CN102692239B

CN102692239B - Fiber optic gyroscope eight-position calibration method based on rotating mechanism

Info

Publication number: CN102692239B
Application number: CN201210194566.3A
Authority: CN
Inventors: 孙伟; 徐爱功; 高扬; 杨琳
Original assignee: Liaoning Technical University
Current assignee: Liaoning Technical University
Priority date: 2012-06-14
Filing date: 2012-06-14
Publication date: 2015-03-04
Anticipated expiration: 2032-06-14
Also published as: CN102692239A

Abstract

The invention provides an eight-position calibration method of an optical fiber gyroscope based on a rotating mechanism. Fasten the fiber optic gyro assembly to the table of the indexing mechanism, and level the table and side of the indexing mechanism to ensure that the coordinate system of the gyroscope coincides with the coordinate system of the indexing mechanism; determine the initial position parameters of the carrier through GPS, and bind to the navigation computer; the strapdown inertial navigation system prepares for warm-up, collects the data output by the fiber optic gyroscope and the quartz accelerometer and processes the data; uses the sensitive gravitational acceleration component of the accelerometer to determine the horizontal attitude angle of the carrier; establishes the fiber optic gyroscope The simple error model of the gyroscope is used; the eight-position indexing scheme is designed by using the dual-axis indexing mechanism; the output data of the gyro assembly collected by the computer at each position is processed by Matlab software, and various error parameters of the gyro assembly are obtained. The invention utilizes the eight-position calibration method provided by the indexing mechanism to accurately calculate each error coefficient of the fiber optic gyroscope, and completes the short-time and high-precision calibration of the fiber optic gyroscope under the condition that the attitude of the carrier is unknown.

Description

An Eight-Position Calibration Method for Fiber Optic Gyroscope Based on Rotating Mechanism

(一)技术领域 (1) Technical field

本发明涉及的是一种测量方法，尤其涉及的是一种基于旋转机构的光纤陀螺八位置标定方法。The present invention relates to a measurement method, in particular to an eight-position calibration method of an optical fiber gyroscope based on a rotating mechanism.

(二)背景技术 (2) Background technology

捷联惯导系统标定主要是系统中的惯性仪表标定。光纤陀螺仪是捷联惯导系统中的主要惯性仪表，它是系统硬件中最关键的部件，陀螺仪敏感载体的姿态角速率，其性能直接关系到系统的一系列性能指标。惯性仪表的误差是影响惯性系统精度的主要因素。因此提高惯性仪表的精度是高精度的惯导系统产生的必要条件。目前，为了提高惯性仪表的精度，主要有硬件、软件两条途径，硬件方面一是对原有惯性仪表从物理结构及工艺上进行改进，二是研究开发新型的、性能更为优越的惯性仪表。软件方面是对惯性仪表进行测试，建立误差模型方程，通过误差补偿来提高仪表的实际使用精度。然而，单靠改进仪表的设计来提高惯性仪表的精度在加工、制造、装配及调试中遇到的困难越来越多，成本也越来越高。因此利用软件补偿来提高实际使用精度成为一条可行的途径。这样，惯性仪表和惯性系统的测试技术的重要日益突出，根据测试数据，通过误差补偿措施提高使用精度，这个过程也就是标定。The calibration of the strapdown inertial navigation system is mainly the calibration of the inertial instruments in the system. The fiber optic gyroscope is the main inertial instrument in the strapdown inertial navigation system. It is the most critical component in the system hardware. The attitude rate of the gyroscope sensitive carrier is directly related to a series of performance indicators of the system. The error of the inertial instrument is the main factor affecting the accuracy of the inertial system. Therefore, improving the precision of the inertial instrument is a necessary condition for the production of a high-precision inertial navigation system. At present, in order to improve the accuracy of inertial instruments, there are mainly two ways of hardware and software. In terms of hardware, one is to improve the physical structure and technology of the original inertial instruments, and the other is to research and develop new types of inertial instruments with better performance. . In terms of software, the inertial instrument is tested, the error model equation is established, and the actual use accuracy of the instrument is improved through error compensation. However, improving the precision of the inertial instrument by improving the design of the instrument alone encounters more and more difficulties in processing, manufacturing, assembling and debugging, and the cost is also increasing. Therefore, using software compensation to improve the actual use accuracy becomes a feasible way. In this way, the importance of the testing technology of inertial instruments and inertial systems has become increasingly prominent. According to the test data, the accuracy of use can be improved through error compensation measures. This process is also called calibration.

标定技术本质上是一种误差补偿技术。所谓误差补偿技术就是建立惯性元件的误差数学模型，通过一定的试验来确定模型系数，进而通过软件算法来消除误差。目前惯性元件的标定技术已经比较成熟，系统标定指从惯导系统精度出发，考虑到由惯性元件构成惯导系统时安装轴向不垂直以及载体运动环境的复杂恶劣性等因素的影响，建立惯性元件的误差数学模型，最后实现误差补偿的过程。系统级标定则利用陀螺仪和加速度计的输出进行导航解算，以导航误差作为观测量来标定系统的误差参数。Calibration technology is essentially an error compensation technology. The so-called error compensation technology is to establish the error mathematical model of inertial components, determine the model coefficients through certain experiments, and then eliminate the errors through software algorithms. At present, the calibration technology of inertial components is relatively mature. System calibration refers to starting from the accuracy of the inertial navigation system. Considering the influence of factors such as non-vertical installation axis and the complex and harsh environment of the carrier movement when the inertial components constitute the inertial navigation system, the inertial components are established. The error mathematical model of the component, and finally realize the process of error compensation. The system-level calibration uses the output of the gyroscope and accelerometer for navigation calculation, and uses the navigation error as an observation to calibrate the error parameters of the system.

标定技术又存在着多种分类方法。根据标定的场所不同可以分为内场标定和外场标定，这是标定的两个不同阶段，内场标定是外场标定的基础。根据标定的层次可以分为元件标定和系统标定。系统标定根据观测量的不同又可以分为分立标定法和系统级标定法。但是，随着光纤陀螺捷联惯导系统的发展，捷联惯导系统对光纤陀螺标定的要求越来越高，传统的标定方法引进了较大的转位机构速率误差和标定参数耦合误差，已不再满足高精度光纤陀螺组件标定的要求。There are many classification methods for calibration technology. According to different calibration places, it can be divided into infield calibration and outfield calibration. These are two different stages of calibration. Infield calibration is the basis of outfield calibration. According to the level of calibration, it can be divided into component calibration and system calibration. System calibration can be divided into discrete calibration method and system-level calibration method according to different observations. However, with the development of the fiber optic gyro strapdown inertial navigation system, the strapdown inertial navigation system has higher and higher requirements for the fiber optic gyroscope calibration. The traditional calibration method introduces a large indexing mechanism speed error and calibration parameter coupling error. The requirements for calibration of high-precision fiber optic gyroscope components are no longer met.

(三)发明内容 (3) Contents of the invention

本发明的技术解决问题是：克服现有技术的不足，提供一种基于旋转机构的光纤陀螺八位置标定方法。The technical problem of the present invention is: to overcome the deficiencies of the prior art, and to provide an eight-position calibration method of the fiber optic gyroscope based on a rotating mechanism.

