A fast rotation calibration method for MEMS accelerometer

Abstract

The invention discloses a fast rotation calibration method of a MEMS accelerometer, which belongs to the field of acceleration measurement technology, including establishing a calibration model of the accelerometer; establishing an error optimal estimation model based on the least square method; adjusting the three axes of the accelerometer to the horizontal direction as reference axes respectively, and pointing to the first orientation and the second orientation respectively; when the reference axis points to the first orientation or the second orientation, the remaining two axes rotate around the reference axis as sensitive axes, and the rotation plane is perpendicular to the horizontal plane; collecting the actual measurement value output by the sensitive axis during the rotation process, and calculating the corresponding theoretical output value, substituting it into the error optimal estimation model based on the least square method, fitting and calculating the calibration parameters, substituting them into the calibration model, and completing the calibration process. The method can perform error calibration on the accelerometer during the rotation process, so it can be calibrated synchronously with the gyroscope, simplifying the calibration process, and improving the calibration efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of acceleration measurement, and in particular relates to a fast rotation calibration method of a MEMS accelerometer. Background Art

[0002] With the increasing demand for integration and miniaturization of modern electronic devices, the development of MEMS (Micro-Electro-Mechanical Systems) is changing with each passing day. MEMS accelerometers, as acceleration measurement devices in the field of micro-electromechanical systems, are usually used together with MEMS gyroscopes to form MEMS inertial groups, which provide information about the object's motion state by measuring the acceleration and angular velocity of the object. MEMS inertial groups have significant advantages such as small size, low power consumption, easy integration and low cost. Therefore, they have been increasingly widely used in attitude measurement, navigation control and other fields. However, MEMS accelerometers themselves have problems such as low accuracy and large zero bias. Before use, they need to be calibrated to determine the error compensation parameters, thereby improving performance indicators and improving accuracy.

[0003] In the existing MEMS inertial group calibration process, the calibration of MEMS accelerometers and MEMS gyroscopes is usually carried out independently. The calibration methods of MEMS accelerometers mainly include multi-position static calibration method, centrifuge calibration method and impact calibration method for large-range accelerometers. Among them, the multi-position static calibration method requires a platform with high horizontal accuracy; the centrifuge calibration method and the impact calibration method require the use of uncommon equipment such as centrifuges and impact tables to complete. The calibration method of MEMS gyroscopes mainly adopts the rotation calibration method, and the equipment usually used is a turntable. Obviously, in the existing method, the MEMS accelerometer cannot be synchronized with the rotation calibration of the MEMS gyroscope, which leads to the calibration work of the MEMS inertial group. There are problems such as complicated procedures and long calibration time. Moreover, the static calibration method of the MEMS accelerometer is overly dependent on the horizontal accuracy of the platform, which makes the implementation of batch calibration difficult. Summary of the invention

[0004] In order to solve the problem that the existing MEMS inertial group calibration method has a complicated calibration process and a long time consumption due to the inability to synchronize the accelerometer and the gyroscope, the present invention proposes a fast rotation calibration method for a MEMS accelerometer, which completes the calibration of the MEMS accelerometer error during the rotation process.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions to achieve the above problems:

[0006] A fast rotation calibration method for a MEMS accelerometer, comprising:

[0007] Establish the calibration model of the three-axis MEMS accelerometer:

[0008] ;

[0009] in, is the theoretical output value of the three-axis sensor; is the linear scale factor error; is the actual measurement value of the three-axis sensor; is zero bias;

[0010] Establish the error optimal estimation model based on the least squares method:

[0011] ;

[0012] in, is the coefficient matrix The optimal solution, coefficient matrix ; is the measurement data matrix, and ;

[0013] The x-axis, y-axis, and z-axis of the MEMS accelerometer are respectively used as reference axes, adjusted to the horizontal direction, and pointed to the first orientation and the second orientation with a horizontal angle difference of 180° respectively;

[0014] When the reference axis points to the first orientation or the second orientation, the remaining two axes rotate around the reference axis as sensitive axes, and the rotation plane is perpendicular to the horizontal plane;

[0015] Collect the actual measurement values ​​output by the sensitive axis during rotation and combine them to form the actual measurement values ​​of the three-axis sensor ;

[0016] According to the rotation angle and initial angle of the sensitive axis, calculate the angle of the sensitive axis relative to the direction pointing to the sky ;

[0017] Use the following formula to calculate the theoretical output value corresponding to the actual measured value:

[0018] ;

[0019] in, is the local gravity acceleration value;

[0020] The actual measured value And the corresponding theoretical output value Substitute the error optimal estimation model based on the least squares method into the fitting calculation to obtain the linear scaling factor error and zero bias ;

[0021] The calculated linear scale factor error and zero bias Substitute into the calibration model to complete the calibration process.

