CN115876225A

CN115876225A - MEMS IMU calibration method and system based on two-degree-of-freedom turntable

Info

Publication number: CN115876225A
Application number: CN202211653720.9A
Authority: CN
Inventors: 肖永丽; 余平; 陈应凯; 李展
Original assignee: Chongqing Starnav Systems Co ltd
Current assignee: Chongqing Starnav Systems Co ltd
Priority date: 2022-12-22
Filing date: 2022-12-22
Publication date: 2023-03-31

Abstract

The application provides an MEMS IMU calibration method and system based on a two-degree-of-freedom turntable, which are applied to the field of inertial measurement, acceleration measurement errors caused by a lever arm effect can be obtained through calculation, the acceleration measurement errors are used for compensating acceleration errors of an MEMS IMU module which is not at the center of the turntable in a rate experiment, an MEMS IMU gyro error model is established according to the acceleration measurement errors, the angular velocity detection sensitivity can be greatly improved, an MEMS IMU accelerometer error model is established, gyro error terms and accelerometer error terms are calculated according to the MEMS IMU gyro error model and the MEMS IMU accelerometer error model respectively, and further, the MEMS IMU module can be accurately, quickly and batch-type calibrated according to the gyro error terms and the accelerometer error terms.

Description

MEMS IMU calibration method and system based on two-degree-of-freedom turntable

Technical Field

The application relates to the field of inertia measurement, in particular to an MEMS IMU calibration method and system based on a two-degree-of-freedom turntable.

Background

The MEMS IMU is an inertia measurement unit manufactured by utilizing a micro motor technology, comprises a three-axis gyroscope and a three-axis accelerometer, and can respectively measure the angular velocity and the acceleration of a carrier. The MEMS IMU has the advantages of small volume, low power consumption, low cost, suitability for mass production and the like, gradually replaces the traditional inertia device in the field of high-precision navigation guidance, becomes an important direction for the development of the field of inertia, and has greatly increased production and manufacturing quantity in recent years.

Before the IMU is used, errors of the device are eliminated through calibration, and the inertia quantity of the output is closer to a true value. In the beginning of the development of MEMS IMU, the traditional calibration method is mainly used for reference. The traditional calibration method generally treats the calibration of the two as two independent processes, and the acceleration and the angular velocity are not influenced mutually. However, for a high-sensitivity MEMS gyroscope, the mass of a sensitive component is not negligible, the acceleration sensitive coefficient of the gyroscope is not considered in the MEMS calibration in the conventional method, the calibration method is not suitable for the high-sensitivity MEMS gyroscope, and a new accurate, fast and efficient calibration method needs to be established for the characteristics of the MEMS IMU to adapt to the actual production.

Disclosure of Invention

In view of the defects of the prior art, the application provides an MEMS IMU calibration method and system based on a two-degree-of-freedom turntable, the MEMS IMU calibration method and system are applied to the field of inertial measurement, acceleration measurement errors caused by lever arm effects are calculated, an MEMS IMU gyro error model is established according to the acceleration measurement errors, an MEMS IMU accelerometer error model is established, gyro error terms and accelerometer error terms are calculated according to the MEMS IMU gyro error model and the MEMS IMU accelerometer error model respectively, further, an MEMS IMU module can be calibrated according to the gyro error terms and the accelerometer error terms, and the method can accurately, quickly and batch-wise finish MEMS IMU calibration.

In a first aspect, the present application provides a method for calibrating an MEMS IMU based on a two-degree-of-freedom turntable, the method comprising the steps of:

s1: calculating acceleration measurement errors caused by lever arm effects;

s2: establishing an MEMS IMU gyro error model according to the acceleration measurement error;

s3: establishing an error model of an MEMS IMU accelerometer;

s4: calculating an accelerometer error item according to the MEMS IMU accelerometer error model, and calculating a gyro error item according to the MEMS IMU gyro error model;

and S5, calibrating the MEMS IMU module according to the gyro error term and the accelerometer error term.

By the MEMS IMU calibration method based on the two-degree-of-freedom turntable, acceleration measurement errors caused by a lever arm effect can be calculated and obtained, the acceleration measurement errors in a rate experiment of the MEMS IMU module which is not in the center of the turntable are compensated, an MEMS IMU gyro error model is established according to the acceleration measurement errors, the angular velocity detection sensitivity can be greatly improved, an MEMS IMU accelerometer error model is established, a gyro error item and an accelerometer error item are calculated according to the MEMS IMU gyro error model and the MEMS IMU accelerometer error model respectively, and further, the MEMS IMU module can be calibrated accurately, quickly and in batch mode according to the gyro error item and the accelerometer error item.

Preferably, in the MEMS IMU calibration method based on a two-degree-of-freedom turntable provided in the present application, the step S1 includes the steps of:

fixing N MEMS IMU modules on the plane of an inner frame of the turntable;

acquiring a lever arm L from at least one MEMS IMU module to the center of a rotating shaft of the inner frame;

a space rectangular coordinate system is established by taking the center of the rotating shaft of the inner frame as an origin, and the coordinate information of the lever arm L in the space rectangular coordinate system is

；

The acceleration measurement error is calculated from the coordinate information of the lever arm L.

