CN107655493A - A kind of position system level scaling methods of optical fibre gyro SINS six - Google Patents
A kind of position system level scaling methods of optical fibre gyro SINS six Download PDFInfo
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Abstract
本发明公开了一种光纤陀螺SINS六位置系统级标定方法,本通过对惯性组件误差传播规律进行分析,设计转台的六位置旋转,计算得到系统速度误差和姿态误差,通过卡尔曼滤波器对各项误差进行滤波估计。本发明的有益效果为:基于系统级方法可准确地标定出光纤陀螺的零位误差、刻度因数误差、安装误差和加速度计的零位误差、刻度因数误差和安装误差;本发明给出了最简便的位置编排,同时给出了标定位置编排的原因,标定原理清晰,能够一次性标定。
The invention discloses a six-position system-level calibration method for fiber optic gyroscope SINS. By analyzing the error propagation law of the inertial component, the six-position rotation of the turntable is designed, and the system speed error and attitude error are obtained through calculation. The item error is filtered and estimated. The beneficial effects of the present invention are: based on the system level method, the zero error, scale factor error, installation error of the fiber optic gyroscope and the zero error, scale factor error and installation error of the accelerometer can be accurately calibrated; the present invention provides the most Simple position arrangement, and the reason for the calibration position arrangement is given at the same time. The calibration principle is clear and can be calibrated at one time.
Description
技术领域technical field
本发明涉及标定技术领域,尤其是一种光纤陀螺SINS六位置系统级标定方法。The invention relates to the technical field of calibration, in particular to a six-position system-level calibration method for an optical fiber gyro SINS.
背景技术Background technique
捷联惯性导航系统是一种利用陀螺和加速度计测量载体角运动和线运动,经过积分运算求出载体瞬时姿态、速度和位置的导航设备,它完全依靠自身的惯性组件完成导航任务,无需依赖任何外界信息,是一种完全自主的导航系统。捷联惯导系统由于其自主性高、隐蔽性好、全天候、稳定性好和短期精度高等优点,被广泛应用于国防科技领域。捷联惯导系统的特点是用数学平台替代平台式惯性导航的物理平台来模拟导航坐标系,由于其本质上是航位推算系统,其误差会随着时间的增加而积累。The strapdown inertial navigation system is a navigation device that uses gyroscopes and accelerometers to measure the angular motion and linear motion of the carrier, and obtains the instantaneous attitude, velocity and position of the carrier through integral calculations. It completely relies on its own inertial components to complete navigation tasks without relying on Any external information is a completely autonomous navigation system. Strapdown inertial navigation system is widely used in the field of national defense technology due to its advantages of high autonomy, good concealment, all-weather, good stability and high short-term accuracy. The feature of the strapdown inertial navigation system is to use a mathematical platform to replace the physical platform of the platform inertial navigation to simulate the navigation coordinate system. Since it is essentially a dead reckoning system, its error will accumulate with time.
根据捷联式惯性导航的原理可知,其关键技术包括惯性仪表技术、惯性组件误差补偿技术、初始对准技术和捷联矩阵更新算法。惯性组件误差占系统误差的90%左右,惯性组件误差补偿技术的方法就是标定。标定的目的是确定惯性组件的误差,并将标定误差补偿到惯性组件中,提高系统的导航精度。目前,所使用的光纤陀螺标定方法主要为分立式标定和系统级标定。分立式标定一般是依靠高精度转台提供位置和速率参考;系统级标定主要是通过观测导航误差反推出误差模型中的各项参数。该方法是基于导航解算的,对转台的精度要求很低,但是该方法原理复杂,并且一般标定时间较长。According to the principle of strapdown inertial navigation, its key technologies include inertial instrument technology, inertial component error compensation technology, initial alignment technology and strapdown matrix update algorithm. Inertial component errors account for about 90% of system errors, and the method of inertial component error compensation technology is calibration. The purpose of calibration is to determine the error of the inertial component and compensate the calibration error into the inertial component to improve the navigation accuracy of the system. At present, the fiber optic gyroscope calibration methods used are mainly discrete calibration and system-level calibration. Discrete calibration generally relies on high-precision turntables to provide position and velocity references; system-level calibration mainly derives various parameters in the error model by observing navigation errors. This method is based on navigation calculation and requires very low accuracy of the turntable, but the principle of this method is complex, and generally the calibration time is long.
