Gyro and quartz accelerometer system calibration method for precision centrifuge measuring device

Abstract

The application discloses a precision centrifugal measuring device gyroscope and quartz accelerometer system calibration method, aiming at the specific situation of three-axis gyroscope and single-axis accelerometer in the precision centrifugal measuring device, establishes a system error model, designs an error calibration method, improves the measurement result accuracy, provides a more accurate acceleration reference for the accelerometer test, and reduces the precision requirement for the centrifugal machine. The calibration method comprises the following steps: pointing the three-axis gyroscope to the sky, respectively, and recording the gyroscope output in the positive and negative rotation of the sky direction axis at a fixed angular velocity; turning the three-axis gyroscope by six positions, and recording the gyroscope and accelerometer output; calculating the gyroscope zero offset, scale factor and installation error, the accelerometer zero offset and installation angle after measuring the corresponding output; and calculating the acceleration reference value. The calibration method is convenient to realize, can guarantee the calibration precision of the three-axis gyroscope and single-axis accelerometer inertial navigation system under the existing precision of the rotary table, and has strong practicability.

Description

Technical Field

[0001] This invention relates to a coordinate transformation and error calibration method for a triaxial gyroscope and a quartz accelerometer in a precision centrifugal measuring device. More specifically, it refers to a method for high-precision error calibration of inertial navigation systems in the context of centrifugal device applications, belonging to the fields of inertial sensor measurement and inertial navigation system error calibration. Background Technology

[0002] Quartz flexible accelerometers are force-balanced closed-loop servo-controlled accelerometers characterized by simple structure and high measurement accuracy, and are widely used in various inertial navigation systems. In the design and manufacturing of quartz flexible accelerometers, several key parameters are often considered, including measurement range, overload capacity, and quadratic coefficient. According to GJB1037A-2004, the measurement of these parameters requires a precision centrifuge. To more accurately measure the acceleration provided by the centrifuge, a three-axis high-precision fiber optic gyroscope is proposed to be mounted on the centrifuge, forming a precision centrifuge measurement device. The fiber optic gyroscope measures the centrifuge's rotational angular velocity. Considering that both the fiber optic gyroscope and the accelerometer under test have zero-bias error, scaling factor error, and installation error, the sensitive axis of the accelerometer under test must be unified to the gyroscope coordinate system, and the aforementioned error terms must be calibrated to improve measurement accuracy.

[0003] Calibration techniques are generally divided into discrete calibration and system-level calibration. System-level calibration requires filtering and analysis of system navigation results. In this invention, only a three-axis gyroscope is used, and there is no complete inertial measurement unit, so effective navigation information cannot be output. Therefore, system-level calibration methods are not applicable. Discrete calibration mainly relies on a turntable to provide standard input information to the system, which requires high precision of the test equipment. Since high calibration accuracy is required under the application context of this invention, it is necessary to analyze the impact of turntable error on the calibration results and minimize the impact as much as possible through calibration path design. Summary of the Invention

[0004] The purpose of this invention is to establish a systematic error model and design an error calibration method for the specific cases of triaxial gyroscopes and single-axis accelerometers under test in precision centrifugal measuring devices, thereby improving the accuracy of measurement results, providing a more accurate acceleration reference for accelerometer testing, and reducing the precision requirements of centrifuges.

[0005] To achieve the above objectives, based on the analysis of the error model, a calibration method incorporating six-position static tests and three-position rate tests was designed. This method can calibrate the zero bias, scale factor, and installation error of the three-axis gyroscope and the instrument under test in the simplest position, considering turntable errors. The specific scheme is as follows:

[0006] A calibration method for a precision centrifugal measuring device gyroscope and quartz accelerometer system includes the following steps:

[0007] S1, perform gyroscope rotation calibration to obtain the three-axis gyroscope output;

[0008] S2, perform static position calibration of the gyroscope and the accelerometer under test, and obtain the output of the gyroscope and the accelerometer;

[0009] S3. Based on the data obtained in steps S1 and S2, perform error estimation to obtain the gyroscope and accelerometer zero bias, gyroscope scaling factor and installation error, and accelerometer installation angle.

