CN101514899B

CN101514899B - Error Suppression Method of Fiber Optic Gyro Strapdown Inertial Navigation System Based on Single-axis Rotation

Info

Publication number: CN101514899B
Application number: CN2009100717333A
Authority: CN
Inventors: 孙枫; 孙伟; 张鑫; 高伟; 奔粤阳; 柴永利; 王文静; 孙巧英; 李国强; 赵彦雷
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2009-04-08
Filing date: 2009-04-08
Publication date: 2010-12-01
Anticipated expiration: 2029-04-08
Also published as: CN101514899A

Abstract

The invention provides an error suppression method for a fiber optic gyroscope strapdown inertial navigation system based on single-axis rotation. Determine the initial position parameters of the carrier; collect the data output by the fiber optic gyroscope and the quartz accelerometer; determine the attitude information of the carrier and complete the system initial Alignment; the inertial measurement unit coordinate system rotates 45 degrees positively around the carrier coordinate system oy _b axis and determines the initial relative position between the two coordinate systems; the IMU rotates around the carrier coordinate system azimuth axis oz _b positively at an angular velocity s rotates continuously; convert the data generated by the fiber optic gyroscope and quartz accelerometer after the IMU rotates to the carrier coordinate system, and obtain the modulation form of the constant value deviation of the inertial device; use the output value ωi _b ^b of the fiber optic gyroscope to the strapdown matrix T _b ⁿ is updated; the speed and position of the carrier after the IMU rotation modulation are calculated; the present invention modulates the constant value deviation of the inertial device in the three-axis direction to improve the navigation and positioning accuracy.

Description

Error Suppression Method of Fiber Optic Gyro Strapdown Inertial Navigation System Based on Single-axis Rotation

(一)技术领域(1) Technical field

本发明涉及的是一种误差抑制方法，特别是涉及一种基于单轴旋转的光纤陀螺捷联惯性导航系统的误差抑制方法。The invention relates to an error suppression method, in particular to an error suppression method based on a fiber optic gyro strapdown inertial navigation system based on single-axis rotation.

(二)背景技术(2) Background technology

捷联惯性导航系统SINS是一种完全自主的导航系统，利用陀螺仪和加速度计测量载体相对惯性空间的线运动和角运动参数，在给定初始条件下，由计算机进行积分运算，连续、实时地提供位置、速度和姿态信息。由于SINS完全依靠自身的惯性元件，不依靠任何外界信息测量导航参数，因此，它具有隐蔽性好，Strapdown Inertial Navigation System SINS is a completely autonomous navigation system. It uses gyroscopes and accelerometers to measure the linear and angular motion parameters of the carrier relative to the inertial space. provide position, velocity and attitude information accurately. Since SINS completely relies on its own inertial components and does not rely on any external information to measure navigation parameters, it has good concealment and

不受气候条件限制，不受干扰等优点，是一种完全自主式、全天候的导航系统，已广泛应用于航空、航天、航海等领域。根据SINS的基本原理，SINS在导航过程中惯性器件常值偏差的存在是导致惯导系统导航精度难以提高的主要因素。如何有效限制惯性导航误差发散、提高惯性导航系统精度是惯性导航领域一项非常重要的课题。Not limited by weather conditions, free from interference and other advantages, it is a completely autonomous, all-weather navigation system, which has been widely used in aviation, aerospace, navigation and other fields. According to the basic principle of SINS, the existence of the constant value deviation of the inertial device in the navigation process of SINS is the main factor that makes it difficult to improve the navigation accuracy of the inertial navigation system. How to effectively limit the divergence of inertial navigation errors and improve the accuracy of inertial navigation systems is a very important topic in the field of inertial navigation.

为了提高捷联系统自身的精度，一方面可以提高惯性元件的精度，但是由于受加工技术水平的限制，无限制的提高元件的精度是很难实现的；另一方面就是采取捷联惯性导航系统的误差抑制技术，自动抵消惯性器件的误差对系统精度的影响。这样就可以应用现有精度的惯性元件构成较高精度的捷联惯性导航系统。In order to improve the accuracy of the strapdown system itself, on the one hand, the accuracy of the inertial components can be improved, but due to the limitation of the processing technology level, it is difficult to achieve unlimited improvement of the accuracy of the components; on the other hand, the strapdown inertial navigation system is adopted The advanced error suppression technology can automatically offset the influence of the error of the inertial device on the system accuracy. In this way, the existing high-precision inertial components can be used to form a higher-precision strapdown inertial navigation system.

惯导系统的误差抑制，不是依赖于外部辅助对误差状态进行估计，而是研究惯性导航误差在特定运动条件下的传播规律，并依据此规律限制误差发散，提高导航精度的方法。转动抑制是最典型的误差抑制方法：通过绕一个轴或多个轴转动惯性测量单元(IMU)，对导航误差进行调制，达到控制导航误差发散、提高导航精度的目的。The error suppression of the inertial navigation system does not rely on external assistance to estimate the error state, but to study the propagation law of inertial navigation errors under specific motion conditions, and based on this law to limit the error divergence and improve navigation accuracy. Rotation suppression is the most typical error suppression method: by rotating the inertial measurement unit (IMU) around one or more axes, the navigation error is modulated to control the divergence of navigation errors and improve navigation accuracy.

单轴旋转仅能补偿两个敏感轴方向上惯性器件的常值偏差；双轴旋转虽然可以补偿三个敏感轴方向上惯性器件的常值偏差，但是旋转机构的复杂化导致了系统的可靠性及导航解算效率的降低。因此，如何设计合理的单轴旋转补偿方式提高光纤惯导系统的导航精度有重要的意义。Single-axis rotation can only compensate for the constant value deviation of inertial devices in the directions of two sensitive axes; although dual-axis rotation can compensate for the constant value deviation of inertial devices in the directions of three sensitive axes, the complexity of the rotating mechanism leads to the reliability of the system And the reduction of navigation solution efficiency. Therefore, how to design a reasonable single-axis rotation compensation method to improve the navigation accuracy of the fiber optic inertial navigation system is of great significance.

(三)发明内容(3) Contents of the invention

本发明的目的在于提供一种将惯性测量单元绕载体方位轴连续旋转，既保证了三个敏感轴方向上惯性器件的常值偏差得以调制，又避免了双轴旋转所需的复杂的旋转机构及导航解算算法的基于单轴旋转的光纤陀螺捷联惯性导航系统误差抑制方法。The purpose of the present invention is to provide a continuous rotation of the inertial measurement unit around the azimuth axis of the carrier, which not only ensures that the constant value deviation of the inertial device in the direction of the three sensitive axes can be modulated, but also avoids the complicated rotation mechanism required for dual-axis rotation An error suppression method for fiber optic gyroscope strapdown inertial navigation system based on single-axis rotation and navigation solution algorithm.

