least one accelerometer on the carrier being subtracted. Preferably, the variations in angular speed are determined by at least two accelerometers, and the heading is considered fixed on average.

[0050] According to one embodiment, the rotation command is applied in one direction according to the angular range of kπ radians and then in the opposite direction according to the angular range of kπ radians. Alternatively, according to a preferred embodiment, the rotation command is always applied in the same direction.

[0051] According to one embodiment, the correction method comprises an additional step consisting, the wearer not necessarily being stationary, of:G correcting the mean electrical scale factor FEem by the variation ΔFEem of the mean electrical scale factor error between strong dynamics and weak or zero dynamics, said variation ΔFEem being determined by spectrally separating the angular velocity command of the wave Ωc from the actual angular value Ωv.

[0052] A second object of the invention is an inertial angular sensor, said inertial sensor being arranged on a carrier and comprising a resonator extending around two axes x and y perpendicular to each other defining an xy sensor reference frame and comprising: - at least one vibrating mobile mass, said at least one mobile mass comprising at least two parts configured to vibrate in phase opposition to a vibration pulse and in a direction x' defining a wave reference x'y', the vibration wave along x' making an electrical angle θ relative to the x axis; - a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, including 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 servocontrols from the detected movements, configured to maintain the wave at a constant amplitude via an amplitude command and, where appropriate, to rotate said vibration wave via a precession command; the inertial angular sensor further comprising: a control and / or processing unit adapted to implement the steps of the correction method according to the first subject of the invention.;

[0053] According to one embodiment, the inertial sensor is axisymmetric.

[0054] According to one embodiment, the inertial sensor comprises at least two vibrating moving masses forming the at least two parts configured to vibrate in phase opposition with respect to each other, one moving mass being able to be arranged around another moving mass.

[0055] The correction method and the inertial sensor according to the invention may comprise any of the characteristics previously stated, taken in isolation or in any technically possible combination with other characteristics.

[0056] The following description presents several exemplary embodiments of the device of the invention: these examples are not limiting of the scope of the invention. These exemplary embodiments present both the essential characteristics of the invention as well as additional characteristics linked to the embodiments considered. BRIEF DESCRIPTION OF THE FIGURES

[0057] Other characteristics, details and advantages of the invention will emerge from reading the description given with reference to the appended figures given by way of example and which represent, respectively: [ Fig. 1 ] There Figure 1 already cited illustrates the axisymmetric resonator of a state-of-the-art MEMS inertial sensor, consisting of two vibrating moving masses arranged around each other. Fig. 2 ] There Figure 2 already cited illustrates the structure of a state-of-the-art MEMS inertial sensor with an axisymmetric resonator around two x and y axes defining a sensor frame. Fig. 3 ] There Figure 3 already cited illustrates the operation of an inertial sensor according to the state of the art. [ Fig. 4 ] There Figure 4 illustrates a correction method according to the invention.

[0058] Throughout these figures, like references may designate identical or similar elements.

[0059] Furthermore, the different parts represented in the figures are not necessarily on a uniform scale, to make the figures more readable. DETAILED DESCRIPTION OF THE INVENTION

[0060] The correction method according to the invention applies to an inertial angular sensor comprising a resonator Res associated with means for setting the resonator into vibration and with means for detecting an orientation of the vibration (vibration wave) relative to a reference point of the sensor.

[0061] The invention can be applied in particular to one of the sensors presented previously, in relation to the figures 1 to 2 , or to sensors according to the variants also previously described (at least one mass or at least two masses, axisymmetric or non-axisymmetric sensor, planar or non-planar structure, the MEMS sensor being an exemplary embodiment).

[0062] Such an angular sensor is arranged on a carrier in order to measure the angle and / or angular velocity values ​​of said carrier. The carrier may be all or part of an airplane, a boat, a train, a car, a satellite or any other air, land or sea vehicle.

[0063] Furthermore, one can still refer to the general functioning of the Figure 3 , the processing unit UT being configured to apply the steps of the method according to the invention. It may be one or more modules added in the UT to carry out the steps of the correction method according to the invention.

[0064] The vibration wave OV vibrates according to a vibration pulse ω. The correction method according to the invention applies to an inertial sensor operating in gyrometer mode or in gyroscope mode, the servocontrols of the excitation controls being in operation.

[0065] In a vibrating inertial angular sensor, in particular an axisymmetric one, two reference frames are distinguished: the xy sensor reference frame, the x and y axes of which are the axes containing the excitation and detection transducers of the sensor, and the x'y' wave reference frame, in which the x' axis is the vibration axis of the OV wave and the y' axis is the axis perpendicular to x' in the plane of the sensor. The x' axis makes an angle θ with the x axis, called the "electric angle", and the x'y' reference frame is called the "wave reference frame".