In order to calibrate MEMS IMUs in a batch mode, N MEMS IMU modules can be fixed on an inner frame plane of a turntable, at least (N-1) MEMS IMU modules are not positioned in the center of an inner frame rotating shaft, a lever arm from the MEMS IMU modules to the center of the rotating shaft is L, and as additional measurement errors are brought to an accelerometer by a lever arm effect in a speed experiment, measurement errors brought by the lever arm effect are deducted in the speed experiment, so that acceleration measurement errors can be calculated according to the lever arm L, and errors brought to the lever arm effect in subsequent speed experiments are facilitatedThe difference is compensated. The lever arm L is represented by: a space rectangular coordinate system can be established by taking the center of the inner frame rotating shaft as an origin, and the coordinate information of the lever arm L in the space rectangular coordinate system is

The coordinate information is used for representing the lever arm L, the distance of the lever arm L can be digitally marked, and the lever arm L is abstracted into concrete, so that the subsequent calculation is facilitated.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, the step of calculating an acceleration measurement error according to coordinate information of a lever arm L includes:

the relationship between the acceleration measurement error and the angular velocity is calculated according to the coordinate information of the lever arm L as follows:

wherein is present>

Are respectively the theoretical value of the three-axis gyro>

Respectively, is a three-axis angular rate differential>

For acceleration measurement errors, is>

，/>

，

Measuring the error for three axes of the accelerometer, respectively>

，/>

，/>

The values of the lever arm L on three axes in a rectangular spatial coordinate system are respectively shown.

By the fact that a direct ratio relation exists between the existing theoretical acceleration measurement error and the angular velocity, after the coordinate information of the lever arm L is determined, a relation formula of the acceleration measurement error and the angular velocity is obtained through derivation:

wherein, in the process,

are respectively the theoretical value of a three-axis gyroscope>

The three-axis angular rate differential is respectively used, and the specific numerical value of the acceleration measurement error can be calculated after the theoretical value of the three-axis gyroscope, the three-axis angular rate differential and the coordinate information of the lever arm L are obtained in a rate experiment through the formula.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, and step S2 includes the steps of:

acquiring a gyro acceleration sensitive item, a scale factor error and a non-orthogonal error of the MEMS IMU module;

and establishing an MEMS IMU gyro error model according to the gyro acceleration sensitive item, the scale factor error, the non-orthogonal error and the acceleration measurement error.

For the MEMS gyroscope with higher sensitivity, the mass of the sensitive part is larger, and the gyroscope acceleration sensitive item is also an important factor causing a gyroscope error under the working condition of large motor, so that an MEMS IMU gyroscope error model can be established according to the gyroscope acceleration sensitive item, the scale factor error and the non-orthogonal error, a gyroscope true value can be calculated and obtained in subsequent rate experiments, and the gyroscope true value is further substituted into the MEMS IMU gyroscope error model to calculate and obtain the gyroscope error item.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, and step S3 includes the steps of:

acquiring a scale factor error, a zero offset error and a non-orthogonal error of the accelerometer;

and establishing an error model of the MEMS IMU accelerometer according to the scale factor error, the zero offset error and the non-orthogonal error.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, the method further comprising the steps of: determining the installation direction of each shaft of the MEMS IMU module and determining the direction and the rotation direction of each shaft of the turntable;

the steps of determining the installation direction of each axis of the MEMS IMU module and determining the direction and the rotating direction of each axis of the turntable comprise:

when the turntable is in a zero position, the Z axis of the MEMS IMU module is perpendicular to the plane of the inner frame, the X axis and the Y axis are parallel to the plane of the inner frame, the inner frame rotates in the plane formed by the X axis and the Y axis, and the outer frame rotates in the plane formed by the Z axis and the Y axis.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, and step S4 includes the steps of:

acquiring a first data file of a position experiment;

calculating a theoretical output value of an acceleration mean value accelerometer of the accelerometer according to the first data file;

and constructing a first matrix according to the acceleration mean value of the accelerometer and the theoretical output value of the accelerometer, and substituting the result of the first matrix into an MEMS IMU accelerometer error model to calculate an accelerometer error item.

Preferably, the present application provides a MEMS IMU calibration method based on a two-degree-of-freedom turntable, and step S4 further includes the steps of:

acquiring a second data file of the rate experiment;

calculating a gyro acceleration average value, a gyro angular velocity average value and a gyro theoretical output value according to the second data file, wherein the gyro theoretical output value is an output value obtained by deducting an acceleration measurement error from the gyro;

and constructing a second matrix according to the gyro acceleration mean value, the gyro angular velocity mean value and the gyro theoretical output value, and substituting the second matrix result into the MEMS IMU gyro error model to calculate a gyro error item.

In a second aspect, a MEMS IMU calibration system based on a two-degree-of-freedom turntable includes:

a first calculation module: the method is used for calculating acceleration measurement errors caused by lever arm effects;

the first modeling module: the MEMS IMU gyroscope error model is established according to the acceleration measurement error;

a second modeling module: the method comprises the steps of establishing an MEMS IMU accelerometer error model;

a second calculation module: the accelerometer error term is calculated according to the MEMS IMU accelerometer error model, and the gyro error term is calculated according to the MEMS IMU gyro error model;

a calibration module: and the MEMS IMU module is calibrated according to the gyro error term and the accelerometer error term.

Preferably, the present application provides a MEMS IMU calibration system based on a two-degree-of-freedom turntable, the system further comprising a direction determining module: the method is used for determining the installation direction of each axis of the MEMS IMU module and determining the direction and the rotation direction of each axis of the turntable.

