### Post by kellyyu on Jan 11, 2024 3:57:31 GMT -5

MEMS gyroscope is a key component in navigation systems. Inertial navigation systems are widely used in aerospace, petroleum logging, mining, surveying, and other fields. Improving its accuracy is of great significance to improving the performance of navigation systems.

Generally speaking, there are two ways to improve the accuracy of MEMS gyroscopes: one is to improve its accuracy from the perspective of instrument research and development, and study new mechanisms, new effects, and new processes, but the investment is often large and the output is small; the second is to establish MEMS gyroscope error parameter model, arrange a reasonable test path, and use high-precision test equipment such as a three-axis turntable to calibrate the parameters in the error model to compensate the MEMS gyroscopes. MEMS gyro calibration is to give the MEMS gyro a stable angular rate input through the input of the turntable, then collect the output of the MEMS gyro, and estimate various error parameters of the MEMS gyro through data processing. In fact, due to the inaccuracy of the three-axis turntable of the test equipment and the influence of environmental factors, there will be errors in the calibration results. For example, the axis verticality error of the turntable, the inclination rotation error, and the motion control accuracy error will all affect the performance of the MEMS gyro during calibration. output, thus affecting the calibration accuracy.

Therefore, this article analyzes the impact of turntable error on MEMS gyro calibration. The following will analyze the three-axis turntable model, three-axis turntable error analysis, and MEMS gyro calibration principles and processes.

Figure 1 is the three-axis turntable model analyzed in this article. Ideally, the axis of the outer frame is always perpendicular to the ground, and the three axes are perpendicular to each other. However, in fact, due to factors such as processing and assembly, manufacturing accuracy, motion control, and environment, three-axis turntables often have various errors. When the turntable rotates, the motion errors generated by the three axes can be represented by the axis rotation error. The verticality of the axis is often converted into the verticality between the axes and the intersection of the axes between the axes due to the motion characteristics of the turntable frame.

Figure 1 Three-axis turntable model

Assume the geographical coordinate system is body 0, and define the low sequence operator as shown in Figure 2. The base coordinate is marked as body 1, the axis system of the outer frame is marked as body 2, the axis system of the middle frame is marked as body 3, and the axis system of the inner frame is marked as body 4. It is a 4-body structure, and the MEMS gyroscope is directly installed under the inner frame axis coordinate system. By performing coordinate transformation on the obtained low-order body array of the three-axis turntable, the motion and position relationship between any two individuals can be obtained.

Figure 2 Three-axis turntable low-sequence array

According to the schematic diagram of motion error analysis between two bodies in Figure 3, the position matrix of a certain point can be expressed in the geographical coordinate system using the following formula:

In the formula: {re0} is the initial position of a given point, [AJK]p is the attitude transformation matrix between the low-order body coordinate system and the adjacent reference system, which is used to describe the movement of the low-order body relative to its adjacent low-order body , [AJK]sp and [AJK]pe are the motion error transformation matrix and position error transformation matrix between adjacent low-order bodies, including 3 angular displacement and 3 linear displacement error terms respectively.

Figure 3 Analysis of motion error between two bodies

1. Inclination rotation error

During the movement of the turntable, the shaking and deviation of each axis system have a greater impact on the calibration equipment. Therefore, the inclination angle rotation error is stipulated. When the three-axis turntable is running, the main axis of the axis system at any time includes two movements. One is the rotation around the turntable. Its own rotation axis rotates, and secondly, its own rotation axis and main shaft have axial, radial and inclination movements with respect to the average axis of the rotation shaft.

2. Verticality error

The difference between the angle between the two axes and 90° is defined as the verticality error. The pointing accuracy of the turntable is mainly affected by the verticality of the axis. Therefore, high requirements will be placed on the verticality of the axis when accepting the turntable. When the turntable is actually running, the movement between each axis will produce inter-axis coupling. The instantaneous rotation axis verticality between the axes is related to the average rotation axis verticality and the angular position of the two axes.

3. Angular position error

Angular position error refers to the difference between the theoretical rotation angle and the actual rotation angle.

4. MEMS gyroscopealignment error

MEMS gyroscope alignment error refers to the angle difference between each rotation axis of the gyroscope and the reference system defined by the system. The gyroscope alignment error is mainly related to the processing technology and installation non-orthogonality.

During gyroscope calibration, when the angular rate of the turntable is large, the rotation time is short, and the earth’s rotation angular rate is much greater than the drift amount of MEMS gyroscopes, so the drift of the gyroscope and the scale factor matrix can be calibrated separately. The common method is to install the gyroscope on the inner frame of the turntable, control the three axes of the turntable to rotate forward and reverse for n turns, set the unit time, collect the gyro angular rate output, and use the output pulse of the forward rotation of the gyro to the reverse rotation of the gyro. The output pulse is poor, weakening the influence of the earth’s rotation angular rate and the drift of the gyroscope itself. The turntable used for calibration is a three-axis turntable with a U-O-O shape. The three axes can rotate continuously 360°. MEMS gyroscope is installed on the inner frame and is installed as shown in Figure 4. During calibration, the outer frame continuously rotates. By controlling the middle frame and the inner frame, the calibration axis coincides with the axis of the outer frame in sequence.

