CN112648995A - Modulation method and terminal of optical fiber gyroscope rotary inertial navigation system - Google Patents

Modulation method and terminal of optical fiber gyroscope rotary inertial navigation system Download PDF

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CN112648995A
CN112648995A CN202011625768.XA CN202011625768A CN112648995A CN 112648995 A CN112648995 A CN 112648995A CN 202011625768 A CN202011625768 A CN 202011625768A CN 112648995 A CN112648995 A CN 112648995A
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error
modulation
gyroscope
scale factor
inertial navigation
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CN112648995B (en
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吴志聪
吴宜荣
黄奇家
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Fujian Xinghai Communication Technology Co Ltd
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Fujian Xinghai Communication Technology Co Ltd
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    • G01—MEASURING; TESTING
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Abstract

The invention provides a modulation method and a terminal of a fiber optic gyroscope rotational inertial navigation system, which are used for acquiring a first output error of a gyroscope component, a second output error of an accelerometer and a scale factor error of the gyroscope component; acquiring the carrier attitude of a carrier where an inertial navigation system is located; after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result; and if the first modulation result meets a preset threshold value, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation. The method obtains the main error value which has larger influence on the final output result in the inertial navigation system and brings the main error value into the alternative modulation equation for calculation, realizes the isolation of the influence on the attitude of the carrier, and finally realizes the high-precision system modulation of the inertial navigation system.

Description

Modulation method and terminal of optical fiber gyroscope rotary inertial navigation system
Technical Field
The invention relates to the field of gyroscope modulation, in particular to a modulation method and a terminal of an optical fiber gyroscope rotary inertial navigation system.
Background
In an inertial navigation system of a fiber-optic gyroscope, a rotation modulation technology is usually adopted to eliminate device errors, and the rotation modulation technology modulates the inertial device errors by introducing deterministic mechanical rotation, so that the method is a technical means for eliminating the device errors from the system angle; the technology can reduce the influence of the error of the inertia device on the system performance on one hand, and can relax the requirement on the performance of the inertia device on the other hand, thereby reducing the system cost; compared with a conventional inertial navigation system, the inertial navigation system adopting the rotation modulation technology is expected to greatly improve the system precision under the same device level, so that the navigation requirements of a ship on the inertial navigation system during long-term navigation and high precision are met, but the rotation modulation needs to be considered from the system perspective, and the existing rotation modulation method mostly has the problem of incomplete consideration factors and influences on the final modulation effect.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: a modulation method and a terminal of an optical fiber gyroscope rotation inertial navigation system are provided, and high-precision rotation modulation is achieved.
In order to solve the technical problems, the invention adopts a technical scheme that:
a modulation method of an optical fiber gyroscope inertial navigation system comprises the following steps:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result;
and S4, if the first modulation result meets a preset threshold, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation.
In order to solve the technical problem, the invention adopts another technical scheme as follows:
a modulation terminal of a fiber optic gyroscope inertial navigation system, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the following steps when executing the computer program:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result;
and S4, if the first modulation result meets a preset threshold, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation.
The invention has the beneficial effects that: respectively obtaining output errors of a gyro component and an accelerometer, obtaining a scale factor error of the gyro component, obtaining a carrier attitude of a carrier where an inertial navigation system is located, bringing the output errors and the scale factor error into a preset alternative modulation equation for analysis under the condition of isolating the carrier attitude, namely demodulating the carrier attitude to obtain a first modulation result, taking a corresponding alternative modulation scheme as a final modulation scheme for modulating the inertial navigation system if the first modulation result meets a threshold value, obtaining a main error value which has a large influence on the final output result in the inertial navigation system and bringing the main error value into the alternative modulation equation for calculation, if the obtained modulation result meets the threshold value, showing that all kinds of errors can be balanced at the moment so that the output result meets the precision requirement, further setting different threshold values according to different precision requirements to realize system modulation of the inertial navigation system, the carrier attitude is also considered to influence the system modulation, so that the modulation precision of the inertial navigation system is further improved, and the method is particularly suitable for modulating the inertial navigation system on a mobile carrier such as a ship.
Drawings
Fig. 1 is a flowchart illustrating steps of a modulation method of an optical fiber gyroscope rotational inertial navigation system according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a modulation terminal of an optical fiber gyroscope rotational inertial navigation system according to an embodiment of the present invention;
FIG. 3 is a graph of carrier roll and IMU rotation about a horizontal axis according to an embodiment of the present invention;
FIG. 4 is a graph of the relationship between carrier roll and IMU rotation about the zenith axis according to an embodiment of the present invention;
FIG. 5 is a graph of the relationship between carrier pitch and IMU rotation about a horizontal axis according to an embodiment of the present invention;
FIG. 6 is a graph of the relationship between carrier pitch and IMU rotation about the zenith axis according to an embodiment of the present invention;
FIG. 7 is a graph illustrating the relationship between carrier heading movement and IMU rotation about a horizontal axis, in accordance with an embodiment of the present invention;
FIG. 8 is a graph illustrating the relationship between carrier heading movement and IMU rotation about the zenith axis, in accordance with an embodiment of the present invention;
FIG. 9 is a schematic diagram of a rotational modulation sequence according to an embodiment of the present invention;
FIG. 10 is a schematic diagram of biaxial 64-order rotation angle changes according to an embodiment of the present invention;
FIG. 11 is a signal flow diagram during carrier isolation according to an embodiment of the present invention;
FIG. 12 is a flow chart of carrier isolation according to an embodiment of the present invention;
FIG. 13 is a schematic diagram illustrating coordinate system definition according to an embodiment of the present invention;
description of reference numerals:
1. a modulation terminal of an optical fiber gyroscope inertial navigation system; 2. a processor; 3. a memory.
Detailed Description
In order to explain technical contents, achieved objects, and effects of the present invention in detail, the following description is made with reference to the accompanying drawings in combination with the embodiments.
Referring to fig. 1, a modulation method of an optical fiber gyroscope inertial navigation system includes the steps of:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result;
and S4, if the first modulation result meets a preset threshold, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation.
From the above description, the beneficial effects of the present invention are: respectively obtaining output errors of a gyro component and an accelerometer, obtaining a scale factor error of the gyro component, obtaining a carrier attitude of a carrier where an inertial navigation system is located, bringing the output errors and the scale factor error into a preset alternative modulation equation for analysis under the condition of isolating the carrier attitude, namely demodulating the carrier attitude to obtain a first modulation result, taking a corresponding alternative modulation scheme as a final modulation scheme for modulating the inertial navigation system if the first modulation result meets a threshold value, obtaining a main error value which has a large influence on the final output result in the inertial navigation system and bringing the main error value into the alternative modulation equation for calculation, if the obtained modulation result meets the threshold value, showing that all kinds of errors can be balanced at the moment so that the output result meets the precision requirement, further setting different threshold values according to different precision requirements to realize system modulation of the inertial navigation system, the carrier attitude is also considered to influence the system modulation, so that the modulation precision of the inertial navigation system is further improved, and the method is particularly suitable for modulating the inertial navigation system on a mobile carrier such as a ship.