本发明的技术解决方案为：一种基于旋转机构的光纤陀螺八位置标定方法，其特征在于实际工作环境中载体姿态信息未知，通过利用旋转机构设计八位置标定路径，分离光纤陀螺仪误差参数之间的耦合影响并激励出光纤陀螺组件误差模型的12个误差系数，以此实现对光纤陀螺误差参数的现场标定。其具体步骤如下：The technical solution of the present invention is: an eight-position calibration method for an optical fiber gyroscope based on a rotating mechanism, which is characterized in that the attitude information of the carrier in the actual working environment is unknown, and the eight-position calibration path is designed by using the rotating mechanism to separate the error parameters of the optical fiber gyroscope. The coupling between them affects and excites 12 error coefficients of the error model of the fiber optic gyroscope components, so as to realize the on-site calibration of the fiber optic gyroscope error parameters. The specific steps are as follows:

(1)将光纤陀螺组件紧固于双轴转位机构的台面，并对转位机构进行台面调平和侧面调平，保证陀螺仪坐标系与转位机构坐标系重合，实验开始前调整转位机构使其平行于当地水平面；(1) Fasten the fiber optic gyro assembly to the table of the biaxial indexing mechanism, and level the table and side of the indexing mechanism to ensure that the coordinate system of the gyroscope coincides with the coordinate system of the indexing mechanism, and adjust the indexing before the experiment starts mechanism so that it is parallel to the local water level;

(2)利用全球定位系统GPS确定载体的初始位置参数，将它们装订至导航计算机中；(2) Utilize the global positioning system GPS to determine the initial position parameters of the carrier, and bind them into the navigation computer;

(3)捷联惯导系统进行预热准备，采集光纤陀螺仪和石英加速度计输出的数据并对数据进行处理；(3) The strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and the quartz accelerometer are collected and processed;

(4)建立光纤陀螺仪简略误差模型；(4) Establish a simple error model of the fiber optic gyroscope;

光纤陀螺与机械陀螺不同，通过光的传输来敏感角速度的变化，不需要任何转动部件，是一种真正的全固态陀螺，其性能从理论上不受加速度的影响。因此，光纤陀螺的主要误差源包括标度因数误差、安装误差和零位误差，其误差模型为：Different from the mechanical gyroscope, the optical fiber gyroscope is sensitive to the change of angular velocity through the transmission of light, and does not need any rotating parts. It is a real all-solid-state gyroscope, and its performance is not affected by acceleration in theory. Therefore, the main error sources of the fiber optic gyroscope include scale factor error, installation error and zero position error, and its error model is:

$[\begin{matrix} {N N}_{gx gx} \\ {N N}_{gy gy} \\ {N N}_{gz gz} \end{matrix}] = = [\begin{matrix} {k k}_{x x} & {k k}_{xy xy} & {k k}_{xz xz} \\ {k k}_{yx yx} & {k k}_{y the y} & {k k}_{yz yz} \\ {k k}_{zx zx} & {k k}_{zy zy} & {k k}_{z z} \end{matrix}] [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}] + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

其中，ω_i(i＝x，y，z)分别为陀螺仪三个敏感轴的输入角速率，N_gi(i＝x，y，z)为光纤陀螺组件的输出，k_i(i＝x，y，z)为陀螺的标度因数，k_ij(i，j＝x，y，z且i≠j)为陀螺的安装误差，D_i(i＝x，y，z)分别为光纤陀螺仪的零位。Among them, ω _i (i=x, y, z) is the input angular rate of the three sensitive axes of the gyroscope, N _gi (i=x, y, z) is the output of the fiber optic gyroscope component, k _i (i=x , y, z) is the scaling factor of the gyroscope, k _ij (i, j=x, y, z and i≠j) is the installation error of the gyroscope, D _i (i=x, y, z) are the fiber optic gyroscope zero position of the meter.

(5)利用加速度计敏感的重力加速度分量确定出载体水平姿态角；(5) Utilize the gravitational acceleration component sensitive to the accelerometer to determine the horizontal attitude angle of the carrier;

当载体相对导航坐标系存在固定姿态角时，可建立载体坐标系与导航坐标系转换矩阵捷联矩阵中元素C_ij(i，j＝1，2，3)可表示为：When the carrier has a fixed attitude angle relative to the navigation coordinate system, the transformation matrix between the carrier coordinate system and the navigation coordinate system can be established The elements C _ij (i, j=1, 2, 3) in the strapdown matrix can be expressed as:

$\{\begin{matrix} {C C}_{1111} = = cos cos γ γ cos cos ψ ψ - - sin sin γ γ sin sin θ θ sin sin ψ ψ \\ {C C}_{1212} = = - - cos cos θ θ sin sin ψ ψ \\ {C C}_{1313} = = sin sin γ γ cos cos ψ ψ + + cos cos γ γ sin sin θ θ sin sin ψ ψ \\ {C C}_{21 twenty one} = = cos cos γ γ sin sin ψ ψ + + sin sin γ γ sin sin θ θ cos cos ψ ψ \\ {C C}_{22 twenty two} = = cos cos θ θ cos cos ψ ψ \\ {C C}_{23 twenty three} = = sin sin γ γ sin sin ψ ψ - - cos cos γ γ sin sin θ θ cos cos ψ ψ \\ {C C}_{3131} = = - - sin sin γ γ cos cos θ θ \\ {C C}_{3232} = = sin sin θ θ \\ {C C}_{3333} = = cos cos γ γ cos cos θ θ \end{matrix}$

其中，γ、θ、ψ分别为载体的三个姿态角。通过利用加速度计敏感的重力加速度分量可确定载体水平姿态角γ、θ，如下式。Among them, γ, θ, ψ are the three attitude angles of the carrier respectively. The horizontal attitude angles γ and θ of the carrier can be determined by using the gravitational acceleration component sensitive to the accelerometer, as shown in the following formula.

$\{\begin{matrix} γ γ = = {sin sin}^{- - 11} (({g g}_{x x} / / g g)) \\ θ θ = = {sin sin}^{- - 11} (({g g}_{y the y} / / g g)) \end{matrix}$

其中，g_x、g_y分别为水平方向上x、y陀螺仪敏感的重力加速度分量。结合式转换矩阵描述的载体姿态角与的函数关系可确定出转换矩阵中的元素C₃₁、C₃₂、C₃₃。Among them, g _x and g _y are the gravitational acceleration components sensitive to the x and y gyroscopes in the horizontal direction, respectively. The elements C ₃₁ , C ₃₂ , and C ₃₃ in the conversion matrix can be determined by the functional relationship between the carrier attitude angle and described by the combined conversion matrix.

(6)利用转位机构设计八位置转位方案；(6) Use the indexing mechanism to design the eight-position indexing scheme;

根据三轴光纤陀螺组件静态误差数学模型，设计八位置标定方案标定高精度光纤陀螺，按照本发明所设计的标定方案编定转位机构的转位程序，在工控机上设定转位机构控制程序，调用工控机转位机构程序实现对转位机构按如下具体转位方案进行控制：According to the static error mathematical model of the three-axis fiber optic gyroscope assembly, an eight-position calibration scheme is designed to calibrate the high-precision fiber optic gyroscope, and the indexing program of the indexing mechanism is compiled according to the calibration plan designed in the present invention, and the control program of the indexing mechanism is set on the industrial computer. , call the program of the indexing mechanism of the industrial computer to realize the control of the indexing mechanism according to the following specific indexing scheme:

初始时刻IMU坐标系与载体坐标系重合，即IMU处于位置1，然后绕z_b轴分别正向转位90°依次得到位置2、位置3、位置4；将位置1绕y_b轴正向转位180°得到位置5；在位置5的基础上绕z_b轴分别正向转位90°依次得到位置6、位置7、位置8(附图3)。At the initial moment, the IMU coordinate system coincides with the carrier coordinate system, that is, the IMU is at position 1, and then rotates positively by 90° around the z _b axis to obtain position 2, position 3, and position 4 in turn; rotate position 1 forward around the y _b axis position 180° to obtain position 5; on the basis of position 5, respectively positively rotate 90° around z _{and b} axes respectively to obtain position 6, position 7, and position 8 (accompanying drawing 3).

