CN1908584A - Method for determining initial status of strapdown inertial navigation system - Google Patents

Method for determining initial status of strapdown inertial navigation system Download PDF

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CN1908584A
CN1908584A CN 200610112526 CN200610112526A CN1908584A CN 1908584 A CN1908584 A CN 1908584A CN 200610112526 CN200610112526 CN 200610112526 CN 200610112526 A CN200610112526 A CN 200610112526A CN 1908584 A CN1908584 A CN 1908584A
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position
sins
angle
initial
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CN100516775C (en
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房建成
宫晓琳
盛蔚
杨胜
徐帆
刘百奇
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北京航空航天大学
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Abstract

The initial attitude determination method for SINS comprises: rotating the SINS from initial position to any one position round arbitrary 3D axis; according to SINS output on first position and the relation of earth rotational angular velocity and acceleration of gravity, determining the initial attitude primarily; then, using Kalman filter to estimate the gyro constant drift and other values for more accurate initial attitude. This invention improves observability and precision.

Description

一种捷联惯性导航系统初始姿态确定方法 The method of determining a gesture of initial strapdown inertial navigation system

技术领域 FIELD

本发明涉及一种捷联惯性导航系统(SINS)初始姿态的确定方法,可用于各种中高精度的捷联惯性导航系统的初始姿态确定,特别适合于机载SINS安装时无转位机构,或转位机构精度不高、转角有限的情况。 The present invention relates to a method of determining the initial posture strapdown inertial navigation system (SINS), can be used in various high-precision initial attitude strapdown inertial navigation system to determine, especially for non-airborne SINS indexing mechanism during installation, or indexing means is not high precision, limited angle circumstances.

背景技术 Background technique

捷联惯性导航系统(SINS)的基本原理是根据牛顿提出的相对惯性空间的力学定律,利用陀螺仪、加速度计测量载体相对惯性空间的线运动和角运动参数,在给定的运动初始条件下,由计算机进行积分运算,连续、实时地提供位置、速度和姿态信息。 The basic principles of the strapdown inertial navigation system (of SINS) is based on the laws with respect to inertial space Newtonian proposed mechanics, the use of a gyroscope, a line motion relative to inertial space accelerometers measure vector and angular motion parameters at a given motion initial conditions , integral calculation performed by a computer, continuous, provide position, velocity and attitude information in real time. SINS完全依靠自身的惯性敏感元件,不依赖任何外界信息测量导航参数,因此,它具有隐蔽性好,不受气候条件限制,无信号丢失,不受干扰等优点,是一种完全自主式、全天候的导航系统,已广泛应用于航空、航天、航海等领域。 SINS entirely on their own inertia sensitive element, not dependent on any external information measuring navigation parameters, so it has good concealment, from weather conditions, no loss of signal, without interference, etc., is a fully autonomous, all-weather the navigation system has been widely used in aviation, aerospace, marine and other fields. 根据SINS的基本原理,SINS在导航定位解算之前必须获得初始信息,包括初始位置、速度和姿态。 The basic principle of the SINS, SINS initial information must be obtained before calculation navigation solution, including the initial position, velocity and attitude. SINS的初始位置和速度信息较初始姿态容易获得,初始姿态确定后的精度就是SINS进入导航工作状态时的初始精度。 SINS initial position and velocity information is more readily available initial posture, attitude determination accuracy after initial is the initial accuracy of navigation SINS enters the working state. 因此,SINS开始工作时进行快速精确的初始姿态确定是十分重要的一步。 Therefore, fast and accurate initial attitude determination is a very important step when SINS work.

现有的捷联惯导系统初始姿态确定可分为粗对准和精对准两个阶段。 Initial posture conventional strapdown inertial navigation system can be divided into coarse alignment and determining the fine alignment in two stages. 粗对准阶段就是在静基座条件下,将单个位置或两个位置上(固定两位置或任意两位置)的陀螺仪和加速度计输出直接引入计算机,计算出载体的初始姿态。 Coarse alignment stage is the base under static conditions, a single position or two positions (two positions or any two fixed positions) of the gyroscope and accelerometer output is introduced directly into the computer, calculating the initial attitude vector. 用此方法时,常常忽略陀螺仪与加速度计的误差及外部干扰因素,然而这些因素会导致误差,因此初始姿态计算精度不高。 When using this method, the error is often ignored and the external disturbance factors gyroscope and accelerometer, however, these factors can lead to errors, so the initial attitude calculation accuracy. 特别地,当采用固定两位置上的陀螺仪和加速度计的输出进行计算时,要求SINS绕Z轴旋转180度或90度,这就需要将SINS安装在一个转位机构上,利用转位机构实现180度或者90度的转动,工程使用时极不方便,而且转位机构的精度不高,转动角度也无法精确测量,降低了初始姿态确定的精度。 In particular, when using a gyro on two fixed positions and accelerometer output calculated in claim SINS rotation about the Z axis by 90 degrees or 180 degrees, which requires to be installed on a SINS indexing mechanism, the indexing mechanism using rotated 180 degrees or 90 degrees to achieve, the use of very inconvenient when the project, and the precision indexing mechanism is not high, the rotational angle can not be accurately measured, decrease the accuracy of determining the initial attitude. 由于具体工程中SINS安装位置的限制,还存在转动角度无法满足180度或90度要求的情况,此时,现有的固定两位置初始姿态确定方法将无法应用。 Due to limited to the specific project SINS mounting position, there is a rotation angle of 180 degrees or can not meet the requirement of 90, this time, two conventional fixed initial posture position determining method will not be applied. 此外,当利用任意两位置上的陀螺仪和加速度计输出时,需计算反正弦函数,陀螺仪和加速度计本身的误差以及测量误差等,容易造成计算结果不稳定,出现虚数现象,因此常需要进行多次任意两位置上陀螺仪和加速度计输出的采集和计算,对计算结果进行挑选,取平均值后,作为载体的初始姿态。 Further, when the gyros by any two positions and the accelerometer output, calculate the arc sine function, a gyroscope and accelerometer itself error and a measurement error and the like, is likely to cause the calculation results instability occurs imaginary phenomenon, and therefore often need multiple collection and calculation of any gyro and accelerometer outputs two positions, the selection results of the calculation, the average value, as the initial attitude of the carrier. 这样一来,初始姿态确定的时间将成倍增加,而且初始姿态计算的精度也无法得到保证。 Thus, the initial attitude determination time will be doubled, and initial pose calculation accuracy can not be guaranteed.