Further, the S1 specifically includes:
obtaining the first output error
Figure BDA0002877423320000041
Wherein S isgA scale factor error matrix representing the gyro component,
Figure BDA0002877423320000042
representing the mounting error matrix of the gyro-assembly, T representing the transpose of the matrix,
Figure BDA0002877423320000043
representing the output value, ε, of the gyro-assemblypRepresenting a zero bias value of the gyro component;
obtaining the second output error
Figure BDA0002877423320000044
Wherein S isaA scale factor error matrix representing the accelerometer,
Figure BDA0002877423320000045
a matrix of mounting errors of the accelerometer is represented,
Figure BDA0002877423320000046
represents an output value of the accelerometer +pRepresenting the zero bias value of the accelerometer.
As can be seen from the above description, the first output error is obtained by periodically acquiring data according to the sampling interval, which conforms to the characteristics of the gyroscope in actual use, and the sampling interval, i.e., the period, is taken into consideration, so that the data modulated according to the first output error is closer to the target value actually measured by the gyroscope.
Further, the S1 specifically includes:
acquiring the scale factor error, and obtaining an angular speed error according to the scale factor error;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error and the angle error into a preset alternative modulation equation to obtain a first modulation result.
It can be known from the above description that an error also exists between the measured value and the actual value of the scale factor, which may cause an error of the calculated angular velocity value required for the final measurement, thereby causing an output error of the gyroscope, an angular velocity error is calculated according to the scale factor error, and the angular error is also brought into the alternative modulation equation to obtain a change rule of the angular velocity error under different modulation modes, thereby taking the change of the angular velocity error into consideration, so that the final modulation according to the modulation equation can neutralize the error value to the maximum extent.
Further, the S3 is preceded by:
acquiring a constant drift amount of the gyro component;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error, the scale factor error and the constant drift amount into a preset alternative modulation equation to obtain a first modulation result.
It can be known from the above description that, since the modulation process is system modulation, the constant offset is also brought into the alternative modulation equation to observe the change of the constant offset along with the modulation, thereby avoiding the error possibly caused by the conventional method for compensating the constant offset in the system modulation.
Further, the alternative modulation equation in S3 is:
Figure BDA0002877423320000051
where γ (t) represents the rotation speed.
As can be seen from the above description, the process of system modulation is identified as a rotation matrix, i.e., an alternative modulation equation, and various modulation modes can be directly calculated by changing parameters in the alternative modulation equation, so that numerical calibration calculation can be conveniently performed on the variation values of various errors possibly caused in the system modulation process, and support data can be provided for the determination of the final modulation equation.
Further, the S4 includes:
and judging whether the accumulated error angle and the accumulated error speed in the first modulation result are symmetrical about 0 in one rotation period of the modulation equation, if so, the first modulation result meets a preset threshold value.
As can be seen from the above description, according to the characteristic that the modulation target of the system does not eliminate the error but balances the error so that the final output data is closest to the true value, it is set that as long as the accumulated error angle and the accumulated error speed are symmetric about 0 in one rotation period, it is determined that the alternative modulation equation satisfies the threshold, that is, although a situation that the error is large may occur at some time point in one period, the error can be balanced in one period so that the final output data is not affected by the error value.
Further, the number of the gyro assemblies in S1 is three;
in the step S1, the obtaining the scale factor error and the obtaining the angular velocity error according to the scale factor error specifically include:
obtaining a scale factor error matrix:
Figure BDA0002877423320000061
wherein the content of the first and second substances,
Figure BDA0002877423320000062
representing a symmetry scale factor error of an ith said gyro assembly gyro,
Figure BDA0002877423320000063
representing an asymmetric scale factor error of the ith said gyro assembly;
the angle error
Figure BDA0002877423320000064
Wherein, ω is1、ω2And omega3Respectively representing input angular velocities sensed by the gyro components;
Figure BDA0002877423320000065
from the above description, in a scenario including three gyro assemblies, a scale factor error matrix is constructed according to the difference of the input angular velocity sensed by each gyro assembly, and the angle error is finally obtained by considering the symmetric scale factor error and the asymmetric scale factor error, so that the accuracy of the finally obtained angle error is improved.
Further, the constant drift amount
Figure BDA0002877423320000066
Wherein the content of the first and second substances,
Figure BDA0002877423320000067
representing the constant drift value of the gyroscope on the x-axis of the gyroscope assembly,
Figure BDA0002877423320000068
represents the constant drift value of the gyroscope on the y axis of the gyroscope component,
Figure BDA0002877423320000069
representing the constant drift value of the gyroscope on the z-axis of the gyroscope assembly.
As can be seen from the above description, the error amount of the final value calculated by the constant drift amount is reduced by considering the constant drift amounts on the three axes in different directions and performing calculation using different constant drift amounts according to different axes.
Further, the S3 is preceded by: obtaining installation error
Figure BDA00028774233200000610
Figure BDA00028774233200000611
Wherein, muij(i ═ x, y, z; j ≠ x, y, z; i ≠ j) is the installation error angle of the gyro component on the ith coordinate axis;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error, the scale factor error and the installation error into a preset alternative modulation equation to obtain a first modulation result.
As can be seen from the above description, in the gyro installation process, the gyro components are installed in different directions, and when the gyro components are finally calculated as a coordinate system, there is an error between the installation angle and the coordinate system used in the final calculation, and the installation error is also included in the calculation range, so that the error balancing effect of the finally determined modulation scheme is further improved.
Referring to fig. 2, a modulation terminal of an optical fiber gyroscope inertial navigation system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, where the processor implements the following steps when executing the computer program:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result;
and S4, if the first modulation result meets a preset threshold, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation.
The invention has the beneficial effects that: respectively obtaining output errors of a gyro component and an accelerometer, obtaining a scale factor error of the gyro component, obtaining a carrier attitude of a carrier where an inertial navigation system is located, bringing the output errors and the scale factor error into a preset alternative modulation equation for analysis under the condition of isolating the carrier attitude, namely demodulating the carrier attitude to obtain a first modulation result, taking a corresponding alternative modulation scheme as a final modulation scheme for modulating the inertial navigation system if the first modulation result meets a threshold value, obtaining a main error value which has a large influence on the final output result in the inertial navigation system and bringing the main error value into the alternative modulation equation for calculation, if the obtained modulation result meets the threshold value, showing that all kinds of errors can be balanced at the moment so that the output result meets the precision requirement, further setting different threshold values according to different precision requirements to realize system modulation of the inertial navigation system, the carrier attitude is also considered to influence the system modulation, so that the modulation precision of the inertial navigation system is further improved, and the method is particularly suitable for modulating the inertial navigation system on a mobile carrier such as a ship.