(7)利用Matlab软件对计算机采集的陀螺组件在各个位置上的输出数据进行处理，得到陀螺组件的各项误差参数；(7) Utilize Matlab software to process the output data of the gyro assembly collected by the computer at each position, and obtain each error parameter of the gyro assembly;

根据光纤陀螺误差模型及IMU相对载体固定的八个位置处陀螺仪输入输出，得到光纤陀螺仪在八个位置下的表达式：According to the error model of the fiber optic gyroscope and the input and output of the gyroscope at eight fixed positions of the IMU relative to the carrier, the expression of the fiber optic gyroscope at eight positions is obtained:

位置1：position 1:

$[\begin{matrix} {N N}_{gx gx 11} \\ {N N}_{gy gy 11} \\ {N N}_{gz gz 11} \end{matrix}] = = [\begin{matrix} {K K}_{gx gx} & {K K}_{gxz gxz} & {- - K K}_{gxy gxy} \\ - - {K K}_{gyz gyz} & {K K}_{gy gy} & {K K}_{gyx gyx} \\ {K K}_{gzy gzy} & {- - K K}_{gzx gzx} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置2：position 2:

$[\begin{matrix} {N N}_{gx gx 22} \\ {N N}_{gy gy 22} \\ {N N}_{gz gz 22} \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} & {K K}_{gx gx} & {- - K K}_{gxy gxy} \\ - - {K K}_{gy gy} & - - {K K}_{gyz gyz} & {K K}_{gyx gyx} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置3：position 3:

$[\begin{matrix} {N N}_{gx gx 33} \\ {N N}_{gy gy 33} \\ {N N}_{gz gz 33} \end{matrix}] = = [\begin{matrix} - - {K K}_{gx gx} & {- - K K}_{gxz gxz} & {- - K K}_{gxy gxy} \\ {K K}_{gyz gyz} & - - {K K}_{gy gy} & {K K}_{gyx gyx} \\ {- - K K}_{gzy gzy} & {K K}_{gzx gzx} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置4：position 4:

$[\begin{matrix} {N N}_{gx gx 44} \\ {N N}_{gy gy 44} \\ {N N}_{gz gz 44} \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} & {- - K K}_{gx gx} & {- - K K}_{gxy gxy} \\ {K K}_{gy gy} & {K K}_{gyz gyz} & {K K}_{gyx gyx} \\ - - {K K}_{gzx gzx} & {- - K K}_{gzy gzy} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置5：Position 5:

$[\begin{matrix} {N N}_{gx gx 55} \\ {N N}_{gy gy 55} \\ {N N}_{gz gz 55} \end{matrix}] = = [\begin{matrix} {- - K K}_{gx gx} & {K K}_{gxz gxz} & {K K}_{gxy gxy} \\ {K K}_{gyz gyz} & {K K}_{gy gy} & {- - K K}_{gyx gyx} \\ {- - K K}_{gzy gzy} & {- - K K}_{gzx gzx} & {- - K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置6：Position 6:

$[\begin{matrix} {N N}_{gx gx 66} \\ {N N}_{gy gy 66} \\ {N N}_{gz gz 66} \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} & {- - K K}_{gx gx} & {K K}_{gxy gxy} \\ - - {K K}_{gy gy} & {K K}_{gyz gyz} & - - {K K}_{gyx gyx} \\ {K K}_{gzx gzx} & {- - K K}_{gzy gzy} & {- - K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置7：Position 7:

$[\begin{matrix} {N N}_{gx gx 77} \\ {N N}_{gy gy 77} \\ {N N}_{gz gz 77} \end{matrix}] = = [\begin{matrix} {K K}_{gx gx} & {- - K K}_{gxz gxz} & {K K}_{gxy gxy} \\ - - {K K}_{gyz gyz} & {- - K K}_{gy gy} & - - {K K}_{gyx gyx} \\ {K K}_{gzy gzy} & {K K}_{gzx gzx} & - - {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

位置8：Position 8:

$[\begin{matrix} {N N}_{gx gx 88} \\ {N N}_{gy gy 88} \\ {N N}_{gz gz 88} \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} & {K K}_{gx gx} & {K K}_{gxy gxy} \\ {K K}_{gy gy} & - - {K K}_{gyz gyz} & - - {K K}_{gyx gyx} \\ - - {K K}_{gzx gzx} & {K K}_{gzy gzy} & - - {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}]$

其中，(N_gxi N_gyi N_gzi)^T(i＝1…8)表示光纤陀螺仪输出。地球自转角速度ω_ie北向分量ω_N＝ω_ieiecosL和天向分量ω_U＝ω_iesin L为定值，L表示当地纬度。Wherein, (N _gxi N _gyi N _gzi ) ^T (i=1...8) represents the output of the fiber optic gyroscope. The earth rotation angular velocity ω _ie northward component ω _N ＝ω _ie iecosL and the celestial component ω _U ＝ω _ie sin L are fixed values, and L represents the local latitude.

$ω ω = = [\begin{matrix} {C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u} \\ {C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u} \\ {C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u} \end{matrix}]$

将位置1的输出与位置3的输出相加得到部分陀螺误差表达式：Adding the output from position 1 to the output from position 3 yields a partial gyro error expression:

$\{\begin{matrix} {δN δN}_{gx gx 1313} = = {N N}_{gx gx 11} + + {N N}_{gx gx 33} = = - - 22 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δN}_{gy gy 1313} = = {N N}_{gy gy 11} + + {N N}_{gy gy 33} = = 22 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δN}_{gz gz 1313} = = {N N}_{gz gz 11} + + {N N}_{gz gz 33} = = 22 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix}$

同理可得位置5的输出与位置7的输出相加得到部分陀螺误差表达式：In the same way, the output of position 5 and the output of position 7 can be added to obtain a partial gyro error expression:

$\{\begin{matrix} {δN δN}_{gx gx 5757} = = {N N}_{gx gx 55} + + {N N}_{gx gx 77} = = 22 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δ N}_{gy gy 5757} = = {N N}_{gy gy 55} + + {N N}_{gy gy 77} = = - - 22 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 5757} = = {N N}_{gz gz 55} + + {N N}_{gz gz 77} = = - - 22 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix}$

位置2的输出与位置6的输出相加得到部分陀螺误差表达式：The output from position 2 is added to the output from position 6 to obtain a partial gyro error expression:

$\{\begin{matrix} {δN δ N}_{gx gx 2626} = = {N N}_{gx gx 22} + + {N N}_{gx gx 66} = = - - 22 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δ N}_{gy gy 2626} = = {N N}_{gy gy 22} + + {N N}_{gy gy 66} = = - - 22 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 2626} = = {N N}_{gz gz 22} + + {N N}_{gz gz 66} = = 22 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix}$