[0066] The invention consists of controlling a rotation of the vibration wave OV when the dynamics of the carrier are zero or at least low, so as to be able to eliminate the defects generated on the measurement signal by the control.

[0067] In the remainder of the detailed description, the angular value considered is the angular velocity. The calculation logic would be the same considering the angle instead of the angular velocity (namely, however, that in one embodiment, the calculations are carried out according to the method by considering the angular velocity as the angular value, then returning to the angles by integration; or conversely the calculations are carried out according to the method by considering the angle as the angular value, then returning to the angular velocity by differentiation).

[0068] Whether for the vibration wave or the carrier, the terms "angular velocity" and "rotational velocity" are used interchangeably, designating the same quantity.

[0069] We will describe the process and the dynamic equations in the case where the dynamics are zero, that is to say that the carrier is stationary, with no movement other than the Earth's rotation.

[0070] As known to those skilled in the art, the angular speed Ωe measured by the sensor is: Ωe = 1 + FEmm + FEm θ Ωv + Dm + D θ + Ft Ωc Or : Ωc is the rotational speed of the commanded wave; Ωv is the actual rotational speed of the carrier; FEmm is the average mechanical scale factor error, independent of the angle θ; the mechanical scale factor being the scale factor related to a mechanical rotation; FEm(θ) is the periodic mechanical scale factor error, at zero mean; Dm is the average drift of the sensor, independent of the angle θ; D(θ) is the periodic drift of the sensor at zero mean; and FT(Ωc) corresponds to the commanded rotational speed Ωc passed through the transfer function of the sensor.

[0071] The transfer function can be expressed as follows: FT Ω c = 1 + FEem + FEe θ Ω c Or : FEem is the mean electrical scale factor error; the electrical scale factor being the scale factor related to an electrical rotation; and FEe(θ) is the periodic, zero-mean electrical scale factor error.

[0072] So, the equation Math.1 becomes: Ωe = 1 + FEmm + FEm θ . Ωv + Dm + D θ + 1 + FEem + FEe θ . Ωc

[0073] Knowing the commanded rotation speed Ωc, we can subtract it from the output, which gives: Ωe − Ω c = 1 + FEmm + FEm θ . Ωv + Dm + D θ + FEem + FEe θ . Ω c

[0074] We already know all the terms on the left of the equation, Ωe and Ωc.

[0075] Furthermore, when stationary, the actual angular velocity of the carrier Ωv corresponds to a projection of the Earth's rotation Ωtp considered constant for the calculations.

[0076] Thus, in zero dynamics, the real angular velocity of the carrier Ωv is small and as the scale factor errors are also small, the product (FEmm + FEm (θ))Ω vis negligible compared to the other terms of the equation. By placing the known terms on the left, and neglecting (therefore removing in the equation Math.4) the product (FEmm + FEm ( θ )). Ω v , the equation becomes: Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c

[0077] Furthermore, on average over the angular range of kπ radians that the electrical angle θ spans, the values ​​of the periodic mechanical scale factor error FEm(θ) and the periodic electrical scale factor error FEe(θ) are zero.

[0078] The measured angular velocity Ωe by the sensor can be measured for several electrical angles θ, either for a continuous rotation or for a series of angles distributed, possibly uniformly, over the angular range of kπ radians. We can then determine the average Ωem of the measured angular velocities Ωe over all angles.

[0079] Furthermore, the average Ωem of the measured angular velocities Ωe is found in the following equation in which the terms FEe(θ) and D(θ) have been removed since they are zero on average over the angular range of kπ radians: Ω em − Ω c = Ω vm + Dm + FEem . Ω c

[0080] Ωvm denotes the average of the actual speed over the angular range of kπ radians. At standstill the actual speed is equal to the average speed, so Ωvm = Ωv.

[0081] This equation has three unknowns: Ωv, Dm and FEem, but in practice, only the two values ​​(Ωv + Dm) on the one hand and FEem on the other hand are observable. With two values ​​of Ωc we can deduce these two observable values. The average drift of the sensor Dm is unobservable because it cannot be distinguished from Ωv, and Ωv is unknown since that is what we are looking for. So in the end we have access to (Ωv + Dm) on the one hand, that is to say the real rotation speed of the carrier tainted by the average drift of the sensor and to FEem.Ωc therefore to FEem on the other hand.

