CN102788597B

CN102788597B - Error suppressing method of rotary strap-down inertial navigation system based on space stabilization

Info

Publication number: CN102788597B
Application number: CN201210305208.5A
Authority: CN
Inventors: 孙伟; 徐爱功; 徐宗秋
Original assignee: Liaoning Technical University
Current assignee: Liaoning Technical University
Priority date: 2012-08-16
Filing date: 2012-08-16
Publication date: 2014-10-29
Anticipated expiration: 2032-08-16
Also published as: CN102788597A

Abstract

The invention provides a space-stabilized rotation strapdown inertial navigation system error suppression method. The initial position parameters of the carrier are determined by GPS, and they are bound to the navigation computer; the strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and quartz accelerometer are collected and processed; the fiber optic gyroscope is rotated by the IMU The data generated by the instrument and the quartz accelerometer are converted into the navigation coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained; the scale factor error and installation error of the gyroscope in the space-stable modulation inertial navigation system are analyzed, and the IMU coordinates are calculated. The attitude error caused by the gyroscope scale factor error and installation error during the conversion process between the inertial system and the inertial system. The invention modulates the constant value deviation of the inertial device in the three-axis direction, and at the same time avoids the coupling of the scale factor error and installation error of the gyroscope with the earth's rotation angular velocity, so that the system has better stability and improves the navigation positioning accuracy.

Description

Error Suppression Method for Rotating Strapdown Inertial Navigation System Based on Spatial Stabilization

(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空间稳定的旋转捷联惯导系统误差抑制方法。The invention relates to a measurement method, in particular to a space-stabilized rotation strapdown inertial navigation system error suppression method.

(二)背景技术 (2) Background technology

空间稳定型惯导系统又称解析式惯导系统。它有一个陀螺稳定平台，此平台相对惯性空间稳定，它是利用陀螺仪在惯性空间保持方向不变的定轴性，通过三套随动系统而实现的空间稳定惯性平台。在稳定平台上装有三个相互垂直的加速度计。由于惯性平台相对于惯性空间没有转动角速度，因此加速度计输出讯号不必消除有害加速度的影响。由于平台稳定在惯性空间，在不同位置下地球重力场矢量在惯性系的分量发生变化，这样加速度计的输出讯号内将出现重力加速度分量，所以对重力加速度分量进行补偿后经过积分作用得到载体的速度和位置信息。Space-stabilized inertial navigation system is also called analytical inertial navigation system. It has a gyro-stabilized platform, which is stable relative to the inertial space. It is a space-stabilized inertial platform realized by using the gyroscope to maintain the fixed axis in the inertial space and through three sets of servo systems. Three mutually perpendicular accelerometers are installed on the stable platform. Since the inertial platform has no rotational angular velocity relative to the inertial space, the accelerometer output signal does not have to cancel the effect of unwanted acceleration. Since the platform is stable in the inertial space, the component of the earth's gravity field vector in the inertial system changes at different positions, so the output signal of the accelerometer will appear in the gravitational acceleration component, so after the gravitational acceleration component is compensated, the vector of the carrier is obtained through integral action. speed and position information.

高精度的捷联惯导系统需要采用高性能的惯性传感器与先进的系统技术。由于我国加工工艺和制造水平的限制，制造高性能的惯性器件难度大，同时高性能的惯性器件会导致整个捷联惯导系统的成本提高，因此先进的系统技术一直都是捷联惯导系统的研究热点。由于光纤陀螺相关的光电器件在技术和数量上满足不了陀螺设计的总体要求，光纤陀螺的发展受到了限制，现有的光纤陀螺精度又无法满足长航时、高精度的要求，所以寻找一种在现有陀螺精度条件下提高导航精度的方法是很重要的。A high-precision strapdown inertial navigation system requires the use of high-performance inertial sensors and advanced system technology. Due to the limitations of our country's processing technology and manufacturing level, it is difficult to manufacture high-performance inertial devices. At the same time, high-performance inertial devices will lead to an increase in the cost of the entire strapdown inertial navigation system. Therefore, advanced system technology has always been the strapdown inertial navigation system. research hotspots. Since the photoelectric devices related to fiber optic gyroscopes cannot meet the overall requirements of gyroscope design in terms of technology and quantity, the development of fiber optic gyroscopes is limited, and the accuracy of existing fiber optic gyroscopes cannot meet the requirements of long endurance and high precision. The method of improving the navigation accuracy under the condition of the existing gyro accuracy is very important.