位置4的输出与位置8的输出相加得到部分陀螺误差表达式：The output of position 4 is added to the output of position 8 to obtain a partial gyro error expression:

$\{\begin{matrix} {δN δ N}_{gx gx 4848} = = {N N}_{gx gx 44} + + {N N}_{gx gx 88} = = 22 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δ N}_{gy gy 4848} = = {N N}_{gy gy 44} + + {N N}_{gy gy 88} = = 22 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δN}_{gz gz 4848} = = {N N}_{gz gz 44} + + {N N}_{gz gz 88} = = - - 22 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix}$

将位置1的输出与位置3的输出相加后的结果减去位置5的输出与位置7的输出相加后的结果：Add the output of position 1 and the output of position 3 minus the output of position 5 and the output of position 7:

$\{\begin{matrix} {δN δ N}_{gx gx 1313} + + {δN δ N}_{gx gx 5757} = = 44 {D D.}_{x x} \\ {δN δ N}_{gy gy 1313} + + {δN δN}_{gy gy 5757} = = 44 {D D.}_{y the y} \\ {δN δN}_{gz gz 1313} + + {δN δN}_{gz gz 5757} = = 44 {D D.}_{z z} \end{matrix}$

$\{\begin{matrix} {δN δ N}_{gx gx 1313} - - {δN δN}_{gx gx 5757} = = - - 44 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \\ {δN δ N}_{gy gy 1313} - - {δN δN}_{gy gy 5757} = = 44 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \\ {δN δ N}_{gz gz 1313} - - {δN δ N}_{gz gz 5757} = = 44 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \end{matrix}$

由于C₃₂ω_N+C₃₃ω_U为固定值，通过解算上述方程可以确定出陀螺仪中的误差参数：K_gxy、K_gyx、K_gz、D_z、D_y、D_z。同理分别将位置2的输出与位置6的输出相加后的结果减去位置4的输出与位置8的输出相加后的结果：Since C ₃₂ ω _N +C ₃₃ ω _U is a fixed value, the error parameters in the gyroscope can be determined by solving the above equation: K _gxy , K _gyx , K _gz , D _z , D _y , D _z . Similarly, the result of adding the output of position 2 and the output of position 6 is subtracted from the result of adding the output of position 4 and the output of position 8:

$\{\begin{matrix} {δN δN}_{gx gx 2626} - - {δN δN}_{gx gx 4848} = = - - 44 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gy gy 2626} - - {δN δ N}_{gy gy 4848} = = - - 44 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gz gz 2626} - - {δN δ N}_{gz gz 4848} = = 44 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \end{matrix}$

将上式与位置1和位置2处水平陀螺仪的输出方程建立方程组：Combine the above formula with the output equations of the horizontal gyroscope at position 1 and position 2 to establish a system of equations:

$\{\begin{matrix} {δN δ N}_{gx gx 2626} - - {δN δN}_{gx gx 4848} = = - - 44 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gy gy 2626} - - {δN δ N}_{gy gy 4848} = = - - 44 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gz gz 2626} - - {δN δ N}_{gz gz 4848} = = 44 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {N N}_{gx gx 11} = = {K K}_{gx gx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gxz gxz} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) - - {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gy gy 11} = = - - {K K}_{gyz gyz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gy gy} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) + + {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gx gx 22} = = - - {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gx gx} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) - - {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gy gy 22} = = - - {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) - - {K K}_{gyz gyz} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) + + {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \end{matrix}$

当载体相对导航坐标系存在固定角位置时，C₃₂ω_N+C₃₃ω_U为固定值。但矩阵中含有未知航向角ψ，因此在八位置标定过程中引入了新的未知参数ψ。由于陀螺仪模型中的部分误差参数K_gxy、K_gyx、K_gz、D_x、D_y、D_z已确定，且陀螺仪输出为已知量，载体姿态矩阵的元素C₁₂、C₁₃、C₂₂、C₂₃中均包含未知量ψ。因此，构建的7个方程中含有六个未知量，通过连立求解可确定陀螺仪模型中的误差参数：K_gx、K_gy、K_gxz、K_gzx、K_gyz、ψ。此时陀螺仪误差模型中的12个参数已经计算出11个，确定载体的三个姿态角后，可根据惯性测量单元所处第一位置时的方位陀螺仪输出方程求解误差量K_gzy：When the carrier has a fixed angular position relative to the navigation coordinate system, C ₃₂ ω _N +C ₃₃ ω _U is a fixed value. However, the matrix contains unknown heading angle ψ, so a new unknown parameter ψ is introduced in the eight-position calibration process. Since some of the error parameters K _gxy , K _gyx , K _gz , D _x , D _y , and D _z in the gyroscope model have been determined, and the output of the gyroscope is known, the elements of the carrier attitude matrix C ₁₂ , C ₁₃ , C ₂₂ and C ₂₃ both contain unknown quantity ψ. Therefore, the 7 equations constructed contain six unknown quantities, and the error parameters in the gyroscope model can be determined through simultaneous solution: K _gx , K _gy , K _gxz , K _gzx , K _gyz , ψ. At this time, 11 of the 12 parameters in the gyroscope error model have been calculated. After determining the three attitude angles of the carrier, the error amount K _gzy can be solved according to the azimuth gyroscope output equation when the inertial measurement unit is in the first position:

N_gz1＝K_gzy(C₁₂ω_N+C₁₃ω_U)-K_gzx(C₂₂ω_N+C₂₃ω_U)+K_gz(C₃₂ω_N+C₃₃ω_U)+D_z N _gz1 ＝K _gzy (C ₁₂ ω _N +C ₁₃ ω _U )-K _gzx (C ₂₂ ω _N +C ₂₃ ω _U )+K _gz (C ₃₂ ω _N +C ₃₃ ω _U )+D _z

至此，利用惯性测量单元的八位置转停方案实现对陀螺误差模型中12个参数的标定工作。So far, the 12 parameters in the gyro error model have been calibrated using the eight-position turn-stop scheme of the inertial measurement unit.

本发明与现有技术相比的优点在于：本发明打破了传统标定方案无法在系统实际工作环境下完成器件标定的状况，通过利用旋转捷联惯导系统中旋转机构可提供惯性测量单元相对载体准确角位置特性，利用双轴转位机构提供八位置标定方法可独立地求解出陀螺的各项误差系数和载体航向信息，因此避免了误差参数之间的耦合影响，同时又缩短了系统的标定时间。Compared with the prior art, the present invention has the advantages that: the present invention breaks the situation that the traditional calibration scheme cannot complete device calibration under the actual working environment of the system, and can provide the relative carrier of the inertial measurement unit by using the rotating mechanism in the rotary strapdown inertial navigation system. Accurate angular position characteristics, using the dual-axis indexing mechanism to provide eight-position calibration method can independently solve the error coefficients of the gyroscope and the carrier heading information, thus avoiding the coupling effect between error parameters and shortening the calibration of the system time.

