CN101738203A - Optimal position calibration method of static drifting zero and primary acceleration related term error model of flexible gyroscope - Google Patents
Optimal position calibration method of static drifting zero and primary acceleration related term error model of flexible gyroscope Download PDFInfo
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Abstract
The invention discloses an optimal position calibration method of a static drifting zero and primary acceleration related term error model of a flexible gyroscope, which acquires an optimal test position by adopting a D-optimal test design method. In the invention, the output of the flexible gyroscope is effectively improved by carrying out measured value compensation on acquired optimal space quadrature-12 position drifting coefficients and an acquired flexible gyro static error compensation model G0 under the optimal space quadrature-12 position; the drifting coefficients are acquired by respectively adopting a traditional 8-position method, a full-space quadrature-24 position method and an optimal space quadrature-12 position method in the flexible gyro test process in an inertial navigation center; and the residual square sum of gyro testing values can shows that a solved result of the drifting coefficients after being compensated by utilizing the optimal space quadrature-12 position test design method of the flexible gyroscope is improved by 4 to 5 times compared with the traditional 8-position method, the precision is improved and the test time is shortened by half compared with the full-space quadrate-24 position test method.
Description
Technical Field
The invention relates to a calibration method for a static drift error model of a flexible gyroscope, in particular to a calibration method for determining the optimal position of a DTGs-AID-ADD model by adopting a D-optimal test design method.
Background
The gyro technology plays a great role in the fields of military, aviation and aerospace, is widely applied in other fields of national economy, and plays an important role in the development of national economy. The gyro test is a guarantee measure in the production and application of the gyro, and the development speed of the gyro technology is directly influenced by the test precision.
A flexible gyroscope is a two-degree-of-freedom gyroscope and is widely used in various navigation, guidance, and control systems due to its advantages in terms of precision, volume, cost, reliability, and the like. However, in practical applications, drift errors due to various disturbance moments exist in the angular velocity measurement value of the flexible gyroscope, and the drift errors generally consist of static drift errors, dynamic drift errors and random drift errors, wherein the static drift errors caused by linear motion are a main part of the drift errors of the flexible gyroscope and are also a main factor of the errors of the flexible inertial navigation system. Since the drift error terms related to the acceleration zero order and the acceleration first order are the main parts of the static drift error in the static drift error model of the flexible gyroscope, the error terms related to the acceleration second order can be ignored to obtain the static drift zero order and first order acceleration related term error model, which is abbreviated as DTGs-AID-ADD model. In the DTGs-AID-ADD model, a drift coefficient which is independent of the acceleration is called an acceleration zero-order term drift coefficient, and a drift coefficient which is dependent on the acceleration is called an acceleration primary term drift coefficient.
At present, the DTGs-AID-ADD model test methods mainly comprise two methods: 1) testing is carried out by adopting a traditional eight-position test method specified in IEEE Std813-1988 or the national military standard; 2) and testing by adopting a full-space orthogonal twenty-four position test method. However, the above two methods have the following problems:
the accuracy of the first term drift coefficient in the DTGs-AID-ADD model obtained by the first and traditional eight-position test methods is not high, so that the gyro measurement precision cannot be remarkably improved after the drift coefficient estimated by the method is used for static drift error compensation of the flexible gyro.
Secondly, although the accuracy of the primary term drift coefficient in the DTGs-AID-ADD model estimated by adopting the full-space orthogonal twenty-four position test method is improved compared with that of the traditional eight-position test method, the primary term drift coefficient in the estimation result is not optimal, and in addition, the test process of the method is long in time, the data processing workload is large, and the test cost is high.
The third, conventional eight-position and full-space orthogonal twenty-four-position test method is not the optimal test method, and thus the obtained drift coefficient is not the optimal. With the continuous improvement of the precision requirement, the test efficiency and the test cost requirement of the navigation and guidance system, a DTGs-AID-ADD model calibration method needs to be further researched to obtain a DTGs-AID-ADD model with higher precision in a time-saving and labor-saving manner, so that the navigation precision is effectively improved.
Disclosure of Invention
In order to efficiently and accurately obtain the optimal drift coefficient in the DTGs-AID-ADD model for error compensation of the flexible gyroscope and improvement of navigation precision, the invention provides the optimal position calibration method suitable for the DTGs-AID-ADD model. And performing a flexible gyroscope position experiment according to the optimal position provided by the invention to obtain the optimal drift coefficient in the DTGs-AID-ADD model.
According to the optimal experimental theory, the number of the optimal experimental positions of the DTGs-AID-ADD model is between six positions and twenty-one positions. The optimal position calibration method of the DTGs-AID-ADD model is determined by adopting a D-optimal experimental design method, and the optimal experimental position is used for testing, so that the experimental time is reduced, the testing cost is reduced, and the obtained drift coefficient is closest to the true value.