[0022] In some embodiments of the present application, the ; ; ; ;in, , , They represent the actual measurement values ​​of the x-axis, y-axis, and z-axis sensors in the MEMS accelerometer respectively; , , Respectively represent the theoretical output values ​​of the x-axis, y-axis, and z-axis sensors; , , Represents the linear scale factor errors of the x-axis, y-axis, and z-axis sensors respectively; is the non-orthogonal error; , , They represent the zero bias of the x-axis, y-axis, and z-axis sensors respectively.

[0023] In some embodiments of the present application, the first orientation and the second orientation can be set to geographic east and geographic west respectively; or, the first orientation and the second orientation can be set to geographic north and geographic south respectively, so as to facilitate the use of an existing turntable to perform a rotation test on the MEMS accelerometer.

[0024] In some embodiments of the present application, when the x-axis, y-axis, and z-axis of the MEMS accelerometer are respectively used as reference axes to select a first orientation and a second orientation, some reference axes (such as the x-axis or the y-axis) can be set to select geographic east and geographic west, and some reference axes (such as the z-axis) can be set to select geographic north and geographic south, so as to eliminate calibration errors that may be caused by a single direction.

[0025] In some embodiments of the present application, in order to make the actual measurement value output by the sensitive axis go through the entire cycle from the maximum value to the minimum value and then from the minimum value to the maximum value, so as to select all feature points suitable for calibration, the sensitive axis can be set to rotate at least one circle around the reference axis so that the angle Covering the entire range [0°,360°).

[0026] In some embodiments of the present application, in order to facilitate the calculation of the rotation angle of the sensitive axis, the sensitive axis can be set to rotate at a constant speed around the reference axis, that is, the angle of rotation per second is fixed, so that the rotation angle of the sensitive axis can be calculated based on the sampling time of the actual measurement value and the rotation speed of the sensitive axis.

[0027] In some embodiments of the present application, in order to reduce the amount of calculation and shorten the calibration time, the following feature point selection process may be performed before calculating the theoretical output value corresponding to the actual measurement value:

[0028] Starting from 0°, each rotation angle β is regarded as a selected angle , until the angle Approaching 360°;

[0029] According to the selected angle Determine the corresponding actual measurement value as the calibrated feature point;

[0030] Calculate the theoretical output value corresponding to the feature point for calibration parameters S , B Fitting calculation.

[0031] In some embodiments of the present application, the angle β can be 30° or 45°, so that the actual measurement value output by the sensitive axis can go through the entire cycle from the maximum value to the minimum value and then from the minimum value to the maximum value, thereby improving the calibration accuracy.

[0032] In some embodiments of the present application, feature points may also be selected in the following manner:

[0033] Select multiple representative feature points from actual measurement values ​​output by each sensitive axis within one rotation cycle;

[0034] The representative feature points should at least include the maximum value, the intermediate value during the transition from the maximum value to the minimum value, the minimum value, and the intermediate value during the transition from the minimum value to the maximum value;

[0035] Determine the corresponding angle based on the selected feature point ;

[0036] According to the selected angle Calculate the theoretical output value corresponding to each feature point to fit the linear scale factor error and zero bias .

[0037] In some embodiments of the present application, the representative feature points may further include an intermediate point between the maximum value and each intermediate value, and an intermediate point between the minimum value and each intermediate value, so as to improve the calibration accuracy.

[0038] Compared with the prior art, the advantages and positive effects of the present invention are as follows: the present invention first establishes a calibration model for the MEMS accelerometer, and derives the optimal estimation equation of the error based on the least squares method; then, by analyzing the output law of the accelerometer and taking into account the rotation calibration method of the gyroscope, a fast calibration method based on rotation arrangement is designed, which can enable the MEMS accelerometer to achieve calibration compensation during the rotation process. By conducting a comparative test with the traditional calibration method, it is proved that the rotation calibration method proposed by the present invention can effectively compensate for the measurement errors of each axis sensor, and the compensation accuracy is equivalent to that of the traditional method. However, due to the use of the rotation calibration method, it can be synchronized with the calibration of the gyroscope, thereby simplifying the calibration process and improving the calibration efficiency. It is particularly suitable for application in the calibration process of the MEMS inertial group, so as to solve the problems of the existing MEMS inertial group calibration method, such as the complicated calibration process and long time consumption, which is caused by the inability of the accelerometer to be calibrated synchronously with the gyroscope, better meet the needs of engineering applications, and provide technical support for the calibration and measurement of MEMS accelerometers.