Establish the geographical coordinate system o0x0y0z0, the outer frame axis coordinate system o1x1y1z1, the middle frame axis coordinate system o2x2y2z2, the inner frame axis coordinate system o3x3y3z3 and the MEMS gyro coordinate system OXYI on the three-axis turntable, where X represents the x-axis direction of the MEMS gyro, and Y represents the y-axis direction of the gyroscope, I represents the input axis direction of MEMS gyroscopes. In an ideal state, the three-axis coordinate systems are coincident, the rotation angle is zero, and the MEMS gyroscope is installed on the inner frame axis coordinate system. At the initial moment, the x-axis of the MEMS gyroscope is parallel to the middle frame axis, the y-axis is parallel to the inner frame axis, and the input axis I is parallel to the outer frame axis.

The specific calibration process of MEMS gyroscopes are as follows:

First, the turntable is energized and preheated. After the gyro connected to it runs for a certain time, the unit sampling time is set when the gyro output data is stable. The arrangement path of this calibration is to calibrate parameters by single-axis speed dual-axis position method. The outer frame of the turntable is used as the input axis, input a constant angular rate, the inner frame axis and the middle frame axis are in the angular position state, record the outer frame angular rate, the inner frame Angle position and the middle frame Angle position, and carry out two positive and negative rotation experiments to offset the influence of the earth rotation and the gyro’s own drift.

Figure 4 Schematic diagram of coordinate system

This article establishes a three-axis turntable error model based on multi-body system theory, lists the low-order body array of the turntable system, and analyzes various errors of the three-axis turntable in detail, including geometric errors and motion errors.

It can be seen from the previous article that due to various errors in the three-axis turntable, the output of the MEMS gyros will also be biased, and the coefficients calibrated will also be biased. Therefore, if you want to accurately calibrate the error coefficient of the MEMS gyroscopes, you need to measure the various errors of the turntable, obtain the corresponding error coefficient value, and substitute it into the gyroscope’s full error parameter model to improve the calibration accuracy.

As a developer and manufacturer of gyroscopes, Ericco has adopted strict control measures for the calibration methods of gyroscopes, and will also conduct measurement and debugging of the turntable equipment. Especially the navigation-level ER-MG2-50/100 and ER-MG2-300/400 have excellent accuracy and high calibration accuracy. Their bias instability can reach 0.01-0.02°/hr and 0.03-0.05°/hr respectively.

If you are interested in other knowledge about MEMS gyroscopes, please click on the relevant products and text below to continue learning.

Generally speaking, there are two ways to improve the accuracy of MEMS gyroscopes: one is to improve its accuracy from the perspective of instrument research and development, and study new mechanisms, new effects, and new processes, but the investment is often large and the output is small; the second is to establish MEMS gyroscope error parameter model, arrange a reasonable test path, and use high-precision test equipment such as a three-axis turntable to calibrate the parameters in the error model to compensate the MEMS gyroscopes. MEMS gyro calibration is to give the MEMS gyro a stable angular rate input through the input of the turntable, then collect the output of the MEMS gyro, and estimate various error parameters of the MEMS gyro through data processing. In fact, due to the inaccuracy of the three-axis turntable of the test equipment and the influence of environmental factors, there will be errors in the calibration results. For example, the axis verticality error of the turntable, the inclination rotation error, and the motion control accuracy error will all affect the performance of the MEMS gyro during calibration. output, thus affecting the calibration accuracy.

Therefore, this article analyzes the impact of turntable error on MEMS gyro calibration. The following will analyze the three-axis turntable model, three-axis turntable error analysis, and MEMS gyro calibration principles and processes.

**Three-axis turntable model**

Figure 1 is the three-axis turntable model analyzed in this article. Ideally, the axis of the outer frame is always perpendicular to the ground, and the three axes are perpendicular to each other. However, in fact, due to factors such as processing and assembly, manufacturing accuracy, motion control, and environment, three-axis turntables often have various errors. When the turntable rotates, the motion errors generated by the three axes can be represented by the axis rotation error. The verticality of the axis is often converted into the verticality between the axes and the intersection of the axes between the axes due to the motion characteristics of the turntable frame.

Figure 1 Three-axis turntable model

Assume the geographical coordinate system is body 0, and define the low sequence operator as shown in Figure 2. The base coordinate is marked as body 1, the axis system of the outer frame is marked as body 2, the axis system of the middle frame is marked as body 3, and the axis system of the inner frame is marked as body 4. It is a 4-body structure, and the MEMS gyroscope is directly installed under the inner frame axis coordinate system. By performing coordinate transformation on the obtained low-order body array of the three-axis turntable, the motion and position relationship between any two individuals can be obtained.