The invention relates to an optimal position calibration method of a static drift zero-order and primary acceleration related term error model of a flexible gyroscope, which is characterized in that the flexible gyroscope is arranged on a three-axis position rate turntable and is connected with data acquisition equipment, and the data acquisition equipment is connected with a computer; position measurement software is installed in the computer; the calibration of the optimal position of the DTGs-AID-ADD comprises the following calibration execution steps:
the first step is as follows: determining optimal locations
The optimal test position of the DTGs-AID-ADD model test is obtained by adopting a D-optimal test design method;
the D-optimal test design method is that the optimal test position for the DTGs-AID-ADD model test is obtained by a D-optimal design criterion, wherein the D-optimal design criterion is that the determinant of the test point information matrix reaches the maximum value;
the D-optimal test design method comprises the steps of firstly initializing the number of test positions of a DTGs-AID-ADD model test to 6, carrying out 6-optimal position test design according to a D-optimal design criterion, obtaining and recording 6-optimal positions and corresponding information matrix determinant based on the DTGs-AID-ADD model, then sequentially increasing the number of the test positions to 24, determining the information matrix determinant and corresponding optimal test positions under the number of the 6-24 positions, and finally obtaining the test position, which is the optimal test position, corresponding to the maximum information matrix determinant in the number n of the test positions 6-24 according to the D-optimal criterion; determining that the optimal test positions of the DTGs-AID-ADD model are twelve positions by a D-optimal test design method, wherein the corresponding test positions are the optimal test positions, namely twelve spatially orthogonal positions;
the second step is that: calibrating a spatial orthogonal twelve-position orientation
A first position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 0 degree;
a second position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 180 degrees, and phi is 0 degree;
a third position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is-90 degrees;
the fourth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 90 degrees;
a fifth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is 0 degree;
a sixth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 180 degrees;
a seventh position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is-90 degrees;
an eighth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is 90 degrees;
ninth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is-90 degrees, and phi is 0 degree;
the tenth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is-90 degrees, and phi is 0 degree;
an eleventh position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is-90 degrees, gamma is 90 degrees, and phi is 0 degree;
a twelfth position: the flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest).
The third step: obtaining a drift coefficient
(A) Performing least square method analysis on the DTGs-AID-ADD model on the data at the traditional eight positions to obtain a traditional eight-position drift coefficient;
(B) performing least square method analysis on DTGs-AID-ADD models on data under twenty-four full-space orthogonal positions to obtain a twenty-four full-space orthogonal position drift coefficient;
(C) performing least square method analysis of a DTGs-AID-ADD model on data at the space orthogonal twelve positions to obtain a space orthogonal twelve position drift coefficient;
the DTGs-AID-ADD model is
Wherein, <math><mrow><msub><mi>U</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><msub><mi>U</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac><mo>,</mo></mrow></math>
U0＝U1×D(X)F+U2×D(Y)F，V0＝V1×D(X)F+V2×D(Y)F，
U3＝U1×D(X)X+U2×D(Y)X，U4＝U1×D(X)Y+U2×D(Y)Y，
V3＝V1×D(X)X+V2×D(Y)X，V4＝V1×D(X)Y+V2×D(Y)Y，
U5＝U1×D(X)Z+U2×D(Y)Z，V5＝V1×D(X)Z+V2×D(Y)Z，
the fourth step: compensating for measurements of a spatially orthogonal twelve-position orientation
Model G using flexible gyroscope static error compensation0Compensating the output measured value of the flexible gyroscope by using a twelve-position drift coefficient orthogonal to the space to obtain a compensated measured value;
the static error compensation model of the flexible gyroscope is
The method for calibrating the optimal position of the flexible gyroscope has the advantages that: (1) at present, the drift error estimation result obtained by the DTGs-AID-ADD model test method specified in IEEE Std813-1988 or the national military standard is not optimal, the optimal position test design method is optimal in all position test design methods, and the drift error estimation result obtained by the method is optimal and is closest to the true value; (2) compared with a full-space orthogonal position gyro testing method, the optimal position test design method of the flexible gyroscope is time-saving and labor-saving, and the test cost is greatly reduced; (3) the optimal position test design method of the flexible gyroscope can accurately estimate main factors influencing the precision of the flexible gyroscope, namely the first-order drift coefficients in the DTGs-AID-ADD model, and the precision of the flexible gyroscope can be improved by 4-5 times after the optimal drift coefficients obtained by the optimal position test design method are used for error compensation of the flexible gyroscope; (4) the method for designing the optimal position test of the flexible gyroscope is also suitable for calibrating and solving the first-term drift coefficient of static drift error models of other types of gyroscopes, and has strong universality.
Drawings
FIG. 1 is a schematic diagram of a flexible gyroscope test apparatus.
FIG. 2 is a process flow diagram of the present invention for performing a D-best trial design.
Fig. 3 is a spatial orthogonal twelve position orientation map of the present invention.
Fig. 4 is a conventional orthogonal eight-position orientation diagram.