Has the advantages that:

according to the MEMS IMU calibration method and system based on the two-degree-of-freedom turntable, acceleration measurement errors caused by a lever arm effect can be calculated through the method and used for compensating acceleration errors of an MEMS IMU module which is not located in the center of the turntable in a rate experiment, an MEMS IMU gyro error model is established according to the acceleration measurement errors, the angular velocity detection sensitivity can be greatly improved, an MEMS IMU accelerometer error model is established, gyro error terms and accelerometer error terms are calculated according to the MEMS IMU gyro error model and the MEMS IMU accelerometer error model respectively, and further, the MEMS IMU module can be accurately, quickly and batch-type calibrated according to the gyro error terms and the accelerometer error terms.

Drawings

Fig. 1 is a flowchart of an MEMS IMU calibration method based on a two-degree-of-freedom turntable according to the present application.

FIG. 2 is a diagram of a MEMS IMU module mounting provided herein.

Fig. 3 is a schematic structural diagram of an MEMS IMU calibration system based on a two-degree-of-freedom turntable according to the present application.

Fig. 4 is a schematic structural diagram of a two-degree-of-freedom turntable.

In the figure: 100. an inner frame; 110. item 1 MEMS IMU module; 120. an MEMS IMU module n item, 201, a first calculation module; 202. a first modeling module; 203. a second modeling module; 204. a second calculation module; 205. a calibration module; 206. a multi-channel data acquisition device; 207. and a direction determination module.

Detailed Description

The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. The components of the embodiments of the present application, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present application, the terms "first, second, third, etc. are used only for distinguishing the description, and are not intended to indicate or imply relative importance.

The following disclosure provides many different embodiments or examples to achieve the objectives of the present invention and to solve the problems of the prior art. In view of the composition structures of non-MEMS accelerometers (e.g., quartz flexible accelerometers) and gyros (e.g., mechanical gyros, fiber optic gyros, etc.), the conventional calibration method usually considers the calibration of the two independent processes, and the acceleration and the angular velocity do not affect each other, but actually for highly sensitive MEMS gyroscopes, the quality of the sensitive components is not negligible, and the conventional calibration method is not suitable for highly sensitive MEMS gyroscopes. In order to solve the problem, the application provides an MEMS IMU calibration method and system based on a two-degree-of-freedom turntable, and the method comprises the following steps:

referring to fig. 1, an embodiment of the present application provides a method for calibrating an MEMS IMU based on a two-degree-of-freedom turntable, which is applied to the field of inertial measurement, and is particularly applied to a high-sensitivity MEMS gyroscope, and therefore, the mass of a sensitive component of the MEMS IMU is not negligible, and therefore, an acceleration sensitive coefficient of the gyroscope is also considered during calibration, and a reasonable calibration experiment is designed, so as to implement accurate, fast, and batch-type MEMS IMU calibration.

The MEMS IMU calibration method based on the two-degree-of-freedom turntable comprises the following steps:

s1: calculating acceleration measurement errors caused by lever arm effects;

s3: establishing an MEMS IMU accelerometer error model;

s4: calculating an accelerometer error term according to the MEMS IMU accelerometer error model, and calculating a gyro error term according to the MEMS IMU gyro error model;

s5: and calibrating the MEMS IMU module according to the gyro error term and the accelerometer error term.

In step S1, a lever arm effect of the MEMS IMU module is a system error, which is caused because a sensor of the MEMS IMU is separately and independently installed, and thus when a carrier rotates around an axis, the sensor will be subjected to additional centrifugal acceleration and tangential acceleration, which further causes output errors of an accelerometer and a gyroscope, and calibration must be more accurate by eliminating such errors. In the scheme, the carrier of the accelerometer actually refers to an MEMS IMU module (the MEMS IMU module actually is an inertial measurement unit), and since the MEMS IMU module itself has a certain measurement error, the acceleration measurement error is one of the factors that affect the measurement error of the MEMS IMU module itself.

In step S1, in some preferred embodiments, when calculating the acceleration measurement error caused by the lever arm effect, the relationship between the accelerometer and the angular velocity needs to be determined, so that the step S1 includes:

fixing N MEMS IMU modules on the plane of an inner frame of a turntable;

a space rectangular coordinate system is established by taking the center of a rotating shaft of the inner frame as an original point, and the coordinate information of the lever arm L in the space rectangular coordinate system is

；

In practical application, the two-degree-of-freedom turntable comprises an outer frame and an inner frame, wherein the two degrees of freedom represent that the turntable has two degrees of freedom of pitching and rolling, linkage in two directions is achieved, the outer frame achieves a pitching function (namely the outer frame rotates around a Y axis), the inner frame achieves a platform rolling function (namely the inner frame rotates around a Z axis), and the specific rotating mode refers to the attached figure 4. In order to realize batch type calibration, N MEMS IMU modules are fixed on the inner frame plane of the turntable and at least storedIn order to facilitate calculation of acceleration measurement errors caused by lever arm effects, one of the MEMS IMU modules may be located at the center of the inner frame rotation shaft and represented by item 1 of the MEMS IMU module, and the remaining MEMS IMU modules may be represented by item N of the MEMS IMU modules, where N =2,3,4 \8230, and N (N is an integer). Establishing a space rectangular coordinate system by taking the center of the rotating shaft of the inner frame as an original point, namely establishing the space rectangular coordinate system by taking 1 item of the MEMS IMU module as the original point, taking the distance from n items of the MEMS IMU module to the original point of the coordinate as a lever arm L, and expressing the coordinate information of the lever arm L in the coordinate system as

By combining the coordinate information of the lever arm L and the direct ratio relationship between the acceleration measurement error and the angular velocity in the existing theory, a relational expression between the acceleration measurement error and the angular velocity can be derived.