[0010] S4. Based on the data obtained in step S3, the system calibration of the gyroscope and accelerometer is completed, and the theoretical output value of the accelerometer is obtained, providing a reference value for precision centrifugation testing.

[0011] Furthermore, step S1 includes the following sub-steps:

[0012] S1.1 Point the z-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their average values, denoted as .

[0013] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as .

[0014] S1.2 Point the x-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the output of the three-axis gyroscopes and calculate the average value of each, denoted as .

[0015] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as .

[0016] S1.3 Point the y-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their averages, denoted as .

[0017] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as .

[0018] Furthermore, step S2 includes the following sub-steps:

[0019] S2.1 Rotate the x, y, and z axes to the "East-North-Sky" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows:

[0020] S2.2 Rotate the x, y, and z axes to the "West-South-Sky" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows:

[0021] S2.3 Rotate the x, y, and z axes to the "North-East-Earth" position, collect 3 minutes of static gyroscope and accelerometer outputs, and calculate the average values, denoted as follows:

[0022] S2.4 Rotate the x, y, and z axes to the "South-West-Ground" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows:

[0023] S2.5 Rotate the x, y, and z axes to the "Sky-East-North" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average value of the data.

[0024] S2.6 Rotate the x, y, and z axes to the "Earth-North-East" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average value of the data.

[0025] Furthermore, the gyroscope and accelerometer have zero bias.

[0026]

[0027]

[0028] Where, ε x ε y ε z Indicates zero bias of the gyroscope, ▽ A This indicates that the accelerometer has zero bias.

[0029] The gyroscope scale factor and installation error are:

[0030]

[0031]

[0032]

[0033] Among them, S mn (m,n = x,y,z) is the gyroscope installation error factor; K gx K gy K gz Indicates the gyroscope scale factor;

[0034] The accelerometer installation angle is

[0035]

[0036]

[0037] Where σ1 is the angle between the sensitive axis of the accelerometer under test and the xOy plane of the three-axis orthogonal coordinate system of the gyroscope, and σ2 is the angle between the projection of the sensitive axis of the accelerometer under test onto the xOy plane and the y-axis.

[0038] Furthermore, the theoretical output value of the accelerometer is

[0039]

[0040] Where, N A0 N is the accelerometer output value. gx N gy N gz To compensate for the error, the angular velocity is R, which is the distance from the location of the acceleration to the center of the heart machine rotation, measured by laser rangefinder.

[0041] The advantages of this invention are as follows: A set of rapid calibration methods for laboratory conditions is designed for specific three-axis gyroscopes and single-axis inertial navigation systems with added dial gauges, completing the calibration of device errors and installation errors. Simultaneously, considering the application background of high-precision calibration, this invention also models the turntable angular position error and analyzes the impact of existing high-precision turntable errors on the calibration results through simulation experiments, verifying the calibration residual results under actual application conditions. Simulation results show that this calibration method requires fewer calibration points, is easy to implement, and can guarantee the calibration accuracy of three-axis gyroscopes and single-axis inertial navigation systems with added dial gauges under existing turntable accuracy, demonstrating strong practicality. Attached Figure Description

[0042] Figure 1 It refers to the relative positional relationship of the speed measurement components.

[0043] Figure 2 This is a schematic diagram of gyroscope installation errors.

[0044] Figure 3 This is a schematic diagram of the accelerometer installation angle.

[0045] Figure 4 This is a flowchart of the calibration method for a precision centrifugal measuring device gyroscope and quartz accelerometer system.

[0046] Figure 5 Schematic diagram of the three-position rotation scheme.

[0047] Figure 6 Schematic diagram of a four-position static scheme.

[0048] Figure 7 Schematic diagram of accelerometer calibration supplementary position.