光纤陀螺是光学陀螺的一种,是检测角速度的传感器。光纤陀螺采用的是Sagnac干涉原理,用光纤绕成环形光路并检测出随转动而产生的反相旋转的两路激光束之间的相位差,由此计算出旋转的角速度。光纤陀螺与传统的机械陀螺在原理上有本质的不同,具有机械陀螺无法比拟的优点,目前已经在惯性制导和导航领域内得到广泛应用。Fiber optic gyroscope is a kind of optical gyroscope, which is a sensor for detecting angular velocity. The fiber optic gyroscope adopts the Sagnac interference principle, uses optical fiber to form a circular optical path and detects the phase difference between the two laser beams that rotate in anti-phase with the rotation, and then calculates the angular velocity of the rotation. Fiber optic gyroscopes are essentially different from traditional mechanical gyroscopes in principle, and have incomparable advantages over mechanical gyroscopes. They have been widely used in the fields of inertial guidance and navigation.
发明内容Contents of the invention
本发明所要解决的技术问题在于,提供一种光纤陀螺SINS六位置系统级标定方法,能够准确地标定出光纤陀螺的各种误差,标定原理清晰,能够一次性标定。The technical problem to be solved by the present invention is to provide a SINS six-position system-level calibration method for an optical fiber gyroscope, which can accurately calibrate various errors of the optical fiber gyroscope, has a clear calibration principle, and can be calibrated at one time.
为解决上述技术问题,本发明提供一种光纤陀螺SINS六位置系统级标定方法,包括如下步骤:In order to solve the above-mentioned technical problems, the present invention provides a six-position system-level calibration method for fiber optic gyroscope SINS, comprising the following steps:
(1)将惯性组件安装在转台上,惯性组件初始朝向为东-北-天;惯性组件通电预热,设定采样周期;(1) Install the inertial component on the turntable, and the initial orientation of the inertial component is east-north-sky; the inertial component is powered on and preheated, and the sampling period is set;
(2)开始采集惯性组件数据并建立惯性组件误差模型和捷联惯导系统误差模型;(2) Start to collect inertial component data and establish an inertial component error model and a strapdown inertial navigation system error model;
(3)使惯性组件在步骤(1)中设定的初始位置静置1分钟进行静态导航,然后使惯性组件以10°/的角速度绕X轴正向旋转180°,使惯性组件的朝向为东-南-地,并静置1分钟进行静态导航;(3) Let the inertial component stand still at the initial position set in step (1) for 1 minute for static navigation, and then make the inertial component rotate 180° around the X axis at an angular velocity of 10°/, so that the orientation of the inertial component is East-south-land, and stand still for 1 minute for static navigation;
(4)使惯性组件绕X轴正向旋转90°,使惯性组件的朝向为东-地-北,并静置1分钟进行静态导航,然后是惯性组件以10°/的角速度绕Z轴正向旋转180°,使惯性组件的朝向为西-天-北,并静置1分钟进行静态导航;(4) Make the inertial component rotate 90° positively around the X-axis, make the orientation of the inertial component east-earth-north, and stand still for 1 minute for static navigation, and then the inertial component positively rotates around the Z-axis at an angular velocity of 10°/ Rotate 180° to make the orientation of the inertial assembly west-sky-north, and stand still for 1 minute for static navigation;
(5)使惯性组件绕Z轴正向旋转90°,使惯性组件的朝向为天-东-北,并静置1分钟进行静态导航,然后是惯性组件以10°/的角速度绕Y轴正向旋转180°,使惯性组件的朝向为地-东-南,并静置1分钟进行静态导航,停止采数;(5) Make the inertial component rotate 90° positively around the Z axis, make the orientation of the inertial component be sky-east-north, and stand still for 1 minute for static navigation, and then the inertial component rotates positively around the Y-axis at an angular velocity of 10°/ Rotate 180° to make the orientation of the inertial components ground-east-south, and stand still for 1 minute for static navigation, and stop data collection;
(6)对惯性组件采集的数据进行离线导航解算,并计算系统速度误差和姿态误差;(6) Perform off-line navigation calculation on the data collected by the inertial component, and calculate the system speed error and attitude error;
(7)设计卡尔曼滤波器对惯性组件误差进行滤波估计;(7) Design a Kalman filter to filter and estimate the inertial component error;
(8)将步骤(1)到步骤(5)重复执行,每次重复执行都更换不同的旋转角速度;对每次重复执行采集得到的数据进行导航解算和卡尔曼滤波估计,对计算得到的不同角速度下的惯性组件误差结果取平均值,作为最终的结果。(8) Repeat step (1) to step (5), and replace different rotational angular velocities with each repeated execution; carry out navigation solution and Kalman filter estimation on the data obtained from each repeated execution, and calculate the obtained The error results of the inertial components under different angular velocities are averaged as the final result.