Fig. 5 is a fully spatial orthogonalized twenty-four position orientation map.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in figure 1, the flexible gyroscope is arranged on the three-axis position rate turntable, the flexible gyroscope is connected with the data acquisition equipment, the data acquisition equipment is connected with the data storage computer, and the flexible gyroscope, the data acquisition equipment and the data storage computer form a solving system of the DTGs-AID-ADD model after being connected. The data storage computer is a PC-based device, and operating system software (such as windows XP) and flexible gyroscope position measurement software (the flexible gyroscope position measurement software is written in C language) are installed in the data storage computer. And the data storage computer is used for constructing various attributes of the flexible gyroscope and displaying the test position of the flexible gyroscope. The flexible gyroscope position measurement software is mainly used for storing the acquired position data into a delta dat format so as to facilitate later calling. The position data comprises X-axis pulse number i of the flexible gyroscopexAnd Y-axis pulse number iy。
As shown in FIG. 2, the optimal trial positions for the DTGs-AID-ADD model test are obtained by a D-optimal trial design method. D-the optimal test design method is as follows: the optimal trial positions for the DTGs-AID-ADD model test are derived from the D-optimal design criterion, which means that the determinant of the trial point information matrix (see document a.c. atkinson, a.n. donev. optimal experimental Designs [ M ].95) reaches a maximum. The D-optimal test design method comprises the steps of firstly initializing the number of test positions of a DTGs-AID-ADD model test to 6, carrying out 6-optimal position test design according to a D-optimal design criterion, obtaining and recording 6-optimal positions based on the DTGs-AID-ADD model and a corresponding information array, then sequentially increasing the number of the test positions to 24, determining the information array (see table 1) and the corresponding optimal test positions under the number of the 6-24 positions, and finally obtaining the test position n which is the optimal test position according to the D-optimal criterion when the number of the test positions is the maximum in the information array in the 6-24.
TABLE 1 number of positions and corresponding D-optimum information matrix
| Number of positions | 6 | 7 | 8 | 9 | 10 |
| Information matrix determinant | 97.2500 | 115.6726 | 138.3909 | 127.8953 | 126.9742 |
| Number of positions | 11 | 12 | 13 | 14 | 15 |
| Number of positions | 6 | 7 | 8 | 9 | 10 |
| Information matrix determinant | 133.0324 | 164.0319 | 152.1635 | 146.7139 | 144.1922 |
| Number of positions | 16 | 18 | 20 | 22 | 24 |
| Information matrix determinant | 155.7064 | 158.3635 | 153.0492 | 155.4938 | 164.0319 |
As can be seen from Table 1, the number of the optimal experimental positions of the DTGs-AID-ADD model is twelve, and the corresponding experimental positions are the optimal experimental positions, namely twelve spatially orthogonal positions.
Referring to fig. 3, the spatially orthogonal twelve positions are represented in the following table:
| first position | The flexible gyroscope is rotated by an angle θ of 0 degrees, γ of 0 degrees, and φ of 0 degrees from the initial mounting coordinate system (northwest). |
| Second position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 180 degrees, and phi of 0 degree from the initial installation coordinate system (northwest). |
| Third position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees and phi of-90 degrees from an initial installation coordinate system (northwest). |
| The fourth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of 90 degrees from the initial installation coordinate system (northwest). |
| Fifth position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Sixth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of 180 degrees from the initial installation coordinate system (northwest). |
| Seventh position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of-90 degrees from an initial installation coordinate system (northwest). |
| Eighth position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees, and phi of 90 degrees from the initial installation coordinate system (northwest). |
| Ninth position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of-90 degrees, and phi of 0 degrees from an initial installation coordinate system (northwest). |
| The tenth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of-90 degrees and phi of 0 degree from an initial installation coordinate system (northwest). |
| Eleventh position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 90 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| The twelfth position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
Note: theta is the rotation angle of the X axis, gamma is the rotation angle of the Y axis, and phi is the rotation angle of the Z axis.
X, Y, Z are the X measuring axis, the Y measuring axis and the Z rotation axis of the flexible gyroscope respectively; omegaieIs the angular velocity of rotation, ω, of the earth relative to the inertial spaceNIs the rotational angular velocity omega of the earth at different positionsieThe angular velocity component in the north direction of the flexible gyroscope (north angular velocity for short), ωUIs the rotational angular velocity omega of the earth at different positionsieThe angular velocity component in the sky direction of the flexible gyroscope (abbreviated as the sky direction angular velocity), omega is the autorotation angle of the earth, phi is the local latitude, g is the gravitational acceleration borne by a unit mass object, and the orientation is positive. Wherein the north direction angular velocity omegaNThe autorotation angle omega of the earth and the local latitude phi meet omegaNΩ cos Φ; angular velocity ω in the direction of the skyUThe autorotation angle omega of the earth and the local latitude phi meet omegaU＝Ωsinφ。
TABLE 2 components of Earth's rotational angular velocity and gravity at spatially orthogonal twelve positions
In the present invention, the following steps are performed for the position data acquisition of the spatially orthogonal twelve positions:
firstly, initializing a solving system of a DTGs-AID-ADD model
A flexible gyroscope (model: 973-.
The lowest hardware configuration of the computer is CPU 2GHz, memory 1.24GB and hard disk 10 GB. The operating system is windows XP.