本发明的技术解决方案为：一种捷联惯导系统的单轴旋转调制方法，其特征在于将惯性测量单元绕不与自身重合的载体方位轴连续转动，利用惯性测量单元连续转动过程中IMU坐标系与载体坐标系的相对位置关系，即可确定惯性器件常值偏差的抑制形式，其具体步骤如下：The technical solution of the present invention is: a single-axis rotation modulation method of a strapdown inertial navigation system, which is characterized in that the inertial measurement unit is continuously rotated around the carrier azimuth axis that does not coincide with itself, and the IMU is used during the continuous rotation of the inertial measurement unit. The relative position relationship between the coordinate system and the carrier coordinate system can determine the suppression form of the constant value deviation of the inertial device. The specific steps are as follows:

(1)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；(1) Utilize the global positioning system GPS to determine the initial position parameters of the carrier, and bind them into the navigation computer;

(2)光纤陀螺捷联惯性导航系统进行预热后采集光纤陀螺仪和石英加速度计输出的数据。其中，三个陀螺的常值漂移相等、三个加速度计零位偏差相等。根据加速度计的输出与重力加速度的关系以及陀螺仪输出与地球自转角速率的关系初步确定此时载体的姿态信息(纵摇角θ、横摇角γ和航向角ψ)完成系统的初始对准，建立惯导系统的初始捷联矩阵T_b ⁿ：(2) The fiber optic gyroscope strapdown inertial navigation system collects the output data of the fiber optic gyroscope and quartz accelerometer after warming up. Among them, the constant value drift of the three gyroscopes is equal, and the zero position deviation of the three accelerometers is equal. According to the relationship between the output of the accelerometer and the acceleration of gravity and the relationship between the output of the gyroscope and the angular rate of the earth's rotation, the attitude information of the carrier at this time (pitch angle θ, roll angle γ and heading angle ψ) is initially determined to complete the initial alignment of the system , to establish the initial strapdown matrix T _b ⁿ of the inertial navigation system:

${T T}_{b b}^{n no} = = [\begin{matrix} cos cos γ γ cos cos ψ ψ - - sin sin γ γ sin sin θ θ sin sin ψ ψ & - - cos cos θ θ sin sin ψ ψ & sin sin γ γ cos cos ψ ψ + + cos cos γ γ sin sin θ θ sin sin ψ ψ \\ cos cos γ γ cos cos ψ ψ + + sin sin γ γ sin sin θ θ sin sin ψ ψ & cos cos θ θ cos cos ψ ψ & sin sin γ γ sin sin ψ ψ - - cos cos γ γ sin sin θ θ cos cos ψ ψ \\ - - sin sin γ γ cos cos θ θ & sin sin θ θ & cos cos γ γ cos cos θ θ \end{matrix}]$

(3)惯性测量单元绕载体坐标系oy_b轴正向旋转45度(如附图2)，确定IMU坐标系与载体坐标系之间的初始相对位置：(3) The inertial measurement unit is rotated 45 degrees positively around the oy _b axis of the carrier coordinate system (as shown in Figure 2), and the initial relative position between the IMU coordinate system and the carrier coordinate system is determined:

载体坐标系与IMU坐标系具有同一坐标原点o，oy_s轴与oy_b轴相重合，ox_s轴、oz_s轴、ox_b轴和oz_b轴位于同一平面内，但oz_s轴与oz_b轴的夹角为45°，oz_s轴与ox_b轴的夹角为90°-45°＝45°。The carrier coordinate system and the IMU coordinate system have the same coordinate origin o, the oy _s axis coincides with the oy _b axis, and the ox _s axis, oz _s axis, ox _b axis and oz _b axis are located in the same plane, but the oz _s axis and oz _b The angle between the axes is 45°, and the angle between the oz _s axis and the ox _b axis is 90°-45°=45°.

(4)确定两坐标系相对初始位置关系后，惯性测量单元绕载体坐标系方位轴oz_b正向以角速度ω＝6°/s连续转动(如附图3)：(4) After determining the relative initial position relationship of the two coordinate systems, the inertial measurement unit rotates continuously at an angular velocity ω=6°/s around the azimuth axis oz _b of the carrier coordinate system (as shown in Figure 3):

IMU转动过程中，IMU坐标系到载体坐标系的转换矩阵为：During the rotation of the IMU, the transformation matrix from the IMU coordinate system to the carrier coordinate system is:

(5)将惯性测量单元旋转后光纤陀螺仪和石英加速度计生成的数据转换到载体坐标系下，得到惯性器件常值偏差的调制形式：(5) After the IMU rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted to the carrier coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained:

光纤陀螺仪和加速度计的输出值分别为ω_is ^s和f_is ^s：The output values of the fiber optic gyroscope and accelerometer are ω _is ^s and f _is ^s respectively:

${ω ω}_{is is}^{s the s} = = {(({T T}_{s the s}^{b b}))}^{T T} {ω ω}_{ibd ibd}^{b b} + + {[\begin{matrix} {ϵ ϵ}_{x x} & {ϵ ϵ}_{y the y} & {ϵ ϵ}_{z z} \end{matrix}]}^{T T} + + {ω ω}_{bs bs}^{s the s}$

${f f}_{is is}^{s the s} = = {(({T T}_{s the s}^{b b}))}^{T T} {f f}_{ibd ibd}^{b b} + + {[\begin{matrix} {&dtri; &dtri;}_{x x} & {&dtri; &dtri;}_{y the y} & {&dtri; &dtri;}_{z z} \end{matrix}]}^{T T} + + {f f}_{bs bs}^{s the s}$

其中， $ω_{bs}^{s} = - {(T_{s}^{b})}^{T} ω_{sb}^{b} = {[\begin{matrix} 0 & 0 & ω \end{matrix}]}^{T},$ (·)^T表示矩阵·的转秩，ω_ibd ^b、f_ibd ^b为载体运动的真实输出。ε_x、ε_y、ε_z为陀螺仪的漂移误差，

为加速度计零位误差。由于s系相对b系只有旋转运动，没有相对直线运动，所以

f_{bs}^{s} = 0,

故加速度计输出可表示为：

f_{is}^{s} = T_{b}^{s} f_{ibd}^{b} + {[\begin{matrix} {&dtri;}_{x} & {&dtri;}_{y} & {&dtri;}_{z} \end{matrix}]}^{T} .

in,

ω_{bs}^{the s} = - {(T_{the s}^{b})}^{T} ω_{sb}^{b} = {[\begin{matrix} 0 & 0 & ω \end{matrix}]}^{T},

(·) ^T represents the transformation rank of the matrix ·, ω _ibd ^b , f _ibd ^b are the real output of the carrier motion. ε _x , ε _y , ε _z are the drift errors of the gyroscope,

is the accelerometer zero error. Since the s system has only rotational motion relative to the b system, there is no relative linear motion, so

f_{bs}^{the s} = 0,

So the accelerometer output can be expressed as:

f_{is}^{the s} = T_{b}^{the s} f_{ibd}^{b} + {[\begin{matrix} {&dtri;}_{x} & {&dtri;}_{the y} & {&dtri;}_{z} \end{matrix}]}^{T} .