优选的,步骤(1)中,采样周期为T=0.005s。Preferably, in step (1), the sampling period is T=0.005s.
优选的,步骤(2)中,建立惯性组件误差模型具体为:将光纤陀螺的安装误差、刻度系数误差和常值漂移建入陀螺误差模型,得:Preferably, in step (2), the establishment of the inertial component error model is specifically: the installation error, scale coefficient error and constant value drift of the fiber optic gyroscope are built into the gyroscope error model to obtain:
式中,n为导航坐标系;b为载体坐标系;i为惯性坐标系;εb为载体坐标系下常值漂移;为从载体坐标系至导航坐标系的变换矩阵;为陀螺的输出;[δKG]为陀螺的刻度系数误差,[δG]为安装误差, In the formula, n is the navigation coordinate system; b is the carrier coordinate system; i is the inertial coordinate system; ε b is the constant drift in the carrier coordinate system; is the transformation matrix from the carrier coordinate system to the navigation coordinate system; is the output of the gyro; [δK G ] is the scale factor error of the gyro, [δG] is the installation error,
将加速度计的安装误差、刻度系数误差和常值漂移建入加速度计误差模型,得:The installation error, scale coefficient error and constant value drift of the accelerometer are built into the accelerometer error model to get:
式中,为载体坐标系下常值漂移;fb为加速度计的输出;[δKA]为加速度计的刻度系数误差,[δA]为安装误差, In the formula, is the constant value drift in the carrier coordinate system; f b is the output of the accelerometer; [δK A ] is the scale coefficient error of the accelerometer, [δA] is the installation error,
建立姿态误差方程为:The attitude error equation is established as:
式中,φ为姿态误差角矢量;为导航坐标系相对惯性坐标系的角速度在导航坐标系下的投影;为导航坐标系相对惯性坐标系转动角速度计算误差;为陀螺仪误差在导航坐标系下的投影;In the formula, φ is the attitude error angle vector; is the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system under the navigation coordinate system; Calculate the error for the rotational angular velocity of the navigation coordinate system relative to the inertial coordinate system; is the projection of the gyroscope error in the navigation coordinate system;
建立速度误差方程为:The velocity error equation is established as:
式中,φn为导航坐标系下姿态误差角;fn为导航坐标系下加速度计的输出;为加速度计误差在导航坐标系下的投影;δVn=[δVE δVN δVU]T为东向、北向和天向速度误差;跟随地球旋转的角速度在导航坐标系下的投影;由于载体运动而引起的相对地球的旋转角速度在导航坐标系下的投影;Vn=[VE VN VU]T为东向、北向、天向速度;和为相应的误差。In the formula, φ n is the attitude error angle in the navigation coordinate system; f n is the output of the accelerometer in the navigation coordinate system; is the projection of the accelerometer error in the navigation coordinate system; δV n =[δV E δV N δV U ] T is the eastward, northward and celestial speed error; The projection of the angular velocity following the rotation of the earth in the navigation coordinate system; The projection of the rotational angular velocity relative to the earth due to the movement of the carrier under the navigation coordinate system; V n = [V E V N V U ] T is the eastward, northward, and skyward velocity; with for the corresponding error.
优选的,步骤(3)中,使惯性组件在步骤(1)中设定的初始位置静置1分钟进行静态导航解算,然后使惯性组件以10°/s的角速度绕X轴正向旋转180°,使惯性组件的朝向为东-南-地,并静置1分钟进行静态导航具体为:Preferably, in step (3), let the inertial component stand still for 1 minute at the initial position set in step (1) for static navigation calculation, and then make the inertial component rotate positively around the X-axis at an angular velocity of 10°/s 180°, so that the orientation of the inertial components is east-south-ground, and stand still for 1 minute for static navigation. The details are:
在转台条件下,姿态误差方程省去的表示;仅由陀螺误差引起的姿态误差方程可写成如下形式:Under the turntable condition, the attitude error equation omits The expression of ; the attitude error equation caused only by the gyro error can be written as follows:
仅由加速度计误差引起的速度误差方程可写成如下形式:The velocity error equation due only to accelerometer error can be written as follows:
在东-北-天的朝向时:In the east-north-day orientation:
展开得:expands to:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
绕X轴旋转,转动角度为180°,标定时采用的转速ω约为10°/s,ω远大于地球自转分量ωie(15°/h)和陀螺零偏,所以地球自转分量和陀螺零偏可以忽略不计,ωx≈ω,ωy≈0,ωz≈0,则有:Rotate around the X axis, the rotation angle is 180°, the rotation speed ω used in calibration is about 10°/s, ω is much larger than the earth rotation component ω ie (15°/h) and the gyro zero bias, so the earth rotation component and the gyro zero The bias can be ignored, ω x ≈ ω, ω y ≈ 0, ω z ≈ 0, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在东-南-地的朝向时:After rotation, in the east-south-land orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差解析得到加速度计相关激励误差项。The accelerometer-related excitation error term is resolved from the velocity errors at the two locations in this step.