误差调制技术是基于旋转惯性测量单元(IMU)的一种惯性器件误差自动补偿的一种技术。惯性测量器件的误差是惯性导航系统误差的主要决定因素。受工艺制造水平的限制，制造高性能的惯性器件难度很大，同时研制高性能的惯性器件会使整个捷联惯导系统的成本提高，因此先进的系统技术一直以来都是捷联惯导系统的研究热点。旋转误差调制技术就是一种先进的系统技术，它通过在惯性元件或者IMU外面加上旋转和控制机构，然后利用旋转来平均掉惯性元件的漂移对导航性能的影响。The error modulation technology is a technology for automatic compensation of inertial device errors based on the rotating inertial measurement unit (IMU). The error of the inertial measurement device is the main determinant of the error of the inertial navigation system. Restricted by the manufacturing level of the process, it is very difficult to manufacture high-performance inertial devices. At the same time, the development of high-performance inertial devices will increase the cost of the entire strapdown inertial navigation system. Therefore, advanced system technology has always been the strapdown inertial navigation system. research hotspots. The rotation error modulation technology is an advanced system technology, which adds a rotation and control mechanism outside the inertial element or IMU, and then uses the rotation to average out the influence of the drift of the inertial element on the navigation performance.

(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，提供一种基于空间稳定的旋转捷联惯导系统误差抑制方法。The technical problem of the present invention is to overcome the deficiencies of the prior art and provide a space-stabilized rotation strapdown inertial navigation system error suppression method.

本发明的技术解决方案为：一种基于空间稳定的旋转捷联惯导系统误差抑制方法，其特征在于将惯性测量单元稳定在赤道平面内，采用四环结构隔离载体角运动及地球自转角速度对旋转调制型捷联惯导系统误差调制效果的影响，避免陀螺仪的标度因数误差及安装误差与地球自转角速度的耦合，使系统具有更好的稳定性，有利于系统位置误差逐渐趋于零。其具体步骤如下：The technical solution of the present invention is: a space-stabilized rotation strapdown inertial navigation system error suppression method, which is characterized in that the inertial measurement unit is stabilized in the equatorial plane, and the four-ring structure is used to isolate the angular motion of the carrier and the angular velocity of the earth's rotation. The influence of the error modulation effect of the rotation modulation type strapdown inertial navigation system avoids the coupling between the scale factor error and installation error of the gyroscope and the angular velocity of the earth's rotation, so that the system has better stability and is conducive to the system position error gradually tending to zero . The specific steps are as follows:

(1)通过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) Determine the initial position parameters of the carrier by GPS, and bind them into the navigation computer;

(2)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；(2) The strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and the quartz accelerometer are collected and processed;

(3)将IMU旋转后光纤陀螺仪和石英加速度计生成的数据转换到导航坐标系下，得到惯性器件常值偏差的调制形式；(3) After the IMU rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted into the navigation coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained;

惯性测量单元坐标系的ox_sy_s平面与地球的赤道平面平行，oz_s轴平行于地球自转轴，且指向与地球旋转角速度方向一致(如附图3)，确定出IMU坐标系与导航坐标系的转换关系：The ox _s y _s plane of the inertial measurement unit coordinate system is parallel to the equatorial plane of the earth, the oz _s axis is parallel to the earth's rotation axis, and the direction is consistent with the direction of the earth's rotation angular velocity (as shown in Figure 3), and the IMU coordinate system and navigation coordinates are determined The conversion relationship of the system:

${C C}_{s the s}^{n no} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i}$

基于空间稳定的调制型捷联系统的姿态更新过程可以归结为对矩阵和的求取。其中，为导航坐标系与地球坐标系之间的变换矩阵；为地球坐标系与惯性系之间的转换矩阵，可由载体所在位置的经度λ、纬度L及时间间隔t确定。The attitude update process of the modulated strapdown system based on spatial stabilization can be attributed to the matrix and of seeking. in, is the transformation matrix between the navigation coordinate system and the earth coordinate system; is the transformation matrix between the earth coordinate system and the inertial system, which can be determined by the longitude λ, latitude L and time interval t of the carrier's location.

