CN108387244B - Inertial measurement unit and prism installation error stability determination method - Google Patents

Inertial measurement unit and prism installation error stability determination method Download PDF

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CN108387244B
CN108387244B CN201711393913.4A CN201711393913A CN108387244B CN 108387244 B CN108387244 B CN 108387244B CN 201711393913 A CN201711393913 A CN 201711393913A CN 108387244 B CN108387244 B CN 108387244B
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coordinate system
axis
installation error
stability
prism
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CN108387244A (en
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李志华
王鹏
黄世涛
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Beijing Aerospace Era Laser Navigation Technology Co ltd
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Beijing Aerospace Era Laser Navigation Technology Co ltd
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Abstract

The method can calculate the stability of the installation errors of the instrument and the prism calibrated and aimed by the inertial set on hexahedron calibration equipment and after repeated disassembly and assembly, and eliminate the influence of errors between different test tools of the inertial set and repeated disassembly and assembly on the stability of the installation errors of the instrument and the prism. The method for determining the stability is direct and clear, adopts non-approximate calculation, is suitable for calculating the installation error of the instrument with irregular installation angle and the prism on the body coordinate system and counting the stability, and has universality.

Description

Inertial measurement unit and prism installation error stability determination method
Technical Field
The invention relates to an inertial measurement unit instrument and a method for determining prism installation error stability, and belongs to the field of inertial measurement combination calibration test.
Background
The laser inertial navigation is successfully applied to the fields of carrier rockets, missiles, satellites, airplanes, ships and other civilian use, provides angular velocity and apparent acceleration information for the carrier rockets, the missiles, the satellites, the airplanes, the ships and the like, and is key equipment of the laser inertial navigation. The inertial measurement unit comprises important instruments (a gyroscope and an additional meter), a body, a box body, a shock absorber, an electronic box, a prism and the like, wherein the important instruments (the gyroscope and the additional meter) of the inertial measurement unit are arranged on the body, the body is arranged on the box body through the shock absorber, and the prism is generally arranged on the box body (as shown in figure 1).
The installation error stability of the inertial measurement unit and the prism is strict, and the alignment precision and the flight precision of the aircraft are influenced by the change of the inertial measurement unit and the prism. The stability of the installation errors is generally obtained by the variance of a plurality of groups of installation errors of instruments and prisms which are calibrated and aimed for testing for a plurality of times in a period of months; the stability of the inertial measurement unit before and after various environmental tests is obtained by comparing the mounting error results of calibration and aiming before and after the tests. Some models directly require the provision of mounting tolerances for the inertial instrument and the prism with respect to the body coordinate system.
The inertial measurement unit is repeatedly disassembled and assembled on the hexahedron or the rotary table, or calibration and aiming tests are carried out on different hexahedrons or rotary tables, the position of the shell (with the installation reference) of the inertial measurement unit relative to the hexahedron reference or the rotary table reference changes, namely the installation errors of the instrument and the prism change due to repeated disassembly and assembly or different test tools. Taking the hexahedron calibration example in fig. 2, the inertial measurement unit is installed in a calibration hexahedron (containing a calibration bottom plate), and the calibration and aiming tests can measure the installation error between the inertial measurement unit and the prism relative to the hexahedron external reference (measurement coordinate system); after the inertial measurement unit is repeatedly disassembled and assembled, the mounting errors of the instrument and the prism relative to a hexahedron external reference (a measurement coordinate system) can be changed due to the non-repeatability of mounting in the test, and the mounting errors of the instrument and the prism can be changed due to the fact that the positions of calibration bottom plates among different test tools are different in the test on the other hexahedron or the rotary table. Therefore, a method for counting the stability of the installation errors of the instrument and the prism is needed to be found so as to eliminate the influence of the repeated disassembly and assembly of the inertial measurement unit or the installation errors of different test tools on the stability of the installation errors of the instrument and the prism.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, provides a calculation and statistics method for the stability of the installation errors of the instruments (a gyroscope and an additional meter) and the prisms, adopts a new space analytic geometry calculation method to perform non-approximate calculation of the installation errors of the inertial measurement instrument and the prisms on the body coordinate system, and is convenient for the statistics and calculation of the stability of the installation errors of the instruments and the prisms, which are obtained by calibration test and aiming test of the inertial measurement instrument on different test tools or after multiple times of disassembly and assembly.