[0039] After reading the specific embodiments of the present invention in conjunction with the accompanying drawings, other features and advantages of the present invention will become more clear. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0041] Figure 1 An overall flow chart of an embodiment of the MEMS accelerometer rotation calibration method proposed by the present invention;

[0042] Figure 2 for Figure 1 A flowchart of an embodiment of a MEMS accelerometer rotation arrangement and data sampling process;

[0043] Figure 3 A schematic diagram of the rotation of the sensitive axis of the MEMS accelerometer;

[0044] Figure 4 This is the output signal waveform of the sensitive axis of the MEMS accelerometer during rotation;

[0045] Figure 5 The waveform diagram of the output signal of the MEMS accelerometer measured at different rotation speeds;

[0046] Figure 6 A rotation diagram of an embodiment of a three-axis MEMS accelerometer rotation arrangement scheme; wherein, Figure 6 Part (a) is a schematic diagram of three-axis rotation with the reference axis being the x-axis and pointing to the east; Figure 6 Part (b) is a schematic diagram of three-axis rotation with the reference axis being the x-axis and pointing to the west; Figure 6 Part (c) is a schematic diagram of three-axis rotation with the reference axis being the y-axis and pointing to the north; Figure 6 Part (d) is a schematic diagram of three-axis rotation with the reference axis being the y-axis and pointing to the south; Figure 6 Part (e) is a schematic diagram of three-axis rotation with the reference axis being the z-axis and pointing to the north; Figure 6 Part (f) is a schematic diagram of three-axis rotation with the reference axis being the z-axis and pointing to the south;

[0047] Figure 7 Schematic diagram of three-axis rotation when calibrating a three-axis MEMS accelerometer using the traditional multi-position static calibration method;

[0048] Figure 8 The output effect diagram of the three-axis sensor when pointing to the sky and pointing to the ground after the MEMS accelerometer is calibrated using the traditional multi-position static calibration method;

[0049] Fig. 9 for Figure 8 Calibration error diagram of

[0050] Fig.10 When the x-axis is horizontal and the y-axis and z-axis rotate around the x-axis, the actual measured value of the three-axis sensor is output after calibration and compensation;

[0051] Fig.11 When the y-axis is horizontal and the x-axis and z-axis rotate around the y-axis, the actual measured value of the three-axis sensor is output as a signal waveform after calibration and compensation;

[0052] Fig.12 When the z-axis is horizontal and the x-axis and y-axis rotate around the z-axis, the actual measurement value of the three-axis sensor is output after calibration and compensation. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] The accuracy and stability of MEMS accelerometers are crucial for real-time attitude estimation and navigation positioning, but error parameter calibration and compensation are required before application. This embodiment analyzes the error model and data output law of the accelerometer and proposes a fast rotation calibration method for the MEMS accelerometer. Since the method can calibrate the error of the accelerometer during the rotation process, it can be calibrated synchronously with the gyroscope, thereby simplifying the calibration process of the MEMS inertial group and improving the calibration efficiency.

[0055] The MEMS accelerometer rotation calibration method of this embodiment mainly includes the establishment of a MEMS accelerometer calibration model, optimal error estimation based on the least squares method, MEMS accelerometer rotation arrangement and data sampling, calibration parameter calculation, experimental verification and other processes.

[0056] like Figure 1 The detailed description is as follows:

[0057] S110. Establishment of MEMS accelerometer calibration model.

[0058] Affected by factors such as manufacturing process and installation, the triaxial MEMS accelerometer itself inevitably has various interfering errors. Through calibration, the deviation between the output value and the theoretical value caused by reasons such as processing accuracy and assembly process can be compensated.

[0059] In engineering applications, ignoring the impact of noise on the measurement results, the measurement output of the three-axis MEMS accelerometer can be expressed by the following formula:

[0060] ;

[0061] in, , , They represent the actual measurement values ​​of the three-axis sensors (x-axis, y-axis, and z-axis) in the MEMS accelerometer. , , Respectively represent the theoretical output values ​​of the three-axis sensor; , , They represent the linear scale factor errors of the three-axis sensor respectively; It is a non-orthogonal error, which can also be called cross-axis coupling error; , , They represent the nonlinear scale factor errors of the three-axis sensor respectively; , , They respectively represent the zero bias of the three-axis sensor, that is, the zero position offset parameters.