${C C}_{e e}^{n no} = = [\begin{matrix} - - sin sin λ λ & cos cos λ λ & 00 \\ - - sin sin L L cos cos λ λ & - - sin sin L L sin sin λ λ & cos cos L L \\ cos cos L L cos cos λ λ & cos cos L L sin sin λ λ & sin sin L L \end{matrix}]$

${C C}_{i i}^{e e} = = [\begin{matrix} cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ - - sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ 00 & 00 & 11 \end{matrix}]$

设定初始时刻IMU坐标系与惯性坐标系重合，随后IMU以恒定角速度ω绕惯性坐标系的oz_i轴持续转动，两坐标系的相对位置关系为：It is set that the IMU coordinate system coincides with the inertial coordinate system at the initial moment, and then the IMU continues to rotate around the oz _i axis of the inertial coordinate system at a constant angular velocity ω. The relative position relationship between the two coordinate systems is:

${C C}_{s the s}^{i i} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}]$

当惯性测量单元围绕惯性系连续旋转过程时，可得到陀螺仪常值漂移在导航系上的投影形式：When the inertial measurement unit rotates continuously around the inertial system, the projection form of the gyroscope constant value drift on the navigation system can be obtained:

${ϵ ϵ}^{n no} = = {C C}_{s the s}^{n no} {ϵ ϵ}^{s the s} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i} {ϵ ϵ}^{s the s} = = [\begin{matrix} {ϵ ϵ}_{x x}^{n no} \\ {ϵ ϵ}_{y the y}^{n no} \\ {ϵ ϵ}_{z z}^{n no} \end{matrix}]$

其中，in,

${ϵ ϵ}_{x x}^{n no} = = cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((- - sin sin λ λ cos cos ωt ωt - - cos cos λ λ sin sin ωt ωt)) {ϵ ϵ}_{x x}^{s the s} + + sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ sin sin ω ω t t {ϵ ϵ}_{x x}^{s the s} - -$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) cos cos λ λ cos cos ωt ωt {ϵ ϵ}_{x x}^{s the s} + + cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((cos cos λ λ cos cos ωt ωt - - sin sin λ λ sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} - -$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) ((sin sin λ λ cos cos ωt ωt + + cos cos λ λ sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s}$

${ϵ ϵ}_{y the y}^{n no} = = cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((sin sin λ λ sin sin ωt ωt - - cos cos λ λ cos cos ωt ωt)) {ϵ ϵ}_{x x}^{s the s} + +$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((cos cos λ λ sin sin ωt ωt + + sin sin λ λ cos cos ωt ωt)) {ϵ ϵ}_{x x}^{s the s} - -$

$cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((cos cos λ λ sin sin ωt ωt + + sin sin λ λ cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} + +$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((sin sin λ λ sin sin ωt ωt - - cos cos λ λ cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s}$

${ϵ ϵ}_{z z}^{n no} = = cos cos L L cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((cos cos λ λ cos cos ωt ωt - - sin sin λ λ sin sin ωt ωt + + cos cos L L)) {ϵ ϵ}_{x x}^{s the s} + + sin sin L L {ϵ ϵ}_{z z}^{s the s} + +$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ cos cos ωt ωt {ϵ ϵ}_{x x}^{s the s} - - sin sin ((λ λ + + {ω ω}_{ie ie} t t)) cos cos λ λ sin sin ωt ωt {ϵ ϵ}_{x x}^{s the s} + +$

$cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ ((cos cos L L sin sin ωt ωt - - sin sin L L cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} + +$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ ((cos cos L L cos cos ωt ωt + + sin sin L L sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s}$

水平陀螺仪常值偏差经过惯性测量单元相对惯性空间的转动后在导航坐标系上的分量完全得到调制，经过整周期积分后的作用效果为零；方位轴上的陀螺仪常值偏差与载体所在位置的纬度耦合后在导航坐标系方位轴上产生了常值偏差。After the rotation of the inertial measurement unit relative to the inertial space, the constant value deviation of the horizontal gyroscope is completely modulated on the navigation coordinate system, and the effect is zero after the whole cycle integration; the constant value deviation of the gyroscope on the azimuth axis is the same as The latitude coupling of the position produces a constant value deviation on the azimuth axis of the navigation coordinate system.

