Method for calibrating the scale factor of inertial angular sensors.
The method addresses scale factor errors and biases in inertial angular sensors by using dual angular sensors for controlled rotation and integral calculations, enhancing sensor accuracy and stability.
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2024-04-30
- Publication Date
- 2026-03-27
AI Technical Summary
Inertial angular sensors suffer from scale factor errors and biases that vary over time due to factors like aging and thermal variations, making factory calibration insufficient for optimal performance.
A method for calibrating inertial angular sensors using a first and second angular sensor with parallel sensitive axes, involving controlled rotation and integral calculations to estimate and correct the scale factor, accounting for bias and measurement errors.
The method provides accurate calibration of scale factors, reducing errors and improving sensor performance by compensating for time-varying biases and thermal variations.
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Abstract
Description
Title of the invention: Method for calibrating the scale factor of inertial angular sensors.
[0001] The present invention relates to the field of inertial angular sensors, such as gyroscopes and gyrometers, and more particularly to vibrating resonator inertial angular sensors.
[0002] BACKGROUND OF THE INVENTION
[0003] Inertial angular sensors are commonly used in inertial measurement units on board carrier vehicles to determine the attitude of carrier vehicles.
[0004] Inertial angular sensors with a vibrating resonator are known. The operation of such a sensor relies on controlling and detecting the amplitudes of two natural modes of vibration of the resonator, these two natural modes being coupled to each other by the effect of Coriolis forces generated by rotational movements of the carrier vehicle around an axis orthogonal to these two natural modes. Documents EP-B-2992298 and FR-B-3013442 describe angular sensors comprising a support and seismic bodies that form the resonator and are mounted concentrically around each other and of substantially the same mass. The seismic bodies are mounted to move relative to the support and are associated with electrostatic actuators arranged to excite the seismic bodies and with electrostatic detectors arranged to detect relative movements of the seismic bodies according to each of the vibration modes.
[0005] Such an angular inertial sensor can be used either in a "gyroscope" mode (or whole angle mode in English), or in a "gyrometer" mode (or rate mode in English).
[0006] In gyroscope mode, the vibration wave is free to move around the axis of symmetry of the resonator, this movement being linked to the amplitude of the carrier's movements, and electrodes are used to detect the angular position of the vibration wave. In gyrometer mode, the position of the vibration wave is fixed and maintained by applying a precession command to the electrodes, the amplitude of this precession command being linked to the amplitude of the carrier's movements.
[0007] The measurement values provided by the inertial angular sensor depend on the value of a scale factor associated with the inertial angular sensor. The scale factor is defined as the ratio between, on the one hand, the amplitude of the rotation of the carrier vehicle and, on the other hand, the fundamental rotation amplitude of the vibration of the resonator in gyroscope mode or the amplitude of the precession control in gyroscope mode.
[0008] The rotational speed estimated from the measurements provided by the angular inertial sensor in gyroscope mode is defined as follows:
[0009] q = _ a • Q + b(9e)-FEP-C» scaling factor gyroscope
[0010] The rotational speed estimated from the measurements provided by the angular sensor Inertial gyroscope mode is defined as follows:
[0011] Û= -FEP-(-a-Û + b(ee) ) « FEFa scaling factor gyroscope
[0012] In both of these modes: • O; the true rotational speed; • Q: the estimated rotation speed; Cp^: the precession command (note that in gyroscope mode, a precession command may occasionally be applied in certain cases to put the vibration wave into a predetermined angular position); • FEP; the precession scale factor; • a: the gyroscope scaling factor; • : 'c bias depending on the angular position of the vibration wave, or vibration angle as measured by the electrodes (commonly referred to as electrical angle as opposed to the rotation angle of the carrier commonly called mechanical angle).
[0013] Thus, regardless of the operating mode of the inertial angular sensor, the angular measurement is affected by a scale factor error (gyroscope or gyrometer) and a bias. The bias and scale factor errors can depend on the angle. These errors vary over time (aging, thermal variation, etc.) so that factory calibration during manufacturing is not sufficient to obtain optimal performance in use.