Therefore, in some preferred embodiments, the relationship between the acceleration measurement error and the angular velocity is determined so that when various measurement data of the MEMS IMU module are acquired, the measurement data are substituted into the formula, and the acceleration measurement error is directly and accurately calculated, so that a fast, accurate, and batch calibration effect is achieved when the MEMS IMU module is calibrated, and thus the step of calculating the acceleration measurement error according to the coordinate information of the lever arm L includes:

calculating the relation between the acceleration measurement error and the angular velocity according to the coordinate information of the lever arm L as follows:

（1），

wherein the content of the first and second substances,

are respectively the theoretical value of the three-axis gyro>

Respectively angular rate differential.

In practice shouldIn use, acceleration measurement error

The theoretical value error of the three-axis gyroscope is caused, the theoretical output value of the gyroscope is further caused to have an error, and the theoretical output value of the gyroscope can be obtained through a rate experiment, so that in order to simplify calculation, all axes can be set to rotate at a constant speed in the rate experiment, the angular rate is slightly divided into 0, namely ^ er>

By substituting this for equation (1) above, equation (1) can be simplified to obtain:

（2）。

for example, a spatial rectangular coordinate system is established by taking 1 item of the MEMS IMU module as an origin, the distance from n items of the MEMS IMU module to the origin of coordinates is a lever arm L, when n =4, the coordinate information read to the lever arm L is (0.1, 0), and a theoretical value of a three-axis gyroscope is obtained in a rate experiment

Respectively (141 × 3600), (141 × 3600), 0, with the unit being °/h, and the numerical value is substituted into the above equation (2), the numerical value of the acceleration measurement error of the item 4 of the MEMS IMU module can be calculated conveniently and accurately; or when n =2, reading the coordinate information of the lever arm L as (-0.1, 0), and acquiring the theoretical value of the three-axis gyroscope ^ based on the speed experiment>

The acceleration measurement error of the MEMS IMU module 2 item can be calculated by adopting the same calculation mode as the above calculation mode, wherein the acceleration measurement error is (141 × 3600), (141 × 3600) and 0, and the unit is degree/h; in the batch calibration, coordinate information of lever arms L of a plurality of MEMS IMU modules and a theoretical value of a three-axis gyroscope can be obtained and substituted into a calculation, for example, when n =5, the coordinate information of the lever arms L is (-0.1, 0), and in a rate experiment, the coordinate information of the lever arms L is calculatedAcquiring the theoretical value of the triaxial gyroscope>

Respectively, (141 × 3600), 0, in units of °/h; when n =6, the lever arm L coordinate information is (0.1,0,0), and a triaxial gyro theory value &isobtained in a rate experiment>

Respectively, (141 × 3600), 0, in units of °/h; when n =7, the lever arm coordinate information is (-0.1, -0.1,0), and a triaxial gyro theoretical value &isobtained in a rate experiment>

Respectively (141 × 3600), (141 × 3600) and 0, the unit is degree/h, and the data are input into data analysis processing software in batches and are substituted into the formula (2), so that the gyro error items from the item 5 of the MEMS IMU module to the item 7 of the MEMS IMU module can be efficiently and accurately calculated.

In some preferred embodiments, since the mass of the sensitive part is larger for the MEMS gyroscope with higher sensitivity, the gyroscope acceleration sensitive term is also an important factor causing a gyroscope error under a large-maneuvering condition, and in order to achieve the purpose of batch-type fast calibration, an MEMS IMU gyroscope error model needs to be established, so step S2 includes the steps of:

The gyro acceleration sensitive term actually refers to the output of the sensitive acceleration of the MEMS gyro, which is an error term. Since the MEMS gyroscope is mostly a gyroscope based on mechanical vibration, it is affected by acceleration, and thus a gyroscope acceleration sensitive term is generated. Where the scale factor, also called the scale factor or scaling factor, in practice refers to the ratio between the output (current/voltage) and the input (acceleration, angular rate) of the sensor, which is a component included in the MEMS IMU module. Therefore, the accelerometer and the MEMS gyroscope carry out model conversion through scale factors, and therefore, the error of the scale factors directly brings measured system errors, and the error of the scale factors is one of parameters of an error model of the MEMS gyroscope. The non-orthogonal error, which may be referred to as a non-sensitive axis cross-coupling error, actually refers to an error output generated when an input is provided on a non-sensitive axis of a sensor, and the reason for generating the non-orthogonal error is mostly that a certain non-orthogonality exists or a certain non-perpendicularity exists in the structure of the sensor itself, for example: the acceleration originally generated on the X axis, however, also generates an error on the Y axis or the Z axis due to the non-orthogonality.

In practical application, error sources of the MEMS IMU gyro error model are mainly a gyro acceleration sensitive term, a scale factor error, a non-orthogonal error, and an acceleration measurement error, and therefore, the MEMS IMU gyro error model can be established according to the errors as follows:

（3），

wherein the content of the first and second substances,

is the original output of the three-dimensional gyro, is combined>

Is zero offset and is greater or less than>

Is a true value->

For original output of a three-dimensional accelerometer, based on a comparison of a reference value and a reference value>

For acceleration measurement errors caused by the lever arm>

The MEMS IMU module calibration factor error and the non-orthogonal error are three-dimensional matrixes which respectively represent scale factor errors, non-orthogonal errors and gyro acceleration sensitive items of the MEMS IMU module. Wherein it is present>

The zero offset is also called zero drift, the average output of the actual middle finger gyro without any rotation, namely the deviation from the true value, for a constant deviation, when the integral is carried out, an angle error which grows linearly along with the time can be caused, namely the zero offset error, and the zero offset can be obtained by taking the average value of the long-time output of the gyro under the condition that the gyro is completely static. And/or>