(4)对空间稳定的调制型惯导系统中陀螺仪标度因数误差和安装误差进行分析，计算IMU坐标系与惯性系转换过程中陀螺仪标度因数误差和安装误差引起的姿态误差。(4) Analyze the gyroscope scale factor error and installation error in the spatially stable modulated inertial navigation system, and calculate the attitude error caused by the gyroscope scale factor error and installation error during the conversion process between the IMU coordinate system and the inertial system.

1)惯性测量单元正向连续旋转过程中，由于标度因数误差的存在引起的姿态误差转换到惯性坐标系：1) During the forward continuous rotation of the inertial measurement unit, the attitude error caused by the existence of the scale factor error is converted to the inertial coordinate system:

$δ δ {ω ω}_{is is + +}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} δ δ {K K}_{gx gx} & 00 & 00 \\ 00 & δ δ {K K}_{gy gy} & 00 \\ 00 & 00 & δ δ {K K}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ δ δ {K K}_{gz gz} ω ω \end{matrix}]$

同理可以得到惯性测量单元反向转动中，陀螺仪标度因数误差引起的姿态误差在惯性系的分量：In the same way, the component of the attitude error in the inertial system caused by the scale factor error of the gyroscope during the reverse rotation of the inertial measurement unit can be obtained:

$δ δ {ω ω}_{is is - -}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} δ δ {K K}_{gx gx} & 00 & 00 \\ 00 & δ δ {K K}_{gy gy} & 00 \\ 00 & 00 & δ δ {K K}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ - - δ δ {K K}_{gz gz} ω ω \end{matrix}]$

假设在持续正反转方案中，一个转动周期为T′＝2T，那么由于陀螺仪标度因数误差引起的输出误差在一个完整的正反连续转动周期内经过积分产生的姿态误差角在惯性系的投影为：Assuming that in the continuous forward and reverse rotation scheme, a rotation cycle is T′=2T, then the output error caused by the gyroscope scale factor error is integrated in a complete forward and reverse continuous rotation cycle, and the attitude error angle is in the inertial system The projection of is:

${&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}]$

采用惯性测量单元连续正反旋转，与旋转角速度耦合的标度因数误差被正负相消，由于采用相对赤道平面的空间稳定方法，也就是四框架结构的空间稳定型惯导系统，不存在地球自转角速度与陀螺仪标度因数误差的耦合，惯性系下的姿态误差经过转换过程得到导航系下载体的姿态误差均为零。The inertial measurement unit is used to continuously rotate positively and negatively, and the scale factor error coupled with the rotational angular velocity is positively and negatively canceled. Due to the space stabilization method relative to the equatorial plane, that is, the space-stabilized inertial navigation system with a four-frame structure, there is no earth The coupling of the rotation angular velocity and the gyroscope scale factor error, the attitude error in the inertial system is converted to zero in the attitude error of the navigation system.

2)惯性测量单元相对惯性空间连续正向旋转过程中，陀螺仪安装误差引起的陀螺仪输出误差在惯性坐标系上的分量为：2) During the continuous positive rotation of the inertial measurement unit relative to the inertial space, the component of the gyroscope output error caused by the installation error of the gyroscope on the inertial coordinate system is:

$δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} sin sin ωt ωt + + {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}]$

同理可以得到惯性测量单元连续反向旋转过程中，由于安装误差引起的陀螺仪输出：In the same way, the gyroscope output caused by the installation error during the continuous reverse rotation of the inertial measurement unit can be obtained:

$δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} ω ω sin sin ωt ωt - - {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}]$

采用正向和反向旋转角度均为360°的持续正反转方案，一个完整的转动周期消耗时间为T′＝2T，其中T表示单向完整转动的周期。由于陀螺仪安装误差引起的姿态角误差为：Using a continuous forward and reverse rotation scheme with both forward and reverse rotation angles of 360°, the time consumed for a complete rotation cycle is T′=2T, where T represents the cycle of one-way complete rotation. The attitude angle error caused by the installation error of the gyroscope is:

${&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}]$

采用惯性测量单元相对惯性空间的连续正反转动方案中，陀螺仪安装误差不会引起载体姿态误差。In the continuous positive and negative rotation scheme of the inertial measurement unit relative to the inertial space, the installation error of the gyroscope will not cause the attitude error of the carrier.