The initialization conditions are as follows: the three-axis position rate rotary table, the flexible gyroscope, the data acquisition equipment and the computer are connected according to the method shown in the figure 1, the test device is used for detecting to ensure that the connection is correct, the three-axis position rate rotary table can be in a balanced state after being started, the storage computer can be normally started and can acquire signals transmitted by the data acquisition equipment, and the flexible gyroscope can output measurement signals through the data acquisition equipment.
Second, steady-state testing is performed on the flexible gyroscope
The flexible gyroscope steady-state test comprises an X measuring axis steady-state test and a Y measuring axis steady-state test. The X measuring axis steady-state test and the Y measuring axis steady-state test refer to that the X measuring axis and the Y measuring axis of the flexible gyroscope respectively point to the east to perform n times or more than 6 times of repeated experiments, the time lasts for 3min each time, and the quantity which needs to be collected and calculated in the test process is as follows:
number N of sampling points of X measuring axis and Y measuring axisi(i＝1～n)；
N in ith test of X measurement axis and Y measurement axisi(i ═ 1 to n) individual sample points Xik，Yik(i＝1～n，k＝1～Ni)；
X measuring axis and Y measuring axis Ni(i is an average value D (X) of 1 to n sampling points)0i，D(Y)0i；
X measuring axis and Y measuring axis <math><mrow><mi>N</mi><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>N</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>)</mo></mrow></mrow></math> Average values of sample points d (x), d (y);
sum of squares of error SS of repetition of X measurement axis and Y measurement axiseDX0，SSeDY0。
Wherein:
x measurement axis N in the ith testi(i is 1 to n) average value of sampling points <math><mrow><mi>D</mi><msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><msub><mi>N</mi><mi>i</mi></msub></mfrac><munderover><mi>Σ</mi><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>N</mi><mi>i</mi></msub></munderover><msub><mi>X</mi><mi>ik</mi></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>;</mo></mrow></math>
Y measurement axis N in the ith testi(i is 1 to n) average value of sampling points <math><mrow><mi>D</mi><msub><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><msub><mi>N</mi><mi>i</mi></msub></mfrac><munderover><mi>Σ</mi><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>N</mi><mi>i</mi></msub></munderover><msub><mi>Y</mi><mi>ik</mi></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>;</mo></mrow></math>
X measuring axis <math><mrow><mi>N</mi><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>N</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>)</mo></mrow></mrow></math> Average of sampling points <math><mrow><mover><mi>D</mi><mo>‾</mo></mover><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mi>D</mi><msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><msub><mi>N</mi><mi>i</mi></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>;</mo></mrow></math>
Y measuring axis <math><mrow><mi>N</mi><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>N</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>)</mo></mrow></mrow></math> Average of sampling points <math><mrow><mover><mi>D</mi><mo>‾</mo></mover><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mi>D</mi><msub><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><msub><mi>N</mi><mi>i</mi></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>;</mo></mrow></math>
Sum of squares of repeat errors for the X measurement axis <math><mrow><msub><mi>SS</mi><mrow><mi>eDX</mi><mn>0</mn></mrow></msub><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mrow><mo>[</mo><mi>D</mi><msub><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><mo>-</mo><mover><mi>D</mi><mo>‾</mo></mover><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>]</mo></mrow><mn>2</mn></msup><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>;</mo></mrow></math>
Sum of squares of the repetition errors of the Y measurement axes <math><mrow><msub><mi>SS</mi><mrow><mi>eDY</mi><mn>0</mn></mrow></msub><mo>=</mo><munderover><mi>Σ</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><mrow><mo>[</mo><mi>D</mi><msub><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mrow><mn>0</mn><mi>i</mi></mrow></msub><mo>-</mo><mover><mi>D</mi><mo>‾</mo></mover><mrow><mo>(</mo><mi>Y</mi><mo>)</mo></mrow><mo>]</mo></mrow><mn>2</mn></msup><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>~</mo><mi>n</mi><mo>.</mo></mrow></math>
The flexible gyroscope steady-state test is characterized in that an X measuring axis steady-state test is firstly carried out, the X measuring axis of the flexible gyroscope is adjusted to point to the east, after the flexible gyroscope is electrified for 3 minutes, repeated steady-state tests are continuously carried out for n times, and the data acquisition equipment stores acquired test data in a dat format.
After the X measuring axis steady-state test is finished, a Y measuring axis steady-state test is carried out, the Y measuring axis of the flexible gyroscope is adjusted to point to east, after the flexible gyroscope is electrified for 3min, repeated steady-state tests are continuously carried out for n times, and the data acquisition equipment stores the acquired test data in a dot format;
after the X measuring axis steady test and the Y measuring axis steady test are both completed, reading data collected by the data collecting equipment from the computer, and solving the sum of squares of repeated errors (SS) of the X measuring axis of the flexible gyroscope through a steady test data processing programeDX0Sum of squares of the repeat errors of the Y measurement axes SSeDY0. If the sum of the squared error of repetition for any of the measurement axes is greater than 100 pulses squared, the test is stopped. If the sum of the squares of the two axis repeat errors is less than 100 pulses squared, indicating that the flexible gyroscope is functioning properly, the following test steps may be continued.