[0082] The average is carried out at constant wave rotation speed Ωc, and the carrier also keeps the same speed Ωv, at zero dynamics, so that these terms are unchanged, as are the average values ​​Dm and FEem, by definition. Figure 4 illustrates a correction method 100 comprising the following steps: A controlling a rotation (electrical rotation) of the vibration wave OV according to at least a constant controlled angular velocity Ωc, such that the electrical angle θ uniformly sweeps at least an angular range of kπ radians, k being an integer greater than or equal to 1; then B recovering the angular speeds measured Ωe by the inertial sensor over the angular range of kπ radians of the electrical angle θ, for the commanded angular speed Ωc, and determining an average Ωem of the angular speeds measured over said angular range; then Csubtract the value of the commanded angular speed Ωc from the average of the measured angular speeds Ωem; the operations A has C being carried out for at least two different commanded angular speeds; then D determine FEem and the actual angular velocity Ωv of the wearer affected by the average drift of the sensor Dm, using the formula expressed for each commanded angular velocity Ωc Ω em − Ω c = Ω vm + Dm + FEem . Ω c

[0083] The average drift Dm of the sensor is a factory calibration residual. It can be determined using another more precise angular sensor, or using external information, for example when the wearer is stationary with a known heading.

[0084] Preferably, the commanded angular velocity Ωc can be given values ​​at which the angular sensor is expected to rotate when the carrier is in motion (e.g. during aircraft navigation or vehicle movement). This allows very good FEem accuracy to be achieved.

[0085] Having determined Ωv+Dm and FEem, we move away from the average to return to the equation Math.5 Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c

[0086] In a step E, using several values ​​of Ωe-Ωc observed during a revolution or a fraction of a revolution, we can determine the term D(θ)+FEe(θ).Ωc (function of the electric angle θ) by removing / subtracting the average FEem.Ωc from each Ωe-Ωc observation.

[0087] The term D(θ)+FEe(θ).Ωc being thus obtained for several electrical angles θ (continuous rotation or series of angles in the form of discrete values), it can be modeled in the form of a polynomial function. Alternatively, a correspondence table of the values ​​of D(θ)+FEe(θ).Ωc can be produced as a function of the different electrical angles θ, values ​​obtained by exploiting the equation Math.5, as described previously. Indeed, it is generally difficult to model the term D(θ)+FEe(θ).Ωc given that the errors and drifts present fairly strong non-linearities linked to the fact that the rotation command has a spectrum larger than the bandwidth of the sensor transfer function.

[0088] When the carrier is no longer stationary but in navigation, we can rely on the stability of the term D(θ)+FEe(θ).Ωc which was measured when the carrier was stationary as described above.

[0089] Once this term D(θ)+FEe(θ).Ωc has been determined, in the form of a function of θ or a correspondence table as a function of θ, we can thus in a step F subtract it from the measurement Ωe-Ωc, to deduce and / refine the term Ωv+Dm even when the carrier is no longer stationary.

[0090] Thus, the invention makes it possible to determine a real angular velocity value affected by a lower drift value, since only Dm remains, therefore more precise than the methods of the prior art, and this, without requiring an additional sensor. In addition, the invention makes it possible to have an angular value that is also more precise because it makes it possible to reduce the term D(θ)+FEe(θ).Ωc and thus the angular error that it can generate. The angular error that may remain will be reduced to the extent that it is a time-bounded error, and is thus much more negligible than the drifts that generate divergent errors over time.

[0091] Alternatively or in a complementary manner, one can also consider filtering the rotation command so that it is within the sensor bandwidth in such a way that these non-linearities are much lower.

[0092] We can also consider constructing an equivalent transfer function of the angular sensor, passing the rotation command into this equivalent transfer function to deduce the additional nonlinearities.

[0093] In the case where the dynamics is not zero but is weak, the steps of the process and the equations described above are the same, but the actual angular velocity of the carrier Ωv does not correspond only to a projection of the Earth's rotation. Indeed, weak dynamics are defined as that of a carrier which is not in navigation (for example it is at its parking point), but which can present weak movements linked for example to the movements of the passengers and / or the crew. Thus the weak movements of the carrier are essentially around the two horizontal axes (attitudes). It is then possible to determine the variations in attitudes using accelerometers, in particular horizontal ones, which are generally available in a vehicle. The angular velocity is in this case equal to the variation in measured horizontal acceleration divided by the projection of gravity to which is added the projection of the Earth's rotation.For example, if we have a sinusoidal pitching movement of amplitude Asin(Ωvt.time) on a stationary aircraft (A being the amplitude of the oscillation and Ωvt the angular velocity), the accelerometer following the longitudinal direction of the aircraft will see an acceleration worth g.Asin(Ωvt.time), where g denotes gravity, reflecting a variation in pitch of Asin(Ωvt.time) and therefore an angular velocity of amplitude AΩvt. Thus, even in low dynamics, the real angular velocity can be determined affected by the error Dm.