本发明与现有技术相比的优点在于：本发明打破了传统旋转调制方法不能有效地隔离载体运动和地球自转角运动及不能避免系统出现自锁现象，提出一种将惯性测量单元稳定在赤道平面内的误差旋转调制方案，此时陀螺仪敏感的角速度中仅存在惯性测量单元的转动角速度，而不存在地球自转角速度信息。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 fact that the traditional rotation modulation method cannot effectively isolate the carrier motion and the earth's rotation angle motion and cannot avoid the self-locking phenomenon of the system, and proposes a method for stabilizing the inertial measurement unit at the equator The error rotation modulation scheme in the plane, at this time, only the rotational angular velocity of the inertial measurement unit exists in the angular velocity sensitive to the gyroscope, and there is no information about the angular velocity of the earth's rotation. 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VC++仿真条件下，对该方法进行仿真实验：Under the condition of VC++ simulation, the simulation experiment of this method is carried out:

载体处于静止状态，基于空间稳定的IMU连续正反转的方案的误差模型参数：The carrier is in a static state, and the error model parameters of the scheme based on the spatially stable IMU continuous forward and reverse:

单向正、反转动一周时消耗的时间为：T＝12秒；The time consumed for one-way forward and reverse rotation is: T=12 seconds;

每一个正、反转动转换过程中，加减速时间各为4秒；During each forward and reverse rotation conversion process, the acceleration and deceleration time is 4 seconds;

载体初始位置：北纬42.0124°，东经121.6481°；The initial position of the carrier: 42.0124° north latitude, 121.6481° 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＝6378393.0米；Equatorial radius: R _e = 6378393.0 meters;

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位置误差曲线如图4所示。结果表明基于空间稳定的IMU正反连续转动条件下，采用本发明方法可以获得较高的定位精度。The carrier position error curve obtained by using the method described in the invention is shown in FIG. 4 . The results show that under the condition of continuous forward and reverse rotation of the IMU based on space stability, the method of the invention can obtain higher positioning accuracy.

(四)附图说明 (4) Description of drawings

图1为本发明的基于空间稳定的旋转捷联惯导系统误差抑制方法流程图；Fig. 1 is the flow chart of the method for suppressing the error of the space-stabilized rotating strapdown inertial navigation system of the present invention;

图2为本发明的基于空间稳定的旋转捷联惯导系统示意图；Fig. 2 is the schematic diagram of the rotation strapdown inertial navigation system based on space stabilization of the present invention;

图3为本发明的基于空间稳定的旋转捷联惯导系统坐标系相对位置图；Fig. 3 is the relative position diagram of the coordinate system of the rotation strapdown inertial navigation system based on space stabilization of the present invention;

图4为本发明的基于空间稳定的IMU正反转动方案的载体位置误差与IMU静止状态时载体定位误差的对比实验曲线。FIG. 4 is a comparison experiment curve of the carrier position error of the space-stabilized IMU forward and reverse rotation scheme based on the present invention and the carrier positioning error when the IMU is in a static state.

(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:

${C C}_{s the s}^{n no} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i} - - - - - - ((11))$

${C C}_{e e}^{n no} = = [\begin{matrix} - - sin sin λ λ & cos cos λ λ & 00 \\ - - sin sin L L cos cos λ λ & - - sin sin L L sin sin λ λ & cos cos L L \\ cos cos L L cos cos λ λ & cos cos L L sin sin λ λ & sin sin L L \end{matrix}] - - - - - - ((22))$

${C C}_{i i}^{e e} = = [\begin{matrix} cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ - - sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ 00 & 00 & 11 \end{matrix}] - - - - - - ((33))$

${C C}_{s the s}^{i i} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] - - - - - - ((44))$