对本发明有益的效果说明如下：The beneficial effects of the present invention are described as follows:

首先采用传统标定方法对光纤陀螺系统进行标定，通过角速率试验标定出角速度通道的标度因数和安装误差角，再通过位置试验标定出陀螺零位误差。然后，设定转台平面相对水平面存在任意初始姿态角，利用转动程序使转台只能围绕y、z轴方向进行转位运动，采用本发明提出的八位置高精度标定方法对光纤陀螺进行标定，其中每个固定位置停顿时间为15分钟。分别将不同标定方法得到的光纤陀螺仪误差系数代入姿态测量系统航行状态4.5小时的导航实验数据进行处理，得到不同标定方法对应的姿态误差，八位置标定方法得到的载体姿态信息与实验室传统标定方案得到的姿态信息基本一致。即使纵摇角误差相对较大，但也控制在0.1度范围之内。横摇角和航向角相差很小基本处于重合状态。(附图4)。First, the traditional calibration method is used to calibrate the fiber optic gyroscope system. The scaling factor of the angular velocity channel and the installation error angle are calibrated through the angular rate test, and then the zero position error of the gyro is calibrated through the position test. Then, set the turntable plane to have any initial attitude angle relative to the horizontal plane, use the rotation program to make the turntable only move around the y and z axis directions, and use the eight-position high-precision calibration method proposed by the present invention to calibrate the fiber optic gyroscope, wherein Each fixed position pause time is 15 minutes. The error coefficients of the fiber optic gyroscope obtained by different calibration methods were substituted into the navigation experiment data of the attitude measurement system for 4.5 hours in the navigation state for processing, and the attitude errors corresponding to different calibration methods were obtained. The attitude information obtained by the scheme is basically the same. Even if the pitch angle error is relatively large, it is controlled within 0.1 degrees. The difference between the roll angle and the heading angle is very small and basically coincident. (accompanying drawing 4).

(四)附图说明 (4) Description of drawings

图1为本发明的一种基于旋转机构的光纤陀螺八位置标定方法流程图；Fig. 1 is a kind of flow chart of eight-position calibration method of fiber optic gyroscope based on rotating mechanism of the present invention;

图2为本发明的标定用转位机构示意图；Fig. 2 is a schematic diagram of the indexing mechanism of the present invention;

图3为本发明的八位置标定路径；Fig. 3 is the eight-position calibration path of the present invention;

图4为本发明的标定结果导致的系统姿态对比曲线；Fig. 4 is the system attitude contrast curve that calibration result of the present invention causes;

(五)具体实施方式 (5) Specific implementation methods

下面结合附图对本发明的具体实施方式进行详细地描述：The specific embodiment of the present invention is described in detail below in conjunction with accompanying drawing:

$[\begin{matrix} {N N}_{gx gx} \\ {N N}_{gy gy} \\ {N N}_{gz gz} \end{matrix}] = = [\begin{matrix} {k k}_{x x} & {k k}_{xy xy} & {k k}_{xz xz} \\ {k k}_{yx yx} & {k k}_{y the y} & {k k}_{yz yz} \\ {k k}_{zx zx} & {k k}_{zy zy} & {k k}_{z z} \end{matrix}] [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}] + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((11))$

$\{\begin{matrix} {C C}_{1111} = = cos cos γ γ cos cos ψ ψ - - sin sin γ γ sin sin θ θ sin sin ψ ψ \\ {C C}_{1212} = = - - cos cos θ θ sin sin ψ ψ \\ {C C}_{1313} = = sin sin γ γ cos cos ψ ψ + + cos cos γ γ sin sin θ θ sin sin ψ ψ \\ {C C}_{21 twenty one} = = cos cos γ γ sin sin ψ ψ + + sin sin γ γ sin sin θ θ cos cos ψ ψ \\ {C C}_{22 twenty two} = = cos cos θ θ cos cos ψ ψ \\ {C C}_{23 twenty three} = = sin sin γ γ sin sin ψ ψ - - cos cos γ γ sin sin θ θ cos cos ψ ψ \\ {C C}_{3131} = = - - sin sin γ γ cos cos θ θ \\ {C C}_{3232} = = sin sin θ θ \\ {C C}_{3333} = = cos cos γ γ cos cos θ θ \end{matrix} - - - - - - ((22))$

$\{\begin{matrix} γ γ = = {sin sin}^{- - 11} (({g g}_{x x} / / g g)) \\ θ θ = = {sin sin}^{- - 11} (({g g}_{y the y} / / g g)) \end{matrix} - - - - - - ((33))$

位置1：position 1:

$[\begin{matrix} {N N}_{gx gx 11} \\ {N N}_{gy gy 11} \\ {N N}_{gz gz 11} \end{matrix}] = = [\begin{matrix} {K K}_{gx gx} & {K K}_{gxz gxz} & {- - K K}_{gxy gxy} \\ - - {K K}_{gyz gyz} & {K K}_{gy gy} & {K K}_{gyx gyx} \\ {K K}_{gzy gzy} & {- - K K}_{gzx gzx} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((44))$

位置2：position 2:

$[\begin{matrix} {N N}_{gx gx 22} \\ {N N}_{gy gy 22} \\ {N N}_{gz gz 22} \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} & {K K}_{gx gx} & {- - K K}_{gxy gxy} \\ - - {K K}_{gy gy} & - - {K K}_{gyz gyz} & {K K}_{gyx gyx} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((55))$

位置3：position 3:

$[\begin{matrix} {N N}_{gx gx 33} \\ {N N}_{gy gy 33} \\ {N N}_{gz gz 33} \end{matrix}] = = [\begin{matrix} - - {K K}_{gx gx} & {- - K K}_{gxz gxz} & {- - K K}_{gxy gxy} \\ {K K}_{gyz gyz} & - - {K K}_{gy gy} & {K K}_{gyx gyx} \\ {- - K K}_{gzy gzy} & {K K}_{gzx gzx} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((66))$

位置4：position 4:

$[\begin{matrix} {N N}_{gx gx 44} \\ {N N}_{gy gy 44} \\ {N N}_{gz gz 44} \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} & {- - K K}_{gx gx} & {- - K K}_{gxy gxy} \\ {K K}_{gy gy} & {K K}_{gyz gyz} & {K K}_{gyx gyx} \\ - - {K K}_{gzx gzx} & {- - K K}_{gzy gzy} & {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((77))$

位置5：Position 5:

$[\begin{matrix} {N N}_{gx gx 55} \\ {N N}_{gy gy 55} \\ {N N}_{gz gz 55} \end{matrix}] = = [\begin{matrix} {- - K K}_{gx gx} & {K K}_{gxz gxz} & {K K}_{gxy gxy} \\ {K K}_{gyz gyz} & {K K}_{gy gy} & {- - K K}_{gyx gyx} \\ {- - K K}_{gzy gzy} & {- - K K}_{gzx gzx} & {- - K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((88))$

位置6：Position 6:

$[\begin{matrix} {N N}_{gx gx 66} \\ {N N}_{gy gy 66} \\ {N N}_{gz gz 66} \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} & {- - K K}_{gx gx} & {K K}_{gxy gxy} \\ - - {K K}_{gy gy} & {K K}_{gyz gyz} & - - {K K}_{gyx gyx} \\ {K K}_{gzx gzx} & {- - K K}_{gzy gzy} & {- - K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((99))$

位置7：Position 7:

$[\begin{matrix} {N N}_{gx gx 77} \\ {N N}_{gy gy 77} \\ {N N}_{gz gz 77} \end{matrix}] = = [\begin{matrix} {K K}_{gx gx} & {- - K K}_{gxz gxz} & {K K}_{gxy gxy} \\ - - {K K}_{gyz gyz} & {- - K K}_{gy gy} & - - {K K}_{gyx gyx} \\ {K K}_{gzy gzy} & {K K}_{gzx gzx} & - - {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((1010))$