Figure 2 Three-axis turntable low-sequence array

According to the schematic diagram of motion error analysis between two bodies in Figure 3, the position matrix of a certain point can be expressed in the geographical coordinate system using the following formula:

In the formula: {re0} is the initial position of a given point, [AJK]p is the attitude transformation matrix between the low-order body coordinate system and the adjacent reference system, which is used to describe the movement of the low-order body relative to its adjacent low-order body , [AJK]sp and [AJK]pe are the motion error transformation matrix and position error transformation matrix between adjacent low-order bodies, including 3 angular displacement and 3 linear displacement error terms respectively.

Figure 3 Analysis of motion error between two bodies

**Three-axis turntable error analysis**

1. Inclination rotation error

During the movement of the turntable, the shaking and deviation of each axis system have a greater impact on the calibration equipment. Therefore, the inclination angle rotation error is stipulated. When the three-axis turntable is running, the main axis of the axis system at any time includes two movements. One is the rotation around the turntable. Its own rotation axis rotates, and secondly, its own rotation axis and main shaft have axial, radial and inclination movements with respect to the average axis of the rotation shaft.

2. Verticality error

The difference between the angle between the two axes and 90° is defined as the verticality error. The pointing accuracy of the turntable is mainly affected by the verticality of the axis. Therefore, high requirements will be placed on the verticality of the axis when accepting the turntable. When the turntable is actually running, the movement between each axis will produce inter-axis coupling. The instantaneous rotation axis verticality between the axes is related to the average rotation axis verticality and the angular position of the two axes.

3. Angular position error

Angular position error refers to the difference between the theoretical rotation angle and the actual rotation angle.

4. MEMS gyroscopealignment error

MEMS gyroscope alignment error refers to the angle difference between each rotation axis of the gyroscope and the reference system defined by the system. The gyroscope alignment error is mainly related to the processing technology and installation non-orthogonality.

**MEMS gyroscope calibration principle and process**

During gyroscope calibration, when the angular rate of the turntable is large, the rotation time is short, and the earth’s rotation angular rate is much greater than the drift amount of MEMS gyroscopes, so the drift of the gyroscope and the scale factor matrix can be calibrated separately. The common method is to install the gyroscope on the inner frame of the turntable, control the three axes of the turntable to rotate forward and reverse for n turns, set the unit time, collect the gyro angular rate output, and use the output pulse of the forward rotation of the gyro to the reverse rotation of the gyro. The output pulse is poor, weakening the influence of the earth’s rotation angular rate and the drift of the gyroscope itself. The turntable used for calibration is a three-axis turntable with a U-O-O shape. The three axes can rotate continuously 360°. MEMS gyroscope is installed on the inner frame and is installed as shown in Figure 4. During calibration, the outer frame continuously rotates. By controlling the middle frame and the inner frame, the calibration axis coincides with the axis of the outer frame in sequence.

Establish the geographical coordinate system o0x0y0z0, the outer frame axis coordinate system o1x1y1z1, the middle frame axis coordinate system o2x2y2z2, the inner frame axis coordinate system o3x3y3z3 and the MEMS gyro coordinate system OXYI on the three-axis turntable, where X represents the x-axis direction of the MEMS gyro, and Y represents the y-axis direction of the gyroscope, I represents the input axis direction of MEMS gyroscopes. In an ideal state, the three-axis coordinate systems are coincident, the rotation angle is zero, and the MEMS gyroscope is installed on the inner frame axis coordinate system. At the initial moment, the x-axis of the MEMS gyroscope is parallel to the middle frame axis, the y-axis is parallel to the inner frame axis, and the input axis I is parallel to the outer frame axis.

The specific calibration process of MEMS gyroscopes are as follows:

First, the turntable is energized and preheated. After the gyro connected to it runs for a certain time, the unit sampling time is set when the gyro output data is stable. The arrangement path of this calibration is to calibrate parameters by single-axis speed dual-axis position method. The outer frame of the turntable is used as the input axis, input a constant angular rate, the inner frame axis and the middle frame axis are in the angular position state, record the outer frame angular rate, the inner frame Angle position and the middle frame Angle position, and carry out two positive and negative rotation experiments to offset the influence of the earth rotation and the gyro’s own drift.

Figure 4 Schematic diagram of coordinate system

**Conclusion**

This article establishes a three-axis turntable error model based on multi-body system theory, lists the low-order body array of the turntable system, and analyzes various errors of the three-axis turntable in detail, including geometric errors and motion errors.

It can be seen from the previous article that due to various errors in the three-axis turntable, the output of the MEMS gyros will also be biased, and the coefficients calibrated will also be biased. Therefore, if you want to accurately calibrate the error coefficient of the MEMS gyroscopes, you need to measure the various errors of the turntable, obtain the corresponding error coefficient value, and substitute it into the gyroscope’s full error parameter model to improve the calibration accuracy.

As a developer and manufacturer of gyroscopes, Ericco has adopted strict control measures for the calibration methods of gyroscopes, and will also conduct measurement and debugging of the turntable equipment. Especially the navigation-level ER-MG2-50/100 and ER-MG2-300/400 have excellent accuracy and high calibration accuracy. Their bias instability can reach 0.01-0.02°/hr and 0.03-0.05°/hr respectively.

If you are interested in other knowledge about MEMS gyroscopes, please click on the relevant products and text below to continue learning.