光纤陀螺仪和加速度计的输出从IMU坐标系到载体坐标系的变换可以表示为：The transformation of the output of the fiber optic gyroscope and accelerometer from the IMU coordinate system to the carrier coordinate system can be expressed as:

${ω ω}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {ω ω}_{is is}^{s the s} + + {ω ω}_{sb sb}^{b b},, {f f}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {f f}_{is is}^{s the s}$

惯性测量单元绕载体坐标系oy_b轴正向旋转45度，此时可以得到ε_zcos45°＝ε_xcos(90°-45°)、

载体坐标系oz_b轴方向上不受陀螺常值漂移和加速度计零位偏差的影响，此时载体相对惯性空间的运动角速度及载体相对惯性空间的线运动加速度在载体坐标系的投影分别如下：The inertial measurement unit rotates 45 degrees positively around the oy _b axis of the carrier coordinate system. At this time, ε _z cos45°=ε _x cos(90°-45°),

The direction of the oz _b- axis of the carrier coordinate system is not affected by the constant value drift of the gyroscope and the zero position deviation of the accelerometer. At this time, the projections of the angular velocity of the carrier relative to the inertial space and the linear motion acceleration of the carrier relative to the inertial space on the carrier coordinate system are as follows:

$\{\begin{matrix} {ω ω}_{ib ib}^{bx bx} = = {ω ω}_{ibd ibd}^{bx bx} + + \sqrt{22} / / 22 cos cos ωt ωt (({ϵ ϵ}_{x x} + + {ϵ ϵ}_{z z})) - - sin sin ωt ωt {ϵ ϵ}_{y the y} \\ {ω ω}_{ib ib}^{by by} = = {ω ω}_{ibd ibd}^{by by} + + \sqrt{22} / / 22 sin sin ωt ωt (({ϵ ϵ}_{x x} + + {ϵ ϵ}_{Z Z})) + + cos cos ωt ωt {ϵ ϵ}_{y the y} \\ {ω ω}_{ib ib}^{bz bz} = = {ω ω}_{ibd ibd}^{bz bz} \end{matrix}$

$\{\begin{matrix} {f f}_{ib ib}^{bx bx} = = {f f}_{ibd ibd}^{bx bx} + + \sqrt{22} / / 22 cos cos ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) - - sin sin ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{by by} = = {f f}_{ibd ibd}^{by by} + + \sqrt{22} / / 22 sin sin ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) + + cos cos ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{bz bz} = = {f f}_{ibd ibd}^{bz bz} \end{matrix}$

其中，ω_ib ^bx、ω_ib ^by、ω_ib ^bz分别为载体相对惯性空间的运动角速度在载体坐标系的ox_b轴、oy_b轴、oz_b轴上的分量；f_ib ^bx、f_ib ^by、f_ib ^bz分别为载体相对惯性空间的线加速度在载体坐标系的ox_b轴、oy_b轴、oz_b轴上的分量。Among them, ω _ib ^bx , ω _ib ^by , and ω _ib ^bz are the components of the angular velocity of the carrier relative to the inertial space on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system; f _ib ^bx , f _ib ^by , f _ib ^bz are the components of the linear acceleration of the carrier relative to the inertial space on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system.

至此，载体坐标系中方位轴上惯性器件的常值偏差得到抵消；水平方向上惯性器件的常值偏差被调制成周期变化的量，经过惯导系统中积分环节，该常值偏差对系统的作用为零。So far, the constant value deviation of the inertial device on the azimuth axis in the carrier coordinate system is offset; the constant value deviation of the inertial device in the horizontal direction is modulated into a periodical variable amount, and after the integration link in the inertial navigation system, the constant value deviation has a great influence on the system Effect is zero.

(6)将步骤(5)获得的载体系下光纤陀螺的输出值ω_ib ^b带入惯导系统中采用四元数法对捷联矩阵T_b ⁿ进行更新：(6) Bring the output value ω _ib ^b of the fiber optic gyroscope under the carrier system obtained in step (5) into the inertial navigation system and use the quaternion method to update the strapdown matrix T _b ⁿ :

${ω ω}_{nb nb}^{b b} = = {ω ω}_{ib ib}^{b b} - - {(({T T}_{b b}^{n no}))}^{T T} (({ω ω}_{ie ie}^{n no} + + {ω ω}_{en en}^{n no}))$

其中：ω_ie ⁿ为地球自转角速度在导航系下的分量；ω_en ⁿ为导航坐标系相对地球坐标系的运动角速度在导航系下的分量；ω_nb ^b为载体相对导航坐标系的运动角速度在载体坐标系上的分量。Among them: ω _ie ⁿ is the component of the angular velocity of the earth's rotation in the navigation system; ω _en ⁿ is the component of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation system; ω _nb ^b is the angular velocity of the carrier relative to the navigation coordinate system in Components in the vector coordinate system.

更新四元数和姿态矩阵：Update the quaternion and pose matrix:

设载体坐标系相对导航坐标系的转动四元数为：Let the rotation quaternion of the carrier coordinate system relative to the navigation coordinate system be:

Q＝q₀+q₁i_b+q₂j_b+q₃k_b Q＝q ₀ +q ₁ i _b +q ₂ j _b +q ₃ k _b

其中：i_b、j_b、k_b分别表示载体坐标系ox_b轴、oy_b轴、oz_b轴上的单位方向向量。Where: i _b , j _b , and k _b represent unit direction vectors on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system, respectively.

