CN100554884C - Optimal eight-position calibration method for flexible gyroscopes - Google Patents

Abstract

The invention discloses a flexible gyroscope optimal eight-position calibration method. The flexible gyroscope is installed on a three-axis position rate turntable, the flexible gyroscope is connected with data acquisition equipment, and the data acquisition equipment is connected with a computer; The invention discloses a specific orientation in the calibration of the optimal eight positions, and the compensation of the measured values of the obtained optimal eight position drift coefficients and the static error compensation model G ₀ of the flexible gyroscope effectively improves the output of the flexible gyroscope. In the inertial navigation test center, the drift coefficients obtained by the traditional eight-position method and the optimal eight-position method were respectively used in the flexible gyro test process. The drift coefficients obtained by the two methods were objectively compared with the gyro output compensation of the other three positions in space. The evaluation results show that the residual sum of squares of the gyro measurement values shows that the drift coefficient solved by the optimal eight-position experimental design method of the flexible gyroscope is compensated by 4 to 8 times compared with the traditional eight-position method.

Description

Optimal eight-position calibration method for flexible gyroscopes

technical field

The invention relates to a method for calibrating the optimal eight-position position of a flexible gyroscope. Precisely defining the test position of the flexible gyroscope is an important experimental process in the field of flexible gyroscope testing and modeling, and is an important means to further improve the measurement accuracy of the flexible gyroscope.

Background technique

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. Therefore, designing the position test method of the flexible gyroscope, establishing a reasonable static error model of the flexible gyroscope and making compensation can greatly improve the measurement accuracy of the flexible gyroscope and the navigation accuracy of the flexible inertial navigation system.

At present, there are two methods to solve the drift coefficient in the static error model of the flexible gyroscope: 1) adopt the traditional eight-position test method specified in IEEE Std813-1988 or the national military standard; 2) adopt the twenty-four-position test method. However, the above two methods have the following problems: ①. The traditional eight-position test method cannot accurately obtain the first-order drift coefficient in the static error model of the flexible gyroscope, so that the gyroscope after compensation for the static error of the flexible gyroscope with the estimated drift coefficient The measurement accuracy has not been significantly improved; ②, compared with the traditional eight-position test method, the first-order drift coefficient in the static error model of the flexible gyroscope estimated by the 24-position test method has been improved, but the estimation result is not optimal One-time item drift coefficient, and the calculation time in the test process is long, the calculation workload is large, and the test cost is high.

Contents of the invention

In order to save time and effort and accurately obtain the optimal drift coefficient in the static error model of the flexible gyroscope, the present invention proposes an optimal eight-position calibration method suitable for the flexible gyroscope. The optimal drift coefficient in the static error model of the flexible gyroscope can be obtained by performing the position experiment of the flexible gyroscope at the position of the eight-position list; the drift coefficient obtained by using the optimal eight-position calibration can effectively reduce the workload in the test process and reduce the test time. Cost; using the optimal drift coefficient for compensation improves the accuracy of gyroscope testing.

A flexible gyroscope optimal eight-position calibration method of the present invention is to install the flexible gyroscope on the three-axis position rate turntable, the flexible gyroscope is connected with the data acquisition equipment, and the data acquisition equipment is connected with the computer; Position measurement software is installed in the computer; it is characterized in that the following calibration execution steps are arranged:

Step 1: Calibrate the optimal eight-position orientation

First orientation: the X measurement axis of the flexible gyroscope points to "sky", the Y measurement axis of the flexible gyroscope points to "West", and the Z rotation axis of the flexible gyroscope points to "North";

Second orientation: the X measurement axis of the flexible gyroscope points to "earth", the Y measurement axis of the flexible gyroscope points to "North", and the Z rotation axis of the flexible gyroscope points to "East";

Third orientation: the X measurement axis of the flexible gyroscope points to "north", the Y measurement axis of the flexible gyroscope points to "sky", and the Z rotation axis of the flexible gyroscope points to "east";

The fourth orientation: the X measurement axis of the flexible gyroscope points to "North", the Y measurement axis of the flexible gyroscope points to "Earth", and the Z rotation axis of the flexible gyroscope points to "West";