[0094] So, while in zero dynamics we have the equation Math.5: Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c with Ω v = Ω tp (projected Earth rotation) considered constant for calculations (but not known)

[0095] At low dynamics we also have the equation Math.5: Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c mais avec Ω v = Ω tp + Ω avion where Ω plane (variation in angular speed due to small movements of the carrier, here an airplane) is deduced from the accelerometric values.

[0096] So, we find ourselves in the previous case by subtracting Ω plane: Ωe − Ω c − Ω avion = Ω tp + Dm + D θ + FEem + FEe θ . Ω c

[0097] So, at zero dynamics, we exploit the fact that the real angular velocity of the carrier Ωv is constant (and corresponds to a projection of the Earth's rotation Ωtp), and at low dynamics, we return to the case of zero dynamics by subtracting the variations in angular velocity determined by the accelerometers.

[0098] On the other hand, with strong dynamics, we estimate the value of FEm with another technique because we no longer have an assumption on Ωv, this is explained in the following.

[0099] We will now describe what happens in the carrier when navigating (strong dynamics).

[0100] When the dynamics are no longer zero or low, we can choose to rely on the stability of the average electrical scale factor error FEem.

[0101] Alternatively, in a step G the error can be corrected by measuring the variations ΔFEem of the average electrical scale factor error FEem between the strong dynamics and the weak or zero dynamics. One way to determine the variations ΔFEem is to spectrally separate the actual angular velocity variable Ωv and the angular velocity command of the wave Ωc, that is to say, concretely, to choose an angular velocity command Ωc whose spectrum can be separated by filtering from the useful spectrum of the actual angular velocity Ωv. Ωc can be expressed for example in the form Ωc 0 + Ωcf where Ωc 0 is a constant angular velocity allowing the angle to be rotated and Ωcf is expressed in the form of a harmonic function (sinusoidal for example) chosen outside the useful bandwidth of the sensor.Thus, by filtering, by placing ourselves outside the useful bandwidth of the sensor and around the frequency of the Ωcf function, we can access the variations of the term (FEem+FEe(θ)).Ωcf and thus the value ΔFEem which is the variation of the average electrical scale factor error FEem.

[0102] After correcting FEem and determining the term D(θ)+FEe(θ).Ωc as explained above, we can use the formula Math.4 giving the real speed of the carrier during navigation: Ω e − Ω c − FEe θ . Ω c − FEem . Ω c − D θ = Ωv + FEmm + FEm θ Ωv + Dm

[0103] The determined terms are on the left of the equation, and so the whole of the left term corresponds to a measured and corrected speed.

[0104] The mechanical scale factor errors FEmm+FEm(θ) and Dm can be factory set to be as small as possible in operation.

[0105] This makes it possible to determine a corrected real angular velocity value, i.e. to refine the estimation of said value.

[0106] In other words, the invention makes it possible to obtain a real angular velocity Ωv only affected by the errors FEmm+FEm(θ) and Dm which can be factory-set to be as low as possible, i.e. an angular velocity determined without the errors FEem, D(θ) and FEe(θ). This makes it possible in particular to eliminate the term D(θ) which is much more important than the term Dm.

[0107] The different modes presented can be combined with each other, unless otherwise indicated.

[0108] Furthermore, the present invention is not limited to the embodiments previously described but extends to any embodiment falling within the scope of the claims.

