CN101738203A - Optimal position calibration method of static drifting zero and primary acceleration related term error model of flexible gyroscope - Google Patents

Abstract

The invention discloses a method for calibrating the optimal position of the error model of zero-order static drift and first-order acceleration related items of a flexible gyroscope, which uses a D-optimal test design method to obtain the optimal test position. In the present invention, under the optimal spatial orthogonal twelve positions, the measured value compensation of the obtained optimal spatial orthogonal twelve position drift coefficients and the static error compensation model G _{of the} flexible gyroscope effectively improves the output of the flexible gyroscope . The drift coefficients obtained by using the traditional eight-position method, the full-space orthogonal twenty-four position method and the optimal space orthogonal twelve-position method during the flexible gyroscope test in the inertial navigation test center. It can be seen from the residual sum of squares of the measured values of the gyroscope that the compensation result of the drift coefficient solved by the optimal space orthogonal twelve-position experimental design method of the flexible gyroscope is 4 to 5 times higher than that of the traditional eight-position method, and compared with the full-space positive The accuracy of the twenty-four position test method is improved and the test time is shortened by half.

Description

Optimal Position Calibration Method for Zero-order and First-order Acceleration Dependent Term Error Models of Flexible Gyroscope Static Drift

technical field

The invention relates to a calibration method for a static drift error model of a flexible gyroscope, more particularly, a calibration method for determining the optimal position of a DTGs-AID-ADD model by using a D-optimal test design method.

Background technique

Gyro technology not only plays a huge role in the fields of military, aviation, and aerospace, but also is widely used in other fields of the national economy, playing an important role in the development of the national economy. Gyro testing is a guarantee measure in the production and application of gyroscopes, and the level of testing accuracy directly affects the development speed of gyroscope technology.

The flexible gyroscope is a dual-degree-of-freedom gyroscope, which is widely used in various navigation, guidance and control systems because of its advantages in accuracy, volume, cost and reliability. However, in practical applications, there are drift errors caused by various disturbance torques in the angular velocity measurement value of the flexible gyroscope. These drift errors are generally composed of static drift errors, dynamic drift errors and random drift errors. The static drift error is the main part of the drift error of the flexible gyroscope, and it is also the main factor of the error of the flexible inertial navigation system. Since in the static drift error model of the flexible gyroscope, the drift error items related to the zero order of acceleration and the first power of acceleration are the main part of the static drift error, generally the error items related to the second power of acceleration can be ignored to obtain the zero order of static drift and an error model related to primary acceleration, which is referred to as the DTGs-AID-ADD model for short. In the DTGs-AID-ADD model, the drift coefficient that has nothing to do with acceleration is called the zero-order drift coefficient of acceleration, and the drift coefficient that is related to acceleration is called the first-order drift coefficient of acceleration.

At present, there are two main test methods for the DTGs-AID-ADD model: 1) use the traditional eight-position test method specified in IEEE Std813-1988 or the national military standard for testing; 2) use the full-space orthogonal twenty-four position test method test method for testing. However, the above two methods have the following problems:

First, the accuracy of the first-order drift coefficient in the DTGs-AID-ADD model obtained by the traditional eight-position test method is not high, so that after the drift coefficient estimated by this method is used to compensate the static drift error of the flexible gyro, the gyro measurement Accuracy cannot be improved significantly.

Second, although the accuracy of the first-order drift coefficient in the DTGs-AID-ADD model estimated by the full-space orthogonal twenty-four-position test method is improved compared with the traditional eight-position test method, the estimation results The first-order drift coefficient in is not optimal. In addition, the test process of this method takes a long time, the workload of data processing is large, and the test cost is high.

Third, the traditional eight-position and full-space orthogonal twenty-four-position test methods are not the optimal test methods, and the resulting drift coefficients are also not optimal. With the continuous improvement of navigation and guidance system accuracy requirements, test efficiency and test cost requirements, it is necessary to further study the DTGs-AID-ADD model calibration method to save time and effort to obtain a DTGs-AID-ADD model with higher accuracy, so that Effectively improve navigation accuracy.

Contents of the invention

In order to efficiently and accurately obtain the optimal drift coefficient in the DTGs-AID-ADD model for flexible gyroscope error compensation and improve navigation accuracy, the present invention proposes an optimal drift coefficient suitable for the DTGs-AID-ADD model Optimal position calibration method. The optimal drift coefficient in the DTGs-AID-ADD model can be obtained by performing the flexible gyro position experiment according to the optimal position proposed in the invention.

According to the optimal test theory of the present invention, the number of optimal test positions of the DTGs-AID-ADD model should be between six positions and twenty-one positions. To obtain the best accuracy and optimal drift coefficient of the DTGs-AID-ADD model through the gyroscope position experiment, it is not that the more positions used for testing, the higher the accuracy of the drift coefficient is, and it is not used for testing. The less the number of positions, the better the drift coefficient, but according to a certain test design standard, an optimal test method is determined between six position numbers and twenty-one position numbers. The present invention adopts D-optimum test The design method determines the optimal position calibration method of the DTGs-AID-ADD model, and the test is carried out through the optimal test position, which not only reduces the test time and test cost, but also makes the obtained drift coefficient the closest to the real value.