The true value can be obtained by acquiring data through a rate experiment and calculating. Wherein it is present>

Has the following form:

(4) In which

Is the scale factor error value of the accelerometer on three axes respectively>

Means for determining the acceleration value taken by the accelerometer on the Y-axis or the Z-axis when the acceleration is taken by the accelerometer on the X-axis>

Means for determining the acceleration value taken by the accelerometer on the X-axis or the Z-axis when the accelerometer is taking acceleration on the Y-axis>

Indicating the acceleration of the accelerometer in the Z axis, the X axis or the Y axisA resultant acceleration value +>

Represents the acceleration of any three points on the X axis of the gyro and is combined with the acceleration of the gyro at the X axis>

Represents the acceleration of any three points of the gyro on the Y axis>

Representing the acceleration of the gyroscope at any three points on the Z-axis.

Combining the above equations (3) and (4), and obtaining the following according to the matrix algorithm:

（5），

wherein, the first and the second end of the pipe are connected with each other,

representing the sum of the scale factor error plus the non-quadrature error. For example, taking the item 4 of the MEMS IMU module as an example, the coordinate information of the item 4 of the MEMS IMU module is (0.1, 0), and the error item coefficient of the item 4 of the MEMS IMU module can be calculated by the least square method according to the data acquired by the position experiment and the velocity experiment, and the batch acquisition data is shown in the following table: />

Table 1 MEMS IMU module 4 gyro calibration result table

By using the data in the above table 1, each error term coefficient is substituted into the formula (5), and the three data of the gyro acceleration sensitive term X axis are substituted into the formula (5)

，/>

Substituting the three data of middle and Y axes into->

The three data of the middle and Z axes are respectively substituted into->

Get->

The X-axis data of the sum of the scale factor error and the non-orthogonal error are respectively substituted into ^ greater than or equal to ^ greater than>

Three data of middle and Y axis are respectively substituted into ^ H>

In-between, three data of Z-axis are respectively substituted

And (4) calculating the original output value of the three-dimensional gyroscope of the MEMS IMU module.

In some preferred embodiments, in order to achieve the purpose of batch-type fast calibration, a MEMS IMU accelerometer error model needs to be established, so step S3 includes the steps of:

acquiring scale factor errors, zero offset errors and non-orthogonal errors of the accelerometer;

and establishing an MEMS IMU accelerometer error model according to the scale factor error, the zero offset error and the non-orthogonal error of the accelerometer.

In practical application, therefore, the error model of the MEMS IMU accelerometer is established as follows:

（6），

Is zero offset and is greater or less than>

Is a true value->

All are three-dimensional matrixes which respectively represent scale factor errors and non-orthogonal errors of the accelerometer, and the derivation mode of an MEMS IMU gyro error model is referred to, and the method comprises the following steps:

(7) Wherein is present>

Representing the sum of the scale factor error and the non-quadrature error of the accelerometer.

Wherein the content of the first and second substances,

the true value can be calculated through position experiment data, and the scale factor error, the zero offset error and the non-orthogonal error of the accelerometer can be actually obtained through position experiments. For example: according to data acquired by a position experiment, an error term coefficient of an MEMS IMU module 4 term can be calculated by a least square method, and batch acquisition data is shown in the following table:

table 2 calibration result table for 4 items of accelerometer of MEMS IMU module

Through the data in the table 2, the original output value of the three-dimensional accelerometer can be calculated by substituting each error term coefficient into the formula (7).

In some preferred embodiments, in order to obtain more accurate data in subsequent position experiments and velocity experiments, the method further comprises the steps of: determining the installation direction of each shaft of the MEMS IMU module and determining the direction and the rotation direction of each shaft of the turntable;

the steps of determining the installation direction of each shaft of the MEMS IMU module and determining the direction and the rotation direction of each shaft of the turntable comprise:

In practical application, the MEMS IMU module is arranged on the plane of the inner frame, the inner frame is used for realizing the platform rolling function of the rotary table, the outer frame is used for realizing the pitching function of the rotary table, the rotary table is used for providing a high-precision position and a servo function which can rotate continuously, the test and calibration of the MEMS IMU module are realized, and the MEMS IMU module can be used for performing position experiments and speed experiments.

In some preferred embodiments, the accelerometer error term is calculated according to the MEMS IMU accelerometer error model, the gyro error term is calculated according to the MEMS IMU gyro error model, a first data file of a position experiment and a second data file of a velocity experiment need to be acquired respectively, and the accelerometer error term and the gyro error term are calculated according to the first data file and the second data file, respectively, so that the step S4 includes the steps of:

acquiring a first data file of a position experiment;

and constructing a first matrix according to the acceleration mean value of the accelerometer and the theoretical output value of the accelerometer, and substituting the result of the first matrix into the MEMS IMU accelerometer error model to calculate an accelerometer error item.