Fifth orientation: the X measurement axis of the flexible gyroscope points to "East", the Y measurement axis of the flexible gyroscope points to "South", and the Z rotation axis of the flexible gyroscope points to "Earth";

Sixth orientation: the X measurement axis of the flexible gyroscope points to "south", the Y measurement axis of the flexible gyroscope points to "east", and the Z rotation axis of the flexible gyroscope points to "sky";

The seventh orientation: the X measurement axis of the flexible gyroscope points to "west", the Y measurement axis of the flexible gyroscope points to "south", and the Z rotation axis of the flexible gyroscope points to "sky";

Eighth orientation: the X measurement axis of the flexible gyroscope points to "south", the Y measurement axis of the flexible gyroscope points to "west", and the Z rotation axis of the flexible gyroscope points to "earth";

Step 2: Obtain the drift coefficient

(A) The data under the traditional eight positions are analyzed based on the least squares method to obtain the traditional eight position drift coefficients of the flexible gyroscope static error model _G1 ;

(B) The data under the optimal eight positions are analyzed based on the least squares method to obtain the optimal eight position drift coefficients of the flexible gyroscope static error model _G1 ;

The static error model of the flexible gyroscope

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</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}{\text{<span class="notranslate"> \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</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 ;

Step 3: Compensate the measured value of the optimal eight-position orientation

Using the flexible gyroscope static error compensation model G ₀ and the optimal eight-position drift coefficient 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">\; G</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>{\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>}}<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 the flexible gyroscope optimal eight-position calibration method of the present invention is: (1) the first-order drift coefficient in the flexible gyroscope static error model that the flexible gyroscope optimal eight-position test design method obtains is the same as IEEEStd 813-1988 Or the traditional eight-position test method specified in the national military standard, the accuracy of the primary drift coefficient is 4-8 times higher than that; (2) The optimal eight-position test design method of the flexible gyroscope is different from the traditional 24-position gyroscope test method Compared with time-saving and labor-saving, the test cost is greatly reduced; (3) The optimal eight-position test design method of the flexible gyroscope can accurately estimate the main factors affecting the accuracy of the flexible gyroscope, that is, the primary factor in the static error model of the flexible gyroscope Item drift coefficient, using the optimal drift coefficient obtained by the optimal eight-position test design method for flexible gyro error compensation can improve the accuracy of the flexible gyroscope by 3 to 5 times; (4) The optimal eight-position test of the flexible gyroscope The design method is also suitable for calibrating and solving the first-order drift coefficient of other types of gyroscope static error models, and has strong versatility.

Description of drawings

Figure 1 is a schematic diagram of the structure of the experimental device for solving the static error of the flexible gyroscope.

Fig. 2 is each azimuth diagram of optimum eight positions of the present invention.

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 computer. The connection of the above devices constitutes a system for solving the static error model of the flexible gyroscope . The computer is a PC-based device, with operating system software (such as windows XP) stored in the internal memory, and "position measurement software" suitable for obtaining measurement data in different positions of the flexible gyroscope. The position measurement software mainly It is used to save the position data of traditional eight positions and optimal eight positions collected by (data acquisition equipment) in ^* .dat format, so as to facilitate the operator to call again. The position data includes the X-axis pulse number i _x and the Y-axis pulse number i _y of the flexible gyroscope. In the present invention, the position measurement software installed in the computer is essentially a kind of conventional conversion software of a data storage format, which is relatively common in the market at present, such as converting the word2007 version to the word2003 version or a low-copyright one that can be used A variety of software, such as high and low copyright transfer in drawing, etc.

Acquisition of position data is to solve the static error model system of the flexible gyroscope and initialize it first, then carry out the steady-state test of the flexible gyroscope first, if the steady-state test of the flexible gyroscope is normal (that is, the residual sum of squares of the measured values of the gyroscope is less than 100 pulses Square), the three-axis position rate turntable is rotated according to the traditional eight positions and the optimal eight positions respectively, and the output measurement value of the flexible gyroscope at each position is collected by the data acquisition device and then output to the computer for saving and recalling . After the acquisition of the output measurement values of the flexible gyroscope at all positions is completed, all the collected data of the traditional eight positions and the optimal eight positions are analyzed by the static error model _G1 of the flexible gyroscope based on the least square method to obtain the drift of the traditional eight positions coefficient and the optimal eight-position drift coefficient; then use (A) the compensation model G ₀ and the traditional eight-position drift coefficient, (B) the compensation model G ₀ and the optimal eight-position drift coefficient to compensate the output measurement value of the flexible gyroscope Obtain compensated measurements.

In the present invention, the static error model _G of the flexible gyroscope is:

${\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</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}{\text{<span class="notranslate"> \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</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 number of pulses corresponding to the torque device current of the X measuring axis of the flexible gyroscope,

i _y represents the number of pulses corresponding to the torquer current of the Y measuring axis of the flexible gyroscope,

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 housing 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, the static error compensation model _G of the flexible gyroscope is:

${\mathrm{<span\; class="notranslate">\; G</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>{\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>}}<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\}$

, where 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 related to the first power of 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 related 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 the present invention, for the optimal eight positions, it means that eight spatial position orientations selected from the 24 different gyroscope coordinate system orientations of the orthogonal position test are used as test points, and the optimal eight positions For the schematic diagram of each direction, please refer to Figure 2.

In the present invention, for the optimal drift coefficient in the static error model of the flexible gyroscope, it means that the drift coefficient of the static error model of the flexible gyroscope obtained by the optimal eight-position test data of the flexible gyroscope is closest to the true value of the drift coefficient, by The measurement accuracy of the flexible gyroscope can be further improved after the optimal drift coefficient obtained from the calibration is compensated for the static error of the flexible gyroscope.

In the present invention, the calibration of the optimal eight-position orientation of the flexible gyroscope is as follows (each orientation is as shown in Figure 2):

First orientation: the X measurement axis of the flexible gyroscope points to "sky", the Y measurement axis of the flexible gyroscope points to "west", and the Z rotation axis of the flexible gyroscope points to "north".

Second orientation: the X measurement axis of the flexible gyroscope points to "earth", the Y measurement axis of the flexible gyroscope points to "north", and the Z rotation axis of the flexible gyroscope points to "east".

Third orientation: the X measurement axis of the flexible gyroscope points to "north", the Y measurement axis of the flexible gyroscope points to "sky", and the Z rotation axis of the flexible gyroscope points to "east".

Fourth orientation: the X measurement axis of the flexible gyroscope points to "North", the Y measurement axis of the flexible gyroscope points to "Earth", and the Z rotation axis of the flexible gyroscope points to "West".

Fifth orientation: the X measurement axis of the flexible gyroscope points to "East", the Y measurement axis of the flexible gyroscope points to "South", and the Z rotation axis of the flexible gyroscope points to "Earth".

Sixth orientation: the X measurement axis of the flexible gyroscope points to "south", the Y measurement axis of the flexible gyroscope points to "east", and the Z rotation axis of the flexible gyroscope points to "sky".

The seventh orientation: the X measurement axis of the flexible gyroscope points to "west", the Y measurement axis of the flexible gyroscope points to "south", and the Z rotation axis of the flexible gyroscope points to "sky".

Eighth orientation: the X measurement axis of the flexible gyroscope points to "south", the Y measurement axis of the flexible gyroscope points to "west", and the Z rotation axis of the flexible gyroscope points to "earth".

Described optimal eight positions satisfy the eight position spatial distributions of table 1, wherein, X, Y, Z are respectively the measurement axis (X measurement axis, Y measurement axis) and the rotation axis of flexible gyroscope; ω _ie is that the earth is relative to The rotation angular velocity in inertial space, ω _N is the angular velocity component of the earth's rotation angular velocity ω _ie in the north direction of the flexible gyroscope at different positions (abbreviated as the north angular velocity), and ω _U is the earth rotation angular velocity ω _ie in the flexible gyroscope at different positions The angular velocity component of the celestial direction (referred to as the celestial angular velocity), Ω is the rotation angle of the earth, φ is the local latitude, g is the gravitational acceleration on 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.

In the stable test process of the flexible gyro, the X measurement axis and the Y measurement axis are included, and the X measurement axis and the Y measurement axis point to the east respectively to do n times (n≥6) repeated experiments, each time lasting 10 minutes, Each test procedure includes:

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;

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

The sum of squared errors of the X measurement axis and the Y measurement axis SS _eDX0 , SS _eDY0 , and the average value of N _i (i=1～n) sampling points 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 on the Y measurement axis ${\mathrm{D.}\left(Y\right)}_{0i}=\frac{1}{N_i}\underset{k=1}{\overset{N_i}{\mathrm{\&Sigma;}}}{Y}_{\mathrm{ik}},i=1~\mathrm{no}.$

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

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

The sum of squared errors of the X measuring axis SS _eDX0 = ∑(D(X) _0i -D(X)) ² , i=1～n,

Repeated error sum of squares of the Y measurement axis SS _eDY0 =∑(D(Y) _0i −D(Y)) ² , i=1˜n.

The flexible gyroscope optimal eight-position test design method of the present invention includes the following processing steps:

Step 1: Connect the three-axis position-rate turntable, flexible gyroscope, data acquisition equipment and computer according to the method shown in Figure 1, and ensure that the connection is correct through the testing device;

Step 2: Adjust the X measurement axis of the flexible gyroscope to point to "East". After 3 minutes of power-on, repeat the steady-state test for n times continuously, and the data acquisition device will save the collected test data in the steady-state test.dat format;

Step 3: Adjust the Y measurement axis of the flexible gyroscope to point to "east". After 3 minutes of power-on, repeat the steady-state test for n times continuously, and the data acquisition device will save the collected test data in the steady-state test.dat format;

Step 4: The computer reads the data collected by the data acquisition equipment, and through the steady-state test to test the data processing program, calculate the sum of the squares of the repeated errors of the X measurement axis of the flexible gyroscope SS _eDX0 and the sum of the squares of the repeated errors of the Y measurement axis SS _eDY0 ;

Stop the test if the square of the repetitive error for any axis is greater than 100 pulses squared. If the sum of the squares of the repetitive errors of the two axes is less than 100 pulse squares, proceed to the following steps for testing.

Step 5: Rotate the three-axis position-rate turntable according to the positions in Table 1 to collect data, and eliminate the outliers through the test data processing program in the computer, and then use the pulse measurement values i _X , i _Y and the known ω _X , ω _Y , a _X , a _Y , a _Y , using the least square method to get the drift coefficient in the static error compensation model G ₀ of the flexible gyroscope.

Example

Please refer to Table 2, collect data in each orientation respectively, and analyze the acquired data according to the static error model G ₁ of the flexible gyroscope to obtain the drift coefficient, and then perform compensation according to the static error compensation model G ₀ of the flexible gyroscope . It can be seen that the accuracy of the optimal eight-position test method is greatly improved compared with the traditional eight-position test method.

The present invention proposes a kind of optimal eight-position test design method of flexible gyroscope, utilizes the principle of D-optimum criterion to design the optimum eight-position test that is convenient to estimate the drift coefficient of flexible gyroscope static error model, and table 2 is in inertial The drift coefficients obtained by using the traditional eight-position method and the optimal eight-position test design method in the flexible gyroscope testing process of the guidance test center, Table 3 is the objective output of the gyro at the other three positions in the space using the drift coefficients obtained by the two methods. The evaluation results after compensation can be seen from the residual sum of squares of the gyro measurement values. The drift coefficient calculated by the optimal eight-position experimental design method of the flexible gyroscope is used for compensation, and the result after compensation is 4 to 8 times higher than that of the traditional eight-position method. Therefore, it can be seen that the optimal eight-position test design method of the flexible gyroscope can accurately estimate the drift coefficient of the error model, improve the measurement accuracy of the flexible gyroscope, greatly reduce the test time of the gyroscope, and reduce the test cost. In addition, the invented The optimal eight-position test design method has strong versatility and can be well applied to the calibration process of other types of gyroscopes.