Referring to fig. 1, a first embodiment of the present invention is:
in the specification, nine coordinate systems of biaxial rotational inertial navigation are defined, namely a gyroscope component coordinate system G system, an accelerometer component coordinate system a system, an IMU coordinate system S system and an actual platform coordinate system P system, and a modulation average coordinate system
Figure BDA0002877423320000081
A system, a carrier coordinate system b system, a system base coordinate system O system, a terrestrial coordinate system e system and a navigation coordinate system n system, each coordinate system being defined as shown in fig. 2, and the coordinate systems defined in this section will be applied throughout the entire paper. The coordinate system is described as follows:
g is: the gyroscope assembly coordinate systems o-xgygzg, oxg, oyg and ozg are the sensitive axes of the x gyroscope, the y gyroscope and the z gyroscope respectively;
a is: the accelerometer assembly coordinate systems o-xayaza, oxa, oya, and oza are the sensitive axes of the x-accelerometer, y-accelerometer, and z-accelerometer, respectively;
s is: the IMU coordinate system o-xsyszs, centered at the IMU structure center. At the initial moment, the ys axis is defined to coincide with the yg axis, the xs axis is perpendicular to the ys axis in the plane, and the zs axis, the xs axis and the ys axis satisfy the right-hand coordinate system. S is fixedly connected with the platform and rotates along with the platform;
p is: the actual platform coordinate system o-xpypzp, defined by the two actual axes of the platform. ozp axis is along the rotation axis of the sky, indicating that the sky is positive; oyp along the horizontal axis, pointing forward positive; the oxp axis is determined according to the right hand rule. The coordinate system is centered at the intersection of the two axes. The coordinate system may be expressed as yp×zp,yp,zp}；
Figure BDA0002877423320000082
Comprises the following steps: modulated mean coordinate system
Figure BDA0002877423320000083
Neither the IMU measurement coordinate system nor the actual gyro platform coordinate system. The coordinate system is a fixed coordinate system centered at the IMU accelerometer assembly. At the initial moment in time of the day,
Figure BDA0002877423320000084
the direction is pointed to the day,
Figure BDA0002877423320000085
is directed to the bow and is provided with a bow-shaped guide rail,
Figure BDA0002877423320000086
pointing to the right. And without loss of generality will
Figure BDA0002877423320000087
Coincident with the ozp axis, the coordinate system can be expressed as yP×zP,zP×(yP×zP),zP}; the coordinate system is constructed, so that the study of non-orthogonal angles of the axes can be facilitated;
b is: a carrier coordinate system o-xbybzb, oxb, oyb and ozb respectively points to the right direction, the heading direction and the heaven direction of the ship, and the origin of coordinates is at the centroid of the carrier;
o is: a system base coordinate system o-xoyozo, ozo is vertically arranged on the bottom surface, oyo is parallel to a horizontal shaft of the platform, an oxo axis is determined according to the right-hand rule, and the center of the coordinate system is coincided with the centroid of the base structure;
e is a group: the earth coordinate system o-xeyeze has its origin at the earth center of mass and its coordinates remain fixed with respect to the rotating earth. oxe in the mean astronomical equatorial plane; oye is 90 ° to the east of the x-axis in the mean astronomical equatorial plane; the oze axis, the oxe axis and the oye axis form a right-hand coordinate system;
n is: and selecting a local horizontal north-pointing azimuth coordinate system according to the navigation coordinate system o-xnynzn. The origin of coordinates is at the center of mass of the carrier, oxn points to geodetic east, oyn points to geodetic north, ozn and oxn and oyn satisfy the right-hand rule;
attitude transformation matrix of
Figure BDA0002877423320000091
Figure BDA0002877423320000092
The carrier system b is a coordinate transformation matrix between the base coordinate system O and is determined by the installation error angle;
Figure BDA0002877423320000093
base coordinate system O system and modulation average coordinate system
Figure BDA0002877423320000094
Coordinate transformation matrix between the systems is determined by the frame angle read by the angle reading device;
Figure BDA0002877423320000095
IMU coordinate system S to modulation mean coordinate system
Figure BDA0002877423320000096
A coordinate transformation matrix between the systems is determined by a rolling misalignment angle, an axis non-orthogonal angle and an axis swing angle;
Figure BDA0002877423320000097
modulating a coordinate transformation matrix between an average coordinate system S system and a navigation coordinate system n system;
a modulation method of an optical fiber gyroscope inertial navigation system comprises the following steps:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
in an alternative embodiment, the number of gyro assemblies is three;
in this embodiment, S1 specifically includes:
obtaining the first output error
Figure BDA0002877423320000098
Wherein S isgA scale factor error matrix representing the gyro component,
Figure BDA0002877423320000099
represents the installation error matrix of the gyro component, in the formula, T represents the transposition of the matrix,
Figure BDA00028774233200000910
representing the output value, ε, of the gyro-assemblypRepresenting a zero bias value of the gyro component;
specifically, the output of the gyro assembly is the angular increment pulse number, which is recorded as NgThe output of the gyroscope is the actual angular velocity input while the error term is ignored
Figure BDA00028774233200000911
Wherein, KgA scaling factor representing a gyro component, t representing a sampling interval; the measured output of the gyroscope, taking into account the error term, is
Figure BDA00028774233200000912
Wherein I represents a preset constant; the first output error
Figure BDA00028774233200000913
Obtaining the second output error
Figure BDA00028774233200000914
Wherein I represents a predetermined constant, SaA scaling factor error matrix representing an accelerometer (also called a accelerometer),
Figure BDA00028774233200000915
a matrix of mounting errors of the accelerometer is represented,
Figure BDA00028774233200000916
represents an output value of the accelerometer +pRepresents a zero bias value for the accelerometer;
specifically, the output of the accelerometer is the specific force increment pulse number NaIf the error term is ignored, the output of the accelerometer is the actual specific force
Figure BDA0002877423320000101
Wherein, KaRepresenting an accelerometer scale factor, t representing a sampling interval; the measurement output of the accelerometer, taking into account the error term, is
Figure BDA0002877423320000102
Wherein I represents a preset constant; the second output error is
Figure BDA0002877423320000103
Wherein the content of the first and second substances,
Figure BDA0002877423320000104
obtaining the scale factor error, and obtaining an angular speed error according to the scale factor error:
the scale factor of the inertia element can not be calibrated absolutely accurately, and the scale factor can change along with the time, environment and other factors, so that the scale factor error of the inertia element always exists in the actual system, and the calibration can not be carried out once and for all, the performance of the scale factor is generally measured by the linearity of different rotating speeds and the repeatability of the successive starting of the same rotating speed, and can be expressed as Kgc＝Kg(I+Sg),Kac＝Ka(I+Sa) (ii) a Wherein, KgcCalculated value of scale factor for gyro component, KacIs a scale factor of an accelerometerNumber calculation value, Kg＝diag([Kgx Kgy Kgz]) And Ka＝diag([Kax Kay Kaz]) The actual values of the scale factors for the gyro assembly and the summers,
Figure BDA0002877423320000105
for gyro-component scale factor error matrices, Sa＝diag([Sax Say Saz]) Scaling a factor error matrix for the accelerometer; the measurement error of the gyro component and the measurement error of the accelerometer caused by the error of the scale factor are respectively
Figure BDA0002877423320000106
Due to the influence of factors such as a process, an IMU self-operation principle and the like in the practical application process, general scale factors have positive and negative asymmetry, a certain scale factor asymmetry error can be caused by usually neglecting the asymmetry or directly taking the scale factors as the average value of the positive scale factors and the negative scale factors, and the error matrix is determined by considering the asymmetry error;
acquiring a gyro scale factor error matrix:
Figure BDA0002877423320000107
wherein the content of the first and second substances,
Figure BDA0002877423320000108
representing a symmetry scale factor error of an ith said gyro assembly gyro,
Figure BDA0002877423320000109
representing an asymmetric scale factor error of the ith said gyro assembly;
Figure BDA0002877423320000111
angular rate error of gyro assembly generated by scale factor error
Figure BDA0002877423320000112
Specifically, the method comprises the following steps:
Figure BDA0002877423320000113
wherein, ω is1、ω2And omega3Respectively representing input angular velocities sensed by the gyro components;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error, the angle error and the constant drift amount into a preset alternative modulation equation to obtain a first modulation result;
wherein, the alternative modulation equation is:
Figure BDA0002877423320000114
wherein the content of the first and second substances,
Figure BDA0002877423320000115
represents the rotational speed;
s4, if the first modulation result meets a preset threshold value, marking the alternative modulation equation as a final modulation equation and modulating the fiber optic gyroscope according to the final modulation equation; the method comprises the following steps: and judging whether the accumulated error angle and the accumulated error speed in the first modulation result are symmetrical about 0 in one rotation period of the modulation equation, if so, the first modulation result meets a preset threshold value.