精对准阶段是在粗对准的基础上进行,利用现代控制理论的状态空间法,对陀螺仪和加速度计输出的数据进行处理。 Fine alignment stage is carried out in the rough alignment based on the use of modern control theory state space method, the data output of the gyroscope and accelerometer are processed. 当对单个位置的数据进行处理时,方位失准角的可观度差,收敛速度较慢,所需时间较长,而且陀螺仪和加速度计误差不可观测,因此,无法进行较好的估计,达不到提高初始姿态精度的目的,也不能在初始姿态计算的同时实现对陀螺仪和加速度计的标定。 When the processing of data in a single location, the azimuth angle of considerable misalignment poor, slow convergence takes longer, and a gyroscope and accelerometer errors can not be observed, therefore, can not be a good estimate of not increase the initial attitude accuracy purposes, can not be achieved calibration of gyroscopes and accelerometers while the initial attitude calculation. 当对固定两个位置的数据进行处理时,如上已叙述,现有的固定两位置初始姿态确定方法存在旋转角度的限制,且对转位机构精度要求较高,具体工程中往往不能应用。 When the two fixed positions of the data processing, as already described, there is a limitation of the rotational angle position of the two conventional fixed initial attitude determination method, and the higher accuracy of the indexing means, particularly engineering applications often can not.

发明内容 SUMMARY

本发明的技术解决问题是:克服现有技术的不足,提供一种精确、方便的捷联惯性导航系统初始姿态确定方法。 The technical problem of the present invention are: to overcome the deficiencies of the prior art by providing an accurate method for determining the initial posture, convenience strapdown inertial navigation system.

本发明的技术解决方案为:一种捷联惯性导航系统初始姿态确定方法,具体步骤如下:(1)SINS预热准备,具体准备时间根据不同的系统而不同;(2)SINS准备完毕后,保持SINS在初始位置(称为第一位置)静止不动,采集陀螺仪输出和加速度计输出; Technical Solution The present invention is as follows: initial gesture of strapdown inertial navigation system determination method, the following steps: (1) SINS warming up, depending on the specific preparation time different systems; (2) SINS After completion of the preparation, SINS held in the initial position (referred to as a first position) stationary, and gathering the gyro output accelerometer output;

(3)利用加速度计输出与重力加速度的关系以及陀螺仪输出与地球自转角速率的关系,计算出第一位置的航向角1、俯仰角θ1和横滚角γ1;(4)无需转位机构,通过任意方法将SINS从第一位置绕空间三维任意轴旋转到任意一个位置(称为第二位置),保持SINS在第二位置静止不动,采集陀螺仪输出和加速度计输出;(5)采用卡尔曼滤波技术,将1、θ1和γ1作为初始参数,对两个位置上陀螺仪和加速度计输出的数据进行处理。 (3) the use of accelerometer output, and the relationship between the gravitational acceleration of the Earth from the gyro output angle rate relationship is calculated heading angle 1 a first position, the roll angle and the pitch angle θ1 γ1; (4) without indexing mechanism, the rotation of SINS by any method from a first position the three-dimensional space about any axis to any position (referred to as second position), SINS held stationary in the second position, the gyro output and capture accelerometer output; (5 ) using the Kalman filtering technique, 1, θ1 and γ1 as an initial parameter, the data on two positions gyroscopes and accelerometers output processing. 由于SINS位置的改变,变化了SINS误差模型中的系统矩阵,从而SINS系统的可观测性得到改善,滤波效果得到提高,更好的估计出第二位置时计算地理坐标系n′与真实地理坐标系n之间的误差角(简称为失准角φx、φy和φz)及陀螺仪常值漂移、加速度计常值偏置;(6)利用估计出的φx、φy和φz计算真实地理坐标系n与计算地理坐标系n′之间的转换矩阵Cn′n。 SINS position due to the change, change in the error model SINS system matrix, thereby SINS system observability is improved, the filtering effect is improved, a better estimate of the geographic coordinate system of a computing second position n 'the real geographic coordinates the error angle (simply referred to as misalignment angle φx, φy and Phi] z) gyro drift constant, the accelerometer-based offset between the constant n; (6) using the estimated φx, φy and calculate the true geographic coordinates Phi] z n and calculating a geographic coordinate system transformation matrix Cn'n between n '. 根据陀螺仪输出的角增量或角速度信息,采用四元数方法,计算载体坐标系b与计算地理坐标系n′之间的转换矩阵Cbn′。 The incremental gyro output angle or angular velocity information, using quaternion calculating 'transformation matrix Cbn between' b n coordinate system and geographic coordinates calculated vector. 由Cn′n和Cbn′,计算出载体坐标系b与真实地理坐标系n之间的转换矩阵Cbn,再由Cbn计算第二位置的航向角2、俯仰角θ2和横滚角γ2,将其作为SINS的初始姿态。 And a Cn'n Cbn ', the calculated transformation matrix Cbn coordinate b between the support and the true geographic coordinate system n, the heading angle recalculated by the second position Cbn 2, pitch angle and roll angle θ2 γ2, the as an initial gesture of SINS.