[0049] Figure 8 It is a coordinate transformation relationship including angular position reference error. Detailed Implementation

[0050] The present invention will now be described in further detail with reference to the accompanying drawings.

[0051] The precision centrifugation measurement device consists of a precision centrifuge, a three-axis fiber optic gyroscope, a laser rangefinder, and an accelerometer under test. The three-axis fiber optic gyroscope measures the centrifuge rotation speed, the laser rangefinder measures the radius of rotation, and the acceleration reference value at the accelerometer under test is calculated using the centripetal acceleration calculation formula.

[0052] The relative positions of the speed measurement sections are as follows: Figure 1 As shown, the three-axis orthogonal coordinate system formed by the gyroscope and the three-axis orthogonal coordinate system at the accelerometer are parallel to each other along their corresponding axes. To ensure that the rotational speed output by the gyroscope accurately reflects the true rotational speed at the accelerometer being measured, it is necessary to unify the gyroscope coordinate system and the sensitive axis of the accelerometer, and to calibrate and compensate for the main error terms present in the system.

[0053] The error terms involved in this invention include:

[0054] (1) Device zero bias

[0055] Zero bias refers to the instrument's output value when the true value is zero. x ε y ε z Indicates that the unit is ° / s, and the accelerometer zero bias is expressed in ▽. A Indicates the unit is m / s 2 .

[0056] (2) Device scaling factor

[0057] The scaling factor refers to the proportional relationship between the instrument output and the true value when the input and output coordinate systems are consistent. In the following text, the gyroscope scaling factor is denoted as K. gx K gy K gz The accelerometer scale factor is expressed as K. A .

[0058] (3) Installation error

[0059] Generally, there is an orthogonality requirement for the sensing axes of a three-axis gyroscope, but due to limitations in actual installation conditions, the x-axis of the gyroscope sensing axis... g y g z g There are installation error angles between the x, y, and z axes and the orthogonal coordinate axes, denoted as angles 1-6, such as... Figure 2As shown, this installation error angle will cause the gyroscope installation error factor discussed later. Furthermore, there will be an installation angle between the sensitive axis of the accelerometer under test and the orthogonal coordinate system formed by the three-axis gyroscope, which can be decomposed into the angle σ1 between the sensitive axis of the accelerometer under test and the xOy plane, and the angle σ2 between the projection of the sensitive axis onto the xOy plane and the y-axis, as shown below. Figure 3 As shown.

[0060] Combining the three types of errors, the systematic error model of the three-axis gyroscope and the single-axis accelerometer is established as follows:

[0061]

[0062]

[0063] Among them, S mn (m,n=x,y,z) represents the coefficients before ω, defined as the gyroscope installation error factor, ω x ω y ω z For the gyroscope's standard input, N x N y N z For gyroscope output, v gx v gy v gz This is gyroscope noise; A x A y A z For the accelerometer standard input, N A For the output of the accelerometer under test, v A This is accelerometer noise.

[0064] Based on the above model, the orthogonalization and normalization of the gyroscope and the position transfer between the single-axis accelerometer and the gyroscope coordinate system were completed.

[0065] like Figure 4 As shown, the specific calibration path is as follows:

[0066] Step 1: Gyroscope rotation calibration

[0067] 1.1 Point the z-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their average values, denoted as ω.

[0068] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . like Figure 5 As shown in (a);

[0069] 1.2 Point the x-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the output of the three-axis gyroscopes and calculate the average value of each, denoted as .

[0070] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . like Figure 5 As shown in (b);

[0071] 1.3 Point the y-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their average values, denoted as .

[0072] The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . like Figure 5 As shown in (c).