[0062] It can be seen from the above formula that the measurement output error of the three-axis MEMS accelerometer mainly comes from linear scale factor error, non-orthogonality error, zero bias and nonlinear scale factor error.

[0063] In general, the nonlinear scale factor error of the accelerometer can be ignored, so the above formula can be simplified to:

[0064] ,

[0065] This is the measurement output model of the three-axis MEMS accelerometer.

[0066] make , , , , then the measurement output model of the three-axis MEMS accelerometer can be transformed into:

[0067] .

[0068] The process of restoring the theoretical output value of the three-axis MEMS accelerometer is the calibration process. Therefore, according to the measurement output model of the three-axis MEMS accelerometer, the calibration model can be obtained, and the formula is as follows:

[0069] (1).

[0070] As can be seen from the above formula, the process of calibration compensation of MEMS accelerometer is to solve the linear scale factor error (Including linear scale factor error of three-axis sensor , , and non-orthogonal errors ) and zero bias process.

[0071] S120. Optimal error estimation based on the least squares method.

[0072] From the calibration model formula (1) above, it can be seen that the calibration equation of the three-axis MEMS accelerometer is a linear equation. Therefore, the linear scale factor error can be identified by the optimal estimation based on least squares. and zero bias .

[0073] The least squares estimation method is widely used in linear regression analysis and is one of the main methods for system parameter estimation. Compared with some other analytical methods, the least squares estimation method has a simple principle, good statistical consistency and unbiasedness, and is suitable for widespread use in engineering applications.

[0074] The calibration model of formula (1) is transformed into:

[0075] .

[0076] Let the coefficient matrix , assuming that the measurement data matrix , then the above formula can be transformed into:

[0077] .

[0078] Redefine the function , then the least squares estimation problem in the above equation becomes Minimize the problem.

[0079] According to the least squares theory, we can get:

[0080] ;

[0081] Then the optimal error estimation model based on the least squares method is obtained as follows:

[0082] (2).

[0083] It can be seen from the above formula (2) that by measuring the data matrix D and the theoretical output value The coefficient matrix can be estimated The optimal solution , and then solve for the linear scale factor error and zero bias , which is used to calibrate and compensate the three-axis MEMS accelerometer during actual use.

[0084] S130, MEMS accelerometer rotation arrangement and data sampling.

[0085] After deriving the calibration model (1) of the three-axis MEMS accelerometer and the error optimal estimation model (2) based on the least squares method, the signal output law of the MEMS accelerometer is analyzed.

[0086] Assuming that the MEMS accelerometer rotates around the geographic north direction, the rotation plane is perpendicular to the horizontal plane, and the rotation diagram of the sensitive axis P (that is, the axis of the rotation plane perpendicular to the horizontal plane, which can be the x-axis, y-axis or z-axis of the MEMS accelerometer) is as follows Figure 3 As shown, the waveform of the output signal of the sensitive axis P during rotation is as follows Figure 4 shown.

[0087] Depend on Figure 4It can be seen from the output signal waveform that during the rotation process of the MEMS accelerometer, if its sensitive axis P starts to rotate from the position corresponding to its maximum output value (i.e., the peak), it will pass through the peak, median, trough, median, and finally return to the peak, completing a rotation cycle.

[0088] Combination Figure 3 and Figure 4 As shown, the theoretical output value of the sensitive axis P can be obtained The calculation formula of (acceleration value) is:

[0089] (3);

[0090] in, is the angle of the sensitive axis P relative to the direction pointing to the sky; is the local gravity acceleration value, which can be calculated based on the longitude and latitude and used as the benchmark for MEMS accelerometer calibration.

[0091] Figure 5 The waveform diagram of the output signal of the MEMS accelerometer measured at different rotation speeds. Figure 5 It can be seen that the amplitude of the MEMS accelerometer output signal is the same when the rotation speed is 10° / s, 30° / s, 50° / s, and 100° / s. Therefore, it can be concluded that, regardless of the centrifugal coupling caused by the installation position, within a rotation cycle, the output value of the MEMS accelerometer has nothing to do with the rotation speed, but only with the angle relative to the skyward direction. related.