The second embodiment of the invention is as follows:
a modulation method of an optical fiber gyroscope rotational inertial navigation system, which is different from the first embodiment in that:
before S3, the method further includes:
(1) acquisition instituteConstant drift amount of the gyro component
Figure BDA0002877423320000121
Wherein the content of the first and second substances,
Figure BDA0002877423320000122
representing the constant drift value of the gyroscope on the x-axis of the gyroscope assembly,
Figure BDA0002877423320000123
represents the constant drift value of the gyroscope on the y axis of the gyroscope component,
Figure BDA0002877423320000124
representing a constant drift value of the gyroscope on the z axis of the gyroscope assembly;
(2) obtaining installation error
Figure BDA0002877423320000125
The installation error angle refers to an included angle (generally in the order of arc seconds) between the orientation of the real sensitive axis of the gyroscope and the orientation of the sensitive axis of the gyroscope obtained by calibration calculation, after the calibration work of the inertial measurement combination, the coordinate system ox consisting of the three sensitive axes of the fiber-optic gyroscope is obtainedgygzg(non-orthogonal system) to IMU coordinate system oxpypzp(orthogonal system) transformation matrix
Figure BDA0002877423320000126
Obtained by calibration
Figure BDA0002877423320000127
Not absolutely exact, it is associated with the true oxgygzgTo oxpypzpMatrix of transformation between
Figure BDA0002877423320000128
In a relationship of
Figure BDA0002877423320000129
Figure BDA00028774233200001210
Wherein, muij(i ═ x, y, z; j ≠ x, y, z; i ≠ j) is the installation error angle of the gyroscope on the ith coordinate axis;
(3) obtaining a random drift of the gyro component, epsilon, taking into account only white noise output by the gyro componentw＝[εwxεwy εwz](ii) a Wherein epsilonwxRepresenting the constant drift value, epsilon, of the gyro on the x-axis of the gyro assemblywyRepresenting the constant drift value, epsilon, of the gyro on the y-axis of the gyro assemblywzRepresenting the constant drift value of the gyroscope on the z-axis of the gyroscope assembly.
The third embodiment of the invention is as follows:
a modulation method of an optical fiber gyroscope rotational inertial navigation system is different from the modulation method of the first embodiment or the second embodiment,
the first output error after modulation according to the alternative modulation equation is:
Figure BDA00028774233200001211
wherein the content of the first and second substances,
Figure BDA0002877423320000131
Figure BDA0002877423320000132
wherein the content of the first and second substances,
Figure BDA0002877423320000133
a coordinate transformation matrix representing the navigation coordinate system n to the carrier coordinate system b,
Figure BDA0002877423320000134
representing the gyro angular velocity under the navigation coordinate system n system,
Figure BDA0002877423320000135
representing the equivalent angular velocity of the accelerometer in the navigation coordinate system n,
Figure BDA0002877423320000136
representing the angular velocity of the carrier coordinate system b, namely the angular velocity of the moving carrier;
Figure BDA0002877423320000137
the second output error after modulation according to the alternative modulation equation is:
Figure BDA0002877423320000138
the constant value drift after modulation according to the alternative modulation equation is:
Figure BDA0002877423320000139
it can be seen that in the continuous rotation scenario, the rotation speed
Figure BDA00028774233200001310
Is a constant value, the constant drift on the vertical plane of the rotating shaft is completely modulated in one rotating period, and the constant drift on the rotating shaft can not be modulated; the positive and negative rotation movement of IMU (Inertial Measurement Unit) makes the driving motor of the rotary table generate frequent braking and starting, so that the driving motor of the rotary table generates frequent braking and starting in actual use, and the motor has enough locking time to adapt to and twist back the deformation generated during braking; moreover, in the locking time period, the drift is not modulated into a sine wave form, so as to be capable of preventing the error generated in the locking time periodThe difference counteracts that the sign of the constant drift in the vertical plane of the rotation axis must change during the lock-in time in each rotation period during the entire modulation process; the requirement is that the rotating speed of positive and negative rotation stop and the angular acceleration of braking and starting have an odd symmetry relation with time in each rotation period, and the requirement is that the position of each rotation stop is symmetrical with the rotating shaft; moreover, for a dual-shaft indexing system, when a motor on one shaft rotates, the motor on the other shaft must be locked for a period of time during the positive and negative transition periods;
the random drift after modulation according to the modulation equation of the present declaration is:
Figure BDA0002877423320000141
εwiis Gaussian white noise, has a mean value of 0 and a variance of
Figure BDA0002877423320000142
Has the following characteristics:
Figure BDA0002877423320000143
Figure BDA0002877423320000144
as can be seen from the above formula, after the rotation modulation, the noise variance in each axial direction has no substantial change; in fact, the frequency of the angle sine change is far less than that of white noise, the rotation has no effect of reducing the error amplitude of the rotation on the fast-changing error quantity, and the random drift of the gyroscope cannot be modulated by the double-shaft rotation;
the gyro output error caused by the scale factor error after modulation according to the alternative modulation equation is:
Figure BDA0002877423320000145
the accumulated error angle after one period of rotation when the modulation is obtained by integration in one period of rotation:
Figure BDA0002877423320000146
wherein, ω isieNRepresenting the angular rate of rotation of the earth, ωieURepresenting the angular velocity of the movement of the carrier around the earth, gamma representing the rotational velocity;
from the above equation, it can be seen that the symmetry error of two gyro scale factors in the direction perpendicular to the rotation axis in one rotation period
Figure BDA0002877423320000151
There is still an asymmetric error term for the two gyro scale factors in the direction perpendicular to the axis of rotation
Figure BDA0002877423320000152
But disappeared; namely, under the condition of isolating the motion of the carrier, the asymmetric error effect of all the inertia elements can be averagely removed by the biaxial rotation; in addition, because the east component of the rotation speed of the earth is zero under the static condition, the east angle error cannot be caused, namely the first term in the formula is zero, the error of the asymmetric scale factor of the gyroscope on the plane vertical to the rotating shaft can be modulated, and the symmetric error cannot be modulated;
obtaining a third component in the above equation:
Figure BDA0002877423320000153
due to omegaieU> omega, the formula is simplified to obtain:
Figure BDA0002877423320000154
analyzing the error of the item (1) in the above equation, if the error is always positive (or negative), that is, if the error is always rotated in one direction in the modulation process, the error accumulation is caused, so that the rotation scheme should adopt a positive and negative rotation stop mode; the error of item (2) represents the error generated by the coupling of the symmetry scale factor error and the earth rotation, which is caused by the rotation of the geographic coordinate system relative to the inertial space, so that the error always exists as long as the rotation is around the geographic system; the electrostatic gyro inertial navigation system rotates relative to an inertial coordinate system, so that the error cannot exist; term (3) is the mathematical platform error angle caused by the coupling of the asymmetric scale factor error and the rotational motion;
for the mounting error, the angular velocity error generated by the mounting error after modulation according to the alternative modulation equation is
Figure BDA0002877423320000155
The corresponding angle error in one period is:
Figure BDA0002877423320000156
when the rotating shaft is superposed with the IMU body system, the single-shaft system can automatically compensate mu in 6 installation error anglesxy,μyx,μzy,μzxAnd μxz,μyzCannot be compensated;
in practical systems, the rotating shaft of the indexing mechanism is not coincident with the axis of the IMU coordinate system, and at the moment
Figure BDA0002877423320000161
It will become complicated, assuming that the deviation angles of the coordinate system defined by the rotating shaft of the indexing mechanism from the IMU coordinate system are α, β, θ, respectively, the actual rotation value when modulating according to the alternative modulation equation is:
Figure BDA0002877423320000162
under the assumption that alpha, beta and theta are small angles,
Figure BDA0002877423320000163
can be further simplified into:
Figure BDA0002877423320000164
the actual angle error caused by the mounting error is then:
Figure BDA0002877423320000165
as can be seen from the above equation, when the rotation axis of the indexing mechanism does not coincide with the axis of the IMU coordinate system, the mounting error cannot be modulated. Analysis shows that only orthogonal installation errors exist in the installation error array in the double-shaft rotating system, namely 6 installation error angles satisfy the following relation:
μyz＝μxz,μxy＝μzy,μzx＝μyz；
the second and third terms in the matrix are found to be zero and the dual axis rotation can modulate all three terms to zero. Thus, the dual axis rotation can modulate all orthogonality mounting errors, but not non-orthogonality mounting errors.
Referring to fig. 3, a fourth embodiment of the present invention is:
a modulation method of an optical fiber gyroscope rotational inertial navigation system is different from the other embodiments in that:
two rotation methods are designed: an initial alignment stage rotation method and a navigation stage rotation method; the two rotation methods have different purposes and different considered influence factors;
when the two axes are modulated, the two axes are operated alternately; the condition that the influence on the modulation effect is large is two conditions that the carrier has rolling motion and IMU modulates around an outer ring shaft (namely a rolling shaft) and the carrier has course change and IMU modulates around an inner ring shaft (namely an azimuth shaft);
the design of the rotation method in the initial alignment stage ensures that the alignment precision is effectively improved, and meanwhile, the error of the inertial element is estimated; the design of the navigation stage rotation method ensures that other errors can be modulated as much as possible on the basis of completely modulating all constant errors of the inertial element;
through reasonable biaxial rotation, main error items of an inertial element can be modulated into a sine and cosine form, and an accumulated error angle of a mathematical platform caused by errors of the inertial element can also be modulated into 0 in a rotation period; however, if it is determined whether the influence of the inertial element error on the navigation is eliminated by modulation, and it is further determined whether the accumulated error angle and speed in one rotation period are symmetric about 0, according to the analysis results of the first and second embodiments, the design principle of the optimal modulation method for biaxial rotation is as follows:
1) rotating around two axes alternately, wherein the rotation around each axis has positive and negative properties and symmetry;
2) in each rotation period, the rotation speed of positive and negative rotation and the angular acceleration of braking and starting have an odd symmetry relation with time, and the stop position of each rotation is symmetrical with the rotating shaft;
3) the accumulated angle error or speed error caused by the error of the device in one rotation period is 0, and the average value is also 0;
the size of the stop time not only affects the length of one modulation period, but also relates to the time of transfer alignment;
if it is better to shorten the rotation period without considering the transmission criteria, not only the modulation effect on the constant error is good, but also the system error caused by the drift with a period larger than several times the rotation period or the drift linearly increasing with time can be averaged to a certain extent, for example, if the drift is assumed to be epsilon ═ epsilon0The law of + kt changes, and in a static state of the system, the mathematical platform error angle at a short time t is approximately as follows:
Δθ≈ε0t+kt2/2
if the IMU continuously rotates in a period T to modulate the drift error, the error angle of the mathematical platform after the whole rotation period is approximate to the following angle at the moment T:
Figure BDA0002877423320000171
comparing the above two formulas, the error angle of the mathematic platform in the rotation state is increased and independent of the constant component of the drift in a rotation period, and compared with the static state, the increase speed and the size are greatly reduced. The slower the change rate of the drift is, the shorter the rotation period is, and the better the modulation compensation effect on the error angle is;
in order to implement the optimal rotation method for determining the navigation phase, the influence of the carrier motion on the rotation modulation effect needs to be obtained, and specifically, S2 is specifically: acquiring a first influence model of carrier roll angular motion on a rotation modulation effect, a second influence model of carrier pitch angular motion on the rotation modulation effect and a third influence model of carrier course angular motion on the rotation modulation effect:
wherein when the angular velocity of the modulation rotation is close to the same time as the angular velocity of the carrier motion, the direction is consistent, which causes the direct current component of the gyroscope scale factor to appear in the equivalent gyroscope drift. The component is coupled with the carrier motion angular velocity, so that the equivalent gyroscope drift is increased, and the system precision is reduced, so that the carrier attitude angular velocity is introduced into the control of the rotating mechanism, and the isolation of the carrier motion is realized while the rotation modulation is carried out; the course angular motion of the carrier is not periodic and can continuously and continuously yaw towards one direction, so that under a certain motion combination, the equivalent gyroscope scale factor caused by the course deflection angle is always increased, the system precision is reduced quickly along with the accumulation of time, and the situation is avoided; in the navigation stage, the attitude angular speed of the carrier is introduced into the control of the rotating mechanism, and the isolation of the motion of the carrier is realized while the rotation modulation is carried out. According to the characteristics of sea conditions, only course angular motion is isolated. During isolation, besides the speed and the accumulated time of course change need to be judged, whether course angle is isolated or not is determined, and judgment of two conditions is needed: one is that when the isolation axis is consistent with the modulation axis, the modulation angle and the modulation angular velocity are calculated, and modulation and isolation are realized simultaneously; when the isolation shaft is inconsistent with the modulation shaft, the isolation shaft starts a stable loop to realize the tracking of the carrier course;
in this embodiment, the rotation modulation method includes an initial alignment phase rotation method and a navigation phase rotation method;
(1) IMU rotates around a traversing rocking shaft
Supposing that the carrier only makes sinusoidal angular motion around an axis oyb without any other motion, adjusting a mechanical zero position and an electrical appliance zero position at the moment, calibrating an IMU rolling misalignment angle and compensating an axis non-orthogonal angle in an equal way, so that an IMU coordinate system S system and a carrier coordinate system b system are superposed at the initial moment, supposing that the IMU is installed at the centroid of the carrier and has no lever arm error to be compensated, and the IMU rotates around a transverse rocking axis oyo of a system base coordinate system O system (an OZ is vertically installed on the bottom surface, an OY is parallel to a horizontal axis of a platform, and an OX axis is determined according to right-hand rules) according to a designed rotation modulation mode; defining a coordinate system b 'as a coordinate system after the carrier moves, and then the relationship between the b system and the b' system is shown in fig. 3;
according to the conversion relation between the carrier systems b and b ', a conversion matrix between b and b' can be obtained
Figure BDA0002877423320000191
Comprises the following steps:
Figure BDA0002877423320000192