[0014] It should be noted, however, that by design, gyroscope scale factor errors are smaller and more stable than gyrometer scale factor errors. Indeed, in the gyrometer scale factor, it is the precession scale factor (PSF) errors that are predominant.
[0015] SUBJECT OF THE INVENTION
[0016] The invention is intended in particular to facilitate the calibration of the scale factor. Summary of the invention
[0017] To this end, the invention provides a method for calibrating an inertial measurement system mounted on a carrier and comprising a first angular sensor and at least one second angular sensor having parallel sensitive axes. The angular sensors comprise at least one resonator and actuators connected to at least one electronic control unit to generate a vibration wave in the resonator. The method comprises the steps, performed by the electronic control unit, of: - control the first angular sensor to make the vibration wave rotate by a predetermined angle around the sensitive axis by varying a value of a control parameter of the first angular sensor and calculate the integral of the value of the control parameter; - during the rotation of the vibration base of the first angular sensor, drive the second angular sensor to perform a reference rotation measurement and calculate the integral of the reference rotation measurement; - calculate a difference between the integral of the value of the control parameter and the integral of the reference rotation measurement; - make an estimate of the scale factor of the first angular sensor from a ratio of said difference and the predetermined angle to calibrate the first angular sensor.
[0018] Thus, the second angular sensor makes it possible to measure a so-called reference rotation, which is the rotation undergone by the first angular sensor due to movements of the carrier during the rotation imposed on the vibration wave of the first angular sensor. By calculating the difference between the rotations measured by the two angular sensors and dividing it by the predetermined angle, an estimate of the scale factor of the first angular sensor is obtained.
[0019] According to optional features, used individually or in whole or in combination: - the first angular sensor being controlled by a gyroscope from an angular setpoint forming the control parameter, the rotation of the vibration background is obtained by imposing a variation of the angular setpoint; - the variation of the angular setpoint is linear; - the variation of the angular setpoint is roughly in the shape of a square; - the first angular sensor being controlled by gyroscope from a precession setpoint forming the control parameter to position Vibration Base, the rotation of Vibration Base is obtained by imposing a variation of the precession setpoint, the variation of the precession setpoint being preferably substantially in the shape of a square; - the process includes the step of estimating the quality of the scale factor estimation.
[0020] The invention also relates to an inertial measurement system intended to be carried on a carrier, comprising a first angular sensor and at least a second angular sensor which have parallel sensitive axes and which include at least one resonator and actuators connected to at least one electronic control unit to generate a vibration wave of the resonator for the implementation of this method.
[0021] Other features and advantages of the invention will become apparent from the following description of particular, non-limiting embodiments of the invention. Brief description of the drawings
[0022] Reference will be made to the attached drawings, among which:
[0023] [Fig-1] [Fig.1] is a schematic view of an inertial measurement system according to the invention;
[0024] [Fig.2] [Fig.2] is a flowchart illustrating the process of the invention;
[0025] [Fig.3] [Fig.3] is a time-dependent representation of the variation of control parameter for a gyroscope-controlled angular sensor;
[0026] [Fig.4] [Fig.4] is a time-dependent representation of the variation of control parameter for a gyroscope-controlled angular sensor. DETAILED DESCRIPTION OF THE INVENTION
[0027] With reference to [Fig.1], the invention relates to an inertial measurement system, generally designated as 1, carried on a carrier P. This system can be part of an inertial measurement unit (commonly called IMU or IMU) for example integrated into an inertial navigation system (commonly called CIN).
[0028] The inertial measurement system 1 here comprises a first angular inertial sensor 10 and a second angular inertial sensor 20 having collinear sensitive axes 10', 20'.
[0029] The sensors 10, 20 are here vibrating axisymmetric resonator sensors and more precisely hemispherical resonator type sensors but other types of angular inertial sensors can be used and for example: a concentric mass gyroscope, a double tuning fork gyroscope.