Thirdly, rotating the rotary table according to the twelve space orthogonal positions to acquire data
Firstly, three axes (X, Y and Z) of the gyroscope are respectively directed to the first direction (north west day) shown in figure 3, after one minute of stability, the data is stored, the time for storing the position data is 2min, and the data is stored in the format of dot. Then, the data are processed in sequence according to the directions shown in figure 3, and after the data are stabilized for 1min every time when the data are transferred to a new direction, the position data of the direction are stored for 2min and the data are stored into the format of dot until the last direction is finished.
Fourthly, calculating a drift coefficient of the space orthogonal twelve positions
Extracting the position data (position-data) of each position stored in delta dat format, eliminating outlier by data processing in computer, and combining the position-data with known omegaX、ωY、aX、aY、aYAnd substituting the space orthogonal twelve-position drift coefficients into a DTGs-AID-ADD model, and analyzing by adopting a least square method to obtain the space orthogonal twelve-position drift coefficients.
The mathematical expression of the DTGs-AID-ADD model is as follows:
wherein, <math><mrow><msub><mi>U</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><msub><mi>U</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac></mrow></math>
U0＝U1×D(X)F+U2×D(Y)F，V0＝V1×D(X)F+V2×D(Y)F
U3＝U1×D(X)X+U2×D(Y)X，U4＝U1×D(X)Y+U2×D(Y)Y
V3＝V1×D(X)X+V2×D(Y)X，V4＝V1×D(X)Y+V2×D(Y)Y
U5＝U1×D(X)Z+U2×D(Y)Z，V5＝V1×D(X)Z+V2×D(Y)Z
in the formula:
ixrepresenting the pulse number corresponding to the torquer current of the X measuring axis of the flexible gyroscope;
iyrepresenting the pulse number corresponding to the torquer current of the Y measuring axis of the flexible gyroscope;
ωXrepresenting the component of the angular rate of rotation of the earth on the X measuring axis of the flexible gyroscope;
ωYrepresenting the component of the earth rotation angular velocity on the Y measuring axis of the flexible gyroscope;
aXrepresenting the acceleration component on the X measurement axis of the flexible gyroscope;
aYrepresenting the acceleration component on the measurement axis of the flexible gyroscope Y;
aZrepresenting the acceleration component on the axis of rotation of the flexible gyroscope Z;
(SF)Xthe scale coefficient of a torquer representing the X measuring axis of the flexible gyroscope;
(SF)Ya torquer scale factor representing a Y measurement axis of the flexible gyroscope;
epsilon represents an included angle between the X axis of the torquer of the flexible gyroscope and the X axis of the shell of the flexible gyroscope;
ξ represents the angle between the flexible gyroscope's torquer Y axis and the flexible gyroscope's housing Y axis.
In the present invention, U0、U1、U2、V0、V1And V2Representing the zero-order drift coefficient of acceleration, U3、U4、U5、V3、V4And V5Representing the acceleration first order term drift coefficient.
Fifthly, obtaining the measured value of the flexible gyroscope after error compensation
The space orthogonal twelve-position drift coefficient obtained in the fourth step and a static error compensation model G of the flexible gyroscope0And compensating the output measured value of the flexible gyroscope, and obtaining the compensated measured value through calculation.
Flexible gyroscope static error compensation model G0Comprises the following steps:
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;
D(X)Fa drift coefficient representing the independence of the flexible gyroscope from the acceleration around the X measuring axis;
D(Y)Fa drift coefficient representing the independence of the flexible gyroscope from the acceleration around the Y measuring axis;
D(X)Xa drift coefficient representing the relation between the first time of acceleration and the second time of acceleration of the flexible gyroscope in the X measuring axis around the X measuring axis;
D(X)Ya drift coefficient representing the relation between the first time of acceleration and the second time of acceleration of the flexible gyroscope in the X measuring axis around the Y measuring axis;
D(X)Za drift coefficient which represents the relation between the acceleration first power and the flexible gyroscope around the Z rotation axis in the X measurement axis;
D(Y)Xrepresenting the flexible gyroscope about X in the Y measurement axisMeasuring a drift coefficient of the axis in relation to a first power of acceleration;
D(Y)Ya drift coefficient representing the relation between the first time of acceleration and the second time of acceleration of the flexible gyroscope around the Y measuring axis in the Y measuring axis;
D(Y)Za drift coefficient which represents the relation between the acceleration first power and the flexible gyroscope around the Z rotation axis in the Y measurement axis;
aXrepresenting the acceleration component on the X measurement axis of the flexible gyroscope;
aYrepresenting the acceleration component on the measurement axis of the flexible gyroscope Y;
aZrepresenting the acceleration component on the rotation axis of the flexible gyroscope Z.
In order to verify the effectiveness of the space orthogonal twelve-position calibration method based on the DTGs-AID-ADD model, two main test methods (a traditional eight-position test method and a full-space orthogonal twenty-four-position test method) for the DTGs-AID-ADD model are taken as comparison examples below.