where α ═ ω yt, ω y is the angular velocity of the carrier rotation about axis oyb;
when the IMU is rotated around axis oyb, the transformation matrix between the b' system to the S system is:
Figure BDA0002877423320000193
where β ═ λ yt, λ y is the angular velocity of the carrier rotating around axis oyb, and its value is determined by the rotation modulation method (the rotation modulation method includes the rotation order, rotation angle, rotation angular velocity and stop time of the rotating shaft);
when the carrier rotates only about axis oyb, the angular velocity of the carrier relative to the inertial system
Figure BDA0002877423320000194
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000195
the angular velocity of the carrier relative to the inertial system when the carrier is stationary,
Figure BDA0002877423320000196
the gyroscope measurements in the IMU are
Figure BDA0002877423320000197
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000198
projecting the measurement error of the gyroscope into a navigation coordinate system n from the s system, wherein the first projection expression is as follows:
Figure BDA0002877423320000199
wherein the content of the first and second substances,
Figure BDA00028774233200001910
the first item on the right side of the equation
Figure BDA00028774233200001911
For angular movement of carriers
Figure BDA00028774233200001912
Under the action of scale factor error and installation error, the equivalent gyroscope in the system b drifts; equal sign second item on right
Figure BDA00028774233200001913
As angular velocity of rotation
Figure BDA00028774233200001914
Under the action of scale factors and installation errors, the equivalent gyroscope in the system b drifts; third item on the right of equal sign
Figure BDA00028774233200001915
Equivalent gyroscope drift of the constant drift of the gyroscope under the b system; because the random walk is an unrelated random process, the variance of the random walk is still itself, so the rotation modulation has no modulation effect on the random walk of the gyroscope;
Figure BDA00028774233200001916
for constant values, it is not considered here. In order to simplify and highlight the influence of gyroscope scale factor errors on attitude angular velocity errors under the condition of carrier motion, neglecting installation error terms of the gyroscope components;
converting the matrix
Figure BDA00028774233200001917
And
Figure BDA00028774233200001918
substituting the first projection expression to obtain a first influence model:
Figure BDA0002877423320000201
Figure BDA0002877423320000202
Figure BDA0002877423320000203
Figure BDA0002877423320000204
from the above four equations, it can be known that when the IMU rotates around the roll axis and the carrier has roll angular motion, the scale factor error of the gyroscope on the y axis of the gyro assembly is directly coupled with the rotation angular velocity, so that the measurement error of the gyroscope is increased by two constant values Δ KGyωyAnd Δ KGyλyThe angular velocity error of the system is increased, and then the attitude error of the system is increased, and the equivalent gyro error is in direct proportion to the moment, the angular amplitude and the angular velocity of the roll angular motion of the carrier according to the first equation in the four equations;
(2) the IMU rotates around the steering shaft:
the assumption conditions are the same as those in (1) except that the IMU rotates around the zenith axis ozo in a rotation modulation manner, a coordinate system b' is defined as a coordinate system after the carrier moves, and the relationship between the carrier rotation and the IMU rotation is shown in fig. 4;
when the IMU is rotated about axis ozo, the transformation matrix between the b' system to the S system is
Figure BDA0002877423320000211
Where γ ═ λ zt, λ z is the angular velocity of the carrier rotating around the axis ozo, and its value is determined by the rotation modulation method (the rotation modulation method includes the index sequence, rotation angle, rotation angular velocity, and off-position time of the rotation shaft);
the measurements of the gyroscope in the IMU are:
Figure BDA0002877423320000212
will be provided with
Figure BDA0002877423320000213
The method of (1) and (2)
Figure BDA0002877423320000214
Substituting into the first projection expressionObtaining a first influence model:
Figure BDA0002877423320000215
Figure BDA0002877423320000216
Figure BDA0002877423320000217
Figure BDA0002877423320000218
according to the four equations, when the IMU rotates around the zenith axis and the carrier moves in a roll angle, errors of the z gyroscope and the x and y gyroscopes are coupled with each other, and scale factor errors of the three gyroscopes are excited; the roll angular motion is also introduced into the error of the equivalent gyroscope due to the scale factor error of the gyroscope, and the influence is influenced by the scale factor of the corresponding gyroscope and is also related to the moment, the amplitude and the angular velocity of the roll angular motion, meanwhile, the larger the angular velocity and the amplitude of the roll angular motion of the carrier are, the larger the error of the equivalent gyroscope is, and therefore, the poorer the rotation modulation effect is;
(3) IMU rotates around a traversing rocking shaft
If the carrier only makes a pitch angle motion around oxb, the angular velocity of the reciprocating motion is ω x, and a coordinate system b 'is defined as a coordinate system after the carrier moves, the relationship between the system b and the system b' is shown in fig. 5;
according to the conversion relation between the carrier systems b and b ″, a conversion matrix can be obtained
Figure BDA0002877423320000221
Is composed of
Figure BDA0002877423320000222
Where α ═ ω xt, ω x is the angular velocity of the carrier rotating about axis oxb;
when the IMU is rotated around the real oyb axis, the transformation matrix between the b "system to the S system is:
Figure BDA0002877423320000223
where β ═ λ yt, λ y is the angular velocity of the carrier rotation around axis oyb; also, its value is determined by the rotational modulation mode;
when the carrier is only rotating around the real-time oyb axis, there are
Figure BDA0002877423320000224
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000225
the angular velocity of the carrier relative to the inertial system when the carrier is stationary,
Figure BDA0002877423320000226
the measurement value of the gyro component in the IMU is
Figure BDA0002877423320000227
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000228
according to
Figure BDA0002877423320000229
And
Figure BDA00028774233200002210
projecting the measurement error of the gyroscope into a navigation coordinate system n from the s system, wherein the second projection expression is as follows:
Figure BDA00028774233200002211
wherein the content of the first and second substances,
Figure BDA00028774233200002212
in order to highlight the influence of the gyroscope scale factor error on the attitude angular speed error under the condition of carrier motion, neglecting the installation error term of the gyroscope assembly, the gyroscope assembly is to be used
Figure BDA00028774233200002213
And
Figure BDA00028774233200002214
substituting the second projection expression to obtain a second influence model:
Figure BDA0002877423320000231
Figure BDA0002877423320000232
Figure BDA0002877423320000233
Figure BDA0002877423320000234
from the above four equations, when the IMU rotates around the horizontal axis and the carrier has pitch angular motion, errors of the y gyroscope and the x, z gyroscopes are coupled to each other, and scale factor errors of all the gyroscopes are directly coupled to the rotation angular velocity, that is, the pitch angular velocity excites the scale factor errors of the x, z gyroscopes;
(4) the IMU rotates around the steering shaft:
similarly, a coordinate system b "is defined as a coordinate system after the carrier moves, and when the IMU rotates around the zenith axis, the relationship between the b system and the b" system and the rotation condition of each axis are shown in fig. 6;
when the carrier is only rotating around the real-time oxb axis, there are
Figure BDA0002877423320000235
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000236
the angular velocity of the carrier relative to the inertial system when the carrier is stationary,
Figure BDA0002877423320000237
the gyroscope measurements in the IMU are
Figure BDA0002877423320000238
In the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000239
by
Figure BDA0002877423320000241
And
Figure BDA0002877423320000242
the measurement error of the gyroscope can be projected into a navigation coordinate system n system from the S system, and the third projection expression is as follows:
Figure BDA0002877423320000243
in the formula (I), the compound is shown in the specification,
Figure BDA0002877423320000244
in (3) are
Figure BDA0002877423320000245
The method of (1) and (2)
Figure BDA0002877423320000246
Substituting a third projection expression to obtain a second influence model:
Figure BDA0002877423320000247
Figure BDA0002877423320000248
Figure BDA0002877423320000249
Figure BDA00028774233200002410
from the above four equations, when the IMU rotates around the zenith axis and the carrier has pitch angular motion, the errors of the x gyroscope and the y, z gyroscopes are coupled to each other, and the scale factor errors of all the gyroscopes are directly coupled to the rotation angular velocity, i.e. the pitch angular velocity excites the scale factor errors of the y, z gyroscopes;
(5) IMU modulation around the roll axis:
assuming that the carrier performs turning motion, the turning angular velocity is ω z, the sign is unchanged, the duration is t, the coordinate system after the carrier moves is a b' system, and the relationship between the coordinate systems is shown in fig. 7;
according to the transformation relation between coordinate systems, the transformation matrix between b system and b' system
Figure BDA0002877423320000251
Can be expressed as:
Figure BDA0002877423320000252
in the formula, α ═ ω zt, ω z is the angular speed of the carrier rotating around the ozb axis, and α is the carrier heading angle;
when the IMU is rotated around axis oyb ', the transformation matrix between the b' system to the S system is:
Figure BDA0002877423320000253
in the formula, β ═ λ yt, λ y is the angular velocity of the carrier rotating around the axis oyb', and its value is determined by the rotation modulation mode;
the compound of (5)
Figure BDA0002877423320000254
The method of (5) and
Figure BDA0002877423320000255
and substituting the first projection expression to obtain a third influence model, namely under the action of carrier course angular motion and rotation modulation angular speed, the equivalent gyroscope under the system b drifts:
Figure BDA0002877423320000256
Figure BDA0002877423320000257
Figure BDA0002877423320000261
Figure BDA0002877423320000262
as can be seen from the first equation of the above four equations, the equivalent gyroscope drift in the b system excited by the angular motion of the carrier relative to the inertial system is related to both the modulation angular velocity and the carrier angular velocity; according to a second equation, the equivalent drift of the x, y and z gyroscopes is related to the angular velocity of the carrier angular motion and the IMU rotation angular velocity during modulation, and meanwhile, the error of the attitude angular velocity is in direct proportion to the angular velocity of the carrier course angular motion; according to a third equation, the modulation angular velocity influences the size of the attitude angle error under the action of equivalent scale factor errors of the x and y gyroscopes; according to the fourth equation, the constant drift of the gyroscope does not influence the attitude angular velocity error under the condition that the carrier has course angular motion and modulation motion; in summary, since there is no dc component, the effect of the course angular motion of the carrier on the modulation effect is not too great under such combined motion;
(6) IMU modulation around the zenith axis
When the carrier only has the change of the heading angle and the IMU rotates around the steering shaft, the change of the coordinate system b is shown in FIG. 8;
the transformation matrix between b and S is:
Figure BDA0002877423320000263
the compound of (5)
Figure BDA0002877423320000264
The ones in (6) and
Figure BDA0002877423320000265
substituting the first projection expression to obtain a third influence model, namely equivalent gyroscope drift under the b system:
Figure BDA0002877423320000271
Figure BDA0002877423320000272
Figure BDA0002877423320000273
Figure BDA0002877423320000274
from the first of the four equations above, the errors of the z-gyroscope and the x, y-gyroscope couple with each other due to the heading angular motion, while the heading angular velocity excites the scale factor error of the x, y-gyroscope. The direct current component becomes an unmodulatable component and becomes equivalent constant gyro drift; as can be known from the second equation, due to the course angular motion, the scale factor error of the z-direction gyroscope is directly coupled with the course angular velocity of the carrier, so that the equivalent gyroscope error under the b system is increased and is in direct proportion to the course angular velocity; as can be seen from the third equation, when the carrier moves with a heading and the IMU rotates around the zenith axis, the scale factor error of the z-direction gyroscope and the modulation angular velocity are directly coupled, so that the modulation angular velocity of the IMU increases the equivalent gyroscope error, and the equivalent gyroscope drift will increase accordingly; as can be seen from the fourth equation, the constant drift of the gyroscope does not affect the attitude angular velocity error under the condition that the carrier has course angular motion and modulation motion. Meanwhile, the constant drift of the z-direction gyroscope is not modulated;
combining the above (1) to (6), the effect of the carrier motion on the modulation effect is obtained, and in particular, see table 1, the two axes are alternately operated during modulation. The analysis shows that the condition with large influence on the modulation effect is two conditions that the carrier has rolling motion and IMU modulates around an outer ring shaft (namely a rolling shaft) and the carrier has course change and IMU modulates around an inner ring shaft (namely an azimuth shaft). As for the marine environment, the rolling motion is periodic swing which is symmetrical relative to a keel of the ship, the influence is small, and the worst condition is the condition that the carrier has course motion and needs to be isolated;
isolating the carrier attitude according to the first influence model, the second influence model and the third influence model;
in an alternative embodiment, the carrier attitude angular velocity is introduced into the control of the rotating mechanism during the navigation phase, and the rotation modulation is carried outMeanwhile, the motion of the carrier is isolated; the flow chart of the key signals is shown in FIG. 11, in which the key signals are
Figure BDA0002877423320000282
The signal will participate in the calculation of the rotation control angle of the indexing mechanism;
when the isolation axis is consistent with the modulation axis, calculating a modulation angle and a modulation angular velocity, and realizing modulation and isolation at the same time; when the isolation axis is not consistent with the modulation axis, the isolation axis starts a stabilization loop to realize the tracking of the carrier course, and the flow chart is shown in fig. 12
TABLE 1
Figure BDA0002877423320000281
Figure BDA0002877423320000291
The fifth embodiment of the invention is as follows:
applying the modulation method of the optical fiber gyroscope inertial navigation system to an actual scene to obtain a modulation path: 1. the rotation method in the initial alignment stage comprises the following steps: adopts a double-shaft rotation 3-position alignment observable degree
Step 1: electrifying, self-checking, standing for 15 minutes, and finishing coarse alignment; step 2: rotating 180 degrees around the positive direction of the Z axis, and stopping for 30 minutes; step 3: rotating the X axis for 90 degrees in the opposite direction, stopping for 15 minutes, and finishing fine alignment; step 4: returning the original path, finishing the initial alignment, and switching to a navigation stage; 2. the navigation stage rotation method comprises the following steps: the rotation of the navigation stage adopts a 64-order biaxial indexing scheme, see table 2, the rotation angle change is shown in figure 10, the scheme is odd-symmetrical every 16 orders, even-symmetrical every 32 orders, odd-symmetrical all-period, the rotation angular velocity is 10 degrees/s, and the angular acceleration is 5 degrees/s2The rotation stop time is 5 s;
TABLE 2
Figure BDA0002877423320000292
Figure BDA0002877423320000301
Referring to fig. 2, a fourth embodiment of the present invention is:
a modulation terminal 1 of a fiber-optic gyroscope inertial navigation system comprises a processor 2, a memory 3 and a computer program stored on the memory 3 and capable of running on the processor 2, wherein the processor 2 implements the steps in the first embodiment when executing the computer program.