Claims

1. A method for correcting (100) the measurement of a vibrating inertial sensor (10), said inertial sensor being disposed on a carrier and comprising a resonator (Res) extending around two mutually perpendicular x and y axes defining an xy sensor frame of reference and comprising: - at least one vibrating movable mass (M1), said at least one movable mass comprising at least two portions configured to vibrate in phase opposition at a vibration pulsation (ω) and in a direction x' defining an x'y' wave frame of reference, the vibration wave (OV) along x' forming an electrical angle θ relative to the x-axis; - a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, said transducers comprising at least: -- a pair of detection transducers (Dx, Dy) configured to detect the movements of the vibration wave along x and y; -- a pair of excitation transducers (Ex, Ey), to which excitation forces are respectively applied along x and y, via a plurality of excitation commands determined by automatic controls from the detected movements, configured to maintain the wave at a constant amplitude via an amplitude command (Ca) and, optionally, to rotate said vibration wave via a precession command (Cp); the correction method being applied when the sensor is operating with a vibration wave (OV) vibrating along the x'-axis; characterised in that said method comprises the following steps, when the carrier is substantially stationary, of: A commanding an electrical rotation of the vibration wave (OV) according to a commanded angular value Ωc, such that the electrical angle θ scans at least one angular range of kπ radians, k being an integer greater than or equal to 1, according to which the angular value is comprised in the set comprising an angular velocity and an angle, then B retrieving the measured angular values Ωe measured by the inertial sensor (10) over the angular range of kπ radians of the electrical angle θ for the commanded angular value Ωc, and determining the mean Ωem of the angular values measured over said angular range; then C subtracting the commanded angular value Ωc from the mean Ωem of the measured angular values; steps A to C being carried out for at least two different commanded angular values so as to determine at least two means of the measured angular values; then D determining: - the mean electrical scale factor error FEem, the electrical scale factor corresponding to the ratio of the measured angular value due to the electrical rotation command, to the commanded angular value Ωc; and - the actual angular value Ωv of the carrier plus a drift value Dm of the sensor; said determining being carried out on the basis of the commanded angular values Ωc and of the means Ωem of the measured angular values, according to the following formula: Ωem − Ωc = Ωv + Dm + FEem . Ω c2. The correction method (100) according to claim 1, comprising an additional step, when the carrier is substantially stationary, of: E determining the periodic drift D(θ) of the sensor as a function of the electrical angle θ and the periodic electrical scale factor error FEe(θ) as a function of the electrical angle θ, on the basis of the measured angular values Ωe during at least one turn or fraction of a turn during an electrical rotation at a commanded angular velocity Ωc, according to the following formula: Ωe − Ω c = Ω v + Dm + D θ + FEem + FEe θ . Ω c3. The correction method (100) according to claim 2, comprising an additional step, the carrier not necessarily being stationary, of: F determining the actual angular value Ωv of the carrier plus a drift value Dm of the sensor, by removing the periodic drift D(θ) and the periodic electrical scale factor error FEe(θ) determined in step E.

4. The correction method (100) according to one of claims 1 to 3, the carrier having a zero dynamic range, said actual angular value Ωv being equal to a projection Ωtp in the xy sensor frame of reference of the terrestrial rotation, which is considered to be constant.

5. The correction method (100) according to one of claims 1 to 3, the carrier having a low but non-zero dynamic range, said actual angular value Ωv being equal to a projection Ωtp in the xy sensor frame of reference of the terrestrial rotation, which is considered to be constant, with the variations in angular velocity determined by at least one accelerometer on the carrier being subtracted, the variations in angular velocity preferably being determined by at least two accelerometers and by considering a mean fixed heading.

6. The correction method (100) according to one of claims 1 to 5, the rotation command being always applied in the same direction.

7. The correction method (100) according to one of claims 1 to 6, comprising an additional step, the carrier not necessarily being stationary, of: G correcting the mean electrical scale factor FEem by the variation ΔFEem of the mean electrical scale factor error FEem between the high dynamic range and the low or zero dynamic range, said variation ΔFEem being determined by spectrally separating the angular velocity command of the wave Ωc from the actual angular value Ωv.

8. An inertial angular sensor (10), said inertial sensor being disposed on a carrier and comprising a resonator (Res) extending around two mutually perpendicular x and y axes defining an xy sensor frame of reference and comprising: - at least one vibrating movable mass (M1), said at least one movable mass comprising at least two portions configured to vibrate in phase opposition at a vibration pulsation (ω) and in a direction x' defining an x'y' wave frame of reference, the vibration wave (OV) along x' forming an electrical angle θ relative to the x-axis; - a plurality of electrostatic transducers controlled by electrical voltages and operating along the two axes x or y, including at least, on at least one of the two masses: -- a pair of detection transducers (Dx, Dy) configured to detect the movements of the vibration wave along x and y; -- a pair of excitation transducers (Ex, Ey), to which excitation forces are respectively applied along x and y, via a plurality of excitation commands determined by automatic controls from the detected movements, configured to maintain the wave at a constant amplitude via an amplitude command (Ca) and, optionally, to rotate said vibration wave via a precession command (Cp); the inertial angular sensor further comprising: - a control and / or processing unit adapted to implement the steps of the correction method (100) according to one of claims 1 to 7.

9. The inertial angular sensor (10) according to claim 8, said inertial sensor being axisymmetric.

10. The inertial angular sensor (10) according to claim 8 or claim 9, comprising at least two vibrating movable masses (M1, M2) forming the at least two portions configured to vibrate in phase opposition relative to each other, one movable mass being able to be disposed around another movable mass.