${ϵ ϵ}^{n no} = = {C C}_{s the s}^{n no} {ϵ ϵ}^{s the s} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i} {ϵ ϵ}^{s the s} = = [\begin{matrix} {ϵ ϵ}_{x x}^{n no} \\ {ϵ ϵ}_{y the y}^{n no} \\ {ϵ ϵ}_{z z}^{n no} \end{matrix}] - - - - - - ((55))$

其中，in,

${ϵ ϵ}_{x x}^{n no} = = cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((- - sin sin λ λ cos cos ωt ωt - - cos cos λ λ sin sin ωt ωt)) {ϵ ϵ}_{x x}^{s the s} + + sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λωt λωt sin sin {ϵ ϵ}_{x x}^{s the s} - -$

$sin sin ((λ λ + + {ω ω}_{ie ie} t t)) cos cos λ λ cos cos ωt ωt {ϵ ϵ}_{x x}^{s the s} + + cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((cos cos λ λ cos cos ωt ωt - - sin sin λ λ sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} - - - - - - - - ((66))$

$((77))$

$((88))$

$δ δ {ω ω}_{is is + +}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} δ δ {K K}_{gx gx} & 00 & 00 \\ 00 & δ δ {K K}_{gy gy} & 00 \\ 00 & 00 & δ δ {K K}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ δ δ {K K}_{gz gz} ω ω \end{matrix}] - - - - - - ((99))$

$δ δ {ω ω}_{is is - -}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} δ δ {K K}_{gx gx} & 00 & 00 \\ 00 & δ δ {K K}_{gy gy} & 00 \\ 00 & 00 & δ δ {K K}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ - - δ δ {K K}_{gz gz} ω ω \end{matrix}] - - - - - - ((1010))$

${&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}] - - - - - - ((1111))$

采用惯性测量单元连续正反旋转，与旋转角速度耦合的标度因数误差被正负相消，由于采用相对赤道平面的空间稳定方法，也就是四框架结构的空间稳定型惯导系统，不存在地球自转角速度与陀螺仪标度因数误差的耦合，惯性系下的姿态误差经过转换过程得到导航系下载体的姿态误差均为零。The inertial measurement unit is used to continuously rotate positive and negative, and the scale factor error coupled with the rotational angular velocity is canceled by positive and negative. Due to the space stabilization method relative to the equatorial plane, that is, the space-stabilized inertial navigation system with a four-frame structure, there is no earth The coupling of the rotation angular velocity and the gyroscope scale factor error, the attitude error in the inertial system is converted to zero, and the attitude error of the navigation system is zero.

$δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} sin sin ωt ωt + + {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}] - - - - - - ((1212))$

$δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} - - {K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} ω ω sin sin ωt ωt - - {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}] - - - - - - ((1313))$

${&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}] - - - - - - ((1414))$

Claims

1. A method for suppressing errors of a rotating strapdown inertial navigation system based on space stabilization, characterized in that it comprises the following steps:

(1) Determine the initial position parameters of the carrier by GPS, and bind them into the navigation computer;

(2) The strapdown inertial navigation system is preheated, and the data output by the fiber optic gyroscope and the quartz accelerometer are collected and processed;

(3) After the IMU rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted into the navigation coordinate system, and the modulation form of the constant value deviation of the inertial device is obtained;

The ox _s y _s plane of the inertial measurement unit coordinate system is parallel to the equatorial plane of the earth, the oz _s axis is parallel to the earth's rotation axis, and the direction is consistent with the direction of the earth's rotation angular velocity, and the conversion relationship between the IMU coordinate system and the navigation coordinate system is determined:

{C C}_{s the s}^{n no} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i}

The attitude update process of the modulated strapdown system based on spatial stabilization can be attributed to the matrix and of seeking, among them, is the transformation matrix between the navigation coordinate system and the earth coordinate system; is the conversion matrix between the earth coordinate system and the inertial system, which can be determined by the longitude λ, latitude L and time interval t of the carrier's position;

{C C}_{e e}^{n no} = = [\begin{matrix} - - sin sin λ λ & cos cos λ λ & 00 \\ - - sin sin L L cos cos λ λ & - - sin sin L L sin sin λ λ & cos cos L L \\ cos cos L L cos cos λ λ & cos cos L L sin sin λ λ & sin sin L L \end{matrix}]