Table 1 Spatial distribution of optimal orthogonal eight positions

Table 2 Test results under two different position definitions

Y-axis coefficient U₀ U₁ U₂ U₃ U₄ U₅ Traditional eight positions -88.2917 13.8319 -0.1846 -38.5564 -7.6838 0.3500 The best eight positions -87.5823 13.8895 -0.0325 -38.4089 -4.6462 -0.2833 X-axis coefficient V₀ V₁ V₂ V₃ V₄ V₅ Traditional eight positions -30.0896 0.1062 13.9443 7.6994 -38.7559 0.6646 The best eight positions -31.4083 -0.0263 13.9992 4.6215 -38.6138 1.7708

Table 3 Evaluation Results

Claims (2)

1, a kind of method for standardization of optimum 8 positions of flexure gyroscope is flexure gyroscope to be installed on the three shaft position rate tables, and flexure gyroscope links to each other with data acquisition equipment, and data acquisition equipment links to each other with computing machine; Position measurement software is installed in the described computing machine; It is characterized in that having following demarcation execution in step:

The first step: demarcate the optimum 8 positions orientation

First orientation: the X measurement axis sensing of flexure gyroscope " my god ", the Y measurement axis of flexure gyroscope is pointed to " west ", and the Z axis of rotation of flexure gyroscope points to " north ";

Second orientation: the X measurement axis sensing of flexure gyroscope " ", the Y measurement axis of flexure gyroscope is pointed to " north ", and the Z axis of rotation of flexure gyroscope points to " east ";

The third party position: the X measurement axis of flexure gyroscope is pointed to " north ", the Y measurement axis sensing of flexure gyroscope " my god ", the Z axis of rotation of flexure gyroscope points to " east ";

The position, four directions: the X measurement axis of flexure gyroscope is pointed to " north ", the Y measurement axis sensing of flexure gyroscope " ", the Z axis of rotation of flexure gyroscope points to " west ";

The 5th orientation: the X measurement axis of flexure gyroscope is pointed to " east ", and the Y measurement axis of flexure gyroscope is pointed to " south ", the Z axis of rotation sensing of flexure gyroscope " ";

The 6th orientation: the X measurement axis of flexure gyroscope is pointed to " south ", and the Y measurement axis of flexure gyroscope is pointed to " east ", the Z axis of rotation sensing of flexure gyroscope " my god ";

The 7th orientation: the X measurement axis of flexure gyroscope is pointed to " west ", and the Y measurement axis of flexure gyroscope is pointed to " south ", the Z axis of rotation sensing of flexure gyroscope " my god ";

Eight directional: the X measurement axis of flexure gyroscope is pointed to " south ", and the Y measurement axis of flexure gyroscope is pointed to " west ", the Z axis of rotation sensing of flexure gyroscope " ";

Second step: obtain coefficient of deviation

(A) data under traditional 8 positions are carried out flexible gyroscope static error model G ₁Resolve to obtain traditional 8 positions coefficient of deviation based on least square method;

(B) data under the optimum 8 positions are carried out flexible gyroscope static error model G ₁Resolve to obtain the optimum 8 positions coefficient of deviation based on least square method;

Described flexible gyroscope static error model

$G_1=\left[\begin{array}{c}{i}_x\\ i_y\end{array}\right]=\left[\begin{array}{c}{U}_0\\ V_0\end{array}\right]+\left[\begin{array}{cc}{U}_1& U_2\\ V_1& V_2\end{array}\right]\left[\begin{array}{c}{\mathrm{\&omega;}}_Y\\ {\mathrm{\&omega;}}_X\end{array}\right]+\left[\begin{array}{cc}{U}_3& U_4\\ V_3& V_4\end{array}\right]\left[\begin{array}{c}{a}_X\\ a_Y\end{array}\right]+\left[\begin{array}{c}{U}_5\\ V_5\end{array}\right]a_Z,$