四元数的即时修正可以通过解四元数微分方程 $\overset{\cdot}{Q} = \frac{1}{2} Q ω_{nb}^{b}$ 来实现：On-the-fly corrections to quaternions can be achieved by solving quaternion differential equations $\overset{&Center Dot;}{Q} = \frac{1}{2} Q ω_{nb}^{b}$ to fulfill:

$[\begin{matrix} {\overset{\cdot \cdot}{q q}}_{00} \\ {\overset{\cdot &Center Dot;}{q q}}_{11} \\ {\overset{\cdot &Center Dot;}{q q}}_{22} \\ {\overset{\cdot \cdot}{q q}}_{33} \end{matrix}] = = \frac{11}{22} [\begin{matrix} 00 & - - {ω ω}_{nb nb}^{bx bx} & - - {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bz bz} \\ {ω ω}_{nb nb}^{} & 00 & {ω ω}_{nb nb}^{bz bz} & - - {ω ω}_{nb nb}^{by by} \\ {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{} & 00 & {ω ω}_{nb nb}^{bx bx} \\ {ω ω}_{nb nb}^{bz bz} & {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bx bx} & 00 \end{matrix}] [\begin{matrix} {q q}_{00} \\ {q q}_{11} \\ {q q}_{22} \\ {q q}_{33} \end{matrix}]$

其中：ω_nb ^bx、ω_nb ^by、ω_nb ^bz分别表示载体相对导航系的运动角速度在载体坐标系ox_b轴、oy_b轴、oz_b轴上的分量。Among them: ω _nb ^bx , ω _nb ^by , and ω _nb ^bz represent the components of the angular velocity of the carrier relative to the navigation system on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system, respectively.

姿态矩阵T_b ⁿ的更新过程为：The update process of attitude matrix T _b ⁿ is:

${T T}_{b b}^{n no} = = [\begin{matrix} {q q}_{00}^{22} + + {q q}_{11}^{22} - - {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{11} {q q}_{22} - - {q q}_{00} {q q}_{33})) & 22 (({q q}_{11} {q q}_{33} + + {q q}_{00} {q q}_{22})) \\ 22 (({q q}_{11} {q q}_{22} + + {q q}_{00} {q q}_{33})) & {q q}_{00}^{22} - - {q q}_{11}^{22} + + {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{22} {q q}_{33} - - {q q}_{00} {q q}_{11})) \\ 22 (({q q}_{11} {q q}_{33} - - {q q}_{00} {q q}_{22})) & 22 (({q q}_{22} {q q}_{33} + + {q q}_{00} {q q}_{11})) & {q q}_{00}^{22} - - {q q}_{11}^{22} - - {q q}_{22}^{22} + + {q q}_{33}^{22} \end{matrix}]$

(7)利用石英加速度计的输出值f_ib ^b和步骤(6)计算的姿态矩阵T_b ⁿ，计算出经过IMU旋转调制后载体的速度和位置。(7) Using the output value f _ib ^b of the quartz accelerometer and the attitude matrix T _b ⁿ calculated in step (6), calculate the velocity and position of the carrier after the IMU rotation modulation.

1)计算导航系下加速度：1) Calculate the acceleration under the navigation system:

$[\begin{matrix} {f f}^{nx nx} \\ {f f}^{ny no} \\ {f f}^{nz nz} \end{matrix}] = = {T T}_{b b}^{n no} [\begin{matrix} {f f}_{ib ib}^{bx bx} \\ {f f}_{ib ib}^{by by} \\ {f f}_{ib ib}^{bz bz} \end{matrix}]$

2)计算载体的水平速度和位置：2) Calculate the horizontal velocity and position of the carrier:

根据t₁时刻的载体东向水平速度V_x(t₁)和北向水平速度V_y(t₁)，求取t₁时刻载体水平速度的变化率为：According to the carrier’s eastward horizontal velocity V _x (t ₁ ) and northward horizontal velocity V _y (t ₁ ) at time t ₁ , the rate of change of carrier’s horizontal velocity at time t ₁ is calculated as:

$\{\begin{matrix} {\overset{\cdot &Center Dot;}{V V}}_{x x} (({t t}_{11})) = = {f f}^{nx nx} + + ((22 {ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{y the y} (({t t}_{11})) \\ {\overset{\cdot &Center Dot;}{V V}}_{y the y} (({t t}_{11})) = = {f f}^{ny no} - - ((22 {ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{x x} (({t t}_{11})) \end{matrix}$

在t₂时刻水平速度和载体位置分别为：The horizontal velocity and carrier position at time _t2 are respectively:

$\{\begin{matrix} {V V}_{x x} (({t t}_{22})) = = {V V}_{x x} (({t t}_{11})) + + {\overset{\cdot &Center Dot;}{V V}}_{x x} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \\ {V V}_{y the y} (({t t}_{22})) = = {V V}_{y the y} (({t t}_{11})) + + {\overset{\cdot &Center Dot;}{V V}}_{y the y} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \end{matrix}$

3)计算载体速度误差和位置误差：3) Calculate carrier velocity error and position error:

$\{\begin{matrix} Δ Δ {V V}_{x x} = = {V V}_{x x} (({t t}_{22})) - - {V V}_{x x 00} \\ Δ Δ {V V}_{y the y} = = {V V}_{y the y} (({t t}_{22})) - - {V V}_{y the y 00} \end{matrix}$

其中：V_x0、V_y0分别表示初始时刻载体的东向和北向速度；ΔV_x、ΔV_y分别表示载体东向、北向速度的变化量；

λ₀分别表示初始时刻载体所处位置的经度和纬度；

Δλ分别表示载体的纬度、经度的变化量；R_xp、R_yp分别表示地球子午圈、卯酉圈的曲率半径；t₁、t₂为惯导系统的解算过程中两个相邻的时间点。Among them: V _x0 and V _y0 represent the eastward and northward velocity of the carrier at the initial moment respectively; ΔV _x and ΔV _y represent the variation of the carrier’s eastward and northward velocity respectively;

λ ₀ represents the longitude and latitude of the carrier's position at the initial moment, respectively;

Δλ respectively represent the change of the latitude and longitude of the carrier; R _xp and R _yp represent the curvature radius of the earth's meridian circle and Maoyou circle respectively; t ₁ and t ₂ are two adjacent times in the solution process of the inertial navigation system point.

本发明与现有技术相比的优点在于：本发明打破了传统单轴旋转不能补偿三个方向上惯性器件常值偏差及双轴旋转所需的复杂旋转机构和导航解算算法的约束，提出一种旋转轴与陀螺敏感轴成一定角度的捷联惯导系统误差旋转调制方案，该方法可以将三轴方向上的惯性器件常值偏差进行调制，有效地提高导航定位精度。Compared with the prior art, the present invention has the advantages that: the present invention breaks the constraint that traditional single-axis rotation cannot compensate the constant value deviation of inertial devices in three directions and the complex rotation mechanism and navigation solution algorithm required by dual-axis rotation, and proposes A strapdown inertial navigation system error rotation modulation scheme in which the rotation axis and the gyro sensitive axis form a certain angle, the method can modulate the constant value deviation of the inertial device in the three-axis direction, and effectively improve the navigation positioning accuracy.