[0092] Therefore, as long as the angle Taking values ​​between [0°, 360°) to cover the entire cycle of the accelerometer output value from maximum to minimum and then from minimum to maximum, as the calibrated feature points, the linear scale factor error of the three-axis MEMS accelerometer can be solved according to the error optimal estimation model based on the least squares method derived above. and zero bias .

[0093] To this end, this embodiment specifically designs a rotation arrangement scheme for the MEMS accelerometer, and collects the actual measurement value of the sensitive axis output in real time during the rotation of the accelerometer, determines the corresponding relationship between the rotation angle of the sensitive axis and the actual measurement value, and uses it for subsequent calibration parameters (linear scale factor error and zero bias ) calculation.

[0094] Specifically, if Figure 2 As shown, the following processes may be included:

[0095] S131. Use one of the axes of the three-axis MEMS accelerometer as a reference axis, adjust it to a horizontal direction, and point it to a first direction.

[0096] For example, see Figure 6 In part (a), the x-axis of the three-axis MEMS accelerometer can be first used as the reference axis, adjusted to the horizontal direction, and pointed to the set first orientation.

[0097] In some embodiments, the first orientation may be set to the geographic east, that is, the x-axis of the accelerometer is adjusted to point to the east.

[0098] S132. Use the remaining two axes of the three-axis MEMS accelerometer as sensitive axes and control them to rotate around the reference axis once, with the rotation planes of the two sensitive axes being perpendicular to the horizontal plane.

[0099] like Figure 6 As shown in part (a) of Figure 1, when the reference axis is the x-axis, the y-axis and z-axis of the three-axis MEMS accelerometer can be used as sensitive axes, and the y-axis and z-axis can be controlled to rotate uniformly around the x-axis for at least one revolution. At this time, the rotation planes of the y-axis and the z-axis are perpendicular to the horizontal plane, and the output acceleration value changes sinusoidally with the change of the rotation angle α.

[0100] S133. Collect actual measurement values ​​output by the two sensitive axes during the rotation process.

[0101] In the case where the reference axis is the x-axis, the actual measurement values ​​Fy and Fz output by the y-axis and the z-axis can be collected in real time and saved while the y-axis and the z-axis of the three-axis MEMS accelerometer rotate uniformly around the x-axis.

[0102] S134. Adjust the reference axis in the horizontal direction and rotate it 180° to point to the second orientation.

[0103] The first orientation and the second orientation are set 180° apart in the horizontal direction, and the reference axis is controlled to point to the positive and negative orientations respectively, which can play a role in calibrating and compensating for processing errors and installation errors.

[0104] For the case where the reference axis is the x-axis, such as Figure 6 As shown in part (b) of FIG. 1 , the x-axis can be controlled to rotate 180° in the horizontal direction to point to the set second direction. When the first direction is the geographic east direction, the second direction is the geographic west direction, that is, the x-axis of the accelerometer is adjusted to point to the west direction.

[0105] Of course, the first orientation and the second orientation may also be set to the geographic north and the geographic south, respectively.

[0106] S135 , repeating the processes S132 and S133 , and continuing to collect the actual measurement values ​​output by the two sensitive axes during the rotation process around the reference axis.

[0107] S136, replace the reference axis of the three-axis MEMS accelerometer, and repeat the process S131-S135 until the x-axis, y-axis, and z-axis of the three-axis MEMS accelerometer are all used as reference axes to complete data sampling.

[0108] For example, after the x-axis is used as the reference axis to complete data sampling, the y-axis can be used as the reference axis and adjusted to the horizontal direction and pointing to the north, such as Figure 6 Then, the x-axis and the z-axis are controlled to rotate at least one revolution around the y-axis at a constant speed, and the actual measured values ​​Fx and Fz output by the x-axis and the z-axis are collected in real time and saved.

[0109] Then, adjust the y-axis horizontally to point to the south, such as Figure 6 As shown in part (d) of the figure, the x-axis and the z-axis are controlled to rotate uniformly around the y-axis for at least one revolution again, and the actual measurement values ​​Fx and Fz output by the x-axis and the z-axis are collected in real time and saved.

[0110] Next, you can use the z-axis as the reference axis, adjust it to the horizontal direction and point to the north, such as Figure 6 Then, the x-axis and y-axis are controlled to rotate at a constant speed around the z-axis for at least one revolution, and the actual measurement values ​​Fx and Fy output by the x-axis and y-axis are collected in real time and saved.