[0030] Each sensor 10, 20 is of the MEMS type and comprises, in a known manner, a support 11, 21; a first mass (or seismic body) 12.1, 22.1 and a second mass (or seismic body) 12.2, 22.2 which form the resonator and are suspended from the support 11, 21 by springs 14, 24; and electrostatic actuators and electrostatic detectors 13, 23 distributed between the free edge of the masses 12.1, 22.1, 12.2, 22.2 and the supports 11, 21. The electrostatic actuators The 13 electrostatic detectors are arranged to excite the masses according to two modes of vibration and to detect movements of the masses according to each of the modes of vibration. This structure being known in itself, it will not be detailed further here.
[0031] The electrostatic actuators and electrostatic detectors 13, 23 are connected to an electronic control unit 30 arranged to control the angular sensors 10, 20 by supplying the electrostatic actuators and electrostatic detectors 13, 23 so as to generate a vibration wave of the resonator whose angular position around the axis of symmetry of the resonator depends on the rotational movements of the carrier P around the sensitive axis of the angular sensors 10, 20. The electronic control unit 30 comprises herein, in a manner known in itself, at least one processor and a memory containing computer programs executable by the processor to operate the inertial measurement system in a conventional manner but also to implement the calibration method of the invention.
[0032] With reference to [Fig.2], the method of the invention comprises the steps of: - controlling the first angular sensor 10 to make the vibration wave perform a rotation of a predetermined angle around the sensitive axis by varying a value of a control parameter of the first angular sensor (step 100) and recording the variation of the control parameter in order to calculate the integral of the value of the control parameter during the rotation (step 110); - during the rotation of the vibration base of the first angular sensor, drive the second angular sensor to perform a reference rotation measurement and calculate the integral of the reference rotation measurement (step 130); - calculate a difference between the integral of the value of the control parameter and the integral of the reference rotation measurement; - make an estimate of the scale factor (i.e. an estimated value of the scale factor) of the first angular sensor from the ratio of said difference and the predetermined angle (step 130); - estimate the quality of the scale factor estimation (step 140) and calibrate the first angular sensor if the quality is sufficient.
[0033] The initial step of the calibration process according to the invention (100) therefore consists of driving the first angular sensor 10 to make the vibration wave perform a rotation of a predetermined angle, from an angular position n°1 to an angular position n°2, around the sensitive axis.
[0034] Two modes of implementation are described below: a first mode of implementation in which the first angular sensor 10 is controlled as a gyroscope in relation to the [Fig.3] and a second mode of implementation in which the first angular sensor 10 is controlled as a gyroscope in relation to the [Fig.4].
[0035] According to the first embodiment, the first angular sensor 10 is controlled as a gyroscope based on an angular setpoint 0setpoint, which forms the control parameter of a precession control. The vibration background rotation is thus obtained by applying a variation to the angular setpoint 0setpoint and therefore to the precession control.
[0036] Angular position n°1 corresponds to an instant T0 and angular position n°2 corresponds to an instant T2. The variation of the angular setpoint 0setpoint can be linear between instants T0 and T2 as shown in solid line on [Fig.3] or have an approximately square shape (the change in the setpoint value then occurs at instant T1 between instants T0 and T2) as shown in dashed line on [Fig.3].
[0037] For step 110, in this gyroscope mode with variation of the setpoint angle, the measurement of the estimated angle variation corresponds to the integral of the precession command:
[0038] ^0 = Jq.= a 0cmsign-FEP a-^ dt- JbfeJ -dt error bias
[0039] With: * ^AO: 'a measure of the estimated angle variation; • FJ; the true rotational speed; • Q: the estimated rotation speed; • A ^setpoint: the variation of the angular setpoint; • FEP; the precession scale factor; • a: the gyroscope scaling factor; • • 'c bias depending on the angular position of the vibration wave, or vibration angle 6th.
[0040] By step 120, we seek to determine if the carrier has undergone rotations during the rotation imposed on the rotation of the vibration wave of the first angular sensor 10.
[0041] The second angular sensor 20 therefore makes it possible to measure a so-called reference rotation which is the rotation undergone by the first angular sensor 10 due to movements of the carrier P during the rotation imposed on the rotation of the vibration wave of the first angular sensor 10. The second angular sensor 20 measures the same axis of rotation as the first angular sensor 10.
