CN102788598B

CN102788598B - Error suppressing method of fiber strap-down inertial navigation system based on three-axis rotation

Info

Publication number: CN102788598B
Application number: CN201210305216.XA
Authority: CN
Inventors: 孙伟; 徐爱功; 徐宗秋; 车莉娜
Original assignee: Liaoning Technical University
Current assignee: Liaoning Technical University
Priority date: 2012-08-16
Filing date: 2012-08-16
Publication date: 2014-12-03
Anticipated expiration: 2032-08-16
Also published as: CN102788598A

Abstract

The invention provides an error suppression method for an optical fiber strapdown inertial navigation system based on three-axis rotation. Use the global positioning system (GPS) to determine the initial position parameters of the carrier; collect the data output by the fiber optic gyroscope and the quartz accelerometer; determine 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 attitude information and complete the initial alignment of the system; the IMU uses twelve rotation-stop sequences as a rotation cycle indexing scheme; after the IMU rotates, the data generated by the fiber optic gyroscope and the quartz accelerometer are converted into the navigation coordinate system to obtain the inertia Modulation form of device constant value deviation; use the output value of fiber optic gyroscope strapdown matrix Update; calculate the position information of the carrier after the IMU rotation modulation; the 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 Optical Fiber Strapdown Inertial Navigation System Based on Three-axis Rotation

(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三轴旋转的光纤捷联惯导系统误差抑制方法。The invention relates to a measurement method, in particular to a method for suppressing errors of an optical fiber strapdown inertial navigation system based on three-axis rotation.

(二)背景技术 (2) Background technology

惯性导航是利用惯性敏感元件(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，并在已知初始条件下，用计算机计算出载体的速度、位置和姿态等导航参数。它完全依靠自身的敏感器件完成导航任务，无需依赖任何外界信息，也不向外辐射任何能量，是一种完全自主的导航系统，因此具有隐蔽性好、抗干扰、不受任何气象条件限制的优点。此外，惯导系统还具有数据更新率高、短期精度高和稳定性好的特点。正是由于以上优点，它在航空、航天、航海和很多民用领域得到了广泛应用。在捷联惯性导航系统中，所有的惯性元件直接安装在载体上，惯性元件输出的就是载体相对于惯性空间的角速度和加速度，由计算机将载体坐标系下测得的加速度数据转换到导航坐标系再进行导航解算，相当于利用陀螺仪输出数据在计算机内构建一个数学平台作为导航计算的参考。Inertial navigation is to use inertial sensitive elements (gyroscope and accelerometer) to measure the linear motion and angular motion of the carrier relative to the inertial space, and under the known initial conditions, use the computer to calculate the navigation parameters such as the speed, position and attitude of the carrier. It completely relies on its own sensitive devices to complete navigation tasks, without relying on any external information, and does not radiate any energy. It is a completely autonomous navigation system, so it has good concealment, anti-interference, and is not restricted by any weather conditions. advantage. In addition, the inertial navigation system also has the characteristics of high data update rate, high short-term accuracy and good stability. It is because of the above advantages that it has been widely used in aviation, aerospace, navigation and many civil fields. In the strapdown inertial navigation system, all inertial components are directly installed on the carrier, and the output of the inertial components is the angular velocity and acceleration of the carrier relative to the inertial space, and the computer converts the acceleration data measured in the carrier coordinate system to the navigation coordinate system Carrying out navigation calculation is equivalent to using the gyroscope output data to build a mathematical platform in the computer as a reference for navigation calculation.

光纤陀螺作为一种新型的角速率传感器，与传统的陀螺仪(液浮陀螺仪、动力调谐陀螺仪、静电陀螺仪)相比，具有显著的优点：1)由于没有任何旋转部件，因而结构坚固、抗震动、抗冲击、耐大过载，可靠性高。同时系统功耗低，不需预热，启动时间短，且不需维修，寿命长；2)由于光纤为非金属材料，因此抗辐射性、抗干扰性强，性能稳定，可工作于较为恶劣的电磁环境中；3)由于灵敏度同光纤环的面积成正比，可以通过增加光纤环圈数的办法来增加光纤环的面积，提高陀螺的灵敏度，因此体积小、结构简单、加工工艺简单和成本低；4)动态范围大，不会出现低速率时的闭锁现象，而且可直接输出数字信号，便于利用计算机进行系统组合。As a new type of angular rate sensor, fiber optic gyroscope has significant advantages compared with traditional gyroscopes (liquid floating gyroscopes, dynamic tuning gyroscopes, electrostatic gyroscopes): 1) The structure is firm because it does not have any rotating parts , Anti-vibration, anti-shock, high overload resistance, high reliability. At the same time, the system has low power consumption, no preheating, short start-up time, no maintenance, and long life; 2) Since the optical fiber is made of non-metallic material, it has strong anti-radiation, anti-interference, and stable performance, and can work in harsh environments 3) Since the sensitivity is directly proportional to the area of the fiber optic ring, the area of the fiber optic ring can be increased by increasing the number of fiber ring turns to improve the sensitivity of the gyroscope, so the volume is small, the structure is simple, the processing technology is simple and the cost is low. Low; 4) The dynamic range is large, there will be no blocking phenomenon at low speed, and it can directly output digital signals, which is convenient for system combination by computer.

捷联惯性导航系统中，人们对于构成惯性测量单元的陀螺仪和加速度计等惯性器件的持续研究推动了惯性器件的快速发展。但器件精度越高，进一步提升器件精度的代价就越大。在惯性器件精度达到一定要求后，采用补偿惯性器件偏差的方法来进一步改善系统的性能是实现更高精度导航的一个实现途径。惯性元件的补偿方法有两种：一是利用外信息进行补偿校正，另一种方法是惯性器件偏差的自补偿，旋转调制技术是一种自补偿方法，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。In the strapdown inertial navigation system, people's continuous research on inertial devices such as gyroscopes and accelerometers that constitute the inertial measurement unit has promoted the rapid development of inertial devices. However, the higher the precision of the device, the greater the cost of further improving the precision of the device. After the precision of the inertial device reaches a certain requirement, it is a way to achieve higher precision navigation by using the method of compensating the deviation of the inertial device to further improve the performance of the system. There are two compensation methods for inertial components: one is to use external information for compensation and correction, and the other is to self-compensate for the deviation of inertial components. The measurement unit (IMU) modulates the navigation error to achieve the purpose of controlling the divergence of the navigation error and improving the 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，但是无法避免载体角运动对旋转调制技术的负面影响。因此，如何设计合理的三轴旋转补偿方式对于进一步提高光纤捷联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, it cannot avoid the negative effects of carrier angular motion on rotation modulation technology. Influence. Therefore, how to design a reasonable three-axis rotation compensation method is of great significance for further improving the navigation accuracy of the fiber optic strapdown inertial navigation system.

(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，提供一种基于惯性测量单元三个敏感轴旋转的光纤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 an error suppression method for an optical fiber strapdown inertial navigation system based on the rotation of three sensitive axes of an inertial measurement unit.

本发明的技术解决方案为：一种基于三轴旋转的光纤捷联惯导系统误差抑制方法，其特征在于采用惯性测量单元的三轴转位方案来完全隔离载体角运动，使惯性测量单元相对地理坐标系静止，避免载体角运动对于采用惯性测量单元旋转调制技术的消极影响，即可确定惯性器件常值偏差的抑制形式，以实现更高精度的导航。其具体步骤如下：The technical solution of the present invention is: an error suppression method for optical fiber strapdown inertial navigation system based on three-axis rotation, which is characterized in that the three-axis transposition scheme of the inertial measurement unit is used to completely isolate the carrier angular motion, so that the inertial measurement unit The geographic coordinate system is stationary, avoiding the negative impact of the angular motion of the carrier on the inertial measurement unit rotation modulation technology, and the suppression form of the constant value deviation of the inertial device can be determined to achieve higher precision navigation. 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)IMU采用十二个转停次序为一个旋转周期的转位方案(如附图2)；(3) The IMU adopts an indexing scheme in which twelve rotation-stop sequences are one rotation cycle (as shown in Figure 2);

次序1，IMU从A点出发逆时针转动180°到达位置B，停止时间T_s；次序2，IMU从B点出发逆时针转动180°到达位置C，停止时间T_s；次序3，IMU从C点出发逆时针转动180°到达位置A，停止时间T_s；次序4，IMU从A点出发逆时针转动180°到达位置C，停止时间T_s；次序5，IMU从C点出发逆时针转动180°到达位置B，停止时间T_s；次序6，IMU从B点出发逆时针转动180°到达位置A，停止时间T_s；次序7，IMU从A点出发顺时针转动180°到达位置B，停止时间T_s；次序8，IMU从B点出发顺时针转动180°到达位置C，停止时间T_s；次序9，IMU从C点出发顺时针转动180°到达位置A，停止时间T_s；次序10，IMU从A点出发顺时针转动180°到达位置C，停止时间T_s；次序11，IMU从C点出发顺时针转动180°到达位置B，停止时间T_s；次序12，IMU从B点出发顺时针转动180°到达位置A，停止时间T_s；IMU按照此转动顺序循环进行。Sequence 1, IMU starts from point A and rotates 180° counterclockwise to position B, stop time T _s ; sequence 2, IMU starts from point B to rotate 180° counterclockwise to position C, stop time T _s ; Sequence 3, IMU starts from C Start from point A and turn 180° counterclockwise to reach position A, stop time T _s ; Sequence 4, IMU turn 180° counterclockwise from point A to reach position C, stop time T _s ; Sequence 5, IMU turn counterclockwise 180° from point C ° Arrive at position B, stop time T _s ; Sequence 6, IMU starts from point B and rotates 180° counterclockwise to reach position A, stops at time T _s ; Sequence 7, IMU starts from point A and rotates 180° clockwise to position B, stops Time T _s ; Sequence 8, IMU starts from point B and turns 180° clockwise to reach position C, stop time T _s ; Sequence 9, IMU starts from point C to turn 180° clockwise to reach position A, stop time T _s ; Sequence 10 , the IMU starts from point A and rotates 180° clockwise to reach position C, stop time T _s ; sequence 11, IMU starts from point C to rotate 180° clockwise to reach position B, stop time T _s ; sequence 12, IMU starts from point B Rotate 180° clockwise to reach position A, stop time T _s ; IMU cycles through this rotation sequence.

(4)将惯性测量单元旋转后陀螺仪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；(4) Convert the data generated by the gyroscope after the inertial measurement unit rotates to the carrier coordinate system to obtain the modulation form of the constant value deviation of the inertial device;

假定IMU水平方向上的陀螺常值漂移分别为ε_x和ε_y。载体静止条件下，由于IMU停顿的A、B、C三个位置相对于导航坐标系对称，因此在一个三轴转位周期内的三个固定位置上，三个陀螺仪常值漂移在导航坐标系上投影引起的姿态角误差必然满足：Assume that the gyro constant drifts in the horizontal direction of the IMU are ε _x and ε _y , respectively. Under the static condition of the carrier, since the three positions A, B, and C where the IMU stops are symmetrical with respect to the navigation coordinate system, at three fixed positions within a three-axis indexing cycle, the three gyroscope constants drift in the navigation coordinate system Attach the projection The resulting attitude angle error must satisfy:

$33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{A A} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{B B} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{C C} = = 00$

$33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{A A} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{C C} = = 00$

$33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{A A} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{B B} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{C C} = = 00$

根据IMU三轴转动方案中的转动存在着转动的对称性问题，忽略载体运动的影响并以当地地理坐标系作为参考，12次序转位方案可以表述为：According to the rotation symmetry problem in the IMU three-axis rotation scheme, ignoring the influence of the carrier motion and taking the local geographic coordinate system as a reference, the 12-order transposition scheme can be expressed as:

过程1：次序1、6、7、12，构成的转动周期内，x、y轴的陀螺仪漂移在导航坐标系ox_ny_n平面内呈现出正反各一周的变化规律，因此在整周期的积分过程中产生的常值偏差为零，即：Process 1: Sequence 1, 6, 7, 12, within the rotation period formed, the gyroscope drift of the x and y axes presents a positive and negative cycle of change in the navigation coordinate system ox _n y _n plane, so in the entire cycle The constant deviation produced during the integration of is zero, that is:

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{A A \overset{+ +}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{B B \overset{+ +}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{A A \overset{- -}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{B B \overset{- -}{&RightArrow; &Right Arrow;} A A} = = 00$

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{A A \overset{+ +}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B \overset{+ +}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{A A \overset{- -}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B \overset{- -}{&RightArrow; &Right Arrow;} A A} = = 00$

其中，每个转动过程的时间计为T_z，围绕惯性测量单元敏感坐标轴逆时针转动为+，顺时针转动为-。Wherein, the time of each rotation process is counted as T _z , counterclockwise rotation around the sensitive coordinate axis of the inertial measurement unit is +, and clockwise rotation is -.

过程2：次序2、5、8、11，构成的转动周期内，y、z轴的陀螺仪漂移在导航坐标系oy_nz_n平面内呈现出正反各一周的变化规律，因此在整周期的积分过程中产生的常值偏差为零，即：Process 2: Sequence 2, 5, 8, 11, within the rotation cycle formed, the gyroscope drift of the y and z axes presents a positive and negative cycle change law in the navigation coordinate system oy _n z _n plane, so in the whole cycle The constant deviation produced during the integration of is zero, that is:

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B \overset{+ +}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{C C \overset{+ +}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B \overset{- -}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{C C \overset{- -}{&RightArrow; &Right Arrow;} B B} = = 00$

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{B B \overset{+ +}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{C C \overset{+ +}{&RightArrow; &Right Arrow;} B B} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{B B \overset{- -}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{C C \overset{- -}{&RightArrow; &Right Arrow;} B B} = = 00$

过程3：次序3、4、9、10，构成的转动周期内，x、z轴的陀螺仪漂移在导航坐标系ox_nz_n平面内呈现出正反各一周的变化规律，因此在整周期的积分过程中产生的常值偏差为零，即：Process 3: Sequences 3, 4, 9, 10, within the rotation cycle formed, the gyroscope drift of the x and z axes presents a positive and negative cycle of change in the navigation coordinate system ox _n z _n plane, so in the entire cycle The constant deviation produced during the integration of is zero, that is:

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{C C \overset{+ +}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{A A \overset{+ +}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{C C \overset{- -}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{x x}^{n no} dt dt))}_{A A \overset{- -}{&RightArrow; &Right Arrow;} C C} = = 00$

${(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{C C \overset{+ +}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{A A \overset{+ +}{&RightArrow; &Right Arrow;} C C} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{C C \overset{- -}{&RightArrow; &Right Arrow;} A A} + + {(({&Integral; &Integral;}_{00}^{{T T}_{z z}} {ϵ ϵ}_{z z}^{n no} dt dt))}_{A A \overset{- -}{&RightArrow; &Right Arrow;} C C} = = 00$

十二次序转停过程就是周期性的改变捷联矩阵的值，使三个陀螺仪的敏感轴在一个转动周期内沿转动中心对称分布(如附图3)。直观地证明了一个十二次序转停过程中，陀螺仪常值偏差相对导航坐标系被完全调制，对系统的导航精度不产生影响。同理在一个完整的转停周期内，由于三个固定位置及转动过程的对称分布，可以得到惯性测量单元停止及转位过程中加速度计零位偏差在导航坐标系的类似作用效果。The twelve-order turn-stop process is to periodically change the value of the strapdown matrix, so that the sensitive axes of the three gyroscopes are symmetrically distributed along the rotation center within one rotation period (as shown in Figure 3). It is proved intuitively that during a twelve-sequence turn-to-stop process, the gyroscope constant value deviation is completely modulated relative to the navigation coordinate system, and has no effect on the navigation accuracy of the system. Similarly, in a complete rotation-stop cycle, due to the symmetrical distribution of the three fixed positions and the rotation process, the similar effect of the zero position deviation of the accelerometer in the navigation coordinate system can be obtained during the stop and indexing process of the inertial measurement unit.

(5)将陀螺仪在IMU坐标系下的输出值带入捷联惯性导航系统中，采用等效旋转矢量法对捷联矩阵进行更新：(5) The output value of the gyroscope in the IMU coordinate system Into the strapdown inertial navigation system, using the equivalent rotation vector method to the strapdown matrix Make an update:

${ω ω}_{ns ns}^{s the s} = = {ω ω}_{is is}^{s the s} - - {(({C C}_{s the s}^{n no}))}^{T T} (({ω ω}_{ie ie}^{n no} + + {ω ω}_{en en}^{n no}))$

其中：为地球自转角速度在导航系下的分量；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；为IMU相对导航坐标系的运动角速度在IMU坐标系上的分量。in: is the component of the earth's rotation angular velocity in the navigation system; is the component of the motion angular velocity of the navigation coordinate system relative to the earth coordinate system under the navigation system; is the component of the angular velocity of the motion of the IMU relative to the navigation coordinate system on the IMU coordinate system.

设IMU坐标系相对导航坐标系的等效旋转矢量微分方程为：Let the equivalent rotation vector differential equation of the IMU coordinate system relative to the navigation coordinate system be:

$\overset{\cdot \cdot}{Φ Φ} = = {ω ω}_{ns ns}^{s the s} + + \frac{11}{22} Φ Φ \times \times {ω ω}_{ns ns}^{s the s} + + \frac{11}{1212} Φ Φ \times \times ((Φ Φ \times \times {ω ω}_{ns ns}^{s the s}))$

根据角速度求解出等效的旋转矢量并代替四元数解，According to angular velocity Solve for the equivalent rotation vector and replace the quaternion solution,

$q q = = cos cos \frac{Φ Φ}{22} + + \frac{Φ Φ}{| | Φ Φ | |} sin sin \frac{Φ Φ}{22}$

由于q＝q₀+q₁i+q₂j+q₃k，i、j、k为方向向量。因此姿态矩阵的更新过程为：Since q=q ₀ +q ₁ i+q ₂ j+q ₃ k, i, j, k are direction vectors. Therefore the attitude matrix The update process is:

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

(6)利用石英加速度计的输出值和步骤(5)计算的姿态矩阵计算出经过IMU旋转调制后载体的位置。(6) Utilize the output value of the quartz accelerometer and the attitude matrix calculated in step (5) Calculate the position of the carrier after the IMU rotation modulation.

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

${f f}^{n no} = = {C C}_{s the s}^{n no} {f f}_{is is}^{s the s}$

2)计算载体的位置：2) Calculate the 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t₂时刻载体位置为：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 position of the carrier at time t ₂ is calculated as:

3)计算载体位置误差：3) Calculate the carrier position error:

其中：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_N、R_M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。in: λ ₀ represents the longitude and latitude of the carrier's position at the initial moment, respectively; Δλ respectively represent the variation of the latitude and longitude of the carrier; R _N and R _M represent the curvature radii of the meridian circle and Maoyou circle of the earth respectively; t ₁ and t ₂ are two adjacent times in the process of inertial navigation system solution point.

本发明与现有技术相比的优点在于：本发明打破了传统捷联惯导系统中IMU与载体固连导致系统导航精度受到惯性器件偏差影响的约束，提出一种将IMU绕载体三个方向的敏感轴固定的三个位置正反转停的惯性器件常值偏差调制方案，该方法可以将所有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 the navigation accuracy of the system is affected by the deviation of the inertial device due to the fixed connection between the IMU and the carrier in the traditional strapdown inertial navigation system, and proposes a three-direction IMU around the carrier The constant value deviation modulation scheme of the inertial device with the three fixed positions of the sensitive axis and the forward and reverse stop. This method can modulate the constant value deviation of all inertial devices, effectively improving the navigation and 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，IMU三位置十二次序转停方案的误差模型参数：The carrier is in a static state, and the error model parameters of the IMU three-position twelve-sequence rotation-stop scheme:

三个位置的停顿时间：T_s＝5分钟；Dwell time at three positions: T _s = 5 minutes;

转动180°时消耗的时间：T_z＝12秒；Time consumed when turning 180°: T _z = 12 seconds;

转动180°的过程中，每一个转位中的加减速时间各为4秒；In the process of turning 180°, the acceleration and deceleration time in each index is 4 seconds;

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＝6378393.0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IMU三位置十二次序转停条件下，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 three positions and twelve sequential stops of the IMU, the method of the present invention can obtain higher positioning accuracy.

(四)附图说明 (4) Description of drawings

图1为本发明的一种基于三轴旋转的光纤捷联惯导系统误差抑制方法流程图；Fig. 1 is a flow chart of a method for suppressing errors of an optical fiber strapdown inertial navigation system based on three-axis rotation in the present invention;

图2为本发明的基于三轴旋转的光纤捷联惯导系统IMU转停方案详细步骤图；Fig. 2 is a detailed step diagram of the IMU turn-stop scheme of the optical fiber strapdown inertial navigation system based on three-axis rotation of the present invention;

图3为本发明的基于三轴旋转的光纤捷联惯导系统IMU转停时常值漂移方位分布；Fig. 3 is the distribution of the drift azimuth of the constant value when the IMU of the optical fiber strapdown inertial navigation system IMU based on the three-axis rotation of the present invention is turned off;

图4为本发明的基于三轴旋转的光纤捷联惯导系统的载体位置误差与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 optical fiber strapdown inertial navigation system based on the three-axis rotation of 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:

$33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{A A} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{B B} + + 33 {(({&Integral; &Integral;}_{00}^{{T T}_{s the s}} {ϵ ϵ}_{y the y}^{n no} dt dt))}_{C C} = = 00 - - - - - - ((11))$

$((22))$

$((33))$

$((44))$

${ω ω}_{ns ns}^{s the s} = = {ω ω}_{is is}^{s the s} - - {(({C C}_{s the s}^{n no}))}^{T T} (({ω ω}_{ie ie}^{n no} + + {ω ω}_{en en}^{n no})) - - - - - - ((55))$

$\overset{\cdot \cdot}{Φ Φ} = = {ω ω}_{ns ns}^{s the s} + + \frac{11}{22} Φ Φ \times \times {ω ω}_{ns ns}^{s the s} + + \frac{11}{1212} Φ Φ \times \times ((Φ Φ \times \times {ω ω}_{ns ns}^{s the s})) - - - - - - ((66))$

$q q = = cos cos \frac{Φ Φ}{22} + + \frac{Φ Φ}{| | Φ Φ | |} sin sin \frac{Φ Φ}{22} - - - - - - ((77))$

${C C}_{s the s}^{n no} = = [\begin{matrix} {q q}_{00}^{22} + + {q q}_{11}^{22} - - {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{11} {q q}_{22} - - {q q}_{00} {q q}_{33})) & 22 (({q q}_{11} {q q}_{33} + + {q q}_{00} {q q}_{22})) \\ 22 (({q q}_{11} {q q}_{22} + + {q q}_{00} {q q}_{33})) & {q q}_{00}^{22} - - {q q}_{11}^{22} + + {q q}_{22}^{22} - - {q q}_{33}^{22} & 22 (({q q}_{22} {q q}_{33} - - {q q}_{00} {q q}_{11})) \\ 22 (({q q}_{11} {q q}_{33} - - {q q}_{00} {q q}_{22})) & 22 (({q q}_{22} {q q}_{33} + + {q q}_{00} {q q}_{11})) & {q q}_{00}^{22} - - {q q}_{11}^{22} - - {q q}_{22}^{22} + + {q q}_{33}^{22} \end{matrix}] - - - - - - ((88))$

${f f}^{n no} = = {C C}_{s the s}^{n no} {f f}_{is is}^{s the s} - - - - - - ((99))$

2)计算载体的位置：2) Calculate the position of the carrier:

3)计算载体位置误差：3) Calculate the carrier position error:

Claims

1. the fiber strapdown inertial navigation system system error inhibiting method rotating based on three axles, is characterized in that comprising the following steps:

(1) by GPS, determine the initial position parameters of carrier, they are bound to navigational computer;

(2) strapdown inertial navitation system (SINS) is carried out preheating preparation, gathers the data of fibre optic gyroscope and quartz accelerometer output and data are processed;

(3) 12 of IMU employings turn and stop the transposition scheme that order is a swing circle;

Order 1, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from A point around U axle _s; Order 2, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from B point around E axle _s; Order 3, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from C point around N axle _s; Order 4, IMU rotates counterclockwise 180 ° of in-position C, stand-by time T from A point around N axle _s; Order 5, IMU rotates counterclockwise 180 ° of in-position B, stand-by time T from C point around E axle _s; Order 6, IMU rotates counterclockwise 180 ° of in-position A, stand-by time T from B point around U axle _s; Order 7, IMU clockwise rotates 180 ° of in-position B, stand-by time T from A point around U axle _s; Order 8, IMU clockwise rotates 180 ° of in-position C, stand-by time T from B point around E axle _s; Order 9, IMU clockwise rotates 180 ° of in-position A, stand-by time T from C point around N axle _s; Order 10, IMU clockwise rotates 180 ° of in-position C, stand-by time T from A point around N axle _s; Order 11, IMU clockwise rotates 180 ° of in-position B, stand-by time T from C point around E axle _s; Order 12, IMU clockwise rotates 180 ° of in-position A, stand-by time T from B point around U axle _s; All to look over and determine from the direction over against coordinate axis counterclockwise and clockwise; IMU rotates sequential loop according to this to carry out;

(4) data that after IMU rotation, gyroscope generates are transformed under carrier coordinate system, obtain the modulation format that inertia device is often worth deviation;

Gyroscope constant value drift in IMU horizontal direction is respectively ε _xand ε _y, under carrier quiescent conditions, because tri-positions of A, B, C that IMU pauses are symmetrical with respect to navigation coordinate system, therefore, on three fixed positions within three axle transposition cycles, three gyro drifts are fastened projection at navigation coordinate the attitude error causing must meet:

\begin{matrix} 3 {({&Integral;}_{0}^{T_{s}} ϵ_{x}^{n} dt)}_{A} + 3 {({&Integral;}_{0}^{T_{s}} ϵ_{x}^{n} dt)}_{B} + 3 {({&Integral;}_{0}^{T_{s}} ϵ_{x}^{n} dt)}_{C} = 0 \\ 3 {({&Integral;}_{0}^{T_{s}} ϵ_{y}^{n} dt)}_{A} + 3 {({&Integral;}_{0}^{T_{s}} ϵ_{y}^{n} dt)}_{B} + 3 {({&Integral;}_{0}^{T_{s}} ϵ_{y}^{n} dt)}_{C} = 0 \\ 3 {({&Integral;}_{0}^{T_{s}} ϵ_{z}^{n} dt)}_{A} + 3 {({&Integral;}_{0}^{T_{S}} ϵ_{z}^{n} dt)}_{B} + 3 {({&Integral;}_{0}^{T_{s}} ϵ_{z}^{n} dt)}_{C} = 0 \end{matrix}

According to the rotation in IMU tri-axle scheme of rotation, exist the symmetry problem of rotation, ignore the impact of carrier movement with local geographic coordinate system as a reference, 12 order transposition schemes are expressed as:

Process 1: order 1,6,7,12, in the rotation period of formation, the gyroscopic drift of x, y axle is ox at navigation coordinate _ny _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

\begin{matrix} {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{A \overset{+}{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{B \overset{+}{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{A \bar{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{B \bar{&RightArrow;} A} = 0 \\ {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{A \overset{+}{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{B \overset{+}{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{A \bar{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{B \bar{&RightArrow;} A} = 0 \end{matrix}

Wherein, the time of each rotation process is counted T _z, around the responsive coordinate axis of IMU rotate counterclockwise into+, clockwise rotate into-;

Process 2: order 2,5,8,11, in the rotation period of formation, the gyroscopic drift of y, z axle is oy at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

\begin{matrix} {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{B \overset{+}{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{C \overset{+}{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{B \bar{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{y}^{n} dt)}_{C \bar{&RightArrow;} B} = 0 \\ {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{B \overset{+}{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{C \overset{+}{&RightArrow;} B} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{B \bar{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{C \bar{&RightArrow;} B} = 0 \end{matrix}

Process 3: order 3,4,9,10, in the rotation period of formation, the gyroscopic drift of x, z axle is ox at navigation coordinate _nz _nin plane, present positive and negative each Changing Pattern of week, the normal value deviation therefore producing in the integral process of complete cycle is zero, that is:

\begin{matrix} {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{C \overset{+}{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{A \overset{+}{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{C \bar{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{x}^{n} dt)}_{A \bar{&RightArrow;} C} = 0 \\ {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{C \overset{+}{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{A \overset{+}{&RightArrow;} C} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{C \bar{&RightArrow;} A} + {({&Integral;}_{0}^{T_{z}} ϵ_{z}^{n} dt)}_{A \bar{&RightArrow;} C} = 0 \end{matrix}

It is exactly the value that periodically changes strapdown matrix that 12 order turn the process of stopping, and makes three gyrostatic sensitive axes symmetrical along center of rotation in a rotation period; Proved that intuitively 12 order turn in the process of stopping, gyroscope is often worth deviation Relative Navigation coordinate system to be modulated completely, and the navigation accuracy of system is not exerted an influence; In like manner complete turning in the cycle of stopping, symmetrical due to three fixed positions and rotation process, obtain that IMU stops and transposition process in accelerometer zero drift identical at the action effect of navigation coordinate system;

(5) output valve under IMU coordinate system by gyroscope bring in strapdown inertial navitation system (SINS), adopt equivalent rotating vector method to strapdown matrix upgrade:

ω_{ns}^{s} = ω_{is}^{s} - {(C_{s}^{n})}^{T} (ω_{ie}^{n} + ω_{en}^{n})

Wherein: for the component of rotational-angular velocity of the earth under navigation coordinate system; for navigation coordinate is the motion angular velocity of the relatively spherical coordinate system component under navigation coordinate system; for the motion angular velocity of the IMU Relative Navigation coordinate system component on IMU coordinate system;

The equivalent rotating vector differential equation of IMU coordinate system Relative Navigation coordinate system is:

\overset{\cdot}{Φ} = ω_{ns}^{s} + \frac{1}{2} Φ \times ω_{ns}^{s} + \frac{1}{12} Φ \times (Φ \times ω_{ns}^{s})

According to angular velocity solve equivalent rotating vector and replace hypercomplex number solution,

q = \cos \frac{Φ}{2} + \frac{Φ}{| Φ |} \sin \frac{Φ}{2}

Due to q=q ₀+ q ₁i+q ₂j+q ₃k, i, j, k are direction vector, so attitude matrix renewal process be:

C_{s}^{n} = [\begin{matrix} q_{0}^{2} + q_{1}^{2} - q_{2}^{2} - q_{3}^{2} & 2 (q_{1} q_{2} - q_{0} q_{3}) & 2 (q_{1} q_{3} + q_{0} q_{2}) \\ 2 (q_{1} q_{2} + q_{0} q_{3}) & q_{0}^{2} - q_{1}^{2} + q_{2}^{2} - q_{3}^{2} & 2 (q_{2} q_{3} - q_{0} q_{1}) \\ 2 (q_{1} q_{3} - q_{0} q_{2}) & 2 (q_{2} q_{3} + q_{0} q_{1}) & q_{0}^{2} - q_{1}^{2} - q_{2}^{2} + q_{3}^{2} \end{matrix}]

(6) utilize the output valve of quartz accelerometer and the attitude matrix of step (5) calculating calculate the position of carrier after IMU rotation modulation;

1) calculate the lower acceleration f of navigation coordinate system ⁿ:

f^{n} = C_{s}^{n} f_{is}^{s}

2) calculate the position of carrier:

According to t ₁carrier east orientation horizontal velocity V constantly _x(t ₁) and north orientation horizontal velocity V _y(t ₁), ask for t ₂carrier positions is constantly:

3) calculate carrier positions error:

Wherein: λ ₀the longitude and the latitude that represent respectively initial time carrier present position; Δ λ represents respectively the latitude of carrier, the variable quantity of longitude; R _n, R _mthe radius-of-curvature that represents respectively earth meridian circle, prime vertical; t ₁, t ₂two the adjacent time points in process that resolve for strapdown inertial navitation system (SINS).