[0111] Then, adjust the z-axis horizontally to point to the south, such as Figure 6 As shown in part (f) of the figure, the x-axis and the y-axis are controlled to rotate uniformly around the z-axis for at least one revolution again, and the actual measurement values ​​Fx and Fy output by the x-axis and the y-axis are collected in real time and saved.

[0112] Thus, the actual measurement values ​​Fx, Fy, and Fz output by the three-axis sensor as the rotation angle α changes are obtained, forming the actual measurement value F of the three-axis sensor.

[0113] S140, calibration parameter calculation.

[0114] In calculating the calibration parameters (linear scale factor error and zero bias ), it is necessary to know the actual measured value F and theoretical output value of the three-axis sensor in the MEMS accelerometer According to the theoretical output value From the calculation formula (3), we can see that we need to know the angle that the sensitive axis has rotated relative to the direction pointing to the sky. .

[0115] Because the initial angle of each sensitive axis relative to the skyward direction is known before the MEMS accelerometer is rotated and sampled, the angle of each sensitive axis relative to the skyward direction can be calculated based on the rotation angle α of the sensitive axis and the initial angle. The rotation angle α can be calculated based on the sampling time and the rotation speed of the sensitive axis.

[0116] Then, using the theoretical output value The calculation formula (3) can calculate the theoretical output value corresponding to each actual measured value F. .

[0117] Use the actual measurement value F to form the measurement data matrix , the measured data matrix D and the theoretical output value Substituting the error optimal estimation model based on the least squares method, that is, formula (2), the linear scaling factor error can be fitted and calculated. and zero bias .

[0118] In order to reduce the amount of calculation, you can select a part of the rotation angle The corresponding actual measured value F and theoretical output value As the input of formula (2), the linear scale factor error is calculated by fitting and zero bias .

[0119] In order to obtain more accurate calibration parameters, select the rotation angle When the selected rotation angle is Able to cover the entire range of [0°,360°).

[0120] In some embodiments, each rotation angle β can be selected as a rotation angle starting from 0°. , so that the actual measured value output by the sensitive axis can go through the entire cycle from maximum value to minimum value and then from minimum value to maximum value.

[0121] In some embodiments, the angle β may be 30° or 45°.

[0122] Of course, calibration points may also be selected according to actual measured values ​​output by the sensitive axis for use in calculating calibration parameters.

[0123] In some embodiments, a plurality of representative sampling points may be selected from the actual measurement values ​​output by each sensitive axis within one rotation cycle for use in the calculation of calibration parameters to improve the accuracy of the calculation results.

[0124] The multiple representative sampling points here may include but are not limited to a maximum value, an intermediate value during a transition from a maximum value to a minimum value, a minimum value, an intermediate value during a transition from a minimum value to a maximum value, and the like.

[0125] Of course, an intermediate point can also be selected between the maximum value and each intermediate value, and between the minimum value and each intermediate value as the selected sampling point, so that the actual measurement value output by the sensitive axis can go through the entire cycle from the maximum value to the minimum value and then from the minimum value to the maximum value, so as to further improve the accuracy of the calibration parameter calculation results.

[0126] The rotation angle is calculated based on the sampling time corresponding to the selected actual measurement value and the rotation speed of the sensitive axis. The rotation angle is then calculated based on the initial angle of the sensitive axis relative to the direction pointing to the sky. , substitute into the theoretical output value calculation formula (3), the theoretical output value corresponding to the selected actual measurement value can be obtained, and then substitute into the error optimal estimation model (2) based on the least squares method, the linear scale factor error can be fitted. and zero bias .

[0127] The linear scale factor error is calculated and zero bias Then, the linear scale factor error and zero bias Substituting into the calibration model, that is, formula (1), the final MEMS accelerometer calibration model can be obtained: Here It can be understood as the output value after calibration compensation. The smaller the calibration error, the closer the output value after calibration compensation is to the theoretical output value.

[0128] S150. Experimental verification.

[0129] (1) Traditional multi-position static calibration method.

[0130] Traditional multi-position static calibration methods mainly include six-position method, nine-position method, twelve-position method, twenty-four-position method, etc. The more positions there are, the better the calibration effect. Here, the twenty-four-position static calibration method is taken as an example to calibrate the three-axis MEMS accelerometer. The three-axis directions x, y, and z of the MEMS accelerometer are perpendicular to each other and form the right-hand rule.

[0131] Install the MEMS accelerometer on a three-axis turntable, adjust the turntable, and perform the test according to the following steps:

[0132] (1) Point the x-axis toward the sky, and keep the y-axis and z-axis in the horizontal plane. Control the y-axis and z-axis to rotate around the x-axis, and keep them stationary for 3 minutes after each 90° rotation, and collect data in the stationary state.

[0133] (2) Adjust the x-axis to point to the ground, and keep the y-axis and z-axis in the horizontal plane. Control the y-axis and z-axis to rotate around the x-axis, and keep them stationary for 3 minutes after each 90° rotation, and collect data in the stationary state.

[0134] The schematic diagram of the three-axis rotation of steps (1) and (2) is as follows: Figure 7 shown.

[0135] (3) Direct the y-axis and z-axis toward the sky and the ground respectively, rotate and select the position according to steps (1) and (2), and collect data in a static state.

[0136] In this way, static data of the triaxial accelerometer at twenty-four positions can be obtained.

[0137] After data collection is completed, the following data processing is performed:

[0138] First, the local gravity acceleration value g is calculated according to the longitude and latitude as the reference output for accelerometer calibration;

[0139] Then, the least squares optimal estimation is used for calibration.

[0140] After calibration, the output values ​​of the triaxial MEMS accelerometer in each direction are shown in Table 1. The unit of acceleration in Table 1 is milligravity mg. Milligravity mg refers to one thousandth of the gravitational acceleration g experienced by an object on the surface of the earth.

[0141] Table 1 Output results of the twenty-four position test

[0142] .

[0143] The output errors of the three-axis sensor of the MEMS accelerometer in various directions are calculated as shown in Table 2.

[0144] Table 2 Calibration error of triaxial MEMS accelerometer

[0145] .

[0146] The output effect of the calibrated MEMS accelerometer's three-axis sensor when pointing to the sky and the ground is as follows: Figure 8 As shown, the calibration error is Fig. 9 shown.

[0147] From Table 1, Table 2, Figure 8 , Fig. 9 It can be seen that the calibration effect is good, and the maximum calibration error of the calibrated three-axis accelerometer is 0.185 mg.

[0148] (2) Rotation calibration method of this embodiment.

[0149] The rotation calibration method proposed in this embodiment is used to perform a calibration test on the same group of objects.

[0150] The three-axis MEMS accelerometer is mounted on the turntable according to Figure 6 The machine rotates in the direction and orientation shown, with any rotation speed, 10° / s in this test. When the uniform rotation reaches a stable state, data is collected.

[0151] The data processing stage is within the rotation period of the three-axis MEMS accelerometer, that is, , take a calibration point every 30° rotation, use the optimal estimation model based on the least squares method proposed in this embodiment to calculate the calibration parameters of the accelerometer, and determine the calibration model.

[0152] The output signal waveform of the three-axis sensor of the calibrated MEMS accelerometer is as follows: Figure 10-12 As shown. Among them, Fig.10 When the x-axis is horizontal and the y-axis and z-axis rotate around the x-axis, the actual measured value of the three-axis sensor is output after calibration and compensation; Fig.11 When the y-axis is horizontal and the x-axis and z-axis rotate around the y-axis, the actual measured value of the three-axis sensor is output as a signal waveform after calibration and compensation; Fig.12 When the z-axis is horizontal and the x-axis and y-axis rotate around the z-axis, the actual measurement value of the three-axis sensor is output after calibration and compensation.

[0153] Depend on Figure 10-12 It can be seen that the output signal of the calibrated three-axis MEMS accelerometer fluctuates in the range of ±1000mg with a sinusoidal waveform, which conforms to the output law of the accelerometer.

[0154] To verify the calibration effect, the x-axis, y-axis, and z-axis of the three-axis MEMS accelerometer are pointed to the sky and the ground respectively, the output values ​​after calibration are recorded, and the calibration errors are calculated, as shown in Tables 3 and 4 respectively.

[0155] Table 3 Output results of the three-axis MEMS accelerometer after calibration

[0156] .

[0157] Table 4 Calibration error of triaxial MEMS accelerometer

[0158] .

[0159] It can be seen from Tables 3 and 4 above that the maximum calibration error of the calibrated three-axis MEMS accelerometer is 0.154 mg, which is comparable to the maximum calibration error of 0.185 mg of the traditional multi-position static calibration method.

[0160] By comparing the test with the traditional multi-position calibration method, it is proved that the MEMS accelerometer rotation calibration method proposed in this embodiment can effectively compensate for the errors of each axis sensor, and the compensation accuracy is equivalent to that of the traditional method. However, due to the use of the rotation calibration method, it can be carried out simultaneously with the calibration of the gyroscope, saving calibration time and improving calibration efficiency.

[0161] Of course, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, it is still possible for a person skilled in the art to modify the technical solutions described in the above embodiments, or to replace some of the technical features therein by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions claimed to be protected by the present invention.

Claims

1. A fast rotation calibration method for a MEMS accelerometer, characterized in that: include: Establish the calibration model of the three-axis MEMS accelerometer: ； in, is the theoretical output value of the three-axis sensor; is the linear scale factor error; is the actual measurement value of the three-axis sensor; is zero bias; Establish the error optimal estimation model based on the least squares method: ； in, is the coefficient matrix The optimal solution, coefficient matrix ; is the measurement data matrix, and ; The x-axis, y-axis, and z-axis of the MEMS accelerometer are respectively used as reference axes, adjusted to the horizontal direction, and pointed to the first orientation and the second orientation with a horizontal angle difference of 180° respectively; When the reference axis points to the first or second orientation, the remaining two axes serve as sensitive axes and rotate at least one circle around the reference axis at a uniform speed, so that the angle of rotation of the sensitive axis relative to the direction pointing to the sky is Covering the entire range of [0°, 360°), and the rotation plane is perpendicular to the horizontal plane; Collect the actual measured values ​​output by the sensitive axis during rotation and combine them to form the ; The rotation angle of the sensitive axis is calculated according to the sampling time of the actual measurement value and the rotation speed of the sensitive axis, and the angle is calculated in combination with the initial angle of the sensitive axis. ; Use the following formula to calculate the theoretical output value corresponding to the actual measured value: ； in, is the local gravity acceleration value; The actual measurement value obtained And the corresponding theoretical output value Substitute the error optimal estimation model based on the least squares method into the fitting calculation to obtain the linear scaling factor error and zero bias ; The calculated linear scale factor error and zero bias Substitute into the calibration model to complete the calibration process.

2. The rapid rotation calibration method of a MEMS accelerometer according to claim 1, characterized in that: In the calibration model, ； ； ； ； in, , , They represent the actual measurement values ​​of the x-axis, y-axis, and z-axis sensors in the MEMS accelerometer respectively; , , Respectively represent the theoretical output values ​​of the x-axis, y-axis, and z-axis sensors; , , Represents the linear scale factor errors of the x-axis, y-axis, and z-axis sensors respectively; is the non-orthogonal error; , , They represent the zero bias of the x-axis, y-axis, and z-axis sensors respectively.

3. The rapid rotation calibration method of a MEMS accelerometer according to claim 1, characterized in that: The first direction and the second direction are respectively the geographical east and the geographical west; or, The first orientation and the second orientation are respectively the geographic north and the geographic south.

4. The rapid rotation calibration method of a MEMS accelerometer according to claim 3, characterized in that: When the x-axis, y-axis, and z-axis of the MEMS accelerometer are respectively selected as reference axes for the first orientation and the second orientation, some reference axes select geographic east and geographic west, and some reference axes select geographic north and geographic south.

5. The rapid rotation calibration method of a MEMS accelerometer according to any one of claims 1 to 4, characterized in that: Before calculating the theoretical output value corresponding to the actual measured value, the following feature point selection process is performed: Starting from 0°, each rotation angle β is regarded as a selected angle , until the angle Approaching 360°; According to the selected angle Determine the actual measurement value corresponding thereto as the feature point for calibration; Calculate the theoretical output value corresponding to the characteristic point, which is used to fit the linear scale factor error and zero bias .

6. The rapid rotation calibration method of a MEMS accelerometer according to claim 5, characterized in that: The angle β is 30° or 45°.

7. The rapid rotation calibration method of a MEMS accelerometer according to any one of claims 1 to 4, characterized in that: Before calculating the theoretical output value corresponding to the actual measured value, the following feature point selection process is performed: Select multiple representative feature points from actual measurement values ​​output by each sensitive axis within one rotation cycle; The representative feature points include at least a maximum value, an intermediate value during a transition from a maximum value to a minimum value, a minimum value, and an intermediate value during a transition from a minimum value to a maximum value; Determine the corresponding angle based on the selected feature point ; According to the selected angle Calculate the theoretical output value corresponding to each characteristic point to fit the linear scale factor error and zero bias .

8. The rapid rotation calibration method of a MEMS accelerometer according to claim 7, characterized in that: The representative feature points also include a midpoint between the maximum value and each intermediate value, and a midpoint between the minimum value and each intermediate value.

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