{C C}_{i i}^{e e} = = [\begin{matrix} cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ - - sin sin ((λ λ + + {ω ω}_{ie ie} t t)) & cos cos ((λ λ + + {ω ω}_{ie ie} t t)) & 00 \\ 00 & 00 & 11 \end{matrix}]

It is set that the IMU coordinate system coincides with the inertial coordinate system at the initial moment, and then the IMU continues to rotate around the oz _i axis of the inertial coordinate system at a constant angular velocity ω. The relative position relationship between the two coordinate systems is:

{C C}_{s the s}^{i i} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}]

When the inertial measurement unit rotates continuously around the inertial system, the projection form of the gyroscope constant value drift on the navigation system can be obtained:

{ϵ ϵ}^{n no} = = {C C}_{s the s}^{n no} {ϵ ϵ}^{s the s} = = {C C}_{e e}^{n no} {C C}_{i i}^{e e} {C C}_{s the s}^{i i} {ϵ ϵ}^{s the s} = = [\begin{matrix} {ϵ ϵ}_{x x}^{n no} \\ {ϵ ϵ}_{y the y}^{n no} \\ {ϵ ϵ}_{z z}^{n no} \end{matrix}]

in,

\begin{matrix} {ϵ ϵ}_{x x}^{n no} = = cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((- - sin sin λ λ cos cos ωt ωt - - cos cos λ λ sin sin ωt ωt)) {ϵ ϵ}_{x x}^{s the s} + + sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ sin sin ωt ωt {ϵ ϵ}_{x x}^{s the s} - - \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) cos cos λ λ cos cos ωt ωt {ϵ ϵ}_{x x}^{s the s} + + cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((cos cos λ λ cos cos ωt ωt - - sin sin λ λ sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} - - \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) ((sin sin λ λ cos cos ωt ωt + + cos cos λ λ sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} \end{matrix}

\begin{matrix} {ϵ ϵ}_{y the y}^{n no} = = cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((sin sin λ λ sin sin ωt ωt - - cos cos λ λ cos cos ωt ωt)) {ϵ ϵ}_{x x}^{s the s} + + \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((cos cos λ λ sin sin ωt ωt + + sin sin λ λ cos cos ωt ωt)) {ϵ ϵ}_{x x}^{s the s} - - \\ cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((cos cos λ λ sin sin ωt ωt + + sin sin λ λ cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} + + \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin L L ((sin sin λ λ sin sin ωt ωt - - cos cos λ λ cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} \end{matrix}

\begin{matrix} {ϵ ϵ}_{z z}^{n no} = = cos cos L L cos cos ((λ λ + + {ω ω}_{ie ie} t t)) ((cos cos λ λ cos cos ωt ωt - - sin sin λ λ sin sin ωt ωt + + cos cos L L)) {ϵ ϵ}_{x x}^{s the s} + + sin sin L L {ϵ ϵ}_{z z}^{s the s} + + \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ cos cos ωt ωt {ϵ ϵ}_{x x}^{s the s} - - sin sin ((λ λ + + {ω ω}_{ie ie} t t)) cos cos λ λ sin sin ωt ωt {ϵ ϵ}_{x x}^{s the s} + + \\ cos cos ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ ((cos cos L L sin sin ωt ωt - - sin sin L L cos cos ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} + + \\ sin sin ((λ λ + + {ω ω}_{ie ie} t t)) sin sin λ λ ((cos cos L L cos cos ωt ωt + + sin sin L L sin sin ωt ωt)) {ϵ ϵ}_{y the y}^{s the s} \end{matrix}

After the rotation of the inertial measurement unit relative to the inertial space, the constant value deviation of the horizontal gyroscope is completely modulated on the navigation coordinate system, and the effect is zero after the whole cycle integration; the constant value deviation of the gyroscope on the azimuth axis is the same as The latitude coupling of the position produces a constant value deviation on the azimuth axis of the navigation coordinate system;

(4) Analyze the gyroscope scale factor error and installation error in the spatially stable modulated inertial navigation system, and calculate the attitude error caused by the gyroscope scale factor error and installation error during the conversion process between the IMU coordinate system and the inertial system;