位置8：Position 8:

$[\begin{matrix} {N N}_{gx gx 88} \\ {N N}_{gy gy 88} \\ {N N}_{gz gz 88} \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} & {K K}_{gx gx} & {K K}_{gxy gxy} \\ {K K}_{gy gy} & - - {K K}_{gyz gyz} & - - {K K}_{gyx gyx} \\ - - {K K}_{gzx gzx} & {K K}_{gzy gzy} & - - {K K}_{gz gz} \end{matrix}] ω ω + + [\begin{matrix} {D D.}_{x x} \\ {D D.}_{y the y} \\ {D D.}_{z z} \end{matrix}] - - - - - - ((1111))$

其中，(N_gxi N_gyi N_gzi)^T(i＝1…8)表示光纤陀螺仪输出。地球自转角速度ω_ie北向分量ω_N＝ω_iecosL和天向分量ω_U＝ω_iesinL为定值，L表示当地纬度。Wherein, (N _gxi N _gyi N _gzi ) ^T (i=1...8) represents the output of the fiber optic gyroscope. The earth rotation angular velocity ω _ie northward component ω _N ＝ω _ie cosL and the celestial component ω _U ＝ω _ie sinL are fixed values, and L represents the local latitude.

$ω ω = = [\begin{matrix} {C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u} \\ {C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u} \\ {C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u} \end{matrix}] - - - - - - ((1212))$

$\{\begin{matrix} {δN δN}_{gx gx 1313} = = {N N}_{gx gx 11} + + {N N}_{gx gx 33} = = - - 22 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δN}_{gy gy 1313} = = {N N}_{gy gy 11} + + {N N}_{gy gy 33} = = 22 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 1313} = = {N N}_{gz gz 11} + + {N N}_{gz gz 33} = = 22 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix} - - - - - - ((1313))$

$\{\begin{matrix} {δN δ N}_{gx gx 5757} = = {N N}_{gx gx 55} + + {N N}_{gx gx 77} = = 22 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δ N}_{gy gy 5757} = = {N N}_{gy gy 55} + + {N N}_{gy gy 77} = = - - 22 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 5757} = = {N N}_{gz gz 55} + + {N N}_{gz gz 77} = = - - 22 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix} - - - - - - ((1414))$

$\{\begin{matrix} {δN δN}_{gx gx 2626} = = {N N}_{gx gx 22} + + {N N}_{gx gx 66} = = - - 22 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δN}_{gy gy 2626} = = {N N}_{gy gy 22} + + {N N}_{gy gy 66} = = - - 22 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 2626} = = {N N}_{gz gz 22} + + {N N}_{gz gz 66} = = 22 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix} - - - - - - ((1515))$

$\{\begin{matrix} {δN δN}_{gx gx 4848} = = {N N}_{gx gx 44} + + {N N}_{gx gx 88} = = 22 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {22 D D.}_{x x} \\ {δN δ N}_{gy gy 4848} = = {N N}_{gy gy 44} + + {N N}_{gy gy 88} = = 22 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{y the y} \\ {δN δ N}_{gz gz 4848} = = {N N}_{gz gz 44} + + {N N}_{gz gz 88} = = - - 22 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + 22 {D D.}_{z z} \end{matrix} - - - - - - ((1616))$

$\{\begin{matrix} {δN δ N}_{gx gx 1313} + + {δN δN}_{gx gx 5757} = = 44 {D D.}_{x x} \\ {δN δN}_{gy gy 1313} + + {δN δ N}_{gy gy 5757} = = 44 {D D.}_{y the y} \\ {δN δ N}_{gz gz 1313} + + {δN δN}_{gz gz 5757} = = 44 {D D.}_{z z} \end{matrix} - - - - - - ((1717))$

$\{\begin{matrix} {δN δ N}_{gx gx 1313} - - {δN δ N}_{gx gx 5757} = = - - 44 {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \\ {δN δN}_{gy gy 1313} - - {δN δN}_{gy gy 5757} = = 44 {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \\ {δN δN}_{gz gz 1313} - - {δN δN}_{gz gz 5757} = = 44 {K K}_{gz gz} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) \end{matrix} - - - - - - ((1818))$

由于C₃₂ω_N+C₃₃ω_U为固定值，通过解算上述方程可以确定出陀螺仪中的误差参数：K_gxy、K_gyx、K_gz、D_x、D_y、D_z。同理分别将位置2的输出与位置6的输出相加后的结果减去位置4的输出与位置8的输出相加后的结果：Since C ₃₂ ω _N +C ₃₃ ω _U is a fixed value, the error parameters in the gyroscope can be determined by solving the above equation: K _gxy , K _gyx , K _gz , D _x , D _y , D _z . Similarly, the result of adding the output of position 2 and the output of position 6 is subtracted from the result of adding the output of position 4 and the output of position 8:

$\{\begin{matrix} {δN δN}_{gx gx 2626} - - {δN δN}_{gx gx 4848} = = - - 44 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δN}_{gy gy 2626} - - {δN δ N}_{gy gy 4848} = = - - 44 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gz gz 2626} - - {δN δ N}_{gz gz 4848} = = 44 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \end{matrix} - - - - - - ((1919))$

$\{\begin{matrix} {δN δ N}_{gx gx 2626} - - {δN δ N}_{gx gx 4848} = = - - 44 {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gy gy 2626} - - {δN δ N}_{gy gy 4848} = = - - 44 {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {δN δ N}_{gz gz 2626} - - {δN δN}_{gz gz 4848} = = 44 {K K}_{gzx gzx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) \\ {N N}_{gx gx 11} = = {K K}_{gx gx} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gxz gxz} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) - - {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gy gy 11} = = - - {K K}_{gyz gyz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gy gy} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) + + {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gx gx 22} = = - - {K K}_{gxz gxz} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) + + {K K}_{gx gx} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) - - {K K}_{gxy gxy} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \\ {N N}_{gy gy 22} = = - - {K K}_{gy gy} (({C C}_{1212} {ω ω}_{N N} + + {C C}_{1313} {ω ω}_{U u})) - - {K K}_{gyz gyz} (({C C}_{22 twenty two} {ω ω}_{N N} + + {C C}_{23 twenty three} {ω ω}_{U u})) + + {K K}_{gyx gyx} (({C C}_{3232} {ω ω}_{N N} + + {C C}_{3333} {ω ω}_{U u})) + + {D D.}_{x x} \end{matrix} - - - - - - ((2020))$

N_gz1＝K_gzy(C₁₂ω_N+C₁₃ω_U)-K_gzx(C₂₂ω_N+C₂₃ω_U)+K_gz(C₃₂ω_N+C₃₃ω_U)+D_z (21)N _gz1 ＝K _gzy (C ₁₂ ω _N +C ₁₃ ω _U )-K _gzx (C ₂₂ ω _N +C ₂₃ ω _U )+K _gz (C ₃₂ ω _N +C ₃₃ ω _U )+D _z (21)

至此，利用惯性测量单元八位置转停方案实现对陀螺误差模型中12个参数的标定。So far, the 12 parameters in the gyro error model have been calibrated using the eight-position turn-stop scheme of the inertial measurement unit.

