An inertial measurement unit and its line-angle coupled motion calibration method

Abstract

This invention belongs to the field of inertial measurement technology, specifically an inertial measurement unit and its linear-angular coupling motion calibration method. It includes constructing a non-contact inertial measurement unit linear-angular motion synchronous measurement system. Through a reference cubic prism, a three-dimensional laser vibrometer, a first dual-axis autocollimator, a second dual-axis autocollimator, and a data acquisition module, an attitude transformation matrix is ​​established from the cubic mirror coordinate system to the inertial measurement unit coordinate system. By synchronously triggering the inertial measurement unit, based on the outputs of a three-axis gyroscope and a three-axis accelerometer, the three-axis acceleration measured by the three-dimensional laser vibrometer in the inertial measurement unit coordinate system, and the three-axis angular velocity of the inertial measurement unit measured by the dual-axis autocollimator, the linear-angular coupling motion of the inertial measurement unit is calibrated. This invention avoids the influence of vibration on the accuracy of the measurement system and solves the problem of difficulty in dynamically tracking and monitoring the actual motion of the inertial measurement unit during vibration.

Description

Technical Field

[0001] This invention belongs to the field of inertial measurement technology, specifically an inertial measurement unit and its line-angle coupling motion calibration method. Background Technology

[0002] An inertial measurement unit (IMU) is an autonomous navigation system that calculates a carrier's position, velocity, and attitude by measuring its own angular velocity and acceleration, without relying on external information. IMUs typically operate in highly dynamic, wide-bandwidth vibration environments. To prevent damage to the inertial components (gyroscopes and accelerometers) in such environments, a rubber damping system is usually installed between the IMU and its housing. However, when subjected to carrier acceleration, the damping system deforms, generating coupled angular motion under linear vibration. This results in a non-rigid connection between the IMU and the carrier, leading to deviations in the IMU's attitude and displacement from those of the carrier.

[0003] In an inertial measurement unit (IMU), gyroscopes and accelerometers are mounted on the IMU's support frame to measure angular velocity and acceleration, respectively. Under vibration, the acceleration readings of both the gyroscope and accelerometer are affected to some extent, manifesting as zero-bias error and increased noise. When performing mechanical performance tests on an inertial navigation system (INS), the INS is typically fixed to a vibration table, and the outputs of the inertial devices are collected during and before vibration. The input to the vibration table is a known quantity, but the actual motion of the IMU after passing through the vibration damper is unknown, making it difficult to distinguish the actual motion of the IMU from the measurement error of the inertial devices through their output. Therefore, a non-contact method for monitoring and calibrating the linear-angular coupled motion of the IMU system is needed to measure the actual motion of the IMU with high precision, thus separating it from the measurement error of the inertial devices. Summary of the Invention

[0004] To address the problems existing in the prior art, an inertial measurement unit and its line-angle coupled motion calibration method are proposed. A non-contact inertial measurement unit line-angle motion synchronous measurement system is built, which solves the problem that it is difficult to distinguish between the actual motion of the IMU and the measurement error of the inertial device through the output of the inertial device under vibration test, and realizes real-time high-precision measurement of the multi-degree-of-freedom motion of the IMU system.

[0005] The complete technical solution of this invention includes: An inertial measurement unit line-angle coupled motion calibration method includes: A non-contact inertial measurement unit linear-angular motion synchronous measurement system is constructed, including a reference cubic prism 2, a three-dimensional laser vibrometer 10, a first dual-axis photoelectric autocollimator 8 and a second dual-axis photoelectric autocollimator 9, and a data acquisition module 11; The reference cubic prism 2 is mounted on the inertial measurement unit 1, and the inertial measurement unit 1 is mounted on the vibration table 7 through the vibration reduction system 3; the first dual-axis photoelectric autocollimator 8 and the second dual-axis photoelectric autocollimator 9 are respectively mounted on the vibration-isolated optical platform, and their optical axes are respectively aligned with the mirror surface of the reference cubic prism 2; the three-dimensional laser vibration meter is mounted on the vibration-isolated optical platform. The inertial measurement unit line-angle coupled motion calibration method specifically includes: Establish a cube mirror coordinate system O j X j Y j Z j and inertial measurement unit coordinate system O d X d Y d Z d cubic mirror coordinate system O j X j Y j Z j The three coordinate axes are perpendicular to the three mutually orthogonal mirror surfaces of the reference cubic prism 2; the inertial measurement unit coordinate system O d X d Y d Z d The three coordinate axes coincide with the directions of the three principal axes of inertia, respectively; After calibrating the relative attitude between the reference cubic prism and the inertial measurement unit (IMU), the three-dimensional spatial vector of the laser beam illumination point of the three-dimensional laser vibrometer 10 and the centroid of the IMU 1 in the IMU coordinate system is measured. ; Subsequently, the inertial measurement unit 1, the three-dimensional laser vibrometer 10, the first dual-axis photoelectric autocollimator 8, and the second dual-axis photoelectric autocollimator 9 are synchronously triggered. In the inertial measurement unit 1, the three-axis gyroscope outputs the first angular velocity. The triaxial accelerometer outputs the first acceleration. The 3D laser vibrometer 10 outputs a second acceleration. The first dual-axis photoelectric autocollimator 8 and the second dual-axis photoelectric autocollimator 9 output the dynamic torsion angle vector of the reference cubic prism 2 in the cubic mirror coordinate system. The data acquisition module 11 collects the output data; The dynamic torsion angle vector in the cubic mirror coordinate system Transformed to the coordinate system of the inertial measurement unit to obtain ， Will Differentiation yields the triaxial angular velocities of the inertial measurement unit measured by the first and second dual-axis photoelectric autocollimators. ; Based on three-dimensional spatial vectors The second acceleration output by the three-dimensional laser vibrometer 10 and The triaxial acceleration measured by the three-dimensional laser vibrometer 10 in the coordinate system of the inertial measurement unit was obtained. ; Based on the first angular velocity First acceleration Triaxial acceleration measured in the inertial measurement unit coordinate system Inertial measurement unit triaxial angular velocity The linear-angular coupling motion of the inertial measurement unit is calibrated.

[0006] Furthermore, a first plane mirror 5 and a second plane mirror 6 are respectively installed on two mutually perpendicular surfaces on the side of the inertial measurement unit. By calibrating the relative attitude between the reference cubic prism 2 and the inertial measurement unit 1 using a theodolite, the pitch angle of the cubic mirror coordinate system relative to the inertial measurement unit coordinate system is obtained. yaw angle φ and azimuth γ .

[0007] Furthermore, through the inertial measurement unit coordinate system O d X d Y d Z d And cubic mirror coordinate system O j X j Y j Z j attitude transformation matrix between The dynamic torsion angle vector in the cubic mirror coordinate system Transformed to the coordinate system of the inertial measurement unit to obtain .

[0008] Furthermore, .

[0009] Furthermore, the triaxial acceleration measured in the inertial measurement unit coordinate system for: .

[0010] Furthermore, the linear-angular coupled motion of the inertial measurement unit is calibrated, including the amplitude error, phase delay, and nonlinearity of the inertial device.

[0011] Furthermore, the amplitude error, phase delay, and nonlinearity of the inertial device are calibrated based on the frequency response function H1 estimation.

[0012] Furthermore, an inertial measurement unit is provided, wherein the inertial measurement unit performs line-angle coupled motion calibration using the aforementioned inertial measurement unit line-angle coupled motion calibration method.

[0013] Furthermore, the inertial measurement unit includes a three-axis accelerometer and a three-axis gyroscope, and the vibration error of the three-axis gyroscope is compensated based on the three-axis accelerometer.

[0014] The advantages of the method of the present invention compared with the prior art specifically include: (1) The measuring device is not in contact with the vibration table and the IMU under test, thus avoiding the impact of vibration on the accuracy of the measuring system.

[0015] (2) The proposed method simultaneously measures the three-axis motion and three-axis angular motion of the IMU, and the results can reconstruct the pose changes of the six degrees of freedom of the IMU.

[0016] (3) Both the three-dimensional laser vibration meter and the dual-axis photoelectric autocollimator can acquire data at high speed, which solves the problem of the difficulty in dynamically tracking and monitoring the actual motion of the IMU during vibration.

[0017] (4) The data from the IMU, the three-dimensional laser vibrometer and the dual-axis photoelectric autocollimator are collected synchronously, which ensures the consistency of data time and provides a method for the performance calibration of inertial devices in the IMU. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the inertial navigation system and coordinate system definition of the reference cubic prism of the present invention.

[0019] Figure 2 This is a schematic diagram of the non-contact inertial measurement unit linear-angular motion synchronous measurement system of the present invention.

[0020] In the figure, 1-Inertial Measurement Unit, 2-Reference Cube Prism, 3-Vibration Reduction System, 4-Base, 5-First Plane Mirror, 6-Second Plane Mirror, 7-Vibration Table, 8-First Dual-Axis Photoelectric Autocollimator, 9-Second Dual-Axis Photoelectric Autocollimator, 10-Three-Dimensional Laser Vibration Meter, 11-Data Acquisition Module. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0022] like Figures 1-2 As shown, the non-contact inertial measurement unit linear-angular motion synchronous measurement system disclosed in this invention includes: (1) Reference cubic prism 2: The reference cubic prism 2 is fixed on the inertial measurement unit 1 to be calibrated, and the axis of the reference cubic prism is kept parallel to the axis of the inertial measurement unit 1 by the theodolite calibration.

[0023] (2) Three-dimensional laser vibration meter 10: The laser head of the three-dimensional laser vibration meter 10 is mounted on an optical platform, and its laser beam is aligned with the measurement point close to the center of mass of the inertial measurement unit 1.

[0024] (3) Dual-axis photoelectric autocollimator: including the first dual-axis photoelectric autocollimator 8 and the second dual-axis photoelectric autocollimator 9. The two dual-axis photoelectric autocollimators are installed on the optical platform and collimate the two mirrors of the reference cubic prism 2 that are perpendicular to the vibration table 7 respectively.

[0025] (4) Data acquisition module 11: used to synchronously trigger the inertial devices, three-dimensional laser vibrometer 10, first dual-axis photoelectric autocollimator 8 and second dual-axis photoelectric autocollimator 9 in the inertial measurement unit 1, and to acquire the output data of each device.

[0026] The specific implementation steps for inertial measurement unit (IMU) line-angle coupled motion calibration based on a non-contact IMU line-angle motion synchronization measurement system include: 1. Installation of a non-contact inertial measurement unit linear-angular motion synchronous measurement system, including: (1) Fine-tune the orientation of the reference cubic prism 2 so that the axes of the reference cubic prism 2 and the inertial measurement unit 1 are as parallel as possible to each other. Install the reference cubic prism 2 on the inertial measurement unit 1.

[0027] (2) Connect the inertial measurement unit 1 to the base 4 through the vibration reduction system 3 and install it on the vibration table 7.

[0028] (3) Mount the first dual-axis photoelectric autocollimator 8 and the second dual-axis photoelectric autocollimator 9 on the vibration-isolated optical platform, so that the optical axes of the two dual-axis photoelectric autocollimators are roughly aligned with the mirror surface of the reference cubic prism 2. Fine-tune the autocollimators so that the center of their light spots falls on the center of the plane of the reference cubic prism, and a stable crosshair image can be seen in the data acquisition software. Define the reading at this time as (0,0).

[0029] (4) Mount the laser head of the three-dimensional laser vibrometer on the vibration-isolated optical platform and align its laser beam with the measurement point close to the center of mass of the inertial measurement unit. Adjust the laser head to obtain the strongest reflected signal.

[0030] 2. Relative position calibration of inertial measurement unit, three-dimensional laser vibrometer, and biaxial photoelectric autocollimator. (1) Relative attitude calibration of the reference cubic prism and the inertial measurement unit: Define the cubic prism coordinate system O j X j Y j Z j Its three coordinate axes are perpendicular to the three mutually orthogonal mirror surfaces of the reference cubic prism 2; define the coordinate system of the inertial measurement unit. O d X d Y d Z d Its three coordinate axes coincide with the directions of the three principal axes of inertia, such as... Figure 1 As shown.

[0031] A first plane mirror 5 and a second plane mirror 6 are respectively installed on two mutually perpendicular surfaces on the side of the inertial measurement unit. The relative attitude between the reference cubic prism 2 and the inertial measurement unit 1 is determined by calibrating the theodolite, and the pitch angle of the cubic mirror coordinate system relative to the IMU system coordinate system is obtained. yaw angle φ and azimuth γ .

[0032] (2) Measure the three-dimensional spatial vector of the laser beam irradiation point of the three-dimensional laser vibrometer 10 and the center of mass of the inertial measurement unit 1 in the coordinate system of the inertial measurement unit. That is, the compensating lever arm.

[0033] 3. Synchronous data acquisition from the inertial measurement unit, three-dimensional laser vibrometer, and biaxial photoelectric autocollimator. The inertial measurement unit 1 is synchronously triggered to collect the output data from inertial devices, a three-dimensional laser vibrometer 10, a first dual-axis photoelectric autocollimator 8, a second dual-axis photoelectric autocollimator 9, and a data acquisition module 11. The output of the inertial measurement unit 1 includes the first angular velocity output from the three-axis gyroscope. and the first acceleration output from the triaxial accelerometer The 3D laser vibrometer 10 outputs a second acceleration. ;in This represents the angular velocity output by the three-axis gyroscope. This indicates the acceleration output by the triaxial accelerometer. The subscript indicates the acceleration output by the 3D laser vibrometer 10. , , , representing the X, Y, and Z axes respectively. The output of the first dual-axis photoelectric autocollimator 8 is The output of the second dual-axis photoelectric autocollimator 9 is ,in Represents a reference cubic prism with 2 turns O j i j The angle of axial torsion. Based on the outputs of two dual-axis photoelectric autocollimators, the dynamic torsion angle vector of the reference cubic prism 2 in the cubic mirror coordinate system is obtained. .

[0034] 4. Data Processing and Analysis because , φ and γ All angles are small; establish the coordinate system of the inertial measurement unit. O d X d Y d Z d And cubic mirror coordinate system O j X j Y j Z j The attitude transition matrix between them is:

[0035] This allows the output of the dual-axis photoelectric autocollimator to be converted to the coordinate system of the inertial measurement unit, achieving a unified output reference between the inertial measurement unit and the dual-axis photoelectric autocollimator. The dynamic torsion angle vector in the cubic mirror coordinate system is then converted... Transformed to the coordinate system of the inertial measurement unit to obtain :

[0036] Will Differentiation yields the triaxial angular velocities of the inertial measurement unit measured by the dual-axis photoelectric autocollimator: .

[0037] After the 3D laser vibration meter 10 outputs the compensation rod arm, the triaxial acceleration in the coordinate system of the inertial measurement unit is measured. for:

[0038] At this time, the non-contact inertial measurement unit linear angle motion synchronous measurement system calculates... and Corresponding to the linear and angular motion of the inertial measurement unit (IMU), this dynamically describes the actual multi-degree-of-freedom pose changes of the IMU under vibration, respectively, and correlates with the outputs of the three-axis gyroscope and three-axis accelerometer within the IMU. and Under the same reference coordinate system.

[0039] 5. Inertial Measurement Unit Performance Calibration: [The following is a partial translation of the original text, which is incomplete and requires further context.] and and and By comparing and calibrating, the scaling factor error, phase delay, and nonlinearity of the inertial devices in the inertial measurement unit can be analyzed.

[0040] The measurement error of an inertial measurement unit can typically be modeled as:

[0041] In the formula, and The impulse responses of the three-axis gyroscope and the three-axis accelerometer are respectively. Represents convolution. and These represent the zero-bias errors of the three-axis gyroscope and the three-axis accelerometer, respectively. and These represent the random noise of the three-axis gyroscope and the three-axis accelerometer, respectively. Indicates time.

[0042] First, synchronously acquire a sufficiently long output signal. , , and Then, data preprocessing is performed, including filtering and denoising, detrending, and time synchronization alignment.