Wherein, $U_1=\frac{\cos (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$ $U_2=\frac{\sin (\mathrm{\&epsiv;}+\mathrm{\&xi;})}{{\left(\mathrm{SF}\right)}_Y\cos \mathrm{\&xi;}},$

$V_1=\frac{-\sin \mathrm{\&epsiv;}}{{\left(\mathrm{SF}\right)}_X\cos \mathrm{\&xi;}},$ $V_2=\frac{\cos \mathrm{\&epsiv;}}{{\left(\mathrm{SF}\right)}_X\cos \mathrm{\&xi;}},$

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 _xThe pairing umber of pulse of torquer electric current of expression flexure gyroscope X measurement axis, i _yThe pairing umber of pulse of torquer electric current of expression flexure gyroscope Y measurement axis, ω _XThe component of expression rotational-angular velocity of the earth on flexure gyroscope X measurement axis, ω _YThe component of expression rotational-angular velocity of the earth on flexure gyroscope Y measurement axis, a _XComponent of acceleration on the expression flexure gyroscope X measurement axis, a _YComponent of acceleration on the expression flexure gyroscope Y measurement axis, a _ZComponent of acceleration on the expression flexure gyroscope Z axis of rotation, (SF) _XThe torquer calibration factor of expression flexure gyroscope X measurement axis, (SF) _YThe torquer calibration factor of expression flexure gyroscope Y measurement axis, ε are represented the angle between the housing X-axis of the torquer X-axis of flexure gyroscope and flexure gyroscope, and ξ represents the angle between the housing Y-axis of the torquer Y-axis of flexure gyroscope and flexure gyroscope;

The 3rd step: the measured value to the optimum 8 positions orientation compensates

Utilize flexible gyroscope static error compensation model G ₀The flexure gyroscope outputting measurement value is compensated the measured value that obtains after the compensation with the optimum 8 positions coefficient of deviation;

Described flexible gyroscope static error compensation model is

$G_0=\left\{\begin{array}{c}D\left(X\right)=D{\left(X\right)}_F+D{\left(X\right)}_X{a}_X+D{\left(X\right)}_Y{a}_Y+D{\left(X\right)}_Z{a}_z\\ D\left(Y\right)=D{\left(Y\right)}_F+D{\left(Y\right)}_X{a}_X+D{\left(Y\right)}_Y{a}_Y+D{\left(Y\right)}_Z{a}_z\end{array}\right\},$

In the formula, the drift value of D (X) expression flexure gyroscope X measurement axis, the drift value of D (Y) expression flexure gyroscope Y measurement axis, D (X) _FThe expression flexure gyroscope is around X measurement axis and the irrelevant coefficient of deviation of acceleration, D (Y) _FThe expression flexure gyroscope is around Y measurement axis and the irrelevant coefficient of deviation of acceleration, D (X) _XFlexure gyroscope is around the X measurement axis coefficient of deviation relevant with the acceleration first power, D (X) in the expression X measurement axis _YFlexure gyroscope is around the Y measurement axis coefficient of deviation relevant with the acceleration first power, D (X) in the expression X measurement axis _ZFlexure gyroscope is around the Z axis of rotation coefficient of deviation relevant with the acceleration first power, D (Y) in the expression X measurement axis _XFlexure gyroscope is around the X measurement axis coefficient of deviation relevant with the acceleration first power, D (Y) in the expression Y measurement axis _YFlexure gyroscope is around the Y measurement axis coefficient of deviation relevant with the acceleration first power, D (Y) in the expression Y measurement axis _ZFlexure gyroscope is around the Z axis of rotation coefficient of deviation relevant with the acceleration first power, a in the expression Y measurement axis _XComponent of acceleration on the expression flexure gyroscope X measurement axis, a _YComponent of acceleration on the expression flexure gyroscope Y measurement axis, a _ZComponent of acceleration on the expression flexure gyroscope Z axis of rotation.

2, method for standardization of optimum 8 positions of flexure gyroscope according to claim 1 is characterized in that: gather 6 secondary data at least on each selected orientation, each time remaining 10min.

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