本发明的原理是:SINS在某一个位置保持静止不动时,加速度计输出与重力加速度以及陀螺仪输出与地球自转角速率有如下关系:fx1fy1fz1=Cnb00g...(1)]]>ωx1ωy1ωz1=Cnb0ωiecosLωiesinL...(2)]]>其中,fx1、fy1和fz1以及ωx1、ωy1和ωz1分别为此位置上SINS的X轴、Y轴和Z轴输出的比力和角速率;g为重力加速度;ωie为地球自转角速率,其在东、北、天方向上的投影为Ω=[0 ωiecosL ωiesinL];L为当地纬度;Cnb为导航坐标系到载体坐标系的转换矩阵,Cnb=(Cbn)T=C11C13C13C21C12C23C31C32C33.]]>Cnb可以表达成此位置处航向角1、俯仰角θ1和横滚角γ1的表达式,利用(1)式和(2)式可以计算出此位置处的1、β1和γ1。 The principles of the present invention is: when SINS remain stationary at a certain position, the gravitational acceleration and the accelerometer output the gyro output angle from the Earth rate the following relationship: fx1fy1fz1 = Cnb00g ... (1)]]> & omega; x1 & omega; y1 & omega; z1 = Cnb0 & omega; iecosL & omega; iesinL ... (2)]]> wherein, fx1, fy1 and fz1 and ωx1, ωy1 and ωz1 respectively SINS position of the X-axis, Y-axis and Z-axis output therefor specific force and angular rate; G is the gravitational acceleration; ωie angular rate from the earth, which is projected on the east, north, days direction of Ω = [0 ωiecosL ωiesinL]; L is the local latitude; Cnb navigation coordinate system into a vector coordinate system transformation matrix, Cnb = (Cbn) T = C11C13C13C21C12C23C31C32C33.]]> Cnb can be expressed as the heading angle 1 this position, the pitch angle and roll angle γ1 expression θ1, the use of (1) and (2 ) can be calculated 1, β1 and γ1 at this location. 计算公式如下:由(1)、(2)式可得:C13=fx1g]]>C23=fy1g]]>C33=fz1g]]>C12=ωx1ωiecosL-fx1tanLg]]>C22=ωy1ωiecosL-fy1tanLg...(3)]]>C32=ωz1ωiecosL-fz1tanLg]]>C11=C22C33-C23C32C21=-C12C33+C13C32C31=C12C23-C13C22航向角1、俯仰角θ1和横滚角γ1的主值计算公式为: It is calculated as follows: a (1), (2), we have: C13 = fx1g]]> C23 = fy1g]]> C33 = fz1g]]> C12 = & omega; x1 & omega; iecosL-fx1tanLg]]> C22 = & omega; y1 & omega; iecosL-fy1tanLg ... (3)]]> C32 = & omega; z1 & omega; iecosL-fz1tanLg]]> C11 = C22C33-C23C32C21 = -C12C33 + C13C32C31 = C12C23-C13C22 heading 1, pitch angle θ1 and transverse calculated roll angle of the primary values ​​of γ1: 若航向角1、俯仰角θ1和横滚角γ1的取值范围定义为[0,2π]、 If the heading angle 1, pitch angle and roll angle range θ1 is defined as γ1 [0,2π], [-π,+π],那么1、θ1和γ1的真值可按如下方法确定。 [-Π, + π], then 1, θ1 and γ1 true value can be determined as follows.

θ1=θ1主(5) θ1 = θ1 master (5) 由(5)式确定的1、θ1和γ1即为SINS在此位置上的航向角、俯仰角和横滚角。 Determined by the formula (5) 1, θ1 and γ1 is the heading angle SINS In this position, the pitch angle and roll angle.

由于(1)式和(2)式中未考虑加速度计偏置、陀螺仪漂移以及加速度计和陀螺仪输出信息的测量误差,求得的航向角1、俯仰角θ1和横滚角γ1不能准确描述载体坐标系与当地地理坐标系之间的真实角度关系。 Because (1) and (2) the offset is not considered an accelerometer, gyroscope drift and measurement errors gyroscope and an accelerometer output, the obtained angle [phi] 1 heading, pitch angle and roll angle θ1 can γ1 accurately describe the real angular relationship between the vehicle coordinate system and the local geographic coordinate system. 因此,应当在此基础上,进一步利用现代估计理论将初始姿态失准角从随机误差和随机干扰中估计出来。 Thus, it should be based on this, the further use of modern estimation theory initial attitude misalignment angle estimated from the random errors and random interference.

利用卡尔曼滤波技术,将1、θ1和γ1作为初始参数,可以估计出计算地理坐标系n′与真实地理坐标系n之间的误差角,校正Cbn′后,可获得更为准确的初始姿态。 Kalman filtering techniques, will 1, θ1 and γ1 as the initial parameter can be estimated after calculating the geographic coordinate system n 'and the error angle between the actual geographic coordinate system n, the correction Cbn', obtain a more accurate initial attitude. 但是,当卡尔曼滤波对单个位置的加速度计和陀螺仪输出进行处理时,系统不完全可观测,其中,两个加速度计和一个陀螺仪的误差不可观测,因此估计效果差,达不到提高初始姿态精度的目的。 However, when the Kalman filter process accelerometer and gyroscope output of a single position, the system is not completely observed, wherein the two accelerometers error and a gyroscope can not be observed, so poor is estimated to improve the reach Objective initial attitude accuracy. 本发明通过将SINS从第一位置绕空间三维任意轴旋转到任意一个位置,即改变SINS的位置,来变化SINS误差模型中的系统矩阵,从而改善SINS系统的可观测性,提高卡尔曼滤波效果,更好地估计出失准角及陀螺仪、加速度计的误差。 SINS present invention from a first position by the three-dimensional space around the shaft is rotated to any arbitrary position, i.e. a position change SINS, vary SINS error model system matrix, thereby improving observability SINS system, Kalman filtering to improve the effects of , to better estimate the misalignment angle gyro, accelerometer errors. 利用估计出的失准角对转换矩阵Cbn′进行校正,得到更为准确的航向角、俯仰角和横滚角。 Using the estimated angular misalignment of the transformation matrix Cbn 'is corrected to obtain a more accurate heading angle, pitch angle and roll angle.

本发明与现有技术相比的优点在于:(1)本发明打破了传统固定两位置初始姿态计算需要通过转位机构将SINS绕Z轴旋转180度或90度的约束,而是无需通过转位机构,将SINS绕任意轴旋转到任意位置,是一种空间三维的任意双位置初始姿态计算方法。 Advantage over the prior art that the present invention is: (1) The present invention breaks the traditional two fixed positions need to calculate the initial attitude of the indexing rotation restricting mechanism SINS 90 degrees or 180 degrees about the Z axis, but without the need for transfer bit means, the SINS about an arbitrary axis to an arbitrary position, the three-dimensional space is a two-position any initial pose calculation. 避免了因转位机构精度不高,造成的固定两位置初始姿态计算精度的降低,即提高了初始姿态计算的精度。 Two fixed positions avoiding a deterioration in accuracy due to the initial posture calculating means indexing accuracy is not high, resulting, i.e., improve the accuracy of calculation of the initial pose. 此外,将SINS绕任意轴旋转到任意位置也极大的方便了在实际工程中的应用。 Further, the SINS about an arbitrary axis to an arbitrary position but also greatly facilitate the practical engineering application.

(2)本发明利用两个位置上陀螺仪和加速度计输出的数据,改善SINS系统的可观测性,提高卡尔曼滤波器的滤波效果,更好地估计出失准角及陀螺仪常值漂移、加速度计常值偏置,利用估计出的失准角对姿态矩阵进行校正后,得到更为准确的航向角、俯仰角和横滚角。 (2) The present invention utilizes a gyroscope and accelerometer data output from two positions, improving observability SINS system, the Kalman filter to improve the filtering effect, a better estimate of the misalignment angle, and the gyro constant drift after the accelerometer constant offset, corrected by the posture matrix estimated misalignment angle, obtain a more accurate heading angle, pitch angle and roll angle.

(3)本发明能够在初始姿态计算的同时完成测漂和定标任务,不但提高了系统初始姿态计算的精度,而且定标精度也得到了提高,在SINS导航状态给予补偿,可有效地提高导航定位精度。 (3) The present invention can be done at the same initial pose calculation drift measurement and calibration tasks, not only improve the accuracy of the initial posture calculated by the system, and calibration accuracy is also improved, compensation of SINS navigation state, can effectively improve the navigation and positioning accuracy.

附图说明 BRIEF DESCRIPTION

图1为本发明的初始姿态确定方法的流程图;图2为航向角、俯仰角θ和横滚角γ的示意图,图中Oxnynzn为导航坐标系,即东北天地理坐标系,Oxbybzb为载体坐标系。 A flowchart of a method of determining the initial posture in FIG. 1 of the present invention; FIG. 2 is a heading angle [phi], a schematic view of the pitch angle θ and roll angle γ, and FIG Oxnynzn navigation coordinate system, i.e. Northeast days geographic coordinate system, Oxbybzb carrier Coordinate System. 其中,图2a表示从导航坐标系Oxnynzn绕zn轴逆时针旋转与载体坐标系Oxbybzb重合,即为航向角;图2b表示从导航坐标系Oxnynzn绕xn轴逆时针旋转θ与载体坐标系Oxbybzb重合,θ即为俯仰角;图2c表示从导航坐标系Oxnynzn绕yn轴逆时针旋转γ与载体坐标系Oxbybzb重合,γ即为横滚角。 Wherein Figure 2a shows the navigation frame from the axis zn Oxnynzn rotated counterclockwise about [phi] coincides with the vector coordinates Oxbybzb,  is the heading angle; Figure 2b shows the xn axis is rotated counterclockwise about the θ coordinate system with the support from the navigation coordinate system Oxnynzn Oxbybzb overlap, θ is the pitch angle; FIG. 2c shows the navigation frame about the shaft rotates counterclockwise Oxnynzn yn coordinates Oxbybzb gamma] coincides with the carrier, γ is the roll angle.

具体实施方式 Detailed ways

如图1所示,本发明的具体实施方法如下:1、捷联惯性导航系统的准备SINS开机后,进入准备状态。 As shown in FIG. 1, the specific embodiment of the method of the present invention are as follows: 1, after preparation SINS strapdown inertial navigation system to boot into the ready state.

2、第一位置数据采集SINS准备完毕,保持SINS在初始位置(称为第一位置)静止不动,采集5分钟陀螺仪输出和加速度计输出,如果SINS的精度较低可适当延长采数时间。 2, a first data acquisition SINS ready position, holding the lower accuracy if SINS data acquisition time may be extended SINS initial position (referred to as a first position) stationary, collecting 5 minutes gyro output and an accelerometer output, .

3、第一位置姿态计算导航坐标系取为东北天地理坐标系,第一位置处航向角1、俯仰角θ1和横滚角γ1的定义如图2a、图2b和图2c所示。 3, a first position and posture computing the navigation frame is taken as the Northeast days geographic coordinate system, at a first angular position [phi] 1 heading, pitch angle and roll angle θ1 defined γ1 in FIG. 2a, 2b and 2c.

加速度计输出与重力加速度以及陀螺仪输出与地球自转角速率有如下关系:fx1fy1fz1=Cnb00g...(6)]]>ωx1ωy1ωz1=Cnb0ωiecosLωiesinL...(7)]]>式中,fx1、fy1和fz1以及ωx1、ωy1和ωz1分别为第一个位置上SINS的X轴、Y轴和Z轴输出的比力和角速率;g为重力加速度;ωie为地球自转角速率,其在东、北、天方向上的投影为Ω=[0 ωiecosL ωiesinL],L表示当地纬度;Cnb为导航系到载体系的转换矩阵,可写为:Cnb=(Cbn)T=C11C13C13C21C12C23C31C32C33.]]>由(6)、(7)式可得:C13=fx1g]]>C23=fy1g]]>C33=fz1g]]>C12=ωx1ωiecosL-fx1tanLg]]>C22=ωy1ωiecosL-fy1tanLg...(8)]]> Accelerometer output the gravitational acceleration and the gyroscope output of the Earth's angular rate the following relationship: fx1fy1fz1 = Cnb00g ... (6)]]> & omega; x1 & omega; y1 & omega; z1 = Cnb0 & omega; iecosL & omega; iesinL ... (7) ]]> where, fx1, fy1 and fz1 and ωx1, ωy1 and ωz1 SINS respectively the first position of the X-axis, the specific force and angular rate Y axis and Z axis output; G is the acceleration of gravity; ωie earth since angular rate, which is projected on the east, north, days direction of Ω = [0 ωiecosL ωiesinL], L represents the local latitude; Cnb the navigation system to the transformation matrix carrier system, can be written as: Cnb = (Cbn) T . = C11C13C13C21C12C23C31C32C33]]> of (6), (7), we have: C13 = fx1g]]> C23 = fy1g]]> C33 = fz1g]]> C12 = & omega; x1 & omega; iecosL-fx1tanLg]]> C22 = & omega; y1 & omega; iecosL-fy1tanLg ... (8)]]>

C32=ωz1ωiecosL-fz1tanLg]]>C11=C22C33-C23C32C21=-C12C33+C13C32C31=C12C23-C13C22航向角1、俯仰角θ1和横滚角γ1的主值计算公式为: C32 = & omega; z1 & omega; iecosL-fz1tanLg]]> C11 = C22C33-C23C32C21 = -C12C33 + C13C32C31 = C12C23-C13C22 heading 1, the main value of the pitch angle θ1 calculated roll angle γ1 and formula is: θ1主=arcsin(C23) (9) Main θ1 = arcsin (C23) (9) 若航向角1、俯仰角θ1和横滚角γ1的取值范围定义为[0,2π]、 If the heading angle 1, pitch angle and roll angle range θ1 is defined as γ1 [0,2π], [-π,+π],那么1、θ1和γ1的真值可按如下方法确定。 [-Π, + π], then 1, θ1 and γ1 true value can be determined as follows.

θ1=θ1主(10) θ1 = θ1 primary (10) 由(10)式确定的1、θ1和γ1即为SINS在第一位置上的航向角、俯仰角和横滚角。 Determined by the formula (10) 1, θ1 and γ1 is the heading angle SINS in the first position, the pitch angle and roll angle.

4、第二位置数据采集通过任意方法将SINS从初始位置绕空间三维任意轴旋转到任意一个位置(称为第二位置),保持SINS在第二位置静止不动,采集5分钟陀螺仪输出和加速度计输出。 4, the second location data collection SINS rotation about three spatial axes by any arbitrary method from an initial position to any position (referred to as second position), SINS held stationary in the second position, the gyro output collected 5 minutes and accelerometer output.

5、对两个位置的数据进行滤波处理将1、θ1和γ1作为初始参数,利用卡尔曼滤波技术,对两个位置上陀螺仪和加速度计输出的数据进行处理,精确估计出失准角φx、φy和φz(东北天地理坐标系下是φE、φN和φU)及陀螺仪常值漂移、加速度计常值偏置。 5, the data filtering process is performed two positions will 1, θ1 and γ1 as the initial parameters by Kalman filtering technique, two data positions gyroscopes and accelerometers output processed accurately estimated angular misalignment φx, φy and Phi] z (Northeast days under the geographic coordinate system is φE, φN and phi] U) and the constant drifts of the gyroscope, accelerometer bias constant.

(1)SINS初始姿态确定误差模型的建立导航坐标系取为东北天地理坐标系,位置和垂直速度误差省略,加速度计和陀螺仪的误差视为随机偏置加白噪声过程,此时SINS的误差模型为:δV·EδV·Nφ·Eφ·Nφ·U▿·x▿·yϵ·xϵ·yϵ·z=02ΩU0-g0T11T12000-2ΩU0g00T21T22000000ΩU-ΩN00T11T12T1300-ΩU0000T21T22T2300-ΩN0000T31T32T3300000000000000000000000000000000000000000000000000δVEδVNφEφNφU▿x▿yϵxϵyϵz...(11)]]>式中,下标E、N、U分别表示东、北、天。 (. 1) is determined to establish the initial posture SINS navigation error model coordinate system is taken as the Northeast days geographic coordinate system, the position and vertical velocity error is omitted, the accelerometer and gyroscope errors considered random white noise process plus the offset, then the SINS error model: & delta; V & CenterDot; E & delta; V & CenterDot; N & phi; & CenterDot; E & phi; & CenterDot; N & phi; & CenterDot; U & dtri; & CenterDot; x & dtri; & CenterDot; y & epsiv; & CenterDot; x & epsiv; & CenterDot; y & epsiv; & CenterDot; z = 02 & Omega; U0- g0T11T12000-2 & Omega; U0g00T21T22000000 & Omega; U- & Omega; N00T11T12T1300- & Omega; U0000T21T22T2300- & Omega; N0000T31T32T3300000000000000000000000000000000000000000000000000 & delta; VE & delta; VN & phi; E & phi; N & phi; U & dtri; x & dtri; y & epsiv; x & epsiv; y & epsiv; z ... (11)]]> formula subscripts E, N, U represent the east, north and days. 地球自转角速率ωie在东、北、天方向上的投影为Ω=[0 ωiecosL ωiesinL]=[0 ΩNΩU],L表示当地纬度;下标x、y、z为载体坐标系;Tij(i=1,2,3;j=1,2,3)为姿态矩阵Cbn中的元素,Cbn={Tij}i=1,2,3;j=1,2,3.]]>(2)SINS初始姿态确定卡尔曼滤波模型的建立对于捷联惯导系统,考虑到陀螺仪随机漂移误差和加速度计的随机偏差,将方程(11)修正为如下形式:[X·a(t)X·b(t)]=FTi05×505×5[Xa(t)Xb(t)]+[W′(t)05×1]=AiX(t)+W(t)...(12)]]>式中,W(t)为N(O,Q)的高斯白噪声;状态变量Xa=[δVEδVNφEφNφU]T,Xb=[xyεxεyεz]T;随机噪声状态矢量W′(t)=wδVEwδVNwφEwφNwφUT,]]>其中,δVE、δVN分别为东向和北向速度误差,φE、φN为水平失准角;φU为方位失准角;x、y为加速度计随机常值偏置,εx、εy、εz是陀螺仪随机常值漂移;05×5和05×1均为指定维数的 Of the Earth's angular rate ωie in the east, north and the projection of heaven direction Ω = [0 ωiecosL ωiesinL] = [0 ΩNΩU], L represents the local latitude; subscripts x, y, z is a vector coordinate system; Tij (i = 1,2,3; j = 1,2,3) is the attitude matrix Cbn the elements, Cbn = {Tij} i = 1,2,3;. j = 1,2,3]]> (2) SINS initial posture determination establishing a Kalman filter model for a strapdown inertial navigation system, taking into account the random deviations random gyro drift error and the accelerometer, the (11) the correction equation in the following form: [X & CenterDot; a (t) X & CenterDot; b (t)] = FTi05 & times; 505 & times; 5 [Xa (t) Xb (t)] + [W & prime; (t) 05 & times; 1] = AiX (t) + W (t) ... (12)]]> wherein, W (t) is white Gaussian noise N (O, Q); and a state variable Xa = [δVEδVNφEφNφU] T, Xb = [xyεxεyεz] T; random noise state vector W & prime; (t) = w & delta; VEw & delta; VNw & phi; Ew & phi; Nw & phi; UT,]]> wherein, δVE, δVN respectively velocity error east and north, φE, φN horizontal misalignment angle; phi] U azimuth misalignment angle; x, y acceleration the count value of the bias is often random, εx, εy, εz gyroscope random constant drift; 05 × 5 05 × 1 and are of a specified dimension 零矩阵;F和Ti代表的内容如下:Ti=T11T12000T21T2200000T11T12T1300T21T22T2300T31T32T33,]]>F=02ΩU0-g0-2ΩU0g00000ΩU-ΩN00-ΩU0000ΩN00]]>(12)式为捷联惯导系统初始姿态确定卡尔曼滤波模型的系统方程。 Zero matrix; Content F and representatives of Ti as follows: Ti = T11T12000T21T2200000T11T12T1300T21T22T2300T31T32T33,]]> F = 02 & Omega; U0-g0-2 & Omega; U0g00000 & Omega; U- & Omega; N00- & Omega; U0000 & Omega; N00]]> (12) formula Jie for initial attitude determination system of equations of the Kalman filter model. 为了应用卡尔曼滤波器进行状态向量的最优估计,还需建立系统观测方程。 In order to apply the Kalman filter optimal estimation of the state vector, the need to establish a system of observation equations. 选取两个水平速度误差为观测量,建立的系统观测方程为Z(t)=10000000000100000000XaXb+ηEηN=HX(t)+η(t)...(13)]]>其中,η(t)是系统观测噪声向量,为N(O,R)的高斯白噪声过程。 Select two horizontal velocity error for the concept of measurement, systematic observation equation established for the Z (t) = 10000000000100000000XaXb + & eta; E & eta; N = HX (t) + & eta; (t) ... (13)]]> wherein, η (t) is an observation noise vector system, Gaussian white noise process N (O, R) is.

(3)离散卡尔曼滤波模型的建立根据上述系统方程和观测方程,可建立离散卡尔曼滤波方程如下。 (3) establishing a discrete Kalman filter system model according to the above equations and observation equations, the discrete Kalman filter equations may be established as follows.

滤波方程: Filter equations: 增益方程:Kk=Pk,k-1HkT[HkPk,k-1HkT+Rk]-1...(15)]]>预报误差方差方程:Pk,k-1=Φk,k-1Pk-1Φk,k-1T+Qk-1...(16)]]>滤波误差方差方程:Pk=[I-KkHk]Pk,k-1(17)式中,Φk,k-1为离散化的状态转移矩阵(系统矩阵),Q、R分别为系统噪声和观测噪声的协方差矩阵。 Gain equation: Kk = Pk, k-1HkT [HkPk, k-1HkT + Rk] -1 ... (15)]]> prediction error variance equation: Pk, k-1 = & Phi; k, k-1Pk-1 & Phi ; k, k-1T + Qk-1 ... (16)]]> filtering error variance equation: Pk = [I-KkHk] Pk, (17) k-1 in the formula, Φk, k-1 discretization the state transition matrix (matrix system), Q, R are the covariance matrix of the observation noise and system noise.

(4)滤波初始条件X(0)=010×1;P(0)、Q和R对应中等精度SINS的取值如下: (4) filtering the initial condition X (0) = 010 × 1; P (0), Q and R values ​​corresponding to medium accuracy SINS follows:

P(0)=diag{(0.3m/s)2,(0.3m/s)2,(30′)2,(10″)2,(10″)2,(100μg)2,(100μg)2,(0.1°)2,(0.1°)2,(0.1°)2};Q=diag{(100μg)2,(100μg)2,(0.1°)2,(0.1°)2,(0.1°)2,0,0,0,0,0};R=diag{(0.1m/s)2,(0.1m/s)2}。 P (0) = diag {(0.3m / s) 2, (0.3m / s) 2, (30 ') 2, (10 ") 2, (10") 2, (100μg) 2, (100μg) 2 , (0.1 °) 2, (0.1 °) 2, (0.1 °) 2}; Q = diag {(100μg) 2, (100μg) 2, (0.1 °) 2, (0.1 °) 2, (0.1 °) 2,0,0,0,0,0}; R = diag {(0.1m / s) 2, (0.1m / s) 2}.

6、计算陀螺仪随机常值漂移和加速度计随机常值偏置滤波器估计出的x、y即为加速度计随机常值偏置,εx、εy、εz为陀螺仪随机常值漂移。 6, calculates a gyro random constant drifts and accelerometer random constant offset filter estimated x, y accelerometer that is a random bias constant, εx, εy, εz gyro random constant drift.

7、计算载体坐标系b与计算地理坐标系n′之间的转换矩阵Cbn′可利用陀螺仪输出的角增量或角速度信息,采用四元数方法计算Cbn′,计算步骤如下:(1)利用航向角1、俯仰角θ1和横滚角γ1初始化第一个位置时的姿态,计算初始转换矩阵Cbn′和四元数q,计算公式如下: 7, calculating and computing vector coordinates b geographic coordinate system n 'transformation matrix Cbn between' may be utilized or angular increments of angular velocity information output from the gyro is calculated Cbn quaternion method ', the following calculation steps: (1) using the heading angle [phi] 1, the pitch attitude angle θ1 when the roll angle γ1 and initialize the first position, to calculate the initial transformation matrix Cbn 'and quaternion q, is calculated as follows: 令Cbn′=T11T12T13T21T22T23T31T32T33]]>则有:q0=±121+T11+T22-T33]]>q1=±121+T11+T22-T33]]>q2=±121+T11+T22-T33]]>q3=±121+T11+T22-T33]]>(2)更新四元数q0、q1、q2、q3和转换矩阵Cbn′ So Cbn & prime; = T11T12T13T21T22T23T31T32T33]]> there are: q0 = & PlusMinus; 121 + T11 + T22-T33]]> q1 = & PlusMinus; 121 + T11 + T22-T33]]> q2 = & PlusMinus; 121 + T11 + T22-T33 ]]> q3 = & PlusMinus; 121 + T11 T22-T33]]> (2) + update quaternion q0, q1, q2, q3, and transformation matrix Cbn '

q(n+1)={(1-(Δθ0)28+(Δθ0)4384)I+(12-(Δθ0)248)(Δθ)}q(n)...(19)]]>其中,Δθ=0-Δθx-Δθy-ΔθzΔθx0Δθz-ΔθyΔθy-Δθz0ΔθxΔθzΔθy-Δθx0]]>Δθ0=Δθx2+Δθy2+Δθz2]]>转换矩阵Cbn′的更新公式如下:Cbn′=q02+q12-q22-q322(q1q2-q0q3)2(q1q3+q0q2)2(q1q2+q0q3)q02-q12+q22-q322(q2q3-q0q1)2(q1q3-q0q2)2(q2q3+q0q1)q02-q12-q22+q32...(20)]]>8、计算航向角2、俯仰角θ2和横滚角γ2利用卡尔曼滤波估计出的φE、φN、φU计算真实地理坐标系n与计算地理坐标系n′之间的转换矩阵Cn′n。 q (n + 1) = {(1 - (& Delta; & theta; 0) 28 + (& Delta; & theta; 0) 4384) I + (12 - (& Delta; & theta; 0) 248) (& Delta; theta &;)} q (n) ... (19)]]> wherein, & Delta; & theta; = 0- & Delta; & theta; x- & Delta; & theta; y- & Delta; & theta; z & Delta; & theta; x0 & Delta; & theta; z- & Delta; & theta ; y & Delta; & theta; y- & Delta; & theta; z0 & Delta; & theta; x & Delta; & theta; z & Delta; & theta; y- & Delta; & theta; x0]]> & Delta; & theta; 0 = & Delta; & theta; x2 + & Delta; & theta; y2 + & Delta; & theta; z2]]> transformation matrix Cbn 'the following update equations: Cbn & prime; = q02 + q12-q22-q322 (q1q2-q0q3) 2 (q1q3 + q0q2) 2 (q1q2 + q0q3) q02-q12 + q22 -q322 (q2q3-q0q1) 2 (q1q3-q0q2) 2 (q2q3 + q0q1) q02-q12-q22 + q32 ... (20)]]> 8, computes the heading 2, pitch angle and roll angle θ2 conversion matrix Cn'n γ2 Kalman filter estimated φE, φN, φU calculate the true geographic coordinate system and calculating a geographic coordinate system n n 'between. 根据Cn′n和(20)式计算出的Cbn′,计算载体坐标系b与真实地理坐标系n之间的转换矩阵Cbn,再由Cbn计算第二位置的航向角2、俯仰角θ2和横滚角γ2,将其作为SINS的初始姿态。 Calculated based Cn'n and (20) Cbn ', calculates a transformation matrix Cbn coordinate b between the support and the true geographic coordinate system n, then the heading angle is calculated from the second position Cbn 2, and a pitch angle θ2 roll angle γ2, as the initial attitude of SINS. 具体计算步骤如下:(1)计算真实地理坐标系n与计算地理坐标系n′之间的转换矩阵Cnn′Cn′n=1-φUφNφU1-φE-φNφE1...(21)]]>(2)计算载体坐标系b与真实地理坐标系n之间的转换矩阵CbnCbn=Cn′nCbn′...(22)]]>(3)计算航向角2、俯仰角θ2和横滚角γ2航向角2、俯仰角θ2和横滚角γ2的定义如图2a、图2b和图2c所示。 The calculation steps are as follows: (1) calculate the conversion real geographic coordinate system n and calculating a geographic coordinate system n 'between the matrix Cnn'Cn & prime; n = 1- & phi; U & phi; N & phi; U1- & phi; E- & phi; N & phi; E1 ... (21)]]> (2) calculate the transform matrix CbnCbn coordinate b between the support and the true geographic coordinate system n = Cn & prime; nCbn & prime; ... (22)]]> (3) computes the heading 2, pitch angle and roll angle θ2 heading angle γ2 2, defined pitch angle and roll angle θ2 γ2 in FIG. 2a, 2b and 2c.

将(22)式计算出的Cbn记为 The (22) is calculated by the equation Cbn referred to as

Cbn=T11T12T13T21T22T23T31T32T33...(23)]]>又因为 Cbn = T11T12T13T21T22T23T31T32T33 ... (23)]]> And because 因此,由(23)式和(24)式,可以确定航向角2、俯仰角θ2和横滚角γ2的主值,即 Thus, from (23) and (24), [phi] 2 may be determined heading angle, pitch angle and the roll angle θ2 main value γ2, i.e. 若航向角2、俯仰角θ2和横滚角γ2的取值范围分别定义为[0,2π]、 If the heading angle 2, pitch angle and roll angle θ2 γ2 are defined as the range [0,2], [-π,+π]。 [-Π, + π]. 那么,2、θ2和γ2的真值可由下式确定: Then, 2, θ2 and γ2 true value is determined by the following formula: θ2=θ2主(26) θ2 = θ2 primary (26) 由(26)式确定的2、θ2和γ2即为SINS在第二位置上的航向角、俯仰角和横滚角,将其作为SINS进入导航工作状态的初始姿态。 Determined by the equation (26) 2, θ2 and γ2 is the heading angle SINS in the second position, the pitch angle and roll angle, enters it as a navigation operating state SINS initial posture.

Claims (1)

1.一种捷联惯性导航系统初始姿态确定方法,其特征在于包括以下步骤:(1)SINS预热准备完毕,保持SINS在初始位置,称为第一位置,静止不动,采集陀螺仪输出和加速度计输出;(2)根据加速度计输出与重力加速度的关系以及陀螺仪输出与地球自转角速率的关系,计算出第一位置的航向角1、俯仰角θ1和横滚角γ1;(3)将SINS从第一位置绕空间三维任意轴旋转到任意一个位置,称为第二位置,保持SINS在第二位置静止不动,采集陀螺仪输出和加速度计输出;(4)采用卡尔曼滤波技术,将1、θ1和γ1作为初始参数,对两个位置上陀螺仪和加速度计输出的数据进行处理,估计出第二位置时计算地理坐标系n′与真实地理坐标系n之间的误差角,简称为失准角φx、φy和φz及陀螺仪常值漂移、加速度计常值偏置;(5)利用卡尔曼滤波估计出的φx、φy和φz计算真实地理坐标 An initial posture strapdown inertial navigation system determining method, comprising the steps of: (1) SINS preheating ready, SINS held in the initial position, referred to as a first position, stationary, collecting the gyro output and accelerometer output; (2) the accelerometer output relationship and the relationship between the gravitational acceleration of the Earth from the gyro output angle rate, calculate the heading angle 1 a first position, the roll angle and the pitch angle θ1 [gamma] l; ( 3) from a first position about the SINS three-dimensional space is rotated to any arbitrary axis position, called the second position, a second position at SINS held stationary, and gathering the gyro output accelerometer output; (4) Kalman filtering the 1, θ1 and γ1 as an initial parameter, the data on two positions gyroscopes and accelerometers output processing, calculating estimated geographic coordinate system between the position of the second 'real geographic coordinate system n n the error angle, referred to as the misalignment angle φx, φy and φz and constant drift gyroscope, accelerometer bias constant; using (5) of the Kalman filter estimated φx, φy and φz calculate the true geographic coordinates 系n与计算地理坐标系n′之间的转换矩阵Cn'n,根据陀螺仪输出的角增量或角速度信息,采用四元数方法,计算载体坐标系b与计算地理坐标系n′之间的转换矩阵Cbn′,再由Cbn计算第二位置的航向角2、俯仰角θ2和横滚角γ2,将其作为SINS的初始姿态。 N are calculated based geographic coordinate system n 'conversion matrix between Cn'n The incremental gyro output angle or angular velocity information, quaternion methods, vectors, and calculating the geographic coordinates b n coordinate system calculated' between the the transformation matrix Cbn ', then the heading angle is calculated from the second position Cbn 2, pitch angle and roll angle θ2 γ2, as the initial attitude of SINS.
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