[0073] Step 2: Static position calibration of gyroscope / accelerometer under test

[0074] 2.1 Rotate the x, y, and z axes to the "East-North-Sky" position, collect 3 minutes of static gyroscope and accelerometer outputs, and calculate the average values, denoted as follows: like Figure 6 As shown in (a);

[0075] 2.2 Rotate the x, y, and z axes to the "West-South-Sky" position, collect 3 minutes of static gyroscope and accelerometer outputs, and calculate the average values, denoted as follows: like Figure 6 As shown in (b);

[0076] 2.3 Rotate the x, y, and z axes to the "North-East-Earth" position, collect 3 minutes of static gyroscope and accelerometer outputs, and calculate the average values, denoted as follows: like Figure 6 As shown in (c);

[0077] 2.4 Rotate the x, y, and z axes to the "South-West-Ground" position, collect the static outputs of the gyroscope and accelerometer for 3 minutes, and calculate the average values ​​of the data, denoted as follows: like Figure 6 As shown in (d);

[0078] 2.5 Rotate the x, y, and z axes to the "Sky-East-North" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average value of the data. like Figure 7 As shown in (a);

[0079] 2.6 Rotate the x, y, and z axes to the "Earth-North-East" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average values, denoted as follows: like Figure 7As shown in (b).

[0080] After completing data collection and recording, substitute the results into the following formula to estimate the error.

[0081] (1) Calculate the zero bias of the gyroscope and accelerometer using the results of positions 2.1, 2.2, 2.3, and 2.4;

[0082]

[0083] (2) Calculate the gyroscope scaling factor and installation error using the results from steps 1.1 to 1.3;

[0084]

[0085]

[0086] (3) Calculate the accelerometer installation angle using the position results from 2.1 to 2.6.

[0087]

[0088] After obtaining the installation angle between the accelerometer under test and the gyroscope coordinate system, the acceleration reference value in the sensitive axis direction of the accelerometer under test can be calculated from the gyroscope angular velocity, as shown in equation (6).

[0089]

[0090] Where, N A0 N is the theoretical output value of the accelerometer. gx N gy N gz To compensate for the error, the angular velocity is calculated using equation (1), where R is the distance from the location of the acceleration to the center of the accelerometer rotation, measured by laser ranging. During the calculation, the noise terms of the gyroscope and accelerometer [v] are included. gx v gy v gz ] T v A Since this is a random error, it cannot be obtained through calibration, therefore no compensation is made.

[0091] In high-precision calibration, the rotation operation is mainly performed using a dual-axis rate turntable. Therefore, certain error terms of the turntable will directly affect the calibration accuracy. In order to eliminate the influence of turntable errors and improve calibration accuracy, it is necessary to analyze the model of each error term of the turntable and its impact on the error calibration of inertial devices.

[0092] Generally, turntable errors can be categorized into turntable angular position reference error, positioning error, perpendicularity error, rotation error, and intersection error. During calibration, only the turntable's directional positioning and rotation functions are used; the calibration results are unrelated to the turntable's intersection error, therefore, the intersection error can be disregarded during modeling. The turntable angular position reference error is caused by turntable installation and long-term use, and its magnitude is relatively large, so it will be analyzed in detail later. Other errors are internal turntable errors, generally small and stable in magnitude, and therefore, their impact is temporarily disregarded.

[0093] The angular position reference error of the turntable is divided into east-west horizontal error, north-south horizontal error, and azimuth error. A mathematical relationship between the actual coordinate system (n′ system) and the reference coordinate system (n system) can be established through Euler angle rotation, such as... Figure 8 As shown in the figure. α and β are the horizontal errors of the angular position reference, and γ is the azimuth error of the angular position reference.

[0094] The coordinate system transformation relationship represented by the direction cosine matrix is ​​as follows:

[0095]

[0096] By modeling and analyzing the turntable angular position error, it can be found that under the above calibration path design, the turntable error has no effect on the gyroscope zero bias, scale factor, or installation error calculation, and has no effect on the accelerometer zero bias, but it does have a certain impact on the accelerometer installation angle calibration. However, through simulation calculations, under the current turntable angular second-level accuracy conditions, the calibration error for the installation angle is within 10... -3 The error is within acceptable limits. This analysis further demonstrates the feasibility of the calibration path proposed in this invention.

[0097] Simulation analysis was performed on the above calibration scheme. The initial simulation conditions were set as follows:

[0098] (1) Initial longitude 116.3434°, initial latitude 39.9778°, initial altitude 40m, sampling time 0.1s;

[0099] (2) Gyroscope zero deviation 0.01° / h, scale factor error 10ppm, installation error angle 1';

[0100] (3) Accelerometer zero bias 10μg, installation angle σ1=σ2=0;

[0101] (4) Turntable angle position error [5"; 5"; 5"].

[0102] The calibration results are shown in Table 1 and Table 2.

[0103] Table 1 Calibration results without considering turntable error

[0104]

[0105] Table 2 Calibration results considering turntable error

[0106]

Claims

1. A calibration method for a precision centrifugal measuring device's gyroscope and quartz accelerometer system, characterized in that, Includes the following steps: S1, perform gyroscope rotation calibration to obtain the three-axis gyroscope output; S2, perform static position calibration of the gyroscope and the accelerometer under test, and obtain the output of the gyroscope and the accelerometer; S3. Based on the data obtained in steps S1 and S2, perform error estimation to obtain the gyroscope and accelerometer zero bias, gyroscope scaling factor and installation error, and accelerometer installation angle. S4. Based on the data obtained in step S3, the system calibration of the gyroscope and accelerometer is completed, and the theoretical output value of the accelerometer is obtained to provide a reference value for precision centrifugation test. Step S1 includes the following sub-steps: S1.1 Point the z-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their average values, denoted as . , , ; The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . , , ; S1.2 Point the x-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the output of the three-axis gyroscopes and calculate the average value of each, denoted as . , , ; The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . , , ; S1.3 Point the y-axis gyroscope upwards and rotate it n times around the celestial axis at a fixed angular rate ω. Record the outputs of the three-axis gyroscopes and calculate their averages, denoted as . , , ; The three-axis gyroscopes rotate n times around the celestial axis at the same angular velocity. The outputs of each gyroscope are recorded and their average values ​​are calculated, denoted as . , , ; Step S2 includes the following sub-steps: S2.1 Rotate the x, y, and z axes to the "East-North-Sky" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows: , , , ; S2.2 Rotate the x, y, and z axes to the "West-South-Sky" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows: , , , ; S2.3 Rotate the x, y, and z axes to the "North-East-Earth" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows: , , , ; S2.4 Rotate the x, y, and z axes to the "South-West-Ground" position, collect the gyroscope and accelerometer outputs under static conditions for 3 minutes, and calculate the average values ​​of the data, denoted as follows: , , , ; S2.5 Rotate the x, y, and z axes to the "Sky-East-North" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average value of the data. ; S2.6 Rotate the x, y, and z axes to the "Earth-North-East" position, collect accelerometer output data under static conditions for 3 minutes, and calculate the average value of the data. ; The zero bias of the gyroscope and accelerometer is in, , , This indicates that the gyroscope has zero bias. This indicates that the accelerometer has zero bias. The gyroscope scale factor and installation error are: ， ， ， ， ， ， in, ( ) represents the gyroscope installation error factor; , , Indicates the gyroscope scale factor; The accelerometer installation angle is in, σ 1 represents the angle between the sensitive axis of the accelerometer under test and the xOy plane of the orthogonal coordinate system of the gyroscope. σ 2 represents the angle between the projection of the sensitive axis of the accelerometer under test onto the xOy plane and the y-axis.

2. The calibration method for the gyroscope and quartz accelerometer system of the precision centrifugal measuring device according to claim 1, characterized in that, The theoretical output value of the accelerometer is in, For accelerometer output value, , , The angular velocity after compensating for the error, R The distance from the location of the acceleration to the center of the heartbeat rotation is measured by laser rangefinder.

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