[0043] Taking the output of a three-axis gyroscope as an example, this paper presents the output based on a two-axis optoelectronic autocollimator. Three-axis gyroscope output Calibration method. The calibration method for accelerometer output based on the output of a three-dimensional laser vibrometer is the same, and will... and Replace with and That's all.

[0044] use H 1. Estimator (H1 Estimator for frequency response function):

[0045] in, To pass HThe estimated value of the angular velocity frequency response function calculated by the estimator. For the input frequency, Input-output cross power spectrum. The input power spectrum.

[0046] Scale factor error The calculation method is as follows

[0047] Phase delay The calculation method is as follows:

[0048] Nonlinearity detection and suppression: Calculating the residuals of a linear model :

[0049] To pass H 1. Estimated values ​​of the impulse response function of a three-axis gyroscope obtained by the estimator; This represents the estimated zero-bias error of the three-axis gyroscope. If the residual is related to the input amplitude, it indicates the presence of nonlinearity, which can be compensated for using the Hammerstein model.

[0050] The calibration results of a certain gyroscope based on the above method are as follows: scaling factor error 22ppm; phase delay 36°; nonlinearity 19ppm.

[0051] Furthermore, the present invention also provides an inertial measurement unit, which undergoes linear-angle coupling motion calibration using the aforementioned method before use. The inertial measurement unit includes a triaxial accelerometer and a triaxial gyroscope, and compensates for vibration errors of the triaxial gyroscope based on the triaxial accelerometer. This includes the following steps: (1) Install the triaxial gyroscope and the triaxial accelerometer together; (2) Install the system equipped with a triaxial gyroscope and a triaxial accelerometer onto a linear vibration table, with the vibration direction aligned with the sensitive axis of the triaxial gyroscope. Calibrate the parameters through multiple sets of sinusoidal vibration tests. The specific method of obtaining it is as follows: Six sets of sinusoidal vibration excitations were set up at 160Hz / 2g, 160Hz / 3g, 160Hz / 4g, 160Hz / 5g, 320Hz / 5g, and 480Hz / 5g, with each set of vibration lasting 1 minute. The angular velocity output of the three-axis gyroscope was collected. and the output of the three-axis accelerometer in the direction of the three-axis gyroscope's sensitive axis. The acceleration along the sensitive axis is subjected to the Hilbert transform and then divided by... To obtain the coefficient K The results calculated from each group of sinusoidal vibration tests will then be used to... K The average of the values ​​is calculated as follows: .

[0052] (3) Based on the above results, online compensation for vibration error of the three-axis gyroscope is achieved, specifically as follows: During the vibration test, the gyroscope output was collected as follows: Angular velocity output along the sensitive axis Let the Hilbert transform be denoted as H (·), then the compensated fiber optic gyroscope output angular velocity for:

[0053] H (·) represents the Hilbert transform. This refers to the real-time output angular velocity of the fiber optic gyroscope. This is the real-time output acceleration of the accelerometer along the sensitive axis of the fiber optic gyroscope.

[0054] The above compensation method solves the problem that when a three-axis gyroscope faces a high-dynamic, wide-bandwidth vibration environment, the physical length and refractive index of the optical fiber change under stress, which causes a non-reciprocal phase shift through the elasto-optic effect. This shift is misinterpreted by the gyroscope as a rotational rate, leading to a deterioration in the accuracy of the three-axis gyroscope.