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

在Matlab仿真条件下，对该方法进行仿真实验：Under the condition of Matlab simulation, the simulation experiment of this method is carried out:

载体作三轴摇摆运动。载体以正弦规律绕纵摇轴、横摇轴和航向轴摇摆，其数学模型为：The carrier makes a three-axis rocking motion. The carrier swings around the pitch axis, roll axis and yaw axis in a sinusoidal law, and its mathematical model is:

$\{\begin{matrix} θ θ = = {θ θ}_{m m} sin sin (({ω ω}_{θ θ} + + {φ φ}_{θ θ})) \\ γ γ = = {γ γ}_{m m} sin sin (({ω ω}_{γ γ} + + {φ φ}_{γ γ})) \\ ψ ψ = = {ψ ψ}_{m m} sin sin (({ω ω}_{ψ ψ} + + {φ φ}_{ψ ψ})) + + k k \end{matrix}$

其中：θ、γ、ψ分别表示纵摇角、横摇角和航向角的摇摆角度变量；θ_m、γ_m、ψ_m分别表示相应的摇摆角度幅值；ω_θ、ω_γ、ω_ψ分别表示相应的摇摆角频率；φ_θ、φ_γ、φ_ψ分别表示相应的初始相位；ω_i＝2π/T_i，i＝θ、γ、ψ，T_i表示相应的摇摆周期，k为初始航向角。仿真时取：θ_m＝12°，γ_m＝15°，ψ_m＝10°，T_θ＝8s，T_γ＝10s，T_ψ＝6s，k＝0。Among them: θ, γ, ψ represent the roll angle variables of pitch angle, roll angle and heading angle respectively; _θ _m , _γ _m , _ψ _m represent the corresponding swing angle amplitudes; Indicates the corresponding swing angle frequency; φ _θ , φ _γ , φ _ψ respectively represent the corresponding initial phase; ω _i = 2π/T _i , i = θ, γ, ψ, T _i represents the corresponding swing period, and k is the initial heading horn. During simulation, take: θ _m =12°, γ _m =15°, ψ _m =10°, T _θ =8s, T _γ =10s, T _ψ =6s, k=0.

载体初始位置：北纬45.7796°，东经126.6705°；The initial position of the carrier: 45.7796° north latitude, 126.6705° east longitude;

初始姿态误差角：三个初始姿态误差角均为零；Initial attitude error angle: the three initial attitude error angles are all zero;

赤道半径：R_e＝6378393.0m；Equatorial radius: R _e = 6378393.0m;

椭球度：e＝3.367e-3；Ellipsoid: e=3.367e-3;

由万有引力可得的地球表面重力加速度：g₀＝9.78049；The gravitational acceleration on the earth's surface obtained from the universal gravitation: g ₀ =9.78049;

地球自转角速度(弧度/秒)：7.2921158e-5；Earth rotation angular velocity (rad/s): 7.2921158e-5;

陀螺仪常值漂移：0.01度/小时；Gyroscope constant value drift: 0.01 degrees/hour;

加速度计零偏：10^-4g₀；Accelerometer zero bias: 10 ^-4 g ₀ ;

常数：π＝3.1415926；Constant: π=3.1415926;

利用发明所述方法得到载体姿态角误差曲线、速度误差曲线和位置误差曲线分别如图4、图5、图6所示。结果表明有摇摆干扰条件下，采用本发明方法可以获得较高的定位精度。Using the method described in the invention to obtain carrier attitude angle error curves, velocity error curves and position error curves are shown in Fig. 4, Fig. 5 and Fig. 6 respectively. The results show that under the condition of sway interference, the method of the invention can obtain higher positioning accuracy.

(四)附图说明(4) Description of drawings

图1为本发明的基于IMU单轴旋转的捷联惯性导航系统误差抑制方法流程图；Fig. 1 is the flow chart of the error suppression method of the strapdown inertial navigation system based on IMU uniaxial rotation of the present invention;

图2为初始时刻IMU坐标系与载体坐标系的初始相对位置关系；Figure 2 shows the initial relative positional relationship between the IMU coordinate system and the carrier coordinate system at the initial moment;

图3为IMU转动过程中，IMU坐标系与载体坐标系的相对位置关系；Figure 3 shows the relative positional relationship between the IMU coordinate system and the carrier coordinate system during the rotation of the IMU;

图4为载体摇摆条件下，基于IMU静止时的载体姿态角误差实验曲线；Figure 4 is the experimental curve of the carrier attitude angle error based on the static IMU under the carrier swing condition;

图5为载体摇摆条件下，基于IMU静止时的载体速度误差实验曲线；Figure 5 is the experimental curve of the carrier speed error based on the static IMU under the carrier swing condition;

图6为载体摇摆条件下，基于IMU静止时的载体位置误差实验曲线。Fig. 6 is the experimental curve of the carrier position error based on the static state of the IMU under the carrier swing condition.

图7为载体摇摆条件下，本发明的基于IMU单轴连续旋转的载体姿态角误差实验曲线；Fig. 7 is the experimental curve of the attitude angle error of the carrier based on the single-axis continuous rotation of the IMU under the condition of the carrier swing;

图8为载体摇摆条件下，本发明的基于IMU单轴连续旋转的载体速度误差实验曲线；Fig. 8 is the experimental curve of the carrier speed error based on the IMU single-axis continuous rotation of the present invention under the carrier swing condition;

图9为载体摇摆条件下，本发明的基于IMU单轴连续旋转的载体位置误差实验曲线。FIG. 9 is an experimental curve of the position error of the carrier based on the single-axis continuous rotation of the IMU under the condition of the carrier swinging.

(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:

(1)利用全球定位系统GPS确定载体的初始位置参数(包括经度、纬度)，将它们装订至导航计算机中。(1) Use the global positioning system (GPS) to determine the initial position parameters (including longitude and latitude) of the carrier, and bind them to the navigation computer.