In order to excite various errors of the accelerometer (such as scale factor errors, zero offset errors, non-orthogonal errors, acceleration mean values and theoretical output values of the accelerometer), in other words, to obtain a first data file in a position experiment, the first data file actually refers to position data of the turntable and position data selected on three axes, the position experiment can be designed, in order to check the accuracy of batch calibration, in the position experiment, a plurality of positions are set, and a plurality of groups of experimental data are obtained, for example: designing 8 groups of positions, collecting data of five position points on each axis (zero position, indicating sky, indicating ground, two inclined positions, wherein the indicating sky and the indicating ground respectively represent two directions of a z axis), and further, sequentially carrying out position experiments:

a. the position of the inner frame is 0 degree, the position of the outer frame is 0 degree, the accelerometers of the X axis and the Y axis are in zero positions, and the accelerometer of the Z axis refers to the sky or the ground;

b. the inner frame is kept unchanged, the position of the outer frame is 90 degrees, the accelerometers on the Z axis are positioned on a zero position X axis, one accelerometer on the Y axis is positioned on a zero position, and the other accelerometer on the Y axis is positioned on the sky or the ground;

c. b, keeping the inner frame unchanged, keeping the position of the outer frame at 180 degrees, keeping accelerometers of an X axis and a Y axis at zero positions, and outputting the output opposite to that in the step a, wherein an accelerometer of a Z axis refers to sky or ground;

d. the inner frame is kept unchanged, the position of the outer frame is 270 degrees, the accelerometers in the Z axis are in zero positions, one of the accelerometers in the X axis and the Y axis is in the zero position, the other one of the accelerometers is in the sky or the ground, and the output is opposite to that in the step b;

e. the position of the inner frame is 90 degrees, the position of the outer frame is 90 degrees, the accelerometers of the Z axis are in zero positions, the accelerometers of the X axis and the Y axis are not in the zero positions in the steps b and d, the accelerometers are in the zero positions in the step e, and the other accelerometer refers to the sky or the ground;

f. the inner frame is kept unchanged, the position of the outer frame is 270 degrees, the Z-axis accelerometer is in a zero position, the accelerometers in the X-axis and the Y-axis are in the zero position in the steps b and d, the accelerometers in the zero position in the step f are in the zero position, the other accelerometer refers to the sky or the ground, and the output is opposite to that in the step e;

g. the position of the inner frame is 30 degrees, the position of the outer frame is 60 degrees, and the three-axis accelerometer is in an inclined state;

h. and (e) the position of the inner frame is 0 degrees, the position of the outer frame is 0 degrees, the three-axis accelerometers are all in an inclined state, the directions of the three-axis accelerometers are all opposite to the directions in the step g, and the output of the three-axis accelerometers is opposite to the output of the step g.

The sampling time from step a to step h has no special requirement.

In the position experiment, the turntable position data included in the first data file are the inner frame position data and the outer frame position data in steps a to h, such as: a. the position data of the inner frame is 0 degree and the position of the outer frame is 0 degree, b, the inner frame is kept unchanged, the position of the outer frame is 90 degrees, and the position point data selected on the three axes are position point data on an X axis, a Y axis and a Z axis, such as: the accelerometers of the X axis and the Y axis are in zero positions, the accelerometers of the Z axis refer to the sky or the earth, the accelerometers of the b axis and the Z axis are in zero positions, one of the accelerometers of the X axis and the Y axis is in the zero position, and the other accelerometer of the X axis and the Y axis refers to the sky or the earth.

All error data are acquired by a multi-channel data acquisition device, because a large number of matrix operations are involved, MATLAB can be adopted for batch processing, the mathematical modes involved in the specific operation steps are algebraic operations, and the arithmetic process is only described by not much description:

for an accelerometer:

firstly, reading data collected in the steps a to h of each MEMS IMU module in batch calibration, wherein each module corresponds to 8 data files;

then, in order to reduce the influence of noise, the acceleration mean value of the accelerometer is respectively calculated for 8 groups of data (namely a first data file) of each MEMS IMU module;

further, a theoretical output value of the accelerometer is deduced from the relative position of the MEMS IMU module and the turntable;

and finally, constructing a first matrix according to the acceleration mean value of the accelerometer and the theoretical output value of the accelerometer, wherein the result of the first matrix is the true value in the MEMS IMU accelerometer error model, and then respectively solving the accelerometer error items of each MEMS IMU module in a cyclic mode by a least square method, wherein the calculated accelerometer error items can be referred to the data of 4 items of the MEMS IMU module listed in the table 1.

In some preferred embodiments, step S4 further comprises the steps of:

acquiring a second data file of the rate experiment;

According to the MEMS IMU gyro error model, a gyro acceleration sensitive item is excited by using a position experiment, and in addition, other error items can be excited by designing a rate experiment. In order to improve the calibration efficiency, the position experiment of the gyroscope can directly adopt the first data file of the position experiment in the accelerometer, so that the second data file comprises the first data file, the rotation angle rate data of the turntable and the three-axis rotation angle rate, and the rate experiment of the gyroscope sequentially comprises the following steps:

i. the position of the outer frame is 0 degrees, the inner frame rotates at angular rates of +/-10 degrees/s, +/-100 degrees/s and +/-300 degrees/s respectively, the Z-axis gyroscope is sensitive to the axial angular rate, and the gyroscopes on the X axis and the Y axis are at zero angular rate;

j. the position of the inner frame is 0 degrees, the outer frame rotates at angular rates of +/-10 degrees/s, +/-100 degrees/s and +/-300 degrees/s respectively, one of the X-axis gyroscope and the Y-axis gyroscope is sensitive to the angular rate of the axis, and the other one of the X-axis gyroscope and the Z-axis gyroscope is at zero angular rate;

k. the position of the inner frame is 90 degrees, the outer frame rotates at angular rates of +/-10 degrees/s, +/-100 degrees/s and +/-300 degrees/s respectively, the Z axis and the gyroscope of the sensing axis in the step j are at zero angular rate, and the gyroscope of the other axis senses the angular rate.

The minimum sampling time in steps i, j, k is:

t is in seconds, w is angular rate, in degrees/s, corresponding to a minimum number of points:

f is sampling frequency in Hz, wherein the minimum number of points is as follows: in the rate experiment, selectThe specific position of the gyroscope with three axes can be represented as an ideal point position in calculation, and the minimum point number is the minimum calculation position.

In the speed experiment, the first data file included in the second data file shares data with the first data file in the position experiment, namely the data is the same as the data in the steps a to h; the rotation angular rate data of the turntable includes the positions of the inner and outer frames and the rotation angular rates, such as: i. the position of the outer frame is 0 degree, and the inner frame rotates at the angular rates of +/-10 degrees/s, +/-100 degrees/s and +/-300 degrees/s respectively; the three-axis rotation angular rate data includes X-axis, Y-axis, Z-axis rotation angular rates, such as: the z-axis gyroscope is sensitive to the angular rate of the axis, and the X-axis and Y-axis gyroscopes are at zero angular rate.

Because a large amount of matrix operations are involved, MATLAB can be adopted for batch processing, the mathematical modes involved in the specific operation steps are algebraic operations, and the operation steps are described in a few times and are only described:

for a spinning top:

firstly, reading data collected in steps a to k of each MEMS IMU module in batch calibration, wherein each module corresponds to 26 data files (namely a second data file);

secondly, the data collected in the steps i, j and k are subjected to rounding, namely: determining the number M of points participating in the calculation according to the minimum sampling time and the sampling frequency,

m is the minimum number of points participating in calculation in the speed experiment, and k is the number of cycles rotating for 360 degrees in the whole cycle in the speed experiment;

then, respectively calculating a gyro angular velocity mean value and a gyro acceleration mean value of each MEMS IMU module according to the data after the integration;

further, a theoretical output value of the gyroscope is deduced from the relative position of the MEMS IMU module and the rotary table and the rotary speed of the rotary table, wherein the theoretical output value of the gyroscope is obtained by deducting acceleration measurement errors caused by a lever arm effect;

finally, according to the topConstructing a second matrix by the mean value of the spiral acceleration, the mean value of the gyro angular velocity and the theoretical output value of the gyro, wherein the result of the second matrix is the true value in the MEMS IMU gyro error model

And then, respectively solving the gyro error terms of the MEMS IMU modules in a cyclic mode by a least square method. The calculated gyro error term can be referred to the data of the MEMS IMU module 4 listed in the table 1.

Further, finally, a batch calibration of the MEMS IMU module may be completed through step S5, where a is shown as follows (where a represents an accelerometer, W represents a gyroscope, for example, ax represents an X-axis accelerometer theoretical output value, and X represents a multiplier):

TABLE 3 static Performance verification Table for accelerometer and gyroscope

Table 4 dynamic performance verification table of gyroscope

According to the MEMS IMU calibration method based on the two-degree-of-freedom turntable, acceleration measurement errors caused by lever arm effects can be obtained through calculation, the acceleration measurement errors are used for compensating acceleration errors of an IMU module which is not located in the center of the turntable in a rate experiment, an MEMS IMU gyro error model is established according to the acceleration measurement errors, the angular velocity detection sensitivity can be greatly improved, an MEMS IMU accelerometer error model is established, a gyro error term and an accelerometer error term are calculated according to the MEMS IMU gyro error model and the MEMS IMU accelerometer error model respectively, and further, the MEMS IMU module can be accurately, quickly and massively calibrated according to the gyro error term and the accelerometer error term.

Referring to fig. 3, a MEMS IMU calibration system based on a two-degree-of-freedom turntable includes:

the first calculation module 201: the method is used for calculating acceleration measurement errors caused by lever arm effects;

the first modeling module 202: the MEMS IMU gyroscope error model is established according to the acceleration measurement error;

the second modeling module 203: the method comprises the steps of establishing an MEMS IMU accelerometer error model;

the second calculation module 204: the accelerometer error item is calculated according to the MEMS IMU accelerometer error model, and the gyro error item is calculated according to the MEMS IMU gyro error model;

the calibration module 205: and the MEMS IMU module is calibrated according to the gyro error term and the accelerometer error term.

In practical applications, the system further includes a multi-channel data collecting device 206, which is configured to collect a first data file and a second data file in the position experiment and the velocity experiment, and transmit the data to the first calculating module 201, the first modeling module 202, the second modeling module 203, the second calculating module 204, and the calibrating module 205 for calculation of each item of data. The first calculation module 201, the first modeling module 202, the second modeling module 203, the second calculation module 204, and the calibration module 205 may be data processing programs built in data analysis software, such as common data analysis software MATLAB.

In some preferred embodiments, when the first computing module 201 computes an acceleration measurement error caused by a lever arm effect, the position of each MEMS IMU module, that is, coordinate information of a lever arm L, is first obtained by the multi-channel data acquisition device 206, for example, a spatial rectangular coordinate system is established with the 1 item 110 of the MEMS IMU module as an origin, the 1 item 110 of the MEMS IMU module is fixed at a rotation axis center of the inner frame 100, the lever arm L coordinate information of the n item 120 of the MEMS IMU module is (0.1, 0), and in a rate experiment, the multi-channel data acquisition device 206 may acquire theoretical values of a three-axis gyroscope, that is, (141 × 3600), 0 in units of °/h, and then the multi-channel data acquisition device transmits the above items of data to the first computing module 201, so as to compute a value of the acceleration measurement error of the 4 items of the MEMS IMU module.