Comparative example 1: conventional eight-position test method
The conventional eight-position test was performed according to the conventional eight-position test method specified in IEEE Std813-1988 or the national military standard, the test method and procedure were the same as the above-described twelve-position test method for spatial orthogonality, except that the test orientation was changed to the conventional eight-position test method as shown in table 3, and the collected position-data was shown as X-axis data and Y-axis data in table 3 after removing outliers.
Referring to fig. 4, the conventional eight-position expression is as follows:
| first position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 90 degrees and phi of 0 degree from the initial installation coordinate system (northwest). |
| Second position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 90 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| Third position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| The fourth position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Fifth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 180 degrees from an initial installation coordinate system (northwest). |
| Sixth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of-90 degrees from an initial installation coordinate system (northwest). |
| Seventh position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| Eighth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 90 degrees from an initial installation coordinate system (northwest). |
Note: theta is the rotation angle of the X axis, gamma is the rotation angle of the Y axis, and phi is the rotation angle of the Z axis.
TABLE 3 test data for two measurement axes in the conventional 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 |
| The 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
The test was performed at the full-space orthogonal twenty-four positions shown in table 4, the test method and procedure were the same as the above-described space orthogonal twelve-position test method except that the test orientation was changed to the full-space orthogonal position shown in table 4, and the collected position-data was shown as the X-axis data and the Y-axis data in table 4 after the outliers were removed.
Referring to fig. 5, the full-space orthogonal twenty-four positions are represented as follows:
| first position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Second position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Third position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 90 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| The fourth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 90 degrees and phi of 0 degree from the initial installation coordinate system (northwest). |
| Fifth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of-90 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| Sixth position | Flexible gyroscope from initial installationThe rotation angle theta of the coordinate system (Tianbeixi) is 180 degrees, gamma is-90 degrees, and phi is 0 degree. |
| Seventh position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of-90 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| Eighth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of-90 degrees and phi of 0 degree from an initial installation coordinate system (northwest). |
| Ninth position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees and phi of-90 degrees from an initial installation coordinate system (northwest). |
| The tenth position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Eleventh position | The flexible gyroscope is rotated by an angle theta of 180 degrees, gamma of 0 degrees, and phi of 90 degrees from the initial installation coordinate system (northwest). |
| The twelfth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 180 degrees, and phi of 0 degree from the initial installation coordinate system (northwest). |
| Thirteenth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of 90 degrees from the initial installation coordinate system (northwest). |
| Fourteenth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of 180 degrees from the initial installation coordinate system (northwest). |
| Fifteenth position | The flexible gyroscope is rotated by an angle theta of 0 degree, gamma of 0 degree and phi of-90 degrees from an initial installation coordinate system (northwest). |
| Sixteenth position | The flexible gyroscope is rotated by an angle θ of 0 degrees, γ of 0 degrees, and φ of 0 degrees from the initial mounting coordinate system (northwest). |
| First position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Seventeenth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 90 degrees from an initial installation coordinate system (northwest). |
| Eighteenth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 180 degrees from an initial installation coordinate system (northwest). |
| Nineteenth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of-90 degrees from an initial installation coordinate system (northwest). |
| Twentieth position | The flexible gyroscope is rotated by an angle theta of-90 degrees, gamma of 0 degrees and phi of 0 degrees from an initial installation coordinate system (northwest). |
| Twenty-first position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 0 degrees and phi of-90 degrees from an initial installation coordinate system (northwest). |
| Twentieth position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 0 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest). |
| Twenty-third position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 0 degrees, and phi of 90 degrees from the initial installation coordinate system (northwest). |
| The twenty-fourth position | The flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 0 degrees, and phi of 180 degrees from the initial installation coordinate system (northwest). |
Note: theta is the rotation angle of the X axis, gamma is the rotation angle of the Y axis, and phi is the rotation angle of the Z axis.
TABLE 4 test data for two measurement axes at 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 |
| The 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 |
| The tenth position | 84.6583 | -196.4333 |
| Eleventh position | -248.6750 | -204.8750 |
| The 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 |
| Fifteenth position | -240.0417 | 143.0750 |
| Sixteenth position | 83.7583 | 123.4833 |
| Seventeenth position | -92.7083 | -205.0917 |
| Eighteenth position | -257.8667 | -24.3917 |
| Nineteenth position | -80.6333 | 142.7000 |
| Twentieth position | 84.4167 | -38.0167 |
| Twenty-first position | -83.7250 | 142.2000 |
| Twentieth position | 84.6000 | -35.3667 |
| Twenty-third position | -89.3000 | -205.8167 |
| The twenty-fourth position | -257.6167 | -28.4417 |
Examples
As shown in table 7, it can be seen that the precision of the spatial orthogonal twelve-position test method is greatly improved compared with the conventional eight-position test method, the precision is improved compared with the full-spatial orthogonal twenty-four-position test method, and the test time is shortened by half.
The invention discloses a space orthogonal twelve-position calibration method based on a DTGs-AID-ADD model, which adopts a D-optimal experimental design method to determine that the optimal test position number of the DTGs-AID-ADD model is twelve and the optimal twelve test orientations. Table 5 shows the drift coefficients obtained by testing the flexible gyroscope in the inertial navigation test center by using the conventional eight-position method, the full-space orthogonal twenty-four-position method, and the space orthogonal twelve-position method, respectively. Table 6 shows test point data, which are test points taken from the full orthogonal space and different from any position of the conventional eight-position and optimal position, and are suitable for evaluating the estimation accuracy of the drift coefficient by the conventional eight-position test method, the full-space orthogonal position method, and the optimal position test method. And in the table 7, drift coefficients obtained by the three methods are respectively used for objectively outputting compensated evaluation results of the gyroscope at the test positions listed in the table 6, the residual square sum of the gyroscope measurement values is visible, the result obtained by compensating the drift coefficients solved by the flexible gyroscope optimal position test design method is improved by 4-5 times compared with the traditional eight-position method, the result obtained by compensating the drift coefficients solved by the flexible gyroscope optimal position test design method is improved by a full-space orthogonal position method, and the test time of the flexible gyroscope optimal position test design method is shortened to be half of that of the full-space orthogonal position method. Therefore, 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 the measurement precision of the flexible gyroscope is improved. Meanwhile, the optimal position test design method is optimal in all position test design methods, the drift coefficient of the DTGs-AID-ADD model obtained by the optimal position test method is optimal and is closest to the true value, high measurement precision of the gyroscope is guaranteed, experimental test positions (such as twenty-four positions) are prevented from being increased for improving the measurement precision, testing time of the gyroscope is greatly shortened, and test cost is reduced. In addition, the optimal position test design method provided by the invention has strong universality and can be well applied to the calibration process of other types of gyros.
TABLE 5 test results
TABLE 6 test points test data
| Position of | X measuring axis (pulse/second) | Y measuring axis (pulse/second) |
| Twenty-first position | -83.7250 | 142.2000 |
| Twentieth position | 84.6000 | -35.3667 |
| The twenty-fourth position | -257.6167 | -28.4417 |
Note: the three positions are selected from the twenty-four positions orthogonal in full space.
Table 7 evaluation results
| Test protocol | Sum of squares of errors in the X axis | Sum of squares of Y-axis errors |
| Twelve positions in space orthogonal | 1.5473 | 5.3523 |
| Conventional eight position | 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 one time acceleration related item error model optimal position calibration method is characterized in that a flexible gyroscope is arranged on a three-axis position rate turntable and is connected with a data acquisition device, and the data acquisition device is connected with a computer; position measurement software is installed in the computer; the method is characterized in that: the calibration of the optimal position of the static drift zero-order and primary acceleration related item error model DTGs-AID-ADD of the flexible gyroscope comprises the following calibration execution steps:
the first step is as follows: determining optimal locations
The optimal test position of the DTGs-AID-ADD model test is obtained by adopting a D-optimal test design method;
the D-optimal test design method is that the optimal test position for the DTGs-AID-ADD model test is obtained by a D-optimal design criterion, wherein the D-optimal design criterion is that the determinant of the test point information matrix reaches the maximum value;
the D-optimal test design method comprises the steps of firstly initializing the number of test positions of a DTGs-AID-ADD model test to 6, carrying out 6-optimal position test design according to a D-optimal design criterion, obtaining and recording 6-optimal positions and corresponding information matrix determinant based on the DTGs-AID-ADD model, then sequentially increasing the number of the test positions to 24, determining the information matrix determinant and corresponding optimal test positions under the number of the 6-24 positions, and finally obtaining the test position, which is the optimal test position, corresponding to the maximum information matrix determinant in the number n of the test positions 6-24 according to the D-optimal criterion; determining that the optimal test positions of the DTGs-AID-ADD model are twelve positions by a D-optimal test design method, wherein the corresponding test positions are the optimal test positions, namely twelve spatially orthogonal positions;
the second step is that: calibrating a spatial orthogonal twelve-position orientation
A first position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 0 degree;
a second position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 180 degrees, and phi is 0 degree;
a third position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is-90 degrees;
the fourth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 90 degrees;
a fifth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is 0 degree;
a sixth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is 180 degrees;
a seventh position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is 0 degree, and phi is-90 degrees;
an eighth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is 0 degree, and phi is 90 degrees;
ninth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 180 degrees, gamma is-90 degrees, and phi is 0 degree;
the tenth position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is 0 degree, gamma is-90 degrees, and phi is 0 degree;
an eleventh position: the rotation angle theta of the flexible gyroscope from an initial installation coordinate system (northwest) is-90 degrees, gamma is 90 degrees, and phi is 0 degree;
a twelfth position: the flexible gyroscope is rotated by an angle theta of 90 degrees, gamma of 90 degrees, and phi of 0 degrees from the initial installation coordinate system (northwest).