优选的,步骤(4)中,使惯性组件绕X轴正向旋转90°,使惯性组件的朝向为东-地-北,并静置1分钟进行静态导航,然后是惯性组件以10°/s的角速度绕Z轴正向旋转180°,使惯性组件的朝向为西-天-北,并静置1分钟进行静态导航具体为:Preferably, in step (4), the inertial component is positively rotated 90° around the X axis, so that the orientation of the inertial component is east-ground-north, and it is left to stand for 1 minute for static navigation, and then the inertial component is rotated at 10°/ The angular velocity of s rotates 180° positively around the Z axis, so that the orientation of the inertial components is west-sky-north, and it is left to stand for 1 minute for static navigation. The details are:
在东-地-北的朝向时:In the east-earth-north orientation:
展开得:expands to:
绕Z轴旋转,转动角度为180°,ωx≈0,ωy≈0,ωz≈ω,则有:Rotate around the Z axis, the rotation angle is 180°, ω x ≈ 0, ω y ≈ 0, ω z ≈ ω, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在西-天-北的朝向时:After rotation, in the west-sky-north orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差可以解析得到加速度计相关激励误差项。According to the speed error at the two positions in this step, the accelerometer-related excitation error term can be obtained analytically.
优选的,步骤(5)中,使惯性组件绕Z轴正向旋转90°,使惯性组件的朝向为天-东-北,并静置1分钟进行静态导航,然后是惯性组件以10°/s的角速度绕Y轴正向旋转180°,使惯性组件的朝向为地-东-南,并静置1分钟进行静态导航,停止采数具体为:Preferably, in step (5), the inertial component is positively rotated 90° around the Z axis, so that the orientation of the inertial component is sky-east-north, and it is left to stand for 1 minute for static navigation, and then the inertial component is rotated at 10°/ The angular velocity of s rotates 180° positively around the Y axis, so that the orientation of the inertial components is ground-east-south, and it is left to stand for 1 minute for static navigation. The details of stopping data collection are:
在天-东-北的朝向时:In the sky-east-north orientation:
展开得:expands to:
绕Y轴旋转,转动角度为180°,ωx≈0,ωy≈ω,ωz≈0,则有:Rotate around the Y axis, the rotation angle is 180°, ω x ≈ 0, ω y ≈ ω, ω z ≈ 0, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在地-东-南的朝向时:After rotation, in the ground-east-south orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差可以解析得到加速度计相关激励误差项。According to the speed error at the two positions in this step, the accelerometer-related excitation error term can be obtained analytically.
优选的,步骤(6)中,对惯性组件采集的数据进行离线导航解算,并计算系统速度误差和姿态误差具体为;首先根据上述步骤中陀螺和加速度计测量得到的相对于惯性坐标系的角速度及比力在载体系上投影;之后,经过坐标系转换,得到载体角速度及比力在导航坐标系上投影,经过一次积分,可得载体相对于导航坐标系的瞬时姿态角及线速度;姿态角真值可由转台提供,速度真值设为0。Preferably, in step (6), the offline navigation solution is performed on the data collected by the inertial components, and the system velocity error and attitude error are calculated specifically as follows; The angular velocity and specific force are projected on the carrier system; after that, through coordinate system conversion, the angular velocity and specific force of the carrier are projected on the navigation coordinate system, and after one integration, the instantaneous attitude angle and linear velocity of the carrier relative to the navigation coordinate system can be obtained; The true value of the attitude angle can be provided by the turntable, and the true value of the velocity is set to 0.
优选的,步骤(7)中,设计卡尔曼滤波器对惯性组件误差进行滤波估计具体为:Preferably, in step (7), designing a Kalman filter to filter and estimate the inertial component error is specifically:
建立光纤陀螺系统级标定卡尔曼滤波状态方程:Establish the fiber optic gyroscope system-level calibration Kalman filter state equation:
式中, In the formula,
A1=[A11 A12 A13 A14]A 1 =[A 11 A 12 A 13 A 14 ]
式中,为陀螺产生的随机干扰;Tij(i,j=1,2,3)为姿态矩阵对应元素。In the formula, is the random disturbance generated by the gyroscope; T ij (i,j=1,2,3) is the attitude matrix corresponding element.
建立相应的量测方程:Create the corresponding measurement equation:
Z1(t)=H1X1(t)+V(t)Z 1 (t)=H 1 X 1 (t)+V(t)
式中,In the formula,
式中,θI、γI、ψI分别为导航解算得到的俯仰角、横滚角和航向角信息;θz、γZ、ψZ分别为转台姿态真值;δθ、δγ、δψ分别为导航解算与转台真值之间的误差;V(t)为系统量测噪声;In the formula, θ I , γ I , and ψ I are the pitch angle, roll angle, and heading angle information obtained from the navigation solution; θ z , γ Z , and ψ Z are the true attitude values of the turntable; is the error between the navigation solution and the true value of the turntable; V(t) is the system measurement noise;
建立加速度计系统级标定卡尔曼滤波状态方程:Establish the accelerometer system-level calibration Kalman filter state equation:
式中,In the formula,
A2=[A21 A22 A23 A24]A 2 =[A 21 A 22 A 23 A 24 ]
式中,为加速度计产生的随机干扰;Tij(i,j=1,2,3)为姿态矩阵对应元素;In the formula, is the random disturbance generated by the accelerometer; T ij (i,j=1,2,3) is the attitude matrix corresponding element;
建立相应的量测方程:Create the corresponding measurement equation:
Z2(t)=Vn(t)-0=H2X2(t)+V(t)Z 2 (t)=V n (t)-0=H 2 X 2 (t)+V(t)
式中,In the formula,
Z2(t)=[δVE δVN δVU]T Z 2 (t)=[δV E δV N δV U ] T
式中,δVE、δVN、δVU为导航解算与真值之间的误差;V(t)为系统量测噪声;以步骤(3)中系统误差模型建立24维卡尔曼滤波器,对惯性组件各项误差进行标定;利用卡尔曼滤波器原理,对状态量中各项误差参数进行估计,完成对惯性组件各项误差参数的辨识。In the formula, δV E , δV N , and δV U are the errors between the navigation solution and the true value; V(t) is the system measurement noise; a 24-dimensional Kalman filter is established based on the system error model in step (3), Calibrate the various errors of the inertial components; use the principle of the Kalman filter to estimate the various error parameters in the state quantity, and complete the identification of the various error parameters of the inertial components.
优选的,步骤(8)中,旋转角速度的取值范围为10°/-30°/。Preferably, in step (8), the value range of the rotational angular velocity is 10°/-30°/.
本发明的有益效果为:基于系统级方法可准确地标定出光纤陀螺的零位误差、刻度因数误差、安装误差和加速度计的零位误差、刻度因数误差和安装误差;本发明给出了最简便的位置编排,同时给出了标定位置编排的原因,标定原理清晰,能够一次性标定。The beneficial effects of the present invention are: based on the system level method, the zero error, scale factor error, installation error of the fiber optic gyroscope and the zero error, scale factor error and installation error of the accelerometer can be accurately calibrated; the present invention provides the most Simple position arrangement, and the reason for the calibration position arrangement is given at the same time. The calibration principle is clear and can be calibrated at one time.
附图说明Description of drawings
图1为本发明的标定方法中转台旋转路径编排示意图。Fig. 1 is a schematic diagram of the layout of the rotation path of the turntable in the calibration method of the present invention.
具体实施方式Detailed ways
如图1所示的转台旋转路径编排示意图,本发明通过设计转台的六位置旋转,计算得到系统速度误差,通过卡尔曼滤波器估计惯性组件误差参数,为了确保最终标定结果的准确性,转台重复三次进行六位置旋转,并将三次计算得到的惯性组件误差进行平均作为最终的标定结果,具体标定方法如下:As shown in Figure 1, the schematic diagram of the rotary path arrangement of the turntable, the present invention calculates the system speed error by designing the six-position rotation of the turntable, and estimates the error parameters of the inertial components through the Kalman filter. In order to ensure the accuracy of the final calibration result, the turntable repeats Perform six-position rotation three times, and average the inertial component errors obtained from the three calculations as the final calibration result. The specific calibration method is as follows:
步骤一:将惯性组件安装在转台上,惯性组件初始朝向为东-北-天;惯性组件通电预热,设定采样周期;Step 1: Install the inertial components on the turntable, the initial orientation of the inertial components is east-north-sky; power on the inertial components to preheat, and set the sampling period;
步骤二:开始采集惯性组件数据并建立惯性组件误差模型和捷联惯导系统误差模型;Step 2: Start to collect inertial component data and establish an inertial component error model and a strapdown inertial navigation system error model;
将光纤陀螺的安装误差、刻度系数误差和常值漂移建入陀螺误差模型,得:The installation error, scale coefficient error and constant value drift of the fiber optic gyroscope are built into the gyroscope error model, and we get:
式中,n为导航坐标系;b为载体坐标系;i为惯性坐标系;εb为载体坐标系下常值漂移;为从载体坐标系至导航坐标系的变换矩阵;为陀螺的输出;[δKG]为陀螺的刻度系数误差,[δG]为安装误差, In the formula, n is the navigation coordinate system; b is the carrier coordinate system; i is the inertial coordinate system; ε b is the constant drift in the carrier coordinate system; is the transformation matrix from the carrier coordinate system to the navigation coordinate system; is the output of the gyro; [δK G ] is the scale factor error of the gyro, [δG] is the installation error,
将加速度计的安装误差、刻度系数误差和常值漂移建入加速度计误差模型,得:The installation error, scale coefficient error and constant value drift of the accelerometer are built into the accelerometer error model to get:
式中,为载体坐标系下常值漂移;fb为加速度计的输出;[δKA]为加速度计的刻度系数误差,[δA]为安装误差, In the formula, is the constant value drift in the carrier coordinate system; f b is the output of the accelerometer; [δK A ] is the scale coefficient error of the accelerometer, [δA] is the installation error,
建立姿态误差方程为:The attitude error equation is established as:
式中,φ为姿态误差角矢量;为导航坐标系相对惯性坐标系的角速度在导航坐标系下的投影;为导航坐标系相对惯性坐标系转动角速度计算误差;为陀螺仪误差在导航坐标系下的投影;In the formula, φ is the attitude error angle vector; is the projection of the angular velocity of the navigation coordinate system relative to the inertial coordinate system under the navigation coordinate system; Calculate the error for the rotational angular velocity of the navigation coordinate system relative to the inertial coordinate system; is the projection of the gyroscope error in the navigation coordinate system;
建立速度误差方程为:The velocity error equation is established as:
式中,φn为导航坐标系下姿态误差角;fn为导航坐标系下加速度计的输出;为加速度计误差在导航坐标系下的投影;δVn=[δVE δVN δVU]T为东向、北向和天向速度误差;跟随地球旋转的角速度在导航坐标系下的投影;由于载体运动而引起的相对地球的旋转角速度在导航坐标系下的投影;Vn=[VE VN VU]T为东向、北向、天向速度;和为相应的误差;In the formula, φ n is the attitude error angle in the navigation coordinate system; f n is the output of the accelerometer in the navigation coordinate system; is the projection of the accelerometer error in the navigation coordinate system; δV n =[δV E δV N δV U ] T is the eastward, northward and celestial speed error; The projection of the angular velocity following the rotation of the earth in the navigation coordinate system; The projection of the rotational angular velocity relative to the earth due to the movement of the carrier under the navigation coordinate system; V n = [V E V N V U ] T is the eastward, northward, and skyward velocity; with is the corresponding error;
由于只考虑转台条件下,此时,捷联惯导系统的精确地理位置信息是可知的,因此我们只需要对姿态回路进行结算,不需要对速度和位置回路进行解算,而姿态解算误差只与陀螺误差有关。同时由于转台可以提供精确的姿态信息,因此,在考虑速度误差方程时,可以忽略牵连加速度。Since only the turntable condition is considered, the precise geographic location information of the strapdown inertial navigation system is known at this time, so we only need to calculate the attitude loop, and do not need to calculate the velocity and position loops, and the attitude calculation error Only related to gyro error. At the same time, since the turntable can provide accurate attitude information, the involved acceleration can be ignored when considering the velocity error equation.
步骤三:使惯性组件在步骤一中设定的初始位置静置1分钟进行静态导航解算,然后使惯性组件以10°/的角速度绕X轴正向旋转180°,使惯性组件的朝向为东-南-地,并静置1分钟进行静态导航;Step 3: Let the inertial component stand still at the initial position set in step 1 for 1 minute for static navigation calculation, and then make the inertial component rotate 180° around the X axis at an angular velocity of 10°/, so that the orientation of the inertial component is East-south-land, and stand still for 1 minute for static navigation;
由于是在转台条件下,为了方便分析,姿态误差方程省去的表示。Since it is under the condition of the turntable, for the convenience of analysis, the attitude error equation is omitted representation.
仅由陀螺误差引起的姿态误差方程可写成如下形式:The attitude error equation caused only by gyro error can be written as follows:
仅由加速度计误差引起的速度误差方程可写成如下形式:The velocity error equation due only to accelerometer error can be written as follows:
在东-北-天的朝向时:In the east-north-day orientation:
展开得:expands to:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
绕X轴旋转,转动角度为180°,标定时采用的转速ω约为10°/,ω远大于地球自转分量ωie(15°/h)和陀螺零偏,所以地球自转分量和陀螺零偏可以忽略不计,ωx≈ω,ωy≈0,ωz≈0,则有:Rotate around the X axis, the rotation angle is 180°, the rotation speed ω used in calibration is about 10°/, ω is much larger than the earth rotation component ω ie (15°/h) and the gyro zero bias, so the earth rotation component and the gyro zero bias Can be ignored, ω x ≈ ω, ω y ≈ 0, ω z ≈ 0, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在东-南-地的朝向时:After rotation, in the east-south-land orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差可以解析得到加速度计相关激励误差项。According to the speed error at the two positions in this step, the accelerometer-related excitation error term can be obtained analytically.
步骤四:使惯性组件绕X轴正向旋转90°,使惯性组件的朝向为东-地-北,并静置1分钟进行静态导航,然后是惯性组件以10°/的角速度绕Z轴正向旋转180°,使惯性组件的朝向为西-天-北,并静置1分钟进行静态导航;Step 4: Make the inertial component rotate 90° positively around the X-axis, make the orientation of the inertial component east-earth-north, and stand still for 1 minute for static navigation, and then the inertial component positively rotates around the Z-axis at an angular velocity of 10°/ Rotate 180° to make the orientation of the inertial assembly west-sky-north, and stand still for 1 minute for static navigation;
在东-地-北的朝向时:In the east-earth-north orientation:
展开得:expands to:
绕Z轴旋转,转动角度为180°,ωx≈0,ωy≈0,ωz≈ω,则有:Rotate around the Z axis, the rotation angle is 180°, ω x ≈ 0, ω y ≈ 0, ω z ≈ ω, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在西-天-北的朝向时:After rotation, in the west-sky-north orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差可以解析得到加速度计相关激励误差项。According to the speed error at the two positions in this step, the accelerometer-related excitation error term can be obtained analytically.
步骤五:使惯性组件绕Z轴正向旋转90°,使惯性组件的朝向为天-东-北,并静置1分钟进行静态导航,然后是惯性组件以10°/的角速度绕Y轴正向旋转180°,使惯性组件的朝向为地-东-南,并静置1分钟进行静态导航,停止采数。Step 5: Make the inertial component rotate 90° positively around the Z axis, make the orientation of the inertial component sky-east-north, and stand still for 1 minute for static navigation, and then the inertial component rotates positively around the Y-axis at an angular velocity of 10°/ Rotate 180° to make the orientation of the inertial components earth-east-south, and stand still for 1 minute for static navigation, and stop data collection.
在天-东-北的朝向时:In the sky-east-north orientation:
展开得:expands to:
绕Y轴旋转,转动角度为180°,ωx≈0,ωy≈ω,ωz≈0,则有:Rotate around the Y axis, the rotation angle is 180°, ω x ≈ 0, ω y ≈ ω, ω z ≈ 0, then:
展开得:expands to:
对上面各式进行积分可得:Integrating the above equations, we get:
旋转完后,在地-东-南的朝向时:After rotation, in the ground-east-south orientation:
加速度计引起的速度误差方程:The velocity error equation due to the accelerometer:
展开得:expands to:
根据此步骤中两个位置上的速度误差可以解析得到加速度计相关激励误差项。According to the speed error at the two positions in this step, the accelerometer-related excitation error term can be obtained analytically.
步骤六:对惯性组件采集的数据进行离线导航解算,并计算系统速度误差和姿态误差;Step 6: Perform offline navigation calculation on the data collected by the inertial component, and calculate the system speed error and attitude error;
首先根据上述步骤中陀螺和加速度计测量得到的相对于惯性坐标系的角速度及比力在载体系上投影。之后,经过坐标系转换,得到载体角速度及比力在导航坐标系上投影,经过一次积分,可得载体相对于导航坐标系的瞬时姿态角及线速度。姿态角真值可由转台提供,速度真值设为0。First, the angular velocity and specific force relative to the inertial coordinate system measured by the gyroscope and the accelerometer in the above steps are projected on the carrier body. Afterwards, after coordinate system conversion, the angular velocity and specific force of the carrier are projected on the navigation coordinate system, and after one integration, the instantaneous attitude angle and linear velocity of the carrier relative to the navigation coordinate system can be obtained. The true value of the attitude angle can be provided by the turntable, and the true value of the speed is set to 0.
步骤七:设计卡尔曼滤波器对惯性组件误差进行滤波估计;Step 7: Design a Kalman filter to filter and estimate the inertial component error;
建立光纤陀螺系统级标定卡尔曼滤波状态方程:Establish the fiber optic gyroscope system-level calibration Kalman filter state equation:
式中, In the formula,
A1=[A11 A12 A13 A14]A 1 =[A 11 A 12 A 13 A 14 ]
式中,为陀螺产生的随机干扰;Tij(i,j=1,2,3)为姿态矩阵对应元素。In the formula, is the random disturbance generated by the gyroscope; T ij (i,j=1,2,3) is the attitude matrix corresponding element.
建立相应的量测方程:Create the corresponding measurement equation:
Z1(t)=H1X1(t)+V(t)Z 1 (t)=H 1 X 1 (t)+V(t)
式中,In the formula,
式中,θi、γI、ψI分别为导航解算得到的俯仰角、横滚角和航向角信息;θz、γz、ψZ分别为转台姿态真值;δθ、δγ、δψ分别为导航解算与转台真值之间的误差;V(t)为系统量测噪声。In the formula, θ i , γ I , and ψ I are the pitch angle, roll angle, and heading angle information obtained from the navigation solution respectively; θ z , γ z , and ψ Z are the true attitude values of the turntable; is the error between the navigation solution and the true value of the turntable; V(t) is the system measurement noise.
建立加速度计系统级标定卡尔曼滤波状态方程:Establish the accelerometer system-level calibration Kalman filter state equation:
式中,In the formula,
A2=[A21 A22 A23 A24]A 2 =[A 21 A 22 A 23 A 24 ]
式中,为加速度计产生的随机干扰;Tij(i,j=1,2,3)为姿态矩阵对应元素。In the formula, is the random disturbance generated by the accelerometer; T ij (i,j=1,2,3) is the attitude matrix corresponding element.
建立相应的量测方程:Create the corresponding measurement equation:
Z2(t)=Vn(t)-0=H2X2(t)+V(t)Z 2 (t)=V n (t)-0=H 2 X 2 (t)+V(t)
式中,In the formula,
Z2(t)=[δVE δVN δVU]T Z 2 (t)=[δV E δV N δV U ] T
式中,δVE、δVN、δVU为导航解算与真值之间的误差;V(t)为系统量测噪声。In the formula, δV E , δV N , and δV U are the errors between the navigation solution and the true value; V(t) is the system measurement noise.
以步骤三中系统误差模型建立24维卡尔曼滤波器,对惯性组件各项误差进行标定Establish a 24-dimensional Kalman filter with the system error model in step 3, and calibrate the errors of the inertial components
利用卡尔曼滤波器原理,对状态量中各项误差参数进行估计,完成对惯性组件各项误差参数的辨识。Using the principle of Kalman filter, the error parameters in the state quantity are estimated, and the identification of the error parameters of the inertial components is completed.
步骤八:将步骤一到步骤五重复执行,每次重复执行都更换不同的旋转角速度;对每次重复执行采集得到的数据进行导航解算和卡尔曼滤波估计,方法与步骤六和步骤七相同;对计算得到的不同角速度下的惯性组件误差结果取平均值,作为最终的结果。Step 8: Repeat step 1 to step 5, and change the rotational angular velocity for each repetition; perform navigation calculation and Kalman filter estimation on the data collected by each repetition, the method is the same as step 6 and step 7 ; Take the average of the calculated inertial component error results under different angular velocities as the final result.
尽管本发明就优选实施方式进行了示意和描述,但本领域的技术人员应当理解,只要不超出本发明的权利要求所限定的范围,可以对本发明进行各种变化和修改。Although the present invention has been illustrated and described in terms of preferred embodiments, those skilled in the art should understand that various changes and modifications can be made to the present invention without departing from the scope defined by the claims of the present invention.
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