Claims

1., based on a fiber optic gyroscope eight-position calibration method for rotating mechanism, it is characterized in that comprising the following steps:

(1) optic fiber gyroscope component is anchored on the table top of twin shaft indexing mechanism, and table top leveling and side leveling are carried out to indexing mechanism, ensure that gyroscope coordinate system overlaps with indexing mechanism coordinate system, before experiment starts, adjustment indexing mechanism makes it be parallel to local level;

(2) initial position parameters of global position system GPS determination carrier is utilized, by their bookbindings in navigational computer;

(3) strapdown inertial navitation system (SINS) carries out preheating preparation, gathers the data of fibre optic gyroscope and quartz accelerometer output and processes data;

(4) fiber optic gyroscope brief error model is set up;

Optical fibre gyro is different from mechanical gyro, the change of sensitive angular is carried out by the transmission of light, without any need for rotatable parts, it is a kind of all solid state gyro really, its performance is not theoretically by the impact of acceleration, therefore, the main error source of optical fibre gyro comprises scale factor error, alignment error and the error of zero, and its error model is:

[\begin{matrix} N_{gx} \\ N_{gy} \\ N_{gz} \end{matrix}] = [\begin{matrix} k_{x} & k_{xy} & k_{xz} \\ k_{yx} & k_{y} & k_{yz} \\ k_{zx} & k_{zy} & k_{z} \end{matrix}] [\begin{matrix} ω_{x} \\ ω_{y} \\ ω_{z} \end{matrix}] + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Wherein, ω _i(i=x, y, z) is respectively the input angle speed of gyroscope three sensitive axes, N _githe output error that (i=x, y, z) is optic fiber gyroscope component, k _ithe scale factor error that (i=x, y, z) is gyro, k _ijthe alignment error that (i, j=x, y, z and i ≠ j) is gyro, D _i(i=x, y, z) is respectively the error of zero of fibre optic gyroscope;

(5) gravitational acceleration component of accelerometer sensitive is utilized to determine carrier levels attitude angle;

When carrier Relative Navigation coordinate system exists Fixed posture angle, carrier coordinate system and navigational coordinate system transition matrix can be set up , Elements C in strap-down matrix _ij(i, j=1,2,3) can be expressed as:

\{\begin{matrix} C_{11} = \cos γ \cos ψ - \sin γ \sin θ \sin ψ \\ C_{12} = - \cos θ \sin ψ \\ C_{13} = \sin γ \cos ψ + \cos γ \sin θ \sin ψ \\ C_{21} = \cos γ \sin ψ + \sin γ \sin θ \cos ψ \\ C_{22} = \cos θ \cos ψ \\ C_{23} = \sin γ \sin ψ - \cos γ \sin θ \cos ψ \\ C_{31} = - \sin γ \cos θ \\ C_{32} = \sin θ \\ C_{33} = \cos γ \cos θ \end{matrix}

Wherein, γ, θ, ψ are respectively three attitude angle of carrier, by utilizing the gravitational acceleration component of accelerometer sensitive can determine carrier levels attitude angle γ, θ, as shown in the formula:

\{\begin{matrix} γ = \sin^{- 1} (g_{x} / g) \\ θ = \sin^{- 1} (g_{y} / g) \end{matrix}

Wherein, g _x, g _ybe respectively the gravitational acceleration component of x, y gyroscope sensitivity in horizontal direction, in the attitude of carrier angle described in conjunction with transition matrix and matrix, the funtcional relationship of element can determine the Elements C in transition matrix ₃₁, C ₃₂, C ₃₃;

(6) indexing mechanism is utilized to design 8 positions transposition scheme;

According to three axis optical fibre gyro assembly static error mathematical model, design eight position measuring scheme demarcates high-precision optical fiber gyro, the transposition program of indexing mechanism is compiled and edited according to designed scaling scheme, industrial computer sets indexing mechanism control program, calls industrial computer indexing mechanism program and realize controlling by following concrete transposition scheme indexing mechanism:

Initial time IMU coordinate system overlaps with carrier coordinate system, and namely IMU is in position 1, then around z _baxle respectively forward transposition 90 ° obtains position 2, position 3, position 4 successively; By position 1 around y _baxle forward transposition 180 ° obtains position 5; Around z on the basis of position 5 _baxle respectively forward transposition 90 ° obtains position 6, position 7, position 8 successively;

(7) utilize Matlab software to process the output data of the gyrounit of computer acquisition on each position, obtain every error parameter of gyrounit;

According to eight position gyroscope input and output that optical fibre gyro error model and IMU opposite carrier are fixed, obtain the expression formula of fibre optic gyroscope under eight positions:

Position 1:

[\begin{matrix} N_{gx 1} \\ N_{gy 1} \\ N_{gz 1} \end{matrix}] = [\begin{matrix} K_{gx} & K_{gxz} & - K_{gxy} \\ - K_{gyz} & K_{gy} & K_{gyx} \\ K_{gzy} & - K_{gzx} & K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 2:

[\begin{matrix} N_{gx 2} \\ N_{gy 2} \\ N_{gz 2} \end{matrix}] = [\begin{matrix} - K_{gxz} & K_{gx} & - K_{gxy} \\ - K_{gy} & {- K}_{gyz} & K_{gyx} \\ K_{gzx} & - K_{gzy} & K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 3:

[\begin{matrix} N_{gx 3} \\ N_{gy 3} \\ N_{gz 3} \end{matrix}] = [\begin{matrix} - K_{gx} & - K_{gxz} & - K_{gxy} \\ K_{gyz} & - K_{gy} & K_{gyx} \\ - K_{gzy} & K_{gzx} & K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 4:

[\begin{matrix} N_{gx 4} \\ N_{gy 4} \\ N_{gz 4} \end{matrix}] = [\begin{matrix} K_{gxz} & - K_{gx} & - K_{gxy} \\ K_{gy} & K_{gyz} & K_{gyx} \\ - K_{gzx} & - K_{gzy} & K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 5:

[\begin{matrix} N_{gx 5} \\ N_{gy 5} \\ N_{gz 5} \end{matrix}] = [\begin{matrix} - K_{gx} & K_{gxz} & K_{gxy} \\ K_{gyz} & K_{gy} & - K_{gyx} \\ - K_{gzy} & - K_{gzx} & - K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 6:

[\begin{matrix} N_{gx 6} \\ N_{gy 6} \\ N_{gz 6} \end{matrix}] = [\begin{matrix} - K_{gxz} & - K_{gx} & K_{gxy} \\ - K_{gy} & K_{gyz} & - K_{gyx} \\ K_{gzx} & - K_{gzy} & - K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 7:

[\begin{matrix} N_{gx 7} \\ N_{gy 7} \\ N_{gz 7} \end{matrix}] = [\begin{matrix} K_{gx} & - K_{gxz} & K_{gxy} \\ - K_{gyz} & - K_{gy} & - K_{gyx} \\ K_{gzy} & K_{gzx} & - K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Position 8:

[\begin{matrix} N_{gx 8} \\ N_{gy 8} \\ N_{gz 8} \end{matrix}] = [\begin{matrix} K_{gxz} & K_{gx} & K_{gxy} \\ K_{gy} & - K_{gyz} & - K_{gyx} \\ - K_{gzx} & K_{gzy} & - K_{gz} \end{matrix}] ω + [\begin{matrix} D_{x} \\ D_{y} \\ D_{z} \end{matrix}]