${T T}_{b b}^{n no} = = [\begin{matrix} cos cos γ γ cos cos ψ ψ - - sin sin γ γ sin sin θ θ sin sin ψ ψ & - - cos cos θ θ sin sin ψ ψ & sin sin γ γ cos cos ψ ψ + + cos cos γ γ sin sin θ θ sin sin ψ ψ \\ cos cos γ γ cos cos ψ ψ + + sin sin γ γ sin sin θ θ sin sin ψ ψ & cos cos θ θ cos cos ψ ψ & sin sin γ γ sin sin ψ ψ - - cos cos γ γ sin sin θ θ cos cos ψ ψ \\ - - sin sin γ γ cos cos θ θ & sin sin θ θ & cos cos γ γ cos cos θ θ \end{matrix}] - - - - - - ((11))$

(5)将惯性测量单元旋转后光纤陀螺仪和石英加速度计生成的数据转换到载体坐标系下，得到惯性器件常值偏差的调制形式：(5) After the inertial measurement unit rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted to the carrier coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained:

${f f}_{is is}^{s the s} = = {(({T T}_{s the s}^{b b}))}^{T T} {f f}_{ibd ibd}^{b b} + + {[\begin{matrix} {&dtri; &dtri;}_{x x} & {&dtri; &dtri;}_{y the y} & {&dtri; &dtri;}_{z z} \end{matrix}]}^{T T} + + {f f}_{bs bs}^{s the s} - - - - - - ((33))$

f_{bs}^{s} = 0,

故加速度计输出可表示为：

f_{is}^{s} = T_{b}^{s} f_{ibd}^{b} + {[\begin{matrix} {&dtri;}_{x} & {&dtri;}_{y} & {&dtri;}_{z} \end{matrix}]}^{T} .

in,

ω_{bs}^{the s} = - {(T_{the s}^{b})}^{T} ω_{sb}^{b} = {[\begin{matrix} 0 & 0 & ω \end{matrix}]}^{T},

f_{bs}^{the s} = 0,

So the accelerometer output can be expressed as:

f_{is}^{the s} = T_{b}^{the s} f_{ibd}^{b} + {[\begin{matrix} {&dtri;}_{x} & {&dtri;}_{the y} & {&dtri;}_{z} \end{matrix}]}^{T} .

${ω ω}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {ω ω}_{is is}^{s the s} + + {ω ω}_{sb sb}^{b b},, {f f}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {f f}_{is is}^{s the s} - - - - - - ((44))$

惯性测量单元绕载体坐标系oy_b轴正向旋转45度，三个陀螺的常值漂移相等，三个加速度计零位偏差相等，此时可以得到ε_zcos 45°＝ε_xcos(90°-45°)、

载体坐标系oz_b轴方向上不受陀螺常值漂移和加速The inertial measurement unit rotates 45 degrees positively around the oy _b axis of the carrier coordinate system, the constant drift of the three gyroscopes is equal, and the zero position deviation of the three accelerometers is equal. At this time, ε _z cos 45° = ε _x cos(90° -45°),

The carrier coordinate system is not subject to gyro constant drift and acceleration in the direction of the oz _b axis

度计零位偏差的影响，此时载体相对惯性空间的运动角速度及载体相对惯性空间The impact of the zero position deviation of the metric, at this time the angular velocity of the carrier relative to the inertial space and the relative inertial space of the carrier

的线运动加速度在载体坐标系的投影分别如下：The projections of the linear motion acceleration on the carrier coordinate system are as follows:

$\{\begin{matrix} {f f}_{ib ib}^{bx bx} = = {f f}_{ibd ibd}^{bx bx} + + \sqrt{22} / / 22 cos cos ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) - - sin sin ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{by by} = = {f f}_{ibd ibd}^{by by} + + \sqrt{22} / / 22 sin sin ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) + + cos cos ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{bz bz} = = {f f}_{ibd ibd}^{bz bz} \end{matrix} - - - - - - ((55))$

${ω ω}_{nb nb}^{b b} = = {ω ω}_{ib ib}^{b b} - - {(({T T}_{b b}^{n no}))}^{T T} (({ω ω}_{ie ie}^{n no} + + {ω ω}_{en en}^{n no})) - - - - - - ((66))$

更新四元数和姿态矩阵：Update the quaternion and pose matrix:

Q＝q₀+q₁i_b+q₂j_b+q₃k_b (7)Q＝q ₀ +q ₁ i _b +q ₂ j _b +q ₃ k _b (7)

四元数的即时修正可以通过解四元数微分方程 $\overset{\cdot}{Q} = \frac{1}{2} Q ω_{nb}^{b}$ 来实现：On-the-fly corrections to quaternions can be achieved by solving quaternion differential equations $\overset{\cdot}{Q} = \frac{1}{2} Q ω_{nb}^{b}$ to fulfill:

$[\begin{matrix} {\overset{\cdot \cdot}{q q}}_{00} \\ {\overset{\cdot \cdot}{q q}}_{11} \\ {\overset{\cdot \cdot}{q q}}_{22} \\ {\overset{\cdot \cdot}{q q}}_{33} \end{matrix}] = = \frac{11}{22} [\begin{matrix} 00 & - - {ω ω}_{nb nb}^{bx bx} & - - {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bz bz} \\ {ω ω}_{nb nb}^{bx bx} & 00 & {ω ω}_{nb nb}^{bz bz} & - - {ω ω}_{nb nb}^{by by} \\ {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{} & 00 & {ω ω}_{nb nb}^{bx bx} \\ {ω ω}_{nb nb}^{bz bz} & {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bx bx} & 00 \end{matrix}] [\begin{matrix} {q q}_{00} \\ {q q}_{11} \\ {q q}_{22} \\ {q q}_{33} \end{matrix}] - - - - - - ((88))$

姿态矩阵T_b ⁿ的更新过程如下：The update process of attitude matrix T _b ⁿ is as follows:

${T T}_{b b}^{n no} = = [\begin{matrix} {q q}_{00}^{22} + + {q q}_{11}^{22} - - {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{11} {q q}_{22} - - {q q}_{00} {q q}_{33})) & 22 (({q q}_{11} {q q}_{33} + + {q q}_{00} {q q}_{22})) \\ 22 (({q q}_{11} {q q}_{22} + + {q q}_{00} {q q}_{33})) & {q q}_{00}^{22} - - {q q}_{11}^{22} + + {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{22} {q q}_{33} - - {q q}_{00} {q q}_{11})) \\ 22 (({q q}_{11} {q q}_{33} - - {q q}_{00} {q q}_{22})) & 22 (({q q}_{22} {q q}_{33} + + {q q}_{00} {q q}_{11})) & {q q}_{00}^{22} - - {q q}_{11}^{22} - - {q q}_{22}^{22} + + {q q}_{33}^{22} \end{matrix}] - - - - - - ((99))$

$[\begin{matrix} {f f}^{nx nx} \\ {f f}^{ny no} \\ {f f}^{nz nz} \end{matrix}] = = {T T}_{b b}^{n no} [\begin{matrix} {f f}_{ib ib}^{bx bx} \\ {f f}_{ib ib}^{by by} \\ {f f}_{ib ib}^{bz bz} \end{matrix}] - - - - - - ((1010))$

$\{\begin{matrix} {\overset{\cdot \cdot}{V V}}_{x x} (({t t}_{11})) = = {f f}^{nx nx} + + ((22 {ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{y the y} (({t t}_{11})) \\ {\overset{\cdot \cdot}{V V}}_{y the y} (({t t}_{11})) = = {f f}^{ny no} - - ((22 {ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{x x} (({t t}_{11})) \end{matrix} - - - - - - ((1111))$