1) During the forward continuous rotation of the inertial measurement unit, the attitude error caused by the existence of the scale factor error is converted to the inertial coordinate system:

δ δ {ω ω}_{is is + +}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} {δK δK}_{gx gx} & 00 & 00 \\ 00 & {δK δK}_{gy gy} & 00 \\ 00 & 00 & {δK δK}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ {δK δK}_{gz gz} ω ω \end{matrix}]

In the same way, the component of the attitude error caused by the gyroscope scale factor error in the inertial system can be obtained during the reverse rotation of the inertial measurement unit:

δ δ {ω ω}_{is is - -}^{i i}^{' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} {δK δK}_{gx gx} & 00 & 00 \\ 00 & {δK δK}_{gy gy} & 00 \\ 00 & 00 & {δK δK}_{gz gz} \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} 00 \\ 00 \\ {- - δK δK}_{gz gz} ω ω \end{matrix}]

Assuming that in the continuous forward and reverse rotation scheme, a rotation cycle is T′=2T, then the output error caused by the gyroscope scale factor error is integrated in a complete forward and reverse continuous rotation cycle, and the attitude error angle is in the inertial system The projection of is:

{&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}]

The inertial measurement unit is used to continuously rotate positive and negative, and the scale factor error coupled with the rotational angular velocity is canceled by positive and negative. Due to the space stabilization method relative to the equatorial plane, that is, the space-stabilized inertial navigation system with a four-frame structure, there is no earth The coupling of the rotation angular velocity and the gyroscope scale factor error, the attitude error of the inertial system is converted to get the attitude error of the navigation system to be zero;

2) During the continuous positive rotation of the inertial measurement unit relative to the inertial space, the component of the gyroscope output error caused by the installation error of the gyroscope on the inertial coordinate system is:

δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is + +}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & - - sin sin ωt ωt & 00 \\ sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ ω ω \end{matrix}] = = [\begin{matrix} {K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} sin sin ωt ωt + + {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}]

In the same way, the gyroscope output caused by the installation error during the continuous reverse rotation of the inertial measurement unit can be obtained:

δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} = = {C C}_{s the s}^{i i} δ δ {ω ω}_{is is - -}^{s the s}^{' '' '' '} = = [\begin{matrix} cos cos ωt ωt & sin sin ωt ωt & 00 \\ - - sin sin ωt ωt & cos cos ωt ωt & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 00 & {K K}_{gxy gxy} & {K K}_{gxz gxz} \\ {K K}_{gyx gyx} & 00 & {K K}_{gyz gyz} \\ {K K}_{gzx gzx} & {K K}_{gzy gzy} & 00 \end{matrix}] [\begin{matrix} 00 \\ 00 \\ - - ω ω \end{matrix}] = = [\begin{matrix} {- - K K}_{gxz gxz} ω ω cos cos ωt ωt - - {K K}_{gyz gyz} ω ω sin sin ωt ωt \\ {K K}_{gxz gxz} ω ω sin sin ωt ωt - - {K K}_{gyz gyz} ω ω cos cos ωt ωt \\ 00 \end{matrix}]

Using a continuous positive and negative rotation scheme with both forward and reverse rotation angles of 360°, the time consumed for a complete rotation cycle is T′=2T, where T represents the cycle of one-way complete rotation; the attitude caused by the installation error of the gyroscope The angular error is:

{&Integral; &Integral;}_{00}^{{T T}^{' '}} δ δ {ω ω}_{is is}^{i i}^{' '' '' '} dt dt = = {&Integral; &Integral;}_{00}^{{T T}^{' '} / / 22} δ δ {ω ω}_{is is + +}^{i i}^{' '' '' '} dt dt + + {&Integral; &Integral;}_{{T T}^{' '} / / 22}^{{T T}^{' '}} δ δ {ω ω}_{is is - -}^{i i}^{' '' '' '} dt dt = = [\begin{matrix} 00 \\ 00 \\ 00 \end{matrix}]

In the continuous positive and negative rotation scheme of the inertial measurement unit relative to the inertial space, the installation error of the gyroscope will not cause the attitude error of the carrier.