Wherein, (N _gxin _gyin _gzi) ^t(i=1 ... 8) fibre optic gyroscope output error is represented, rotational-angular velocity of the earth ω _ienorth component ω _n=ω _iecosL and sky are to component ω _u=ω _iesinL is definite value, and L represents local latitude;

ω = [\begin{matrix} C_{12} ω_{N} + C_{13} ω_{U} \\ C_{22} ω_{N} + C_{23} ω_{U} \\ C_{32} ω_{N} + C_{33} ω_{U} \end{matrix}]

The output of position 1 is added with the output of position 3 and obtains part gyro error expression formula:

\{\begin{matrix} {δN}_{gx 13} = N_{gx 1} + N_{gx 3} = - 2 K_{gxy} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{x} \\ {δN}_{gy 13} = N_{gy 1} + N_{gy 3} = 2 K_{gyx} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{y} \\ {δN}_{gz 13} = N_{gz 1} + N_{gz 3} = 2 K_{gz} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{z} \end{matrix}

The output that in like manner can obtain position 5 is added with the output of position 7 and obtains part gyro error expression formula:

\{\begin{matrix} {δN}_{gx 57} = N_{gx 5} + N_{gx 7} = 2 K_{gxy} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{x} \\ {δN}_{gy 57} = N_{gy 5} + N_{gy 7} = - 2 K_{gyx} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{y} \\ {δN}_{gz 57} = N_{gz 5} + N_{gz 7} = - 2 K_{gz} (C_{32} ω_{N} + C_{33} ω_{U}) + 2 D_{z} \end{matrix}

The output of position 2 is added with the output of position 6 and obtains part gyro error expression formula:

\{\begin{matrix} {δN}_{gx 26} = N_{gx 2} + N_{gx 6} = - 2 K_{gxz} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{x} \\ {δN}_{gy 26} = N_{gy 2} + N_{gy 6} = - 2 K_{gy} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{y} \\ {δN}_{gz 26} = N_{gz 2} + N_{gz 6} = 2 K_{gzx} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{z} \end{matrix}

The output of position 4 is added with the output of position 8 and obtains part gyro error expression formula:

\{\begin{matrix} {δN}_{gx 48} = N_{gx 4} + N_{gx 8} = 2 K_{gxz} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{x} \\ {δN}_{gy 48} = N_{gy 4} + N_{gy 8} = 2 K_{gy} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{y} \\ {δN}_{gz 48} = N_{gz 4} + N_{gz 8} = - 2 K_{gzx} (C_{12} ω_{N} + C_{13} ω_{U}) + 2 D_{z} \end{matrix}

Result after results added after the output of position 1 being added with the output of position 3 and the output deducting position 5 are added with the output of position 7:

\{\begin{matrix} {δN}_{gx 13} + {δN}_{gx 57} = 4 D_{x} \\ {δN}_{gy 13} + {δN}_{gy 57} = 4 D_{y} \\ {δN}_{gz 13} + {δN}_{gz 57} = 4 D_{z} \end{matrix}

\{\begin{matrix} {δN}_{gx 13} - {δN}_{gx 57} = - 4 K_{gxy} (C_{32} ω_{N} + C_{33} ω_{U}) \\ {δN}_{gy 13} - {δN}_{gy 57} = 4 K_{gyx} (C_{32} ω_{N} + C_{33} ω_{U}) \\ {δN}_{gz 13} - {δN}_{gz 57} = 4 K_{gz} (C_{32} ω_{N} + C_{33} ω_{U}) \end{matrix}

Due to C ₃₂ω _n+ C ₃₃ω _ufor fixed value, error parameter in gyroscope can be determined by resolving above formula: K _gxy, K _gyx, K _gz, D _x, D _y, D _z; Result after the output that result after in like manner the output of position 2 being added with the output of position 6 respectively deducts position 4 is added with the output of position 8:

\{\begin{matrix} {δN}_{gx 26} - {δN}_{gx 48} = - 4 K_{gxz} (C_{12} ω_{N} + C_{13} ω_{U}) \\ {δN}_{gy 26} - {δN}_{gy 48} = - 4 K_{gy} (C_{12} ω_{N} + C_{13} ω_{U}) \\ {δN}_{gz 26} - {δN}_{gz 48} = 4 K_{gzx} (C_{12} ω_{N} + C_{13} ω_{U}) \end{matrix}

The output equation of above formula and position 1 and position 2 place horizontal gyro is set up system of equations:

\{\begin{matrix} {δN}_{gx 26} - {δN}_{gx 48} = - 4 K_{gxz} (C_{12} ω_{N} + C_{13} ω_{U}) \\ {δN}_{gy 26} - {δN}_{gy 48} = - 4 K_{gy} (C_{12} ω_{N} + C_{13} ω_{U}) \\ {δN}_{gz 26} - {δN}_{gz 48} = 4 K_{gzx} (C_{12} ω_{N} + C_{13} ω_{U}) \\ N_{gx 1} = K_{gx} (C_{12} ω_{N} + C_{13} ω_{U}) + K_{gxz} (C_{22} ω_{N} + C_{23} ω_{U}) - K_{gxy} (C_{32} ω_{N} + C_{33} ω_{U}) + D_{x} \\ N_{gy 1} = - K_{gyz} (C_{12} ω_{N} + C_{13} ω_{U}) + K_{gy} (C_{22} ω_{N} + C_{23} ω_{U}) + K_{gyx} (C_{32} ω_{N} + C_{33} ω_{U}) + D_{x} \\ N_{gx 2} = - K_{gxz} (C_{12} ω_{N} + C_{13} ω_{U}) + K_{gx} (C_{22} ω_{N} + C_{23} ω_{U}) - K_{gxy} (C_{32} ω_{N} + C_{33} ω_{U}) + D_{x} \\ N_{gy 2} = - K_{gy} (C_{12} ω_{N} + C_{13} ω_{U}) - K_{gyz} (C_{22} ω_{N} + C_{23} ω_{U}) + K_{gyx} (C_{32} ω_{N} + C_{33} ω_{U}) + D_{x} \end{matrix}

When there is fixed angular positions in carrier Relative Navigation coordinate system, C ₃₂ω _n+ C ₃₃ω _ufor fixed value, but containing unknown course angle ψ in matrix, therefore in eight position measuring process, introduce new unknown parameter ψ; Due to the fractional error parameter K in gyroscope model _gxy, K _gyx, K _gz, D _x, D _y, D _zdetermine, and gyroscope exports as known quantity, attitude of carrier entry of a matrix element C ₁₂, C ₁₃, C ₂₂, C ₂₃in all comprise unknown quantity ψ; Therefore, containing six unknown quantitys in 7 equations of structure, solve by connecting to stand the error parameter can determined in gyroscope model: K _gx, K _gy, K _gxz, K _gzx, K _gyz, and ψ; 12 parameters now in gyro error model have calculated 11, after determining three attitude angle of carrier, can solve error parameter K according to the azimuth gyroscope output equation residing for Inertial Measurement Unit during primary importance _gzy:

N _gz1＝K _gzy(C ₁₂ω _N+C ₁₃ω _U)-K _gzx(C ₂₂ω _N+C ₂₃ω _U)+K _gz(C ₃₂ω _N+C ₃₃ω _U)+D _z

So far, the staking-out work of 8 positions rotation-stop scheme realization to 12 parameters in gyroscope error model of Inertial Measurement Unit is utilized.