The third step: obtaining a drift coefficient
(A) Performing least square method analysis on the DTGs-AID-ADD model on the data at the traditional eight positions to obtain a traditional eight-position drift coefficient;
(B) performing least square method analysis on DTGs-AID-ADD models on data under twenty-four full-space orthogonal positions to obtain a twenty-four full-space orthogonal position drift coefficient;
(C) performing least square method analysis of a DTGs-AID-ADD model on data at the space orthogonal twelve positions to obtain a space orthogonal twelve position drift coefficient;
the DTGs-AID-ADD model is
Wherein, <math><mrow><msub><mi>U</mi><mn>1</mn></msub><mo>=</mo><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac><mo>,</mo></mrow></math> <math><mrow><msub><mi>U</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>+</mo><mi>ξ</mi><mo>)</mo></mrow></mrow><mrow><msub><mrow><mo>(</mo><mi>SF</mi><mo>)</mo></mrow><mi>Y</mi></msub><mi>cos</mi><mi>ξ</mi></mrow></mfrac><mo>,</mo></mrow></math>
U0＝U1×D(X)F+U2×D(Y)F，V0＝V1×D(X)F+V2×D(Y)F，
U3＝U1×D(X)X+U2×D(Y)X，U4＝U1×D(X)Y+U2×D(Y)Y，
V3＝V1×D(X)X+V2×D(Y)X，V4＝V1×D(X)Y+V2×D(Y)Y，
U5＝U1×D(X)Z+U2×D(Y)Z，V5＝V1×D(X)Z+V2×D(Y)Z，
in the formula: i.e. ixRepresenting the number of pulses, i, corresponding to the torquer current of the X measuring axis of the flexible gyroscopeyRepresenting the number of pulses, omega, corresponding to the torquer current in the Y measuring axis of the flexible gyroscopeXRepresenting the component of the angular velocity of rotation of the earth, omega, in the X measuring axis of a flexible gyroscopeYRepresenting the component of the angular velocity of rotation of the earth in the Y measuring axis of a flexible gyroscopeXRepresenting the acceleration component in the X measuring axis of the flexible gyroscope, aYRepresenting the acceleration component in the Y measuring axis of the flexible gyroscope, aZRepresenting the acceleration component of the flexible gyroscope Z axis of rotation (SF)XTorquer scale factor representing flexible gyroscope X measuring axis, (SF)YTorquer scale factor representing flexible gyroscope Y measurement axisEpsilon represents an included angle between the X axis of the torquer of the flexible gyroscope and the X axis of the shell of the flexible gyroscope, and xi represents an included angle between the Y axis of the torquer of the flexible gyroscope and the Y axis of the shell of the flexible gyroscope;
the fourth step: compensating for measurements of a spatially orthogonal twelve-position orientation
Model G using flexible gyroscope static error compensation0Compensating the output measured value of the flexible gyroscope by using a twelve-position drift coefficient orthogonal to the space to obtain a compensated measured value;
the static error compensation model of the flexible gyroscope is Wherein 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)FRepresenting the drift coefficient of the flexible gyroscope about the X measuring axis independent of the acceleration, D (Y)FRepresenting acceleration-independent drift of a flexible gyroscope about a Y measurement axisCoefficient, D (X)XExpressing the drift coefficient of the flexible gyroscope in the X measurement axis about the X measurement axis in relation to the first power of the acceleration, D (X)YExpressing the drift coefficient of the flexible gyroscope in the X measurement axis about the Y measurement axis in relation to the first power of acceleration, D (X)ZExpressing the drift coefficient of the flexible gyroscope in the X measurement axis about the Z rotation axis in relation to the acceleration first power, D (Y)XExpressing the drift coefficient of the flexible gyroscope in the Y measurement axis about the X measurement axis in relation to the first power of acceleration, D (Y)YExpressing the drift coefficient of the flexible gyroscope in the Y measurement axis about the Y measurement axis in relation to the first power of acceleration, D (Y)ZRepresenting the drift coefficient of the flexible gyroscope about the axis of rotation Z in the Y measurement axis, aXRepresenting the acceleration component in the X measuring axis of the flexible gyroscope, aYRepresenting the acceleration component in the Y measuring axis of the flexible gyroscope, aZRepresenting the acceleration component on the rotation axis of the flexible gyroscope Z.
2. The method for calibrating the optimal position of the error model of the static drift zero order and the primary acceleration related terms of the flexible gyroscope according to claim 1, is characterized in that: at least 6 data acquisitions were made at each selected orientation, each time lasting 10 min.
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2009
- 2009-12-08 CN CN2009102421377A patent/CN101738203B/en not_active Expired - Fee Related
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| CN103884356B (en) * | 2014-03-25 | 2016-06-01 | 北京航天控制仪器研究所 | A kind of method demarcating strap down inertial navigation combination gyrostat combination |
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| CN111854752A (en) * | 2019-04-30 | 2020-10-30 | 意法半导体公司 | Dead reckoning by determining misalignment angle between moving direction and sensor traveling direction |
| CN111854752B (en) * | 2019-04-30 | 2024-06-04 | 意法半导体公司 | Dead reckoning by determining a misalignment angle between a direction of movement and a direction of sensor travel |
| CN111595309A (en) * | 2020-04-24 | 2020-08-28 | 中电投电力工程有限公司 | System and method for improving verticality measurement precision by using multiple micro-mechanical gyroscopes |
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