The technical solution of the invention is as follows:
an inertial measurement unit and prism installation error stability determination method comprises the following steps:
(1) defining an inertial measurement unit body coordinate system S system, an inertial measurement unit measurement coordinate system F system and an installation error angle EgαβAnd the installation error angle EaαβWherein β ═ x, y, z; α ≠ β:
inertial measurement unit body coordinate system S system: o isSXSTaking inertial unit X plus meter input shaft direction, OSYSIn the plane of the input shaft of the inertial measurement unit X, Y plus meter and OSXSPerpendicular, pointing in the direction of the Y plus the input axis of the meter, OSZSThe axis is determined by the right hand rule;
installation error angle EgαβFor an alpha-direction gyroscope input shaft and an inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes; installation error angle EaαβFor alpha to add table input shaft and inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes;
inertial measurement coordinate system F system: the inertial measurement unit is arranged on the hexahedron for calibration, and O is takenFXFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial measurement unit X plus the meter; taking OFYFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial measurement unit Y plus the meter; taking OFZFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertia unit Z plus the meter;
the definition of the installation error of the inertial measurement unit under the coordinate system F is shown in the table 1, and the installation error under the system F is obtained by a calibration test:
TABLE 1 installation error definitions
Symbol Physical significance
Dxx X-axis installation error of X-gyro relative measurement coordinate system
Dxy Y-axis installation error of X-gyro relative measurement coordinate system
Dxz Z-axis installation error of X-gyro relative measurement coordinate system
Dyx X-axis installation error of Y-gyroscope relative measurement coordinate system
Dyy Y-axis installation error of Y gyroscope relative measurement coordinate system
Dyz Z-axis installation error of Y-gyroscope relative measurement coordinate system
Dzx X-axis installation error of Z-gyro relative measurement coordinate system
Dzy Y-axis installation error of Z gyroscope relative measurement coordinate system
Dzz Z-axis installation error of Z-gyro relative measurement coordinate system
Exx X-axis installation error of X-plus-meter relative measurement coordinate system
Exy Y-axis installation error of X-adding table relative measurement coordinate system
Exz Z-axis installation error of X-adding table relative measurement coordinate system
Eyx X-axis installation error of Y-plus-meter relative measurement coordinate system
Eyy Y-axis installation error of Y-plus-meter relative measurement coordinate system
Eyz Z-axis installation error of Y-plus-meter relative measurement coordinate systemDifference (D)
Ezx X-axis installation error of Z-plus-meter relative measurement coordinate system
Ezy Y-axis installation error of Z-plus-meter relative measurement coordinate system
Ezz Z-axis installation error of Z-plus-meter relative measurement coordinate system
(2) Determining a conversion matrix R of an inertial measurement unit body coordinate system S system to a measurement coordinate system F system as follows:
Figure BDA0001518072700000031
wherein, OSXS(1)、OSXS(2)、OSXS(3) Is a vector
Figure BDA0001518072700000032
X in the F seriesF、YF、ZFAn on-axis component; o isSYS(1)、OSYS(2)、OSYS(3) Is a vector
Figure BDA0001518072700000033
X in the F seriesF、YF、ZFAn on-axis component; o isSZS(1)、OSZS(2)、OSZS(3) Is a vector
Figure BDA0001518072700000034
X in the F seriesF、YF、ZFAn on-axis component;
namely, it is
Figure BDA0001518072700000035
The unit vectors of the X axis, the Y axis and the Z axis of the body coordinate system S system in the measurement coordinate system F system are respectively, and the unit vectors comprise:
Figure BDA0001518072700000036
Figure BDA0001518072700000037
Figure BDA0001518072700000041
at the same time, the user can select the desired position,
Figure BDA0001518072700000042
is composed of
Figure BDA0001518072700000043
The normalized unit vector is obtained by the following steps,
Figure BDA0001518072700000044
is composed of
Figure BDA0001518072700000045
Normalized unit vectors;
Figure BDA0001518072700000046
adding a unit vector of the table in the measurement coordinate system to X, and
Figure BDA0001518072700000047
Figure BDA0001518072700000048
adding a unit vector of the table in the measurement coordinate system to Y, and
Figure BDA0001518072700000049
Figure BDA00015180727000000410
(3) calculating the installation error beta of the prism to the S system of the body coordinate systemsAnd alphasThe method specifically comprises the following steps:
Figure BDA00015180727000000411
Figure BDA00015180727000000412
wherein, OLS(1)、OLS(2)、OLS(3) Is composed of
Figure BDA00015180727000000413
The components on the Xs, Ys, and Zs axes of the S system,
Figure BDA00015180727000000414
to make the ridge vector under the system of measurement coordinate system F
Figure BDA00015180727000000415
Transformed into a vector in the system of the body coordinate system S, and has
Figure BDA00015180727000000416
OLS(2)，OLS(3) ); the vector of the ridge in the measuring coordinate system F is represented as:
Figure BDA00015180727000000417
alpha is the parallelism error of the edge line of the aiming prism relative to the positioning reference around the X axis, and the polarity of the error is that the overlooking prism rotates anticlockwise to be positive; beta is the parallelism error of the edge line of the aiming prism relative to the positioning reference around the Y axis, and the polarity of the parallelism error is that the right height of the front-view prism is positive; both α and β are determined by aiming tests.