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[0052] In this case, the reference rotation is given by the integral of the reference rotation measurement A07 = - J £2 ■ dt + measurement error ref With : • q: the measurement of the estimated reference rotation; • £2; the true rotational speed; • measurement error ref; the error affecting the rotation measurement. Step 130 allows us to estimate the scale factor, which is written as: ü^-~FEP-a+ order measurement error (ref.), bias error t^amsign This method estimates the entire scaling factor of the angular sensor operating in gyroscope mode. According to the second implementation, the first angular sensor 10 is gyroscope-controlled based on a precession setpoint Cpconsigne, which forms the control parameter for positioning the vibration wave. The vibration wave's rotation is thus obtained by applying a variation to the precession setpoint Cpconsigne. The variation of the precession setpoint Cpconsigne can be essentially a sharp square wave between times T0 and T2, as shown by the solid line in [Fig. 4], or a smoothed square wave as shown by the dashed line in [Fig. 4]. With the sharp square wave, the precession setpoint Cpconsigne goes from 0° / s to the maximum value Cpmax at time T0 and then returns from the maximum value Cpmax to 0° / s at time T1 (position #2 is therefore reached at time T1). The smoothed square wave is obtained by applying a low-pass filter to the sharp square wave and then multiplying it by a gain to obtain the same angular variation as the sharp square wave. For step 110, in this gyroscope mode with varying precession setpoint, the estimated angle change measurement corresponds to the integral of the rotation measurement of the first angular sensor 10 during the imposed rotation: A 6 = Jû = FEP ■ Cpc(ms • A t - a ■ fû dt- Jb(ôe) • dt ^^tomigne error bias With : * Tf): 'a measure of the estimated angle variation; • £2; the true rotational speed; • Q: the estimated rotation speed; • Ep: the precession command instruction; • FEP; the precession scale factor; • a: the gyroscope scaling factor;
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[0064] • : 'c bias depending on the angular position of the vibration wave, or vibration angle 6th. Step 120 is carried out as in the first implementation method. Step 130 allows us to estimate the scale factor, which is written as: A8-A8ref ppp, measurement error ref bias error A4 rGl “TA / ; TA / 9 ^^Cfnvagne '■X'conta gne consigne This method only estimates the errors of the precession scaling factor (PSF). It does not include the gyroscope scaling factor error that occurs during fixed-position measurements. However, the impact on the estimation is limited because, in most vibrating angular sensors, the stability of the gyroscope scaling factor is significantly better than that of the gyroscope scaling factor. In both implementation methods, the estimation of the scale factor is used to Recalibrate the gyroscope scale factor. This is called calibration. However, as we have seen, the estimation of the scale factor is tainted by bias errors and errors in the reference measure. A mechanism for monitoring the estimated bias and measured rotation can be implemented to detect excessive degradation in the scale factor estimate and correct the error recalibration. EP-A-2 225 534 describes the use of measurements in multiple positions to estimate the angular sensor bias requiring recalibration. Similarly, it is possible to apply to the second angular sensor 20 an identical or similar procedure to that described above in order to estimate the scale factor error and bias of the reference measurement. The reference measurement error is given by: Estimated reference measurement error - (estimated reference FEP error) ■ A 0 reference + estimated reference bias error With : * ^Qrèf : 'a measure of the estimated reference rotation; • estimated FEP ref error; estimated scaling factor error; • estimated ref bias error: the estimated bias error; • Estimated reference measurement error – the estimated error affecting the rotation measurement reference. In the preferred version of the method according to the invention, the electronic processing unit calculates a quality indicator of the scaling factor estimation during step 140. The calculation of the quality indicator for the scaling factor estimation can be implemented in the following ways: - if the estimated bias and / or measured rotation exceeds a threshold, the indicator indicates insufficient quality (KO: no calibration) and, conversely, sufficient quality (OK: perform calibration); - A quality indicator can be calculated in the following form with adjustable parameters (y, |3) and H a function:
[0065] jquaUty = y H() + fi.H( ) J * \ ^'instruction / \ ^'instruction /
[0066] For example, H can be the absolute value function, or the square function.