In summary, the present invention provides a modulation method and a terminal for an optical fiber gyroscope rotational inertial navigation system, wherein a first output error, a scale factor error, a mounting error and a constant drift amount of a gyroscope assembly are obtained, a second output error of an accelerometer is obtained, the values are respectively substituted into preset alternative modulation equations to obtain a first modulation result, the first modulation result is analyzed to obtain an influence of settings of different values on a modulation balance result of each error in a modulation period in a rotational modulation process, when the first modulation result satisfies a threshold value, that is, in a rotation period, an accumulated error angle and an accumulated error velocity are symmetric with respect to 0, the alternative modulation equation at the time is indicated to enable errors in a period to be balanced with each other, so that an error of a final output quantity is minimized, an output numerical value is maximized, the alternative modulation equation satisfying the condition is marked as a final modulation equation, and inertial navigation is performed according to the final modulation equation The double-shaft rotation modulation of the system can perform system modulation on the optical fiber gyroscope rotary inertial navigation system, and the modulation results of all errors are integrated instead of considering all errors separately, so that the measurement accuracy of the optical fiber gyroscope rotary inertial navigation system in the subsequent actual use scene is improved.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to the related technical fields, are included in the scope of the present invention.

Claims (10)

1. A modulation method of an optical fiber gyroscope rotational inertial navigation system is characterized by comprising the following steps:
s1, acquiring a first output error of a gyro assembly, a second output error of an accelerometer and a scale factor error of the gyro assembly;
s2, acquiring the carrier attitude of the carrier where the inertial navigation system is located;
s3, after isolating the carrier attitude, bringing the first output error, the second output error and the scale factor error into a preset alternative modulation equation to obtain a first modulation result;
and S4, if the first modulation result meets a preset threshold, marking the alternative modulation equation as a final modulation equation and modulating the inertial navigation system according to the final modulation equation.
2. The method for modulating an optical fiber gyroscope rotational inertial navigation system according to claim 1, wherein the S1 is specifically:
obtaining the first output error
Figure FDA0002877423310000011
Wherein S isgA scale factor error matrix representing the gyro component,
Figure FDA0002877423310000012
representing the mounting error matrix of the gyro-assembly, T representing the transpose of the matrix,
Figure FDA0002877423310000013
representing the output value, ε, of the gyro-assemblypRepresenting a zero bias value of the gyro component;
obtaining the second output error
Figure FDA0002877423310000014
Wherein S isaA scale factor error matrix representing the accelerometer,
Figure FDA0002877423310000015
a matrix of mounting errors of the accelerometer is represented,
Figure FDA0002877423310000016
is representative of the output value of the accelerometer,
Figure FDA0002877423310000017
representing the zero bias value of the accelerometer.
3. The method for modulating an optical fiber gyroscope rotational inertial navigation system according to claim 1, wherein the S1 is specifically:
acquiring the scale factor error, and obtaining an angular speed error according to the scale factor error;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error and the angle error into a preset alternative modulation equation to obtain a first modulation result.
4. The method for modulating an optical fiber gyroscope rotational inertial navigation system according to claim 1, wherein the S3 is preceded by:
acquiring a constant drift amount of the gyro component;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error, the scale factor error and the constant drift amount into a preset alternative modulation equation to obtain a first modulation result.
5. The modulation method of the fiber optic gyroscope inertial rotation system according to claim 1, wherein the alternative modulation equation in S3 is:
Figure FDA0002877423310000021
where γ (t) represents the rotation speed.
6. The method for modulating an optical fiber gyroscope rotational inertial navigation system according to claim 1, wherein the S4 includes:
and judging whether the accumulated error angle and the accumulated error speed in the first modulation result are symmetrical about 0 in one rotation period of the modulation equation, if so, the first modulation result meets a preset threshold value.
7. The modulation method of a fiber optic gyroscope rotational inertial navigation system according to claim 3, wherein the number of the gyroscope components in the S1 is three;
in the step S1, the obtaining the scale factor error and the obtaining the angular velocity error according to the scale factor error specifically include:
obtaining a scale factor error matrix:
Figure FDA0002877423310000022
wherein the content of the first and second substances,
Figure FDA0002877423310000023
representing a symmetry scale factor error of an ith said gyro assembly gyro,
Figure FDA0002877423310000024
representing an asymmetric scale factor error of the ith said gyro assembly;
the angle error
Figure FDA0002877423310000025
Wherein, ω is1、ω2And omega3Respectively representing input angular velocities sensed by the gyro components;
Figure FDA0002877423310000026
8. the method for modulating an optical fiber gyroscope inertial rotation system according to claim 4, wherein the constant drift amount
Figure FDA0002877423310000031
Wherein the content of the first and second substances,
Figure FDA0002877423310000032
representing the constant drift value of the gyroscope on the x-axis of the gyroscope assembly,
Figure FDA0002877423310000033
represents the constant drift value of the gyroscope on the y axis of the gyroscope component,
Figure FDA0002877423310000034
representing the constant drift value of the gyroscope on the z-axis of the gyroscope assembly.
9. The method for modulating an optical fiber gyroscope rotational inertial navigation system according to claim 1, wherein the S3 is preceded by: obtaining installation error
Figure FDA0002877423310000035
Figure FDA0002877423310000036
Wherein, muij(i ═ x, y, z; j ≠ x, y, z; i ≠ j) is the installation error angle of the gyro component on the ith coordinate axis;
the S3 specifically includes:
and after isolating the carrier attitude, bringing the first output error, the second output error, the scale factor error and the installation error into a preset alternative modulation equation to obtain a first modulation result.
10. A modulation terminal of an optical fiber gyroscope rotational inertial navigation system, comprising a memory, a processor and a computer program stored in the memory and operable on the processor, wherein the processor implements the modulation terminal of the optical fiber gyroscope rotational inertial navigation system according to any one of claims 1 to 9 when executing the computer program.
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