[0055] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for calibrating the linear-angular coupling motion of an inertial measurement unit, characterized in that, include: A non-contact inertial measurement unit linear-angle motion synchronous measurement system is constructed, including a reference cubic prism (2), a three-dimensional laser vibrometer (10), a first dual-axis photoelectric autocollimator (8), a second dual-axis photoelectric autocollimator (9), and a data acquisition module (11). The reference cubic prism (2) is mounted on the inertial measurement unit (1), and the inertial measurement unit (1) is mounted on the vibration table (7) through the vibration reduction system (3); the first dual-axis photoelectric autocollimator (8) and the second dual-axis photoelectric autocollimator (9) are respectively mounted on the vibration-isolated optical platform, and their optical axes are respectively aligned with the mirror surface of the reference cubic prism (2); the three-dimensional laser vibration meter is mounted on the vibration-isolated optical platform; The inertial measurement unit line-angle coupled motion calibration method specifically includes: Establish a cube mirror coordinate system O j X j Y j Z j and inertial measurement unit coordinate system O d X d Y d Z d cubic mirror coordinate system O j X j Y j Z j The three coordinate axes are perpendicular to the three mutually orthogonal mirror surfaces of the reference cubic prism (2); the coordinate system of the inertial measurement unit. O d X d Y d Z d The three coordinate axes coincide with the directions of the three principal axes of inertia, respectively; After calibrating the relative attitude between the reference cubic prism and the inertial measurement unit, the three-dimensional spatial vector of the laser beam irradiation point of the three-dimensional laser vibrometer (10) and the centroid of the inertial measurement unit (1) in the coordinate system of the inertial measurement unit is measured. ; Subsequently, the inertial measurement unit (1), the three-dimensional laser vibrometer (10), the first dual-axis photoelectric autocollimator (8), and the second dual-axis photoelectric autocollimator (9) are synchronously triggered. In the inertial measurement unit (1), the three-axis gyroscope outputs the first angular velocity. The triaxial accelerometer outputs the first acceleration. The three-dimensional laser vibrometer (10) outputs the second acceleration. The first dual-axis photoelectric autocollimator (8) and the second dual-axis photoelectric autocollimator (9) output the dynamic torsion angle vector of the reference cubic prism (2) in the cubic mirror coordinate system. The data acquisition module (11) collects the output data; The dynamic torsion angle vector in the cubic mirror coordinate system Transformed to the coordinate system of the inertial measurement unit to obtain ,Will Differentiation yields the triaxial angular velocity of the inertial measurement unit measured by the first and second dual-axis photoelectric autocollimators. ; Based on three-dimensional spatial vectors The second acceleration output by the three-dimensional laser vibrometer (10) and The triaxial acceleration measured by the three-dimensional laser vibrometer (10) in the coordinate system of the inertial measurement unit was obtained. ; Based on the first angular velocity First acceleration Triaxial acceleration measured in the inertial measurement unit coordinate system Inertial measurement unit triaxial angular velocity The linear-angular coupling motion of the inertial measurement unit is calibrated.

2. The inertial measurement unit line-angle coupling motion calibration method according to claim 1, characterized in that, A first plane mirror (5) and a second plane mirror (6) are installed on two mutually perpendicular surfaces on the side of the inertial measurement unit. The relative attitude between the reference cubic prism (2) and the inertial measurement unit (1) is determined by calibrating the theodolite, and the pitch angle of the cubic mirror coordinate system relative to the inertial measurement unit coordinate system is obtained. yaw angle and azimuth .

3. The inertial measurement unit line-angle coupling motion calibration method according to claim 2, characterized in that, Through the coordinate system of the inertial measurement unit O d X d Y d Z d And cubic mirror coordinate system O j X j Y j Z j attitude transformation matrix between The dynamic torsion angle vector in the cubic mirror coordinate system Transformed to the coordinate system of the inertial measurement unit to obtain .

4. The inertial measurement unit line-angle coupling motion calibration method according to claim 3, characterized in that, 。 5. The inertial measurement unit line-angle coupling motion calibration method according to claim 4, characterized in that, Triaxial acceleration measured in the inertial measurement unit coordinate system for: .

6. The inertial measurement unit line-angle coupling motion calibration method according to claim 5, characterized in that, Calibrate the linear-angular coupled motion of the inertial measurement unit, including the amplitude error, phase delay, and nonlinearity of the inertial device.

7. The inertial measurement unit line-angle coupling motion calibration method according to claim 6, characterized in that, The amplitude error, phase delay, and nonlinearity of inertial devices are calibrated based on the frequency response function H1 estimation.

8. An inertial measurement unit, characterized in that, The inertial measurement unit is calibrated using the line-angle coupling motion calibration method described in any one of claims 1-7.

9. An inertial measurement unit according to claim 8, characterized in that, The inertial measurement unit includes a three-axis accelerometer and a three-axis gyroscope, and the vibration error of the three-axis gyroscope is compensated based on the three-axis accelerometer.

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