(4) Calculating the installation error of each gyroscope to the S system of the body coordinate system, specifically:
Egxy＝OSXG(2)；
Egyx＝OSYG(1)；
Egzx＝OSZG(1)；
Egxz＝OSXG(3)；
Egyz＝OSYG(3)；
Egzy＝OSZG(2)；
OSXG(1)、OSXG(2)、OSXG(3) is composed of
Figure BDA0001518072700000051
The component on the Xs, Ys, Zs axis of the S system, OSYG(1)、OSYG(2)、OSYG(3) Is composed of
Figure BDA0001518072700000052
The component on the Xs, Ys, Zs axis of the S system, OSZG(1)、OSZG(2)、OSZG(3) Is composed of
Figure BDA0001518072700000053
The components on the Xs, Ys, and Zs axes of the S system.
Figure BDA0001518072700000054
Respectively is the vector of each gyro under the system of a measuring coordinate system F
Figure BDA0001518072700000055
Figure BDA0001518072700000056
Transformed into a vector in the system of the body coordinate system S:
Figure BDA0001518072700000057
Figure BDA0001518072700000058
Figure BDA0001518072700000059
Figure BDA00015180727000000510
unit vectors of the X gyroscope, the Y gyroscope and the Z gyroscope in a measurement coordinate system are respectively as follows:
Figure BDA00015180727000000511
(5) calculating the installation error of each additional table to the S system of the body coordinate system, specifically:
Eayx＝OSYA(1)；
Eazx＝OSZA(1)；
Eazy＝OSZA(2)；
OSYA(1)、OSYA(2)、OSYA(3) is composed of
Figure BDA00015180727000000512
The component on the Xs, Ys, Zs axis of the S system, OSZA(1)、OSZA(2)、OSZA(3) Is composed of
Figure BDA00015180727000000513
The components on the Xs, Ys, Zs axes of the S system;
Figure BDA00015180727000000514
for each adding table to be under the system of measurement coordinate system F
Figure BDA00015180727000000515
Transformed into a vector in the system of the body coordinate system S:
Figure BDA00015180727000000516
Figure BDA00015180727000000517
Figure BDA00015180727000000518
respectively is a unit vector of the Y plus table and the Z plus table under a measurement coordinate system:
Figure BDA00015180727000000519
(6) and (5) repeating the steps (1) to (5) to obtain the installation errors of a plurality of groups of prisms, gyroscopes and addition tables in the system of the body coordinate system S, and determining the stability of the prisms, the gyroscopes and the addition tables:
according to a plurality of groups alphaSValue calculation of alphaSVariance σ ofαsI.e. represents the stability of α;
according to multiple groups of betaSValue calculation of betaSVariance σ ofβsI.e. represents the stability of β;
calculating the variance σ of Egxy according to the values of multiple groups of EgxyEgxyRepresents the stability of Dxy;
calculating the variance σ of Egyx from the values of the plurality of groups of EgyxEgyxRepresenting Dyx stability;
calculating the variance σ of Egzx from the values of the plurality of groups of EgzxEgzxRepresenting Dzx stability;
calculating the variance σ of Egxz from the values of the plurality of groups of EgxzEgxzRepresenting Dxz stability;
calculating the variance σ of Egyz from the values of the plurality of groups of EgyzEgyzRepresenting Dyz stability;
calculating the variance σ of Egzy from the values of the plurality of groups of EgzyEgzyRepresenting Dzy stability;
calculating the variance σ of Eayx according to the values of the plurality of groups of EayxEayxRepresenting Eyx stability;
calculating the variance σ of Eazx according to the values of the plurality of groups of EazxEazxRepresenting Ezx stability;
calculating the variance σ of Eazy according to the values of the plurality of groups of EazyEazyRepresenting the stability of Ezy.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention provides a statistical method for the stability of installation errors, which enables the statistics of the stability of the installation errors of instruments and prisms obtained by testing an inertial measurement unit on different testing tools or after the same tool is disassembled and assembled for multiple times to be possible.
(2) The statistical calculation method for the stability of the installation errors is direct and clear, adopts non-approximate calculation, has more indirect complex steps in the derivation process of the prior similar technical scheme, has multi-step approximate calculation, and does not analyze the influence of the comprehensive errors brought by each approximate calculation.
(3) Compared with the prior similar technical scheme, the method is suitable for a system for calculating and stabilizing the installation error of the instrument with irregular installation angle and the prism on the body coordinate system, and has universality.
Drawings
FIG. 1 is a schematic diagram of the basic components of a laser inertial measurement unit;
FIG. 2 is a schematic diagram of laser inerter hexahedron calibration;
fig. 3 is a schematic view of the mounting error definition of the collimating prism.
Detailed Description
The inertial instrument (at least 3 orthogonally-mounted gyros and at least 3 orthogonally-mounted summers) and the sighting prism are mounted on the inertial set. The inertial measurement unit calibration test can measure the installation error (the included angle between the sensitive axis of the instrument and the axis of the measurement coordinate system) of the sensitive axis of each instrument relative to the inertial measurement unit measurement coordinate system, and the inertial measurement unit aiming test can measure the installation error (the included angle between the prism ridge and the axis of the measurement coordinate system) of the prism ridge relative to the inertial measurement unit measurement coordinate system; the inertial measurement unit is arranged on a hexahedron or a rotary table for calibration and aiming test, and the measurement coordinate system is a hexahedron reference coordinate system or a rotary table reference coordinate system. The inertial measurement unit is repeatedly disassembled and assembled on a hexahedron or a rotary table, or calibration and aiming tests are carried out on different hexahedrons or rotary tables, the position of the shell (with an installation reference) of the inertial measurement unit relative to the hexahedron reference or the rotary table reference changes, namely the installation errors of the instrument and the prism change due to repeated disassembly and assembly or different test tools; in the application of the inertial measurement unit, strict requirements are imposed on the stability of installation errors of the instrument and the prism, and the position of the instrument and the prism relative to the shell is required to be stable and unchanged.
The adding tables are small in size and are installed on a metal base together, the relative position relation among the adding tables is stable, in practical application, a adding table coordinate system can be defined according to the space position relation of 2 approximate orthogonal adding tables, and the adding table coordinate system is used as a reference to count the installation errors of the adding tables, the gyroscope and the prism so as to eliminate the influence of the installation errors of the inertial measurement unit on the stability of the installation errors of the instrument and the prism.
The error stability method provided by the invention comprises the following steps:
(1) definition of coordinate system and mounting error:
defining an inertial measurement unit body coordinate system S system, an inertial measurement unit measurement coordinate system F system and an installation error angle EgαβAnd the installation error angle Eaαβ(wherein β ═ x, y, z ≠ β):
inertial measurement unit body coordinate system S system: o isSXSTaking inertial unit X plus meter input shaft direction, OSYSIn the plane of the input shaft of the inertial measurement unit X, Y plus meter and OSXSPerpendicular, pointing in the direction of the Y plus the input axis of the meter, OSZSThe axis is determined by the right hand rule;
installation error angle EgαβFor an alpha-direction gyroscope input shaft and an inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes; installation error angle EaαβFor alpha to add table input shaft and inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes;
inertial measurement coordinate system F system: the inertial measurement unit is arranged on the hexahedron for calibration, and O is takenFXFIs parallel to the measuring reference surface of the corresponding direction of the hexahedron,and the direction of the input shaft is consistent with that of the input shaft of the inertia set X plus meter; taking OFYFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial measurement unit Y plus the meter; taking OFZFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertia unit Z plus the meter;
the mounting error definition table 1 is obtained by the inertial measurement unit under the coordinate system F, and the mounting error under the system F is obtained by a calibration test.
TABLE 1 installation error definitions
Symbol Physical significance
Dxx X-axis installation error of X-gyro relative measurement coordinate system
Dxy Y-axis installation error of X-gyro relative measurement coordinate system
Dxz Z-axis installation error of X-gyro relative measurement coordinate system
Dyx X-axis installation error of Y-gyroscope relative measurement coordinate system
Dyy Y-axis installation error of Y gyroscope relative measurement coordinate system
Dyz Z-axis installation error of Y-gyroscope relative measurement coordinate system
Dzx X-axis installation error of Z-gyro relative measurement coordinate system
Dzy Y-axis installation error of Z gyroscope relative measurement coordinate system
Dzz Z-axis installation error of Z-gyro relative measurement coordinate system
Exx X-axis installation error of X-plus-meter relative measurement coordinate system
Exy Y-axis installation error of X-adding table relative measurement coordinate system
Exz Z-axis installation error of X-adding table relative measurement coordinate system
Eyx X-axis installation error of Y-plus-meter relative measurement coordinate system
Eyy Y-axis installation error of Y-plus-meter relative measurement coordinate system
Eyz Z-axis installation error of Y-plus-meter relative measurement coordinate system
Ezx X-axis installation error of Z-plus-meter relative measurement coordinate system
Ezy Y-axis installation error of Z-plus-meter relative measurement coordinate system
Ezz Z-axis installation error of Z-plus-meter relative measurement coordinate system
In Table 1, Dxx2+Dxy2+Dxz2＝1、Dyx2+Dyy2+Dyz2＝1、Dzx2+Dzy2+Dzz2＝1、Exx2+Exy2+Exz2＝1、Eyx2+Eyy2+Eyz2＝1、Ezx2+Ezy2+Ezz21, each installation error in table 1 can be directly obtained through a calibration test; installation error angle Egαβ、EaαβDerived from the calculation.
(2) Calculating a transformation matrix of the body coordinate system to the measurement coordinate system:
the unit vectors of the X adding table, the Y adding table and the Z adding table in a measurement coordinate system are respectively set as
Figure BDA0001518072700000091
Figure BDA0001518072700000092
Then:
Figure BDA0001518072700000093
Figure BDA0001518072700000094
let the unit vectors of X-axis, Y-axis and Z-axis of the body coordinate system under the measurement coordinate system be
Figure BDA0001518072700000095
According to the definition of the S system (OsXsYsZs) of the inertial measurement system body coordinate system
Figure BDA0001518072700000096
Then
Figure BDA0001518072700000097
Figure BDA0001518072700000098
Normalized unit vector, namely:
Figure BDA0001518072700000099
Figure BDA00015180727000000910
Figure BDA00015180727000000911
wherein O isSXS(1)、OSXS(2)、OSXS(3) Is composed of
Figure BDA00015180727000000912
In the F series (O)FFXFYFZ) X of (2)F、YF、ZFAn on-axis component; o isSYS(1)、OSYS(2)、OSYS(3) Is composed of
Figure BDA00015180727000000913
X in the F seriesF、YF、ZFAn on-axis component; o isSZS(1)、OSZS(2)、OSZS(3) Is composed of
Figure BDA00015180727000000914
X in the F seriesF、YF、ZFThe component on the axis.
Then the matrix of the transformation matrix R for transforming the coordinates in the measurement coordinate system F into the coordinates in the body coordinate system S is:
Figure BDA00015180727000000915
in the subsequent steps, vector coordinates of prism edge lines obtained through aiming under a measuring coordinate system F system and vector coordinates of instrument input shafts obtained through calibration test under the measuring coordinate system F system are converted into vector coordinates under a body coordinate system S system through a conversion matrix R, so that installation errors of the prism edge lines and the instrument input shafts under the body coordinate system are directly solved; the method is a geometric calculation method by using space resolution, is directly clear and has no approximate calculation.
(3) Calculating the installation error of the prism to the body coordinate system (S system):
the mounting error of the aiming prism is shown in figure 3, and alpha is the parallelism error of the edge line of the aiming prism relative to the positioning reference around the X axis (the polarity is that the prism rotates anticlockwise to be positive when looking down); beta is the parallelism error of the edge line of the aiming prism relative to the positioning reference around the Y axis (polarity: the right height of the front view prism is positive).
And alpha and beta can be obtained by aiming test, and then the vector of the ridge line under the measuring coordinate system F is represented as:
Figure BDA0001518072700000101
oriented according to the aiming document
Figure BDA0001518072700000102
The definition of (1) specifies; the vector of the ridge in the system of measurement coordinates F
Figure BDA0001518072700000103
Transformed into vectors in the system of the body coordinate system S
Figure BDA0001518072700000104
Figure BDA0001518072700000105
Installation error of the prism to the body coordinate system:
Figure BDA0001518072700000106
Figure BDA0001518072700000107
(4) and (3) calculating the installation error of each gyroscope to the body coordinate system (S system):
the unit vectors of the X gyroscope, the Y gyroscope and the Z gyroscope in a measurement coordinate system are respectively set as
Figure BDA0001518072700000108
Figure BDA0001518072700000109
Then:
Figure BDA00015180727000001010
Figure BDA00015180727000001011
vector of each gyro in measuring coordinate system F system
Figure BDA00015180727000001012
Transformed into vectors in the system of the body coordinate system S
Figure BDA00015180727000001013
Comprises the following steps:
Figure BDA00015180727000001014
Figure BDA00015180727000001015
Figure BDA00015180727000001016
and then the installation error of each gyro to the body coordinate system is as follows:
Egxy＝OSXG(2)
Egyx＝OSYG(1)
Egzx＝OSZG(1)
Egxz＝OSXG(3)
Egyz＝OSYG(3)
Egzy＝OSZG(2)
(5) and calculating the installation error of each additional table to the body coordinate system (S system):
similar to a gyroscope, adding vectors of a table in a measurement coordinate system F
Figure BDA0001518072700000111
Figure BDA0001518072700000112
Transformed into vectors in the system of the body coordinate system S
Figure BDA0001518072700000113
Figure BDA0001518072700000114
Comprises the following steps:
Figure BDA0001518072700000115
Figure BDA0001518072700000116
and adding table to the installation error of the body coordinate system:
Eayx＝OSYA(1)
Eazy＝OSZA(2)
Eazx＝OSZA(1)
the adding tables are small in size and are mounted on a metal base together, the relative position relation among the adding tables is stable, and a body coordinate system is defined by selecting the relation of the adding table input shafts; in the step, because an X adding table and a Y adding table input shaft are used for defining a coordinate system, only three values of Eayx, Eazy and Eazx are taken for the installation errors of the 3 adding tables to the body coordinate system.
(6) And (3) calculating the stability of the prism, each gyro and each additional meter for calibrating the installation error for multiple times:
and (5) repeating the steps (1) to (5) to obtain a plurality of groups of installation errors of the calibrated or aimed prisms, the gyroscopes and the adding tables under the system of the body coordinate system S, and calculating the stability of the prisms, the gyroscopes and the adding tables:
according to a plurality of groups alphaSValue calculation of alphaSVariance σ ofαsI.e. represents the stability of α;
according to multiple groups of betaSValue calculation of betaSVariance σ ofβsI.e. represents the stability of β;
calculating the variance σ of Egxy according to the values of multiple groups of EgxyEgxyRepresents the stability of Dxy;
calculating the variance σ of Egyx from the values of the plurality of groups of EgyxEgyxRepresenting Dyx stability;
calculating the variance σ of Egzx from the values of the plurality of groups of EgzxEgzxRepresenting Dzx stability;
calculating the variance σ of Egxz from the values of the plurality of groups of EgxzEgxzRepresenting Dxz stability;
calculating the variance σ of Egyz from the values of the plurality of groups of EgyzEgyzRepresenting Dyz stability;
calculating the variance σ of Egzy from the values of the plurality of groups of EgzyEgzyRepresenting Dzy stability;
calculating the variance σ of Eayx according to the values of the plurality of groups of EayxEayxRepresenting Eyx stability;
calculating the variance σ of Eazx according to the values of the plurality of groups of EazxEazxRepresenting Ezx stability;
calculating the variance σ of Eazy according to the values of the plurality of groups of EazyEazyRepresenting the stability of Ezy.
Example (b):
as shown in table 2, taking the calculation of the mounting error stability of a certain inertial instrument and prism as an example:
Figure BDA0001518072700000131
the 6 sets of data in table 2 are instrument and prism installation error data calibrated and aimed on different hexahedron tools.
Directly calculating the variance of instrument and prism installation errors (under a measurement coordinate system F) obtained by calibration and aiming tests on 6 groups of different hexahedrons, wherein the stability of the installation errors exceeds a required value (10');
and (5) calculating the installation errors of the instrument and the prism under the S system of the body coordinate system according to the steps (2) to (5), and calculating the stability of the instrument and the prism, wherein the stability meets the requirement (is less than 10 ").
In model application, the requirement on the stability of the installation errors of the inertial instrument and the prism is strict, and the change of the installation errors affects the alignment precision and the flight precision of the aircraft; meanwhile, the stability before and after various environment tests in the production process of the inertial measurement unit is obtained by comparing the mounting error results of calibration and aiming before and after the tests. The inertial measurement unit cannot be repeatedly disassembled and assembled on a tool or a calibration aiming test can be carried out on different hexahedrons and rotary tables in the production process of the inertial measurement unit. Errors of equipment and repeated installation cause that the stability of installation errors of the instrument and the prism cannot be counted, for example, the variance of a test value (in a measurement coordinate system F) of the installation errors is directly counted in the table 2, and the stability is over-poor; the subsequent calculation of the installation error stability system under the body coordinate system S shows that the out-of-stability of the installation error under the measurement coordinate system F is not caused by the change of the installation error of the instrument or the prism but only caused by the tool or the repeated dismounting inertial unit, and the use precision is not influenced. In addition, the current model application also requires the installation error of the prism and the instrument of the conventional set, and a universal and accurate calculation method is needed. The method is convenient for counting the stability of the installation error in the inertial measurement unit production process, has universality and no approximate calculation, and has great application significance.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (7)

1. An inertial measurement unit and prism installation error stability determination method is characterized by comprising the following steps:
(1) defining an inertial measurement unit body coordinate system S system, an inertial measurement unit measurement coordinate system F system and an installation error angle EgαβAnd the installation error angle EaαβWherein β ═ x, y, z; α ≠ β:
(2) determining a transformation matrix R of an inertial measurement unit body coordinate system S to a measurement coordinate system F;
the transformation matrix R of the inertial measurement unit body coordinate system S under the measurement coordinate system F is as follows:
Figure FDA0002610354930000011
wherein, OSXS(1)、OSXS(2)、OSXS(3) Is a vector
Figure FDA0002610354930000012
X in the F seriesF、YF、ZFAn on-axis component; o isSYS(1)、OSYS(2)、OSYS(3) Is a vector
Figure FDA0002610354930000013
X in the F seriesF、YF、ZFAn on-axis component; o isSZS(1)、OSZS(2)、OSZS(3) Is a vector
Figure FDA0002610354930000014
X in the F seriesF、YF、ZFAn on-axis component;
namely, it is
Figure FDA0002610354930000015
Are respectively the bookThe unit vector of X axis, Y axis and Z axis of the body coordinate system S system under the measurement coordinate system F system comprises:
Figure FDA0002610354930000016
Figure FDA0002610354930000017
Figure FDA0002610354930000018
at the same time, the user can select the desired position,
Figure FDA0002610354930000019
Figure FDA00026103549300000110
is composed of
Figure FDA00026103549300000111
The normalized unit vector is obtained by the following steps,
Figure FDA00026103549300000112
is composed of
Figure FDA00026103549300000113
Normalized unit vectors;
Figure FDA00026103549300000114
adding a unit vector of the table in the measurement coordinate system to X, and
Figure FDA00026103549300000115
Figure FDA00026103549300000116
Figure FDA00026103549300000117
adding a unit vector of the table in the measurement coordinate system to Y, and
Figure FDA00026103549300000118
Figure FDA00026103549300000119
(3) calculating the installation error beta of the prism to the S system of the body coordinate systemsAnd alphas；
(4) Calculating the installation error of each gyroscope to the S system of the body coordinate system;
(5) calculating the installation error of each additional table to the S system of the body coordinate system;
(6) and (5) repeating the steps (1) to (5) to obtain the installation errors of the plurality of groups of prisms, gyroscopes and addition tables in the system of the body coordinate system S, and determining the stability of the prisms, the gyroscopes and the addition tables.
2. The method for determining the mounting error stability of the inertial instrument and the prism as claimed in claim 1, wherein: in the step (1):
inertial measurement unit body coordinate system S system: o isSXSTaking inertial unit X plus meter input shaft direction, OSYSIn the plane of the input shaft of the inertial measurement unit X, Y plus meter and OSXSPerpendicular, pointing in the direction of the Y plus the input axis of the meter, OSZSThe axis is determined by the right hand rule;
installation error angle EgαβFor an alpha-direction gyroscope input shaft and an inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes; installation error angle EaαβFor alpha to add table input shaft and inertial measurement unit body coordinate system OSβSNon-orthogonal errors of axes;
inertial measurement coordinate system F system: the inertial measurement unit is arranged on the hexahedron for calibration, and O is takenFXFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial measurement unit X plus the meter; taking OFYFThe direction of the measuring reference plane is parallel to the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial measurement unit Y plus the meter; taking OFZFIs parallel to the measuring reference surface in the corresponding direction of the hexahedron and is consistent with the direction of the input shaft of the inertial unit Z plus the meter.
3. The method for determining the installation error stability of an inertial instrument and a prism as claimed in claim 1 or 2, wherein: the installation error under the inertial measurement coordinate system F is defined as:
dxx is the installation error of the X gyroscope relative to the X axis of the measurement coordinate system;
dxy is the installation error of the X gyroscope relative to the Y axis of the measurement coordinate system;
dxz is the installation error of X gyroscope relative to the Z axis of the measuring coordinate system;
dyx is the installation error of Y gyroscope relative to the X axis of the measuring coordinate system;
dyy is the Y-axis installation error of the Y gyroscope relative to the measurement coordinate system;
dyz is the installation error of Y gyroscope relative to the Z axis of the measuring coordinate system;
dzx is the installation error of Z gyroscope relative to the X axis of the measuring coordinate system;
dzy is the installation error of Z gyroscope relative to the Y axis of the measuring coordinate system;
dzz is the Z axis installation error of the Z gyro relative to the measurement coordinate system;
exx is X plus the relative measurement coordinate system X axis installation error;
exy is the installation error of X plus table relative measurement coordinate system Y axis;
exz is the relative measurement coordinate system Z axis installation error of X plus table;
eyx is Y plus the installation error of the relative measurement coordinate system X axis;
eyy is Y plus the installation error of the relative measurement coordinate system Y axis;
eyz is Y plus the relative measurement coordinate system Z axis installation error;
ezx is Z plus the installation error of the relative measurement coordinate system X axis;
ezy is Z plus table relative measurement coordinate system Y axis installation error;
ezz is Z plus the Z axis installation error of the relative measurement coordinate system.
4. The method for determining the mounting error stability of the inertial instrument and the prism as claimed in claim 1, wherein: the step (3) is used for calculating the installation error beta of the prism to the S system of the body coordinate systemsAnd alphasThe method specifically comprises the following steps:
Figure FDA0002610354930000031
Figure FDA0002610354930000032
wherein, OLS(1)、OLS(2)、OLS(3) Is composed of
Figure FDA0002610354930000033
The components on the Xs, Ys, and Zs axes of the S system,
Figure FDA0002610354930000034
to make the ridge vector under the system of measurement coordinate system F
Figure FDA0002610354930000035
Transformed into a vector in the system of the body coordinate system S, and has
Figure FDA0002610354930000036
The vector of the ridge in the measuring coordinate system F is represented as:
Figure FDA0002610354930000037
alpha is the parallelism error of the edge line of the aiming prism relative to the positioning reference around the X axis, and the polarity of the error is that the overlooking prism rotates anticlockwise to be positive; beta is aiming prism crest lineThe parallelism error of the relative positioning reference around the Y axis has the polarity that the right height of the front-view prism is positive; both α and β are determined by aiming tests.
5. The method for determining the mounting error stability of the inertial instrument and the prism as claimed in claim 1, wherein: the step (4) of calculating the installation error of each gyroscope to the body coordinate system S system specifically comprises the following steps:
Egxy＝OSXG(2)；
Egyx＝OSYG(1)；
Egzx＝OSZG(1)；
Egxz＝OSXG(3)；
Egyz＝OSYG(3)；
Egzy＝OSZG(2)；
OSXG(1)、OSXG(2)、OSXG(3) is composed of
Figure FDA0002610354930000041
The component on the Xs, Ys, Zs axis of the S system, OSYG(1)、OSYG(2)、OSYG(3) Is composed of
Figure FDA0002610354930000042
The component on the Xs, Ys, Zs axis of the S system, OSZG(1)、OSZG(2)、OSZG(3) Is composed of
Figure FDA0002610354930000043
The components on the Xs, Ys, Zs axes of the S system;
Figure FDA0002610354930000044
respectively is the vector of each gyro under the system of a measuring coordinate system F
Figure FDA0002610354930000045
Figure FDA0002610354930000046
Transformed into a vector in the system of the body coordinate system S:
Figure FDA0002610354930000047
Figure FDA0002610354930000048
Figure FDA0002610354930000049
Figure FDA00026103549300000410
unit vectors of the X gyroscope, the Y gyroscope and the Z gyroscope in a measurement coordinate system are respectively as follows:
Figure FDA00026103549300000411
6. the method for determining the mounting error stability of the inertial instrument and the prism as claimed in claim 1, wherein: and (5) calculating the installation error of each additional table to the S system of the body coordinate system, specifically:
Eayx＝OSYA(1)；
Eazx＝OSZA(1)；
Eazy＝OSZA(2)；
OSYA(1)、OSYA(2)、OSYA(3) is composed of
Figure FDA0002610354930000051
The component on the Xs, Ys, Zs axis of the S system, OSZA(1)、OSZA(2)、OSZA(3) Is composed of
Figure FDA0002610354930000052
The components on the Xs, Ys, Zs axes of the S system;
Figure FDA0002610354930000053
for each adding table to be under the system of measurement coordinate system F
Figure FDA0002610354930000054
Transformed into a vector in the system of the body coordinate system S:
Figure FDA0002610354930000055
Figure FDA0002610354930000056
Figure FDA0002610354930000057
respectively is a unit vector of the Y plus table and the Z plus table under a measurement coordinate system:
Figure FDA0002610354930000058
7. the method for determining the mounting error stability of the inertial instrument and the prism as claimed in claim 1, wherein: the step (6) of mounting the plurality of sets of prisms, gyroscopes and additional tables in the body coordinate system S, and determining the stability of the prisms, the gyroscopes and the additional tables specifically comprise the following steps:
according to a plurality of groups alphaSValue calculation of alphaSVariance σ ofαsI.e. represents the stability of α;
according to multiple groups of betaSValue calculation of betaSVariance σ ofβsI.e. represents the stability of β;
calculating the variance σ of Egxy according to the values of multiple groups of EgxyEgxyRepresents the stability of Dxy;
calculating the variance σ of Egyx from the values of the plurality of groups of EgyxEgyxRepresenting Dyx stability;
calculating the variance σ of Egzx from the values of the plurality of groups of EgzxEgzxRepresenting Dzx stability;
calculating the variance σ of Egxz from the values of the plurality of groups of EgxzEgxzRepresenting Dxz stability;
calculating the variance σ of Egyz from the values of the plurality of groups of EgyzEgyzRepresenting Dyz stability;
calculating the variance σ of Egzy from the values of the plurality of groups of EgzyEgzyRepresenting Dzy stability;
calculating the variance σ of Eayx according to the values of the plurality of groups of EayxEayxRepresenting Eyx stability;
calculating the variance σ of Eazx according to the values of the plurality of groups of EazxEazxRepresenting Ezx stability;
calculating the variance σ of Eazy according to the values of the plurality of groups of EazyEazyRepresenting the stability of Ezy.
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