[0067] It should be noted that to guarantee the convergence of the scale factor estimation method, it is sufficient that the bias errors and the reference measurement errors decrease with each estimation. To this end, the method of the invention can be applied alternately to two angular sensors, where each, one after the other, undergoes precession: then, each scale factor estimation will be affected by an increasingly smaller error.
[0068] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.
[0069] In particular, the inertial system may have a different structure from that described.
[0070] The system may comprise several second angular sensors 20, each individually having a sensitive axis not parallel to the sensitive axis of the first sensor. The measurements provided by all the second sensors are then summed, after possible weighting, such that the combination of the second sensors forms a single equivalent second sensor having a sensitive axis parallel to the axis of the first sensor. For example, the system comprises two second sensors having a sensitive axis forming an angle of +30° and -30° respectively with respect to the sensitive axis of the first sensor. It is understood that the sum of the angular measurements provided by the second sensors provides a measurement of the rotation of the carrier P about the sensitive axis of the first sensor.
[0071] The sensors 10 and 20 are not necessarily MEMS concentric mass sensors and may be of another type, such as hemispherical resonant gyroscopes or dual-tuning-fork gyroscopes. Furthermore, the sensors may be of different types: different types of angular sensors may be used simultaneously, such as a hemispherical resonant gyroscope, and / or a concentric mass gyroscope, and / or a dual-tuning-fork gyroscope.
[0072] The system may include one or more electronic control units between which the functions to be performed are distributed.
[0073] The variation of the precession setpoint may have a rough (angular) or smoothed square shape or any other shape suitable for the precession control.
[0074] The step of calculating a quality indicator is optional.
[0075] The invention is usable on any type of carrier: land, air, space, nautical...
Claims
1.
2.
3.
4. Demands A method for calibrating an inertial measurement system (1) which is mounted on a carrier (P) and which comprises a first angular sensor (10) and at least a second angular sensor (20) having parallel sensitive axes, the angular sensors (10, 20) comprising at least one resonator and actuators connected to at least one electronic control unit (30) to generate a vibration wave of the resonator, the method comprising the steps, carried out by the electronic control unit, of: - control the first angular sensor (10) to make the vibration wave perform a rotation of a predetermined angle around the sensitive axis by varying a value of a control parameter of the first angular sensor (10) and calculate the integral of the value of the control parameter; - during the rotation of the vibration wave of the first angular sensor (10), drive the second angular sensor (20) to perform a reference rotation measurement and calculate the integral of the reference rotation measurement; - calculate a difference between the integral of the value of the control parameter and the integral of the reference rotation measurement; - make an estimate of the scale factor of the first angular sensor (10) from a ratio of said difference and the predetermined angle to calibrate the first angular sensor (10). Method according to claim 1, wherein, the first angular sensor (10) being controlled as a gyroscope from an angular setpoint forming the control parameter, the rotation of the vibration wave is obtained by imposing a variation of the angular setpoint. A method according to claim 2, wherein the variation of the angular setpoint is linear. A method according to claim 2, wherein the variation of the angular setpoint is substantially in the shape of a notch.
5. Method according to claim 1, wherein the first angular sensor (10) being controlled by gyroscope from a precession setpoint forming the control parameter for positioning the vibration wave, the rotation of the vibration wave is obtained by imposing a variation of the precession setpoint.
6. Method according to claim 5, wherein the variation of the precession setpoint is substantially in the shape of a notch.
7. A method according to any one of the preceding claims, comprising the step of estimating the quality of the scaling factor estimation.
8. Inertial measurement system (1), intended to be mounted on a carrier (P), comprising a first angular sensor (10) and at least a second angular sensor (20) which have parallel sensitive axes and which comprise at least one resonator and actuators connected to at least one electronic control unit (30) to generate a vibration wave of the resonator, the electronic control unit (30) being arranged to implement the method according to any one of the preceding claims.
9. System according to claim 8, wherein the second angular sensor is formed by a combination of several angular sensors having sensitive axes not parallel to the sensitive axis of the first angular sensor.