$\{\begin{matrix} {V V}_{x x} (({t t}_{22})) = = {V V}_{x x} (({t t}_{11})) + + {\overset{\cdot &Center Dot;}{V V}}_{x x} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \\ {V V}_{y the y} (({t t}_{22})) = = {V V}_{y the y} (({t t}_{11})) + + {\overset{\cdot &Center Dot;}{V V}}_{y the y} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \end{matrix} - - - - - - ((1212))$

$\{\begin{matrix} Δ Δ {V V}_{x x} = = {V V}_{x x} (({t t}_{22})) - - {V V}_{x x 00} \\ Δ Δ {V V}_{y the y} = = {V V}_{y the y} (({t t}_{22})) - - {V V}_{y the y 00} \end{matrix} - - - - - - ((1414))$

λ₀分别表示初始时刻载体所处位置的经度和纬度；

Claims

1. A fiber optic gyroscope strapdown inertial navigation system error suppression method based on single-axis rotation, is characterized in that comprising the following steps:

(1) Utilize the global positioning system GPS to determine the initial position parameters comprising longitude and latitude of the carrier, and bind them into the navigation computer;

(2) Collect the data output by the fiber optic gyroscope and the quartz accelerometer of the fiber optic gyroscope strapdown inertial navigation system. The relationship between the acceleration and the relationship between the output of the gyroscope and the angular rate of the earth's rotation is preliminarily determined at this time. Connected matrix T _b ⁿ :

{T T}_{b b}^{n no} = = [\begin{matrix} cos cos γ γ cos cos ψ ψ - - sin sin γ γ sin sin θ θ sin sin ψ ψ & - - cos cos θ θ sin sin ψ ψ & sin sin γ γ cos cos ψ ψ + + cos cos γ γ sin sin θ θ sin sin ψ ψ \\ cos cos γ γ cos cos ψ ψ + + sin sin γ γ sin sin θ θ sin sin ψ ψ & cos cos θ θ cos cos ψ ψ & sin sin γ γ sin sin ψ ψ - - cos cos γ γ sin sin θ θ cos cos ψ ψ \\ - - sin sin γ γ cos cos θ θ & sin sin θ θ & cos cos γ γ cos cos θ θ \end{matrix}];;

(3) The inertial measurement unit rotates 45 degrees positively around the oy _b axis of the carrier coordinate system to determine the initial relative position between the IMU coordinate system and the carrier coordinate system:

The carrier coordinate system and the IMU coordinate system have the same coordinate origin o, the oy _s axis coincides with the oy _b axis, and the ox _s axis, oz _s axis, ox _b axis and oz _b axis are located in the same plane, but the oz _s axis and oz _b The included angle of the axis is 45°, and the included angle between the oz _s axis and the ox _b axis is 90°-45°=45°;

(4) After determining the relative initial position relationship of the two coordinate systems, the inertial measurement unit rotates continuously around the azimuth axis oz _b of the carrier coordinate system at an angular velocity ω=6°/s;

(5) After the IMU rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted to the carrier coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained:

The output values of the fiber optic gyroscope and accelerometer are ω _is ^s and f _is ^s respectively:

{ω ω}_{is is}^{s the s} = = {(({T T}_{s the s}^{b b}))}^{T T} {ω ω}_{ibd ibd}^{b b} + + {[\begin{matrix} {ϵ ϵ}_{x x} & {ϵ ϵ}_{y the y} & {ϵ ϵ}_{z z} \end{matrix}]}^{T T} + + {ω ω}_{bs bs}^{s the s}

{f f}_{is is}^{s the s} = = {(({T T}_{s the s}^{b b}))}^{T T} {f f}_{ibd ibd}^{b b} + + {[\begin{matrix} {&dtri; &dtri;}_{x x} & {&dtri; &dtri;}_{y the y} & {&dtri; &dtri;}_{z z} \end{matrix}]}^{T T} + + {f f}_{bs bs}^{s the s}

in,

(·) ^T represents the transfer rank of the matrix ·, ω _ibd ^b , f _ibd ^b are the real output of the carrier motion, ε _x , ε _y , ε _z are the drift errors of the gyroscope,

is the zero position error of the accelerometer; since the s system has only rotational motion relative to the b system, there is no relative linear motion, so

So the accelerometer output can be expressed as:

The transformation of the output of the fiber optic gyroscope and accelerometer from the IMU coordinate system to the carrier coordinate system can be expressed as:

{ω ω}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {ω ω}_{is is}^{s the s} + + {ω ω}_{sb sb}^{b b},,

{f f}_{ib ib}^{b b} = = {T T}_{s the s}^{b b} {f f}_{is is}^{s the s}

The inertial measurement unit rotates 45 degrees positively around the oy _b axis of the carrier coordinate system, the constant value drift of the three gyroscopes is equal, and the zero position deviation of the three accelerometers is equal. At this time, ε _z cos45°=ε _x cos(90°- 45°),

\{\begin{matrix} {ω ω}_{ib ib}^{bx bx} = = {ω ω}_{ibd ibd}^{bx bx} + + \sqrt{22} / / 22 cos cos ωt ωt (({ϵ ϵ}_{x x} + + {ϵ ϵ}_{z z})) - - sin sin ωt ωt {ϵ ϵ}_{y the y} \\ {ω ω}_{ib ib}^{by by} = = {ω ω}_{ibd ibd}^{by by} + + \sqrt{22} / / 22 sin sin ωt ωt (({ϵ ϵ}_{x x} + + {ϵ ϵ}_{z z})) + + cos cos ωt ωt {ϵ ϵ}_{y the y} \\ {ω ω}_{ib ib}^{bz bz} = = {ω ω}_{ibd ibd}^{bz bz} \end{matrix}

\{\begin{matrix} {f f}_{ib ib}^{bx bx} = = {f f}_{ibd ibd}^{bx bx} + + \sqrt{22} / / 22 cos cos ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) - - sin sin ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{by by} = = {f f}_{ibd ibd}^{by by} + + \sqrt{22} / / 22 sin sin ωt ωt (({&dtri; &dtri;}_{x x} + + {&dtri; &dtri;}_{z z})) + + cos cos ωt ωt {&dtri; &dtri;}_{y the y} \\ {f f}_{ib ib}^{bz bz} = = {f f}_{ibd ibd}^{bz bz} \end{matrix}

Among them, ω _ib ^bx , ω _ib ^by , and ω _ib ^bz are the components of the angular velocity of the carrier relative to the inertial space on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system; f _ib ^bx , f _ib ^by , f _ib ^bz are the components of the linear acceleration of the carrier relative to the inertial space on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system;