A method for calibrating the optimal position of a flexible gyroscope static drift zero-order and first-order acceleration related item error model of the present invention is to install the flexible gyroscope on a three-axis position rate turntable, and connect the flexible gyroscope to a data acquisition device , the data acquisition device is connected to the computer; position measurement software is installed in the computer; the calibration of the optimal position of the DTGs-AID-ADD includes the following calibration steps:

Step 1: Determine the optimal location

The optimal experimental location of DTGs-AID-ADD model test is obtained by D-optimal experimental design method;

The D-optimal test design method means that the optimal test position for DTGs-AID-ADD model testing is obtained by the D-optimal design criterion, and the so-called D-optimal design criterion refers to making the determinant of the test point information matrix reach the extreme large value;

The D-optimal experimental design method first initializes the number of test locations for the DTGs-AID-ADD model test to 6, and performs the 6 optimal location experimental design according to the D-optimal design criteria, and obtains and records the DTGs-AID-ADD model based on The 6 optimal positions and the corresponding information array determinant, and then increase the number of test test positions to 24 in turn, determine the information array determinant and the corresponding optimal test position under the number of 6 to 24 positions, and finally obtain the test The test position corresponding to the maximum determinant of the information matrix in the number of positions n=6～24 is the optimal test position according to the D-optimal criterion; the DTGs-AID- The optimal number of experimental positions of the ADD model is twelve positions, and the corresponding experimental positions are the optimal experimental positions, that is, twelve spatially orthogonal positions;

Step 2: Calibrate the orientation of the space orthogonal twelve positions

First position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is 0 degrees;

Second position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is 0 degrees, γ is 180 degrees, and φ is 0 degrees;

The third position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is -90 degrees;

The fourth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is 90 degrees;

Fifth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is 0 degrees;

Sixth position: The flexible gyroscope rotates from the initial installation coordinate system (North North West) to 0 degrees, γ to 0 degrees, and φ to 180 degrees;

The seventh position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is -90 degrees;

The eighth position: the rotation angle of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is 90 degrees;

Ninth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is -90 degrees, and φ is 0 degrees;

Tenth position: the rotation angle of the flexible gyroscope from the initial installation coordinate system (North North West) is 0 degrees, γ is -90 degrees, and φ is 0 degrees;

Eleventh position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is -90 degrees, γ is 90 degrees, and φ is 0 degrees;

The twelfth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees.

Step 3: Obtain the drift coefficient

(A) Carry out DTGs-AID-ADD model analysis based on the least squares method on the data under the traditional eight positions to obtain the drift coefficient of the traditional eight positions;

(B) Carrying out the DTGs-AID-ADD model based on the least square method analysis on the data under the full-space orthogonal twenty-four positions to obtain the full-space orthogonal twenty-four position drift coefficients;

(C) Carry out DTGs-AID-ADD model analysis based on the least squares method to the data under the spatial orthogonal twelve positions to obtain the spatial orthogonal twelve position drift coefficients;

The DTGs-AID-ADD model is

$\mathrm{<span\; class="notranslate">\; DTGs</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; AID</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ADD</span>}<span\; class="notranslate">\; =</span>\begin{array}{}\end{array}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00041.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00051.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; ,</span>$

in, $u_1=\frac{\cos (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$ $u_2=\frac{\sin (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00051.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; ,</span>$

U ₀ ＝U ₁ ×D(X) _F +U ₂ ×D(Y) _F , V ₀ ＝V ₁ ×D(X) _F +V ₂ ×D(Y) _F ,

U ₃ =U ₁ ×D(X) _X +U ₂ ×D(Y) _X , U ₄ =U ₁ ×D(X) _Y +U ₂ ×D(Y) _Y ,

V ₃ =V ₁ ×D(X) _X +V ₂ ×D(Y) _X , V ₄ =V ₁ ×D(X) _Y +V ₂ ×D(Y) _Y ,

U ₅ ＝U ₁ ×D(X) _Z +U ₂ ×D(Y) _Z , V ₅ =V ₁ ×D(X) _Z +V ₂ ×D(Y) _Z ,

Step 4: Compensate the measured values of spatially orthogonal 12-position azimuth

Using the flexible gyroscope static error compensation model G ₀ and space orthogonal twelve position drift coefficients to compensate the output measurement value of the flexible gyroscope to obtain the compensated measurement value;

The static error compensation model of the flexible gyroscope is

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G"\; filenames="H2009102421377E00031.png,H2009102421377E00041.png"\; state="\{\{state\}\}">G</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Y</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Z</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\\ \mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Y</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Z</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\end{array}\right\}<span\; class="notranslate">\; .</span>$

The advantage of flexible gyroscope optimal position calibration method of the present invention is: (1) the drift error estimation result obtained by the DTGs-AID-ADD model test method stipulated in the current IEEE Std 813-1988 or the national military standard is not optimal , and the optimal position test design method is the best among all position test design methods, and the drift error estimation result obtained by this method is the best, closest to the true value; (2) The optimal position test design of the flexible gyroscope Compared with the full-space orthogonal position gyro test method, the method saves time and effort, and greatly reduces the test cost; (3) The test design method for the optimal position of the flexible gyroscope can accurately estimate the main factors that affect the accuracy of the flexible gyroscope, that is, DTGs - The first-order drift coefficient in the AID-ADD model, after using the optimal drift coefficient obtained by the optimal position test design method to compensate the error of the flexible gyro, the accuracy of the flexible gyro can be increased by 4 to 5 times; (4) The experimental design method for the optimal position of the gyroscope is also suitable for calibrating and solving the first-order drift coefficient of other types of gyroscope static drift error models, which has strong versatility.

Description of drawings

Figure 1 is a schematic diagram of the structure of the flexible gyroscope test device.

Fig. 2 is a flow chart of the process of performing D-optimal experimental design in the present invention.

Fig. 3 is an azimuth diagram of space orthogonal twelve positions of the present invention.

Figure 4 is an azimuth diagram of a traditional quadrature eight position.

Fig. 5 is an azimuth diagram of the full-space orthogonal twenty-four positions.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

As shown in Figure 1, the flexible gyroscope is installed on the three-axis position rate turntable, the flexible gyroscope is connected to the data acquisition equipment, and the data acquisition equipment is connected to the data storage computer. After the above components are connected, the DTGs-AID-ADD is formed The solution system for the model. Wherein, the data storage computer is a PC-based device, and the data storage computer is installed with operating system software (such as windows XP) and flexible gyroscope position measurement software (the flexible gyroscope position measurement software is written in C language) . The data storage computer is used to construct various properties of the flexible gyroscope, showing the test position of the flexible gyroscope. The flexible gyroscope position measurement software is mainly used to save the collected position data in *.dat format for later recall. The position data includes the X-axis pulse number i _x and the Y-axis pulse number i _y of the flexible gyroscope.

As shown in Fig. 2, the optimal test location for the DTGs-AID-ADD model test was obtained using the D-optimal test design method. The D-optimal experimental design method means that the optimal test location for DTGs-AID-ADD model testing is obtained by the D-optimal design criterion, and the so-called D-optimal design criterion refers to the experimental point information matrix (see literature A.C. ATKINSON, A.N.DONEV.Optimum Experimentai Designs[M].95) the determinant reaches the maximum value. The D-optimal experimental design method first initializes the number of test locations for the DTGs-AID-ADD model test to 6, and performs the 6 optimal location experimental design according to the D-optimal design criteria, and obtains and records the DTGs-AID-ADD model based on The 6 optimal positions and the corresponding information array determinant, and then increase the number of test test positions to 24 in turn, and determine the information array determinant (see Table 1) and the corresponding optimal test under the number of 6 to 24 positions Finally, obtain the test position corresponding to the maximum determinant of the information matrix among the number of test positions n = 6-24. According to the D-optimal criterion, the test position is the optimal test position.

Table 1 Number of positions and corresponding D-optimal information array determinant

Number of locations 6 7 8 9 10 Determinant of information matrix 97.2500 115.6726 138.3909 127.8953 126.9742 Number of locations 11 12 13 14 15

Number of locations 6 7 8 9 10 Determinant of information matrix 133.0324 164.0319 152.1635 146.7139 144.1922 Number of locations 16 18 20 twenty two twenty four Determinant of information matrix 155.7064 158.3635 153.0492 155.4938 164.0319

It can be seen from Table 1 that the optimal number of test positions for the DTGs-AID-ADD model is twelve positions, and the corresponding test positions are the optimal test positions, that is, the twelve space orthogonal positions.

Referring to Figure 3, the twelve spatially orthogonal positions are expressed in the following table:

first position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 0 degrees. second position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 180 degrees, and φ is 0 degrees. third position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is -90 degrees. Fourth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 90 degrees. Fifth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is 0 degrees. sixth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 180 degrees. Seventh position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is -90 degrees. eighth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is 90 degrees. Ninth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is -90 degrees, and φ is 0 degrees. tenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is -90 degrees, and φ is 0 degrees. Eleventh position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 90 degrees, and φ is 0 degrees. Twelfth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees.

Note: θ is the rotation angle of the X axis, γ is the rotation angle of the Y axis, and φ is the rotation angle of the Z axis.

_X , Y, Z are the X measurement axis, Y measurement _axis and Z rotation axis of the flexible gyroscope _respectively ; The northward angular velocity component of the gyroscope (abbreviated as the northward angular velocity), ω _U is the angular velocity component of the earth's rotation angular velocity ω _ie in the celestial direction of the flexible gyroscope (abbreviated as the celestial angular velocity) at different positions, Ω is the earth's rotation angle, and φ is The local latitude, g is the gravitational acceleration experienced by the unit mass object, and it is positive in the downward direction. Among them, the northward angular velocity ω _N , the earth's rotation angle Ω, and the local latitude φ satisfy ω _N = Ωcosφ; the celestial angular velocity ω _U , the earth's rotation angle Ω, and the local latitude φ satisfy ω _U = Ωsinφ.

Table 2 The components of the earth's rotation angular velocity and gravity at the twelve space-orthogonal positions

In the present invention, the following steps are performed on the position data acquisition of the spatially orthogonal twelve positions:

The first step is to initialize the solution system of the DTGs-AID-ADD model

The flexible gyroscope (model: 973-61334, accuracy: 0.005 degrees/hour), three-axis position rate turntable (ATS5000 high-precision three-axis rate position test bench produced by 102 of Aerospace First Academy), data acquisition equipment (resolution : 0.07 arc seconds/pulse, acquisition frequency: 200Hz) and a computer (position measurement software is stored in the computer, and the test data at each test position is obtained by using the software) to connect as shown in Figure 1.

The minimum hardware configuration of the computer is CPU 2GHz, memory 1.24GB, and hard disk 10GB. The operating system is windows XP.

The initialization conditions are as follows: connect the three-axis position-rate turntable, flexible gyroscope, data acquisition equipment, and computer according to the method shown in Figure 1, and check through the test device to ensure that the connection is correct, and the three-axis position-rate turntable can be in balance after starting state, the storage computer can be started normally, and the signal transmitted by the data acquisition device can be collected, and the flexible gyroscope can output the measurement signal through the data acquisition device.

The second step is to conduct a steady-state test on the flexible gyroscope

The flexible gyro steady state test includes the X measuring axis steady state test and the Y measuring axis steady state test. The X measurement axis steady-state test and the Y measurement axis steady-state test refer to the X measurement axis and the Y measurement axis of the flexible gyroscope pointing to the east respectively to do n ≥ 6 repeated experiments, each time lasting 3 minutes. During the test, it is necessary to collect and the calculated quantities are:

The number N _i (i=1~n) of sampling points of the X measurement axis and the Y measurement axis;

A single sampling point X ik , Y _ik (i ₌ 1~n, _k =1~N i ) of the N _i (i=1~n) sampling points in the i-th test of the X measurement axis and the Y measurement axis;

The average value D(X) _0i , D(Y) _0i of the X measurement axis and the Y measurement axis N _i (i=1～n) sampling points;

X measuring axis and Y measuring axis $N=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{N}_i(i=1~\mathrm{no})$ The average value D(X) of sampling points, D(Y);

The sum of squared errors of the X measurement axis and the Y measurement axis SS _eDX0 , SS _eDY0 .

in:

The average value of N _i (i=1~n) sampling points in the i-th test on the X measurement axis $\mathrm{D.}{\left(x\right)}_{0i}=\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\&Sigma;}}}{x}_{\mathrm{ik}},i=1~\mathrm{no};$

The average value of N _i (i=1~n) sampling points in the i-th test on the Y measurement axis $\mathrm{D.}{\left(Y\right)}_{0i}=\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\&Sigma;}}}{Y}_{\mathrm{ik}},i=1~\mathrm{no};$

X measuring axis $N=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{N}_i(i=1~\mathrm{no})$ The average value of sampling points $\stackrel{\&OverBar;}{\mathrm{D.}}\left(x\right)=\frac{1}{N}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\mathrm{D.}{\left(x\right)}_{0i}{N}_i,i=1~\mathrm{no};$

Y measuring axis $N=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{N}_i(i=1~\mathrm{no})$ The average value of sampling points $\stackrel{\&OverBar;}{\mathrm{D.}}\left(Y\right)=\frac{1}{N}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}\mathrm{D.}{\left(Y\right)}_{0i}{N}_i,i=1~\mathrm{no};$

Repeat error sum of squares for X measurement axis ${\mathrm{SS}}_{\mathrm{eDX}}$$0_{}=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{[\mathrm{D.}{\left(x\right)}_{0i}-\stackrel{\&OverBar;}{\mathrm{D.}}\left(x\right)]}^2,i=1~\mathrm{no};$

Repeat error sum of squares for the Y measurement axis ${\mathrm{SS}}_{\mathrm{wxya}}$$0_{}=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{[\mathrm{D.}{\left(Y\right)}_{0i}-\stackrel{\&OverBar;}{\mathrm{D.}}\left(Y\right)]}^2,i=1~\mathrm{no}.$

The stable test of the flexible gyroscope is first carried out with the steady state test of the X measurement axis, and the X measurement axis of the flexible gyroscope is adjusted to point to "East". Data is saved in .dat format.

After the X measurement axis steady state test is completed, carry out the Y measurement axis steady state test, adjust the Y measurement axis of the flexible gyroscope to point to "East", and after 3 minutes of power on, repeat the steady state test for n times continuously, and the data acquisition equipment will collect the test The data is saved in *.dat format;

After the X measurement axis steady state test and the Y measurement axis steady state test are completed, read the data collected by the data acquisition equipment from the computer, and test the data processing program through the steady state test to obtain the X measurement axis of the flexible gyroscope. Repeated error sum of squares SS _eDX0 and repeated error sum of squares SS _eDY0 for the Y measuring axis. Stop the test if the sum of the squared errors of the repeatability of any measurement axis is greater than 100 pulses squared. If the sum of the squares of the repeated errors of the two axes is less than 100 pulse squares, it means that the flexible gyroscope can work normally, and you can proceed to the following test steps.

The third step is to collect data by rotating the turntable according to the spatially orthogonal twelve positions

First, point the three axes (X, Y, Z) of the gyroscope to the first orientation (north and west sky) shown in Figure 3, wait for one minute to stabilize, and then start saving data. The time to save position data is 2 minutes, and the data is stored as *.dat format. Then proceed in sequence according to the orientation shown in Figure 3, after each new orientation, you must wait for 1 minute to stabilize, then save the position data of this orientation for 2 minutes and store the data in *.dat format until the last orientation is completed.

The fourth step is to calculate the spatial orthogonal twelve position drift coefficients

After the position data (referred to as position-data) of each position stored in *.dat format is proposed, the outliers are eliminated through data processing in the computer, and then the position-data after the outliers are eliminated and the known ω _X , ω _Y , a _X , a _Y , a _Y are substituted into the DTGs-AID-ADD model, and the least square method is used to analyze and obtain the space orthogonal twelve position drift coefficients.

The mathematical expression of the DTGs-AID-ADD model is:

$\mathrm{<span\; class="notranslate">\; DTGs</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; AID</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ADD</span>}<span\; class="notranslate">\; =</span>\begin{array}{}\end{array}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00041.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00051.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; ,</span>$

in, $u_1=\frac{\cos (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$ ${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="H2009102421377E00031.png,H2009102421377E00051.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=\frac{\sin (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}}$

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="V"\; filenames="H2009102421377E00031.png,H2009102421377E00051.png"\; state="\{\{state\}\}">V</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}$

U ₀ ＝U ₁ ×D(X) _F +U ₂ ×D(Y) _F , V ₀ ＝V ₁ ×D(X) _F +V ₂ ×D(Y) _F

U ₃ =U ₁ ×D(X) _X +U ₂ ×D(Y) _X , U ₄ =U ₁ ×D(X) _Y +U ₂ ×D(Y) _Y

V ₃ =V ₁ ×D(X) _X +V ₂ ×D(Y) _X , V ₄ =V ₁ ×D(X) _Y +V ₂ ×D(Y) _Y

U ₅ ＝U ₁ ×D(X) _Z +U ₂ ×D(Y) _Z , V ₅ =V ₁ ×D(X) _Z +V ₂ ×D(Y) _Z

In the formula:

i _x represents the number of pulses corresponding to the torquer current of the X measuring axis of the flexible gyroscope;

i _y represents the pulse number corresponding to the torque device current of the flexible gyroscope Y measuring axis;

ω _X represents the component of the earth's rotation angular velocity on the X measurement axis of the flexible gyroscope;

ω _Y represents the component of the earth's rotation angular velocity on the Y measurement axis of the flexible gyroscope;

a _X represents the acceleration component on the X measurement axis of the flexible gyroscope;

a _Y represents the acceleration component on the Y measurement axis of the flexible gyroscope;

a _Z represents the acceleration component on the Z rotation axis of the flexible gyroscope;

(SF) _X represents the torque scale coefficient of the X measuring axis of the flexible gyroscope;

(SF) _Y represents the torque scale coefficient of the Y measuring axis of the flexible gyroscope;

ε represents the angle between the X-axis of the torque device of the flexible gyroscope and the X-axis of the shell of the flexible gyroscope;

ξ represents the angle between the Y-axis of the torque device of the flexible gyroscope and the Y-axis of the shell of the flexible gyroscope.

In the present invention, U ₀ , U ₁ , U ₂ , V ₀ , V ₁ and V ₂ represent the zero-order drift coefficient of acceleration, and U ₃ , U _{4 ,} U 5 , V ₃ , V ₄ and V ₅ represent the first-order acceleration Item drift coefficient.

The fifth step is to obtain the measured value of the flexible gyroscope after error compensation

Compensate the output measurement value of the flexible gyroscope with the space orthogonal twelve position drift coefficients obtained in the fourth step and the static error compensation model G ₀ of the flexible gyroscope, and obtain the measured value after compensation through calculation.

The static error compensation model _G0 of the flexible gyroscope is:

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="G"\; filenames="H2009102421377E00031.png,H2009102421377E00041.png"\; state="\{\{state\}\}">G</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; f</span>}}\\ \mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; f</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ \mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\\ \mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Z</span>}}\\ \mathrm{<span\; class="notranslate">\; D.</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; Z</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}$

In the formula:

D(X) represents the drift of the X measuring axis of the flexible gyroscope;

D(Y) represents the drift of the Y measuring axis of the flexible gyroscope;

D(X) _F represents the drift coefficient of the flexible gyroscope around the X measurement axis that has nothing to do with acceleration;

D(Y) _F represents the drift coefficient of the flexible gyroscope around the Y measurement axis that has nothing to do with acceleration;

D(X) _X represents the drift coefficient of the flexible gyroscope around the X measurement axis in the X measurement axis relative to the first power of the acceleration;

D(X) _Y represents the drift coefficient of the flexible gyroscope around the Y measurement axis in the X measurement axis related to the first power of acceleration;

D(X) _Z represents the drift coefficient of the flexible gyroscope around the Z rotation axis in the X measurement axis related to the first power of acceleration;

D(Y) _X represents the drift coefficient of the flexible gyroscope around the X measurement axis in the Y measurement axis related to the first power of acceleration;

D(Y) _Y represents the drift coefficient of the flexible gyroscope around the Y measurement axis in the Y measurement axis relative to the first power of acceleration;

D(Y) _Z represents the drift coefficient of the flexible gyroscope around the Z rotation axis in the Y measurement axis related to the first power of acceleration;

a _X represents the acceleration component on the X measurement axis of the flexible gyroscope;

a _Y represents the acceleration component on the Y measurement axis of the flexible gyroscope;

a _Z represents the acceleration component on the Z rotation axis of the flexible gyroscope.

In order to verify the effectiveness of the spatially orthogonal 12-position calibration method based on the DTGs-AID-ADD model, the two main test methods of the DTGs-AID-ADD model (traditional eight-position test method, full-space orthogonal 20-position calibration method) will be tested below. Four-position test method) as a control example.

Comparative example 1: traditional eight-position test method

Carry out the traditional eight-position test according to the traditional eight-position test method specified in IEEE Std 813-1988 or the national military standard. The test method and steps are the same as the above-mentioned spatial orthogonal twelve-position test method, except that the test orientation is changed as shown in Table 3 The traditional eight positions of the collected position-data are shown in the X-axis data and Y-axis data in Table 3 after removing wild points.

As shown in Figure 4, the traditional eight positions are expressed in the following table:

first position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 90 degrees, and φ is 0 degrees. second position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 90 degrees, and φ is 0 degrees. third position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 90 degrees, and φ is 0 degrees. Fourth position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees. Fifth position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 180 degrees. sixth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is -90 degrees. Seventh position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 0 degrees. eighth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 90 degrees.

Note: θ is the rotation angle of the X axis, γ is the rotation angle of the Y axis, and φ is the rotation angle of the Z axis.

Table 3 Experimental data of two measuring axes under traditional eight positions

orientation X measuring axis (pulse/second) Y measuring axis (pulse/second) first position -89.1083 128.4667 second position -244.0167 -32.3750 third position -85.0917 -190.9417 Fourth position 69.9583 -30.1167

orientation X measuring axis (pulse/second) Y measuring axis (pulse/second) Fifth position -257.8667 -24.3917 sixth position -80.6333 142.7000 Seventh position 84.4167 -38.0167 eighth position -92.7083 -205.0917

Comparative example 2: full-space orthogonal twenty-four-position test method

Carry out the test according to the full-space orthogonal twenty-four positions shown in Table 4. The test method and steps are still the same as the above-mentioned space orthogonal twelve-position test method, but the test orientation is changed to the full space orthogonal as shown in Table 4. Position, the collected position-data after removing wild points is shown in the X-axis data and Y-axis data in Table 4.

Referring to Figure 5, the full-space orthogonal twenty-four positions are expressed in the following table:

first position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees. second position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 90 degrees, and φ is 0 degrees. third position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 90 degrees, and φ is 0 degrees. Fourth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 90 degrees, and φ is 0 degrees. Fifth position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is -90 degrees, and φ is 0 degrees. sixth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is -90 degrees, and φ is 0 degrees. Seventh position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is -90 degrees, and φ is 0 degrees. eighth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is -90 degrees, and φ is 0 degrees. Ninth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is -90 degrees. tenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is 0 degrees. Eleventh position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 180 degrees, γ is 0 degrees, and φ is 90 degrees. Twelfth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 180 degrees, and φ is 0 degrees. Thirteenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 90 degrees. Fourteenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 180 degrees. 15th position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is -90 degrees. Sixteenth position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North West) is 0 degrees, γ is 0 degrees, and φ is 0 degrees.

first position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees. Seventeenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 90 degrees. 18th position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 180 degrees. Nineteenth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is -90 degrees. twentieth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is -90 degrees, γ is 0 degrees, and φ is 0 degrees. 21st position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 0 degrees, and φ is -90 degrees. 22nd position The rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is 90 degrees, γ is 0 degrees, and φ is 0 degrees. Twenty-third position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 0 degrees, and φ is 90 degrees. Twenty-fourth position The rotation angle of the flexible gyroscope from the initial installation coordinate system (North West) is 90 degrees, γ is 0 degrees, and φ is 180 degrees.

Note: θ is the rotation angle of the X axis, γ is the rotation angle of the Y axis, and φ is the rotation angle of the Z axis.

Table 4. Experimental data of two measurement axes in full-space orthogonal twenty-four positions

orientation X axis (pulse/second) Y axis (pulse/second) first position 69.9583 -30.1167 second position -85.0917 -190.9417 third position -244.0167 -32.3750 Fourth position -89.1083 128.4667 Fifth position 70.7083 -32.5833 sixth position -87.7417 -190.1667 Seventh position -243.8083 -28.1000 eighth position -85.2917 129.6083 Ninth position 74.5167 142.2083 tenth position 84.6583 -196.4333 Eleventh position -248.6750 -204.8750 Twelfth position -258.5000 133.7667 Thirteenth position 66.0250 -206.0500

orientation X axis (pulse/second) Y axis (pulse/second) Fourteenth position -257.7417 -186.4417 15th position -240.0417 143.0750 Sixteenth position 83.7583 123.4833 Seventeenth position -92.7083 -205.0917 18th position -257.8667 -24.3917 Nineteenth position -80.6333 142.7000 twentieth position 84.4167 -38.0167 21st position -83.7250 142.2000 22nd position 84.6000 -35.3667 Twenty-third position -89.3000 -205.8167 Twenty-fourth position -257.6167 -28.4417

Example

Please refer to Table 7. It can be seen that the accuracy of the space-orthogonal twelve-position test method is greatly improved compared with the traditional eight-position test method, and the accuracy of the full-space orthogonal twenty-four-position test method is improved and the test time is shortened by half.

The present invention is a space orthogonal twelve position calibration method based on the DTGs-AID-ADD model, using the D-optimal experimental design method to determine that the number of optimal test positions for the DTGs-AID-ADD model should be twelve and the maximum Excellent twelve test orientation. Table 5 shows the drift coefficients obtained by testing the flexible gyroscope in the inertial navigation test center using the traditional eight-position method, the full-space orthogonal twenty-four-position method and the space orthogonal twelve-position method. Table 6 is the data of test points. These test points are taken from the full-orthogonal space and are different from the test points in the traditional eight-position and the optimal position. They are suitable for evaluating the traditional eight-position test method and the full-space orthogonal position. method and the optimal location test method for the estimation accuracy of the drift coefficient. Table 7 shows the evaluation results of the drift coefficients obtained by the three methods objectively after compensation for the gyro output at the test positions listed in Table 6. It can be seen from the residual sum of squares of the gyro measured values. The optimal position test design of the flexible gyroscope Compared with the traditional eight-position method, the compensation result of the drift coefficient obtained by the method is 4 to 5 times higher than that of the traditional eight-position method. In addition, the test time of the optimal position test design method of the flexible gyroscope is shortened to half of that of the full-space orthogonal position method. Therefore, it can be seen that the optimal position test design method of the flexible gyroscope can accurately estimate the drift coefficient of the static drift error model in a time-saving and labor-saving manner, and improve the measurement accuracy of the flexible gyroscope. Simultaneously the optimal position test design method of the present invention is optimal in all position test design methods, the drift coefficient of the DTGs-AID-ADD model that adopts the optimal position test method to obtain is optimal, the closest to the true value, both guaranteed The high measurement accuracy of the gyroscope is guaranteed, and the increase of test test positions (such as twenty-four positions) is avoided in order to improve the measurement accuracy, which greatly reduces the test time of the gyroscope and reduces the test cost. In addition, the optimal position test design method proposed by the present invention has strong versatility and can be well applied to the calibration process of other types of gyroscopes.

Table 5 Test Results

Table 6 Test data of test points

Location X measuring axis (pulse/second) Y measuring axis (pulse/second) 21st position -83.7250 142.2000 22nd position 84.6000 -35.3667 Twenty-fourth position -257.6167 -28.4417

NOTE: These three positions were selected from the full-space orthogonal twenty-four positions.

Table 7 Evaluation Results

Test plan X-axis error sum of squares Y-axis error sum of squares Spatial Orthogonal Twelve Positions 1.5473 5.3523 Traditional eight positions 9.4539 23.1095 Full-space orthogonal twenty-four positions 1.7890 6.5910

Claims (2)

1. A flexible gyroscope static drift zero-order and first-order acceleration related term error model optimal position calibration method is that the flexible gyroscope is installed on the three-axis position rate turntable, and the flexible gyroscope is connected with the data acquisition equipment. The data acquisition equipment is connected with the computer; the position measurement software is installed in the computer; it is characterized in that: the calibration of the optimal position of the flexible gyroscope static drift zero and primary acceleration related item error model DTGs-AID-ADD includes the following calibration Steps: Step 1: Determine the optimal location The optimal experimental location of DTGs-AID-ADD model test is obtained by D-optimal experimental design method; The D-optimal test design method means that the optimal test position for DTGs-AID-ADD model testing is obtained by the D-optimal design criterion, and the so-called D-optimal design criterion refers to making the determinant of the test point information matrix reach the extreme large value; The D-optimal experimental design method first initializes the number of test locations for the DTGs-AID-ADD model test to 6, and performs the 6 optimal location experimental design according to the D-optimal design criteria, and obtains and records the DTGs-AID-ADD model based on The 6 optimal positions and the corresponding information array determinant, and then increase the number of test test positions to 24 in turn, determine the information array determinant and the corresponding optimal test position under the number of 6 to 24 positions, and finally obtain the test The test position corresponding to the maximum determinant of the information matrix in the number of positions n=6～24 is the optimal test position according to the D-optimal criterion; the DTGs-AID- The optimal number of experimental positions of the ADD model is twelve positions, and the corresponding experimental positions are the optimal experimental positions, that is, twelve spatially orthogonal positions; Step 2: Calibrate the orientation of the space orthogonal twelve positions First position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is 0 degrees; Second position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is 0 degrees, γ is 180 degrees, and φ is 0 degrees; The third position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is -90 degrees; The fourth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is 90 degrees; Fifth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is 0 degrees; Sixth position: The flexible gyroscope rotates from the initial installation coordinate system (North North West) to 0 degrees, γ to 0 degrees, and φ to 180 degrees; The seventh position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 0 degrees, γ is 0 degrees, and φ is -90 degrees; The eighth position: the rotation angle of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is 0 degrees, and φ is 90 degrees; Ninth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (Tianbeixi) is 180 degrees, γ is -90 degrees, and φ is 0 degrees; Tenth position: the rotation angle of the flexible gyroscope from the initial installation coordinate system (North North West) is 0 degrees, γ is -90 degrees, and φ is 0 degrees; Eleventh position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is -90 degrees, γ is 90 degrees, and φ is 0 degrees; The twelfth position: the rotation angle θ of the flexible gyroscope from the initial installation coordinate system (North North West) is 90 degrees, γ is 90 degrees, and φ is 0 degrees. Step 3: Obtain the drift coefficient (A) Carry out DTGs-AID-ADD model analysis based on the least squares method on the data under the traditional eight positions to obtain the drift coefficient of the traditional eight positions; (B) Perform the DTGs-AID-ADD model analysis based on the least squares method on the data under the full-space orthogonal twenty-four positions to obtain the full-space orthogonal twenty-four position drift coefficients; (C) Carry out DTGs-AID-ADD model analysis based on the least squares method to the data under the spatial orthogonal twelve positions to obtain the spatial orthogonal twelve position drift coefficients; The DTGs-AID-ADD model is $\mathrm{<span\; class="notranslate">\; DTGs</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; AID</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ADD</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\end{array}\right]<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\\ {\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; ,</span>$ in, $u_1=\frac{\cos (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$ $u_2=\frac{\sin (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$ ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; SF</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}}<span\; class="notranslate">\; ,</span>$ U ₀ ＝U ₁ ×D(X) _F +U ₂ ×D(Y) _F , V ₀ ＝V ₁ ×D(X) _F +V ₂ ×D(Y) _F , U ₃ =U ₁ ×D(X) _X +U ₂ ×D(Y) _X , U ₄ =U ₁ ×D(X) _Y +U ₂ ×D(Y) _Y , V ₃ =V ₁ ×D(X) _X +V ₂ ×D(Y) _X , V ₄ =V ₁ ×D(X) _Y +V ₂ ×D(Y) _Y , U ₅ ＝U ₁ ×D(X) _Z +U ₂ ×D(Y) _Z , V ₅ =V ₁ ×D(X) _Z +V ₂ ×D(Y) _Z , In the formula: i _x represents the pulse number corresponding to the torquer current of the X measuring axis of the flexible gyroscope, i _y represents the pulse number corresponding to the torquer current of the Y measuring axis of the flexible gyroscope, ω _X represents the angular velocity of the earth’s rotation at The component on the X measurement axis of the flexible gyroscope, ω _Y represents the component of the earth’s rotation angular velocity on the Y measurement axis of the flexible gyroscope, a _X represents the acceleration component on the X measurement axis of the flexible gyroscope, and a _Y represents the flexible gyroscope a _Z represents the acceleration component on the Z rotation axis of the flexible gyroscope, (SF) _X represents the torque scale coefficient of the X measuring axis of the flexible gyroscope, (SF) _Y represents the flexible gyroscope The scale factor of the torquer on the Y measuring axis of the instrument, ε represents the angle between the X-axis of the torquer of the flexible gyroscope and the X-axis of the shell of the flexible gyroscope, and ξ represents the angle between the Y-axis of the torquer of the flexible gyroscope and the flexure The angle between the Y-axis of the shell of the gyroscope; Step 4: Compensate the measured values of spatially orthogonal 12-position azimuth Using the flexible gyroscope static error compensation model G ₀ and space orthogonal twelve position drift coefficients to compensate the output measurement value of the flexible gyroscope to obtain the compensated measurement value; The static error compensation model of the flexible gyroscope is $G_0=\left\{\begin{array}{c}\mathrm{D.}\left(x\right)=\mathrm{D.}{\left(x\right)}_f+\mathrm{D.}{\left(x\right)}_x{a}_x+\mathrm{D.}{\left(x\right)}_Y{a}_Y+\mathrm{D.}{\left(x\right)}_Z{a}_z\\ \mathrm{D.}\left(Y\right)=\mathrm{D.}{\left(Y\right)}_f+\mathrm{D.}{\left(Y\right)}_x{a}_x+\mathrm{D.}{\left(Y\right)}_Y{a}_Y+\mathrm{D.}{\left(Y\right)}_Z{a}_z\end{array}\right\},$ In the formula, D(X) represents the drift amount of the X measuring axis of the flexible gyroscope, D(Y) represents the drift amount of the Y measuring axis of the flexible gyroscope, and D(X) _F represents the distance between the flexible gyroscope around the X measuring axis and Acceleration-independent drift coefficient, D(Y) _F indicates the drift coefficient of the flexible gyroscope around the Y measurement axis that has nothing to do with acceleration, D(X) _X indicates that the flexible gyroscope in the X measurement axis is related to the first power of the acceleration around the X measurement axis D(X) _Y represents the drift coefficient of the flexible gyroscope around the Y measuring axis in the X measuring axis and the first power of acceleration, and D(X) _Z represents the relationship between the flexible gyroscope's rotation around the Z axis and The drift coefficient related to the first power of acceleration, D(Y) _X represents the drift coefficient related to the first power of the acceleration of the flexible gyroscope around the X measurement axis in the Y measurement axis, D(Y) _Y represents the rotation of the flexible gyroscope in the Y measurement axis The drift coefficient of the Y measurement axis related to the first power of acceleration, D(Y) _Z indicates the drift coefficient of the flexible gyroscope around the Z rotation axis in the Y measurement axis related to the first power of acceleration, and a _X indicates the X measurement axis of the flexible gyroscope a _Y represents the acceleration component on the Y measurement axis of the flexible gyroscope, and a _Z represents the acceleration component on the Z rotation axis of the flexible gyroscope. 2. flexible gyroscope static drift zero according to claim 1 and method for calibrating optimal position of first-order acceleration-related term error model, it is characterized in that: gather 6 data at least on each selected orientation, every time The time lasts 10 minutes.

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