In some preferred manners, the first modeling module 202 may establish an MEMS IMU gyro error model, first, acquire data of each error item in a rate experiment through the multi-channel data acquisition device 206, then transmit the data to the first modeling module 202, analyze the data, and establish the MEMS IMU gyro error model, that is, compensate each error item, so as to subsequently calculate a gyro error item according to the MEMS IMU gyro error model, and calibrate the MEMS IMU module.

In some preferred schemes, the second modeling module 203 may establish an MEMS IMU accelerometer error model, first, acquire data of each error item in a position experiment through the multi-channel data acquisition device 206, then transmit the data to the second modeling module 203, analyze the data, and establish the MEMS accelerometer error model, that is, compensate each error item, so as to subsequently calculate an accelerometer error item according to the MEMS IMU accelerometer error model, and calibrate the MEMS IMU module.

In some preferred solutions, the second calculating module 204 may calculate a gyro error term according to the MEMS IMU gyro error model, and calculate an accelerometer error term according to the MEMS accelerometer error model. After the MEMS IMU gyro error model and the MEMS IMU accelerometer error model are respectively established by the first modeling module 202 and the second modeling module 203, the two models are transmitted to the second computing module 204, the first data file and the second data file are also transmitted to the second computing module 204 by the multi-channel data acquisition device 206, and after the models and the data are acquired by the second computing module 204, the accelerometer error item and the gyro error item can be output, and the MEMS IMU module can be calibrated according to the numerical values of the two items.

In some preferred schemes, the system further includes a direction determining module 207, the direction determining module may determine an installation orientation of each axis of the MEMS IMU module and determine an orientation and a rotation direction of each axis of the turntable, in an actual application process, the direction determining module 207 sends the installation orientation of each axis of the MEMS IMU module and the orientation and the rotation direction of each axis of the turntable to the multi-channel data acquiring device 206, and the installation orientation and the rotation direction of each axis of the turntable are used as important parameters to participate in calculation of a gyro error term and an accelerometer error term in a position experiment and a rate experiment.

In this document, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.

The above description is only an example of the present application and is not intended to limit the scope of the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A MEMS IMU calibration method based on a two-degree-of-freedom turntable is characterized by comprising the following steps:

s1: calculating acceleration measurement errors caused by lever arm effects;

s3: establishing an MEMS IMU accelerometer error model;

2. The MEMS IMU calibration method based on the two-degree-of-freedom turntable as claimed in claim 1, wherein the step S1 comprises the steps of:

fixing the N MEMS IMU modules on the plane of the inner frame of the turntable;

obtaining a lever arm L from at least one MEMS IMU module to the center of a rotating shaft of the inner frame;

establishing a space rectangular coordinate system by taking the center of the rotating shaft of the inner frame as an originThe coordinate information of the lever arm L in the rectangular space coordinate system is

；

And calculating the acceleration measurement error according to the coordinate information of the lever arm L.

3. The method of claim 2, wherein the step of calculating the acceleration measurement error according to the coordinate information of the lever arm L comprises:

in which>

Are respectively the theoretical value of a three-axis gyroscope>

Respectively, is a three-axis angular rate differential>

For acceleration measurement errors, based on the measured acceleration value>

，

，/>

Measuring the error for three axes of the accelerometer, respectively>

，/>

，/>

Respectively, the values of the lever arm L on three axes in a spatial rectangular coordinate system.

4. The MEMS IMU calibration method based on the two-degree-of-freedom turntable as claimed in claim 1, wherein the step S2 comprises the steps of:

and establishing the MEMS IMU gyro error model according to the gyro acceleration sensitive item, the scale factor error, the non-orthogonal error and the acceleration measurement error.

5. The MEMS IMU calibration method based on the two-degree-of-freedom turntable as claimed in claim 1, wherein the step S3 comprises the steps of:

and establishing an error model of the MEMS IMU accelerometer according to the scale factor error, the zero offset error and the non-orthogonal error of the accelerometer.

6. The method for MEMS IMU calibration based on two-degree-of-freedom turntable according to claim 1, further comprising the steps of: determining the installation direction of each shaft of the MEMS IMU module and determining the direction and the rotation direction of each shaft of the turntable;

the steps of determining the installation orientation of each axis of the MEMS IMU module and determining the orientation and the rotation direction of each axis of the turntable comprise:

7. The MEMS IMU calibration method based on the two-degree-of-freedom turntable as claimed in claim 6, wherein the step S4 comprises the steps of:

acquiring a first data file of a position experiment;

calculating the acceleration mean value of the accelerometer according to the first data file and the theoretical output value of the accelerometer;

and constructing a first matrix according to the acceleration mean value of the accelerometer and the theoretical output value of the accelerometer, and substituting the result of the first matrix into the MEMS IMU accelerometer error model to calculate the accelerometer error item.

8. The MEMS IMU calibration method based on the two-degree-of-freedom turntable as claimed in claim 7, wherein the step S4 further comprises the steps of:

acquiring a second data file of the rate experiment;

calculating a gyro acceleration mean value, a gyro angular velocity mean value and a gyro theoretical output value according to a second data file, wherein the gyro theoretical output value is an output value obtained by deducting the acceleration measurement error from a gyro;

9. A MEMS IMU calibration system based on a two-degree-of-freedom turntable is characterized by comprising:

10. The MEMS IMU calibration system based on a two-degree-of-freedom turntable as claimed in claim 9, further comprising a direction determination module: the MEMS IMU module is used for determining the installation orientation of each shaft of the MEMS IMU module and determining the orientation and the rotation direction of each shaft of the turntable.