(6) Bring the output value ω _ib ^b of the fiber optic gyroscope under the carrier system obtained in step (5) into the inertial navigation system and use the quaternion method to update the strapdown matrix T _b ⁿ :

{ω ω}_{nb nb}^{b b} = = {ω ω}_{ib ib}^{b b} - - {(({T T}_{b b}^{n no}))}^{T T} (({ω ω}_{ie ie}^{n no} + + {ω ω}_{en en}^{n no}))

Among them: ω _ie ⁿ is the component of the angular velocity of the earth's rotation in the navigation system; ω _en ⁿ is the component of the angular velocity of the navigation coordinate system relative to the earth coordinate system in the navigation system; ω _nb ^b is the angular velocity of the carrier relative to the navigation coordinate system in Components on the carrier coordinate system;

Update the quaternion and pose matrix:

Let the rotation quaternion of the carrier coordinate system relative to the navigation coordinate system be:

Q＝q ₀ +q ₁ i _b +q ₂ j _b +q ₃ k _b

Among them: i _b , j _b , k _b represent the unit direction vectors on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system, respectively;

On-the-fly corrections to quaternions can be achieved by solving quaternion differential equations

to fulfill:

[\begin{matrix} {\overset{\cdot &Center Dot;}{q q}}_{00} \\ {\overset{\cdot &Center Dot;}{q q}}_{11} \\ {\overset{\cdot &Center Dot;}{q q}}_{22} \\ {\overset{\cdot &Center Dot;}{q q}}_{33} \end{matrix}] = = \frac{11}{22} [\begin{matrix} 00 & - - {ω ω}_{nb nb}^{bx bx} & - - {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bz bz} \\ {ω ω}_{nb nb}^{bx bx} & 00 & {ω ω}_{nb nb}^{bz bz} & - - {ω ω}_{nb nb}^{by by} \\ {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bz bz} & 00 & {ω ω}_{nb nb}^{bx bx} \\ {ω ω}_{nb nb}^{bz bz} & {ω ω}_{nb nb}^{by by} & - - {ω ω}_{nb nb}^{bx bx} & 00 \end{matrix}] [\begin{matrix} {q q}_{00} \\ {q q}_{11} \\ {q q}_{22} \\ {q q}_{33} \end{matrix}]

Among them: ω _nb ^bx , ω _nb ^by , ω _nb ^bz represent the components of the angular velocity of the carrier relative to the navigation system on the ox _b axis, oy _b axis, and oz _b axis of the carrier coordinate system, respectively;

The update process of attitude matrix T _b ⁿ is as follows:

{T T}_{b b}^{n no} = = [\begin{matrix} {q q}_{00}^{22} + + {q q}_{11}^{22} - - {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{11} {q q}_{22} - - {q q}_{00} {q q}_{33})) & 22 (({q q}_{11} {q q}_{33} + + {q q}_{00} {q q}_{22})) \\ 22 (({q q}_{11} {q q}_{22} + + {q q}_{00} {q q}_{33})) & {q q}_{00}^{22} - - {q q}_{11}^{22} + + {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{22} {q q}_{33} - - {q q}_{00} {q q}_{11})) \\ 22 (({q q}_{11} {q q}_{33} - - {q q}_{00} {q q}_{22})) & 22 (({q q}_{22} {q q}_{33} + + {q q}_{00} {q q}_{11})) & {q q}_{00}^{22} - - {q q}_{11}^{22} - - {q q}_{22}^{22} + + {q q}_{33}^{22} \end{matrix}];;

(7) Utilize the output value f _ib ^b of the quartz accelerometer and the attitude matrix T _b ⁿ calculated in step (6) to calculate the velocity and position of the carrier after the IMU rotation modulation;

The method for calculating the speed and position of the carrier after IMU rotation modulation is as follows:

1) Calculate the acceleration under the navigation system:

[\begin{matrix} {f f}^{nx nx} \\ {f f}^{ny no} \\ {f f}^{nz nz} \end{matrix}] = = {T T}_{b b}^{n no} [\begin{matrix} {f f}_{ib ib}^{bx bx} \\ {f f}_{ib ib}^{by by} \\ {f f}_{ib ib}^{bz bz} \end{matrix}];;

2) Calculate the horizontal velocity and position of the carrier:

According to the carrier’s eastward horizontal velocity V _x (t ₁ ) and northward horizontal velocity V _y (t ₁ ) at time t ₁ , the rate of change of carrier’s horizontal velocity at time t ₁ is calculated as:

\{\begin{matrix} {\overset{\cdot &Center Dot;}{V V}}_{x x} (({t t}_{11})) = = {f f}^{nx nx} + + (({22 ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{y the y} (({t t}_{11})) \\ {\overset{\cdot &Center Dot;}{V V}}_{y the y} (({t t}_{11})) = = {f f}^{ny no} - - (({22 ω ω}_{ie ie}^{nz nz} + + {ω ω}_{en en}^{nz nz})) {V V}_{x x} (({t t}_{11})) \end{matrix}

The horizontal velocity and carrier position at time _t2 are respectively:

\{\begin{matrix} {V V}_{x x} (({t t}_{22})) = = {V V}_{x x} (({t t}_{11})) + + {\overset{\cdot \cdot}{V V}}_{x x} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \\ {V V}_{y the y} (({t t}_{22})) = = {V V}_{y the y} (({t t}_{11})) + + {\overset{\cdot &Center Dot;}{V V}}_{y the y} (({t t}_{11})) (({t t}_{22} - - {t t}_{11})) \end{matrix}

3) Calculate carrier velocity error and position error:

\{\begin{matrix} {ΔV ΔV}_{x x} = = {V V}_{x x} (({t t}_{22})) - - {V V}_{x x 00} \\ {ΔV ΔV}_{y the y} = = {V V}_{y the y} (({t t}_{22})) - - {V V}_{y the y 00} \end{matrix}

Among them: V _x0 and V _y0 represent the eastward and northward velocity of the carrier at the initial moment respectively; ΔV _x and ΔV _y represent the variation of the carrier’s eastward and northward velocity respectively;

Δλ respectively represent the change of latitude and longitude of the carrier; R _xp and R _yp respectively represent the curvature radius of the meridian circle and Maoyou circle of the earth; t ₁ and t ₂ are two adjacent times in the solution process of the inertial navigation system point.

2. The error suppression method of the fiber optic gyroscope strapdown inertial navigation system based on single-axis rotation according to claim 1, wherein after the relative initial position relationship of the two coordinate systems is determined, the inertial measurement unit rotates around the carrier coordinate system azimuth axis In the step of continuous rotation of oz _b at an angular velocity ω=6°/s in the forward direction, during the rotation of the IMU, the transformation matrix from the IMU coordinate system to the carrier coordinate system is: