CN101514900B - Method for initial alignment of a single-axis rotation strap-down inertial navigation system (SINS) - Google Patents

Method for initial alignment of a single-axis rotation strap-down inertial navigation system (SINS) Download PDF

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CN101514900B
CN101514900B CN 200910071734 CN200910071734A CN101514900B CN 101514900 B CN101514900 B CN 101514900B CN 200910071734 CN200910071734 CN 200910071734 CN 200910071734 A CN200910071734 A CN 200910071734A CN 101514900 B CN101514900 B CN 101514900B
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吕玉红
奔粤阳
孙伟
孙枫
李国强
李雪峰
薛媛媛
赵彦雷
高伟
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哈尔滨工程大学
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Abstract

The invention provides a method for initial alignment of a single-axis rotation strap-down inertial navigation system (SINS). The method comprises the following steps: building a carrier coordinate system and computing a transfer matrix between geographic coordinate systems on the basis of coarse alignment completed by collecting the information output by gyroscopes and accelerometers in the SINSwith the carrier being in a static state; establishing Kalman filtering state equations with speed errors as the state variables and measurement equations with the speed errors as the measurement variables; and estimating the misalignment angles of the carrier by the Kalman filtering technique and feeding back to the SINS to complete the initial alignment of the SINS. The invention can overcome the influence on the estimation precision of the azimuth misalignment angles caused by the equivalent gyroscope drift of the geographic coordinate systems and improve the alignment precision.

Description

一种单轴旋转的捷联惯导系统初始对准方法 One kind of uniaxial rotation SINS Initial Alignment Method

(-)技术领域 (-) FIELD

[0001] 本发明涉及的是一种测量方法,特别是涉及一种单轴旋转的捷联惯性导航系统的初始姿态确定方法。 [0001] The present invention relates to a measuring method, more particularly to a method for determining the initial attitude strapdown inertial navigation system, a single axis of rotation.

(二)背景技术 (B) Background Art

[0002] 旋转式捷联惯性导航系统是一种完全自主的导航系统,利用陀螺仪和加速度计测量惯性测量单元(IMU)相对惯性空间的线运动和角运动参数,在给定初始条件下,结合转动机构提供的IMU相对载体的角度值,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。 [0002] Rotary strapdown inertial navigation system is a completely autonomous navigation system, using an accelerometer and gyroscope measurement inertial measurement unit (IMU) line motion relative to inertial space and angular motion parameters at a given initial condition, IMU rotation mechanism provided in conjunction with the relative angle of the vector value, integral calculation performed by a computer, continuous, real-time to provide position, velocity and attitude information. 由于旋转式捷联惯性导航系统完全依靠自身的惯性元件,不依靠任何外界信息测量导航参数,因此,它具有隐蔽性好,不受气候条件限制,不受干扰等优点,是一种完全自主式、全天候的导航系统,已广泛应用于航空、航天、航海等领域。 Since the rotary strapdown inertial navigation system entirely on their own inertia element, without recourse to any outside information measured navigation parameters, so it has good concealment, from weather conditions, without interference, etc., is a completely self-contained , all-weather navigation system has been widely used in aviation, aerospace, marine and other fields. 初始对准误差是导致惯导系统导航精度难以提高的主要因素,初始对准误差对系统的影响不仅表现在载体姿态测量输出上,而且表现在速度和位置的测量输出上。 Initial alignment error is the main factor leading to difficult to improve the accuracy of navigation guidance system, the effect of the initial alignment error not only in the system on the carrier output attitude measurement, but also in the measuring output speed and position. 因此在旋转捷联惯导系统进入导航状态前,必须首先完成初始对准过程。 Therefore, before rotation strapdown inertial navigation system enters the navigation state, the initial alignment procedure must be completed.

[0003] 根据不同基座的运动状态,初始对准又可以分为静基座对准和动基座对准。 [0003] According to a different state of motion of the base, the initial alignment can be divided into static and dynamic Alignment Alignment. 动基座对准是指在载体机动或存在外界扰动的条件下,捷联惯导系统完成初始对准。 Alignment means is movable in a motor vehicle or the presence of external disturbances, complete SINS initial alignment. 动基座对准常常需要外部信息,对系统的状态变量进行估计,并在滤波稳定后进行姿态修正。 Alignment is often necessary to move the external information, the state variables of the system is estimated, and correcting the posture stabilization after filtering. 静基座对准是指载体在静止的条件下,捷联惯性系统进行初始对准。 Static Alignment is meant the carrier under quiescent conditions, strapdown inertial system the initial alignment.

[0004] 通过分析捷联惯导系统的误差特性可以知道,系统初始对准的难点与重点是方位失准角的估计。 [0004] By analyzing the error characteristics may know SINS, the initial alignment of the difficulties with a focus on the estimated azimuth misalignment angle. 为了提高方位失准角的估计精度及收敛速度,重要的就是要提高方位失准角的可观测度,而方位失准角的可观测度与东向陀螺漂移是密切相关的。 In order to improve the azimuth misalignment angle estimation accuracy and convergence rate, it is important is to improve the azimuth misalignment angle observability, and azimuth misalignment angle observability and east to the gyro drift is closely related. 由于载体静止的条件下进行以速度为观测量的组合对准,系统可观测度不高,特别是地理坐标系下东向陀螺漂移不可观测,导致方位失准角的可观测度难以提高。 Since under conditions of stationary support for the concept of a combination of a speed measuring alignment, considerable measurement system is not high, especially east gyro drift unobservable geographic coordinate system, the azimuth misalignment angle results in considerable measure difficult to improve.

[0005](三)发明内容 [0005] (iii) Disclosure of the Invention

[0006] 本发明的目的在于提供一种能够解决在载体静止的状态下,地理坐标系下东向陀螺漂移不可观测,导致方位失准角的可观测度难以提高的问题的一种单轴旋转的捷联惯导系统初始对准方法。 [0006] The object of the present invention is to provide a carrier solution in a state of rest, the geographic coordinate system east gyro drift can not be observed, the uniaxial orientation leads to a considerable measure of angular misalignment problem is difficult to improve the rotational the initial alignment method of strapdown inertial navigation system.

[0007] 本发明的技术解决方案为:一种单轴旋转的捷联惯导系统初始对准方法,其特征在于将惯性测量单元绕不与自身重合的载体方位轴连续转动,通过改变系统对准模型中的系统矩阵,从而改善惯导系统的可观测性,其具体步骤如下: [0007] The technical solution of the invention is as follows: initial alignment method of strapdown inertial navigation system of a single axis, wherein the vector orientation of the inertial measurement unit about its own axis is not coincident with the continuous rotation by changing system registration model in the system matrix, thereby improving observability inertial navigation system, the specific steps are as follows:

[0008] (1)利用全球定位系统GPS确定载体的初始位置参数,将它们装订至导航计算机中; [0008] (1) using the global positioning system GPS parameters determine the initial position of the carrier, the stapling them to the navigation computer;

[0009] (2)光纤陀螺捷联惯性导航系统进行预热,然后采集光纤陀螺仪和石英加速度计输出的数据; [0009] (2) FOG strapdown inertial navigation system for preheating, and then collect data quartz fiber optic gyroscope and accelerometer output;

[0010] (3)对采集到的光纤陀螺仪和石英加速度计的数据进行处理,采用解析法来完成系统的粗对准,初步确定载体的姿态信息;[0011] 根据加速度计的输出的重力矢量i以及陀螺仪输出与地球自转角速率^的测量值初步确定此时载体的姿态信息完成系统的粗对准,建立载体坐标系b和计算地理坐标系η'之间的转换矩阵Tbn': [0010] (3) a fiber optic gyroscope data and quartz accelerometer collected for processing to complete the analytical method using coarse alignment system, initially identified posture information carrier; [0011] The gravity of the accelerometer output vector i and the gyro output angle from the earth rate measurements ^ initial coarse alignment is determined at this time pose information carrier to complete the system, and to establish a bearer b coordinates calculated geographic coordinates η 'between the conversion matrix Tbn':

[0012] 对于某一纬度树炉<90°),有: [0012] For a certain latitude tree oven <90 °), are:

[0013] ? [0013]? = [0 0 -g]T = [0 0 -g] T

[0014] [0014]

Figure CN101514900BD00061

[0015] 用i和、可以构成一个新的矢量I,即忑= iX^,再根据导航系与载体系之间的方向余弦矩阵可以得: [0015] with i and may constitute a new vector I, i.e. nervous = iX ^, then the direction cosine matrix can be prepared according to the navigation between the system and the system contained:

Figure CN101514900BD00062

[0017] 考虑捷联矩阵的正交性,即 [0017] Consider strapdown orthogonality matrix, i.e.,

[0018] (Γ;)"1 =(Γ„Λ)7'=Γ;' [0018] (Γ;) "1 = (Γ" Λ) 7 '= Γ;'

[0019] [0019]

Figure CN101514900BD00063

[0020] 其中gb、ω 用陀螺和加速度的输出近似代替。 [0020] wherein the output gb, ω gyro and accelerometer approximation instead.

[0021] (4)惯性测量单元绕载体坐标系oyb轴正向旋转45度(如附图2),确定IMU坐标系与载体坐标系之间的初始相对位置; [0021] (4) an inertial measurement unit vector normal rotation axis coordinate system oyb initial relative position between the IMU coordinate system and coordinate vector (e.g., Fig. 2), it is determined about 45 degrees;

[0022] 载体坐标系与IMU坐标系具有同一坐标原点0,oys轴与oyb轴相重合,oxs轴、ozs 轴、OXb轴和OZb轴位于同一平面内,但OZs轴与OZb轴的夹角为45°,OZs轴与oxb轴的夹角为90° -45° = 45°。 [0022] The IMU support coordinate system and a coordinate system with the same coordinate origin 0, oys oyb axis coincides with the axis, the axis OXS, ozs axis, and the axis OXB OZb axis in the same plane, the angle between the axis and OZs axis is OZb 45 °, the angle OZs oxb shaft axis is 90 ° -45 ° = 45 °.

[0023] (5)确定两坐标系相对初始位置关系后,惯性测量单元绕载体坐标系方位轴OZb正向以角速度ω =6° /s连续转动(如附图3); After [0023] (5) determining an initial relative positional relationship between the two coordinate systems, inertial measurement unit around the carrier axis orientation coordinates OZb forward at an angular velocity ω = 6 ° / s continuous rotation (e.g., Figure 3);

[0024] IMU转动过程中,IMU坐标系到载体坐标系的转换矩阵为: [0024] IMU during rotation, IMU coordinate system to coordinate transformation matrix as a carrier:

[0025] [0025]

Figure CN101514900BD00064

[0026] (6)建立以速度误差为状态变量的卡尔曼滤波状态方程及速度误差为量测量的量测方程; [0026] (6) establishing the Kalman filter state equations the speed error and speed error of the state variable measured quantity measurement equation;

[0027] 1)建立卡尔曼滤波的状态方程:[0028] 用一阶线性微分方程来描述旋转捷联惯导系统的状态误差: [0027] 1) established Kalman filter state equations: [0028] by a state order linear differential equation that describes the rotation of the strapdown inertial navigation system error:

[0029] X(t) = A(t)X(t) + 5(0^(0 [0029] X (t) = A (t) X (t) + 5 (0 ^ (0

[0030] 其中X(t)为t时刻系统的状态向量;A(t)和B(t)分别为系统的状态矩阵和噪声矩阵;W(t)为系统噪声向量; State vector [0030] wherein X (t) of the system at time t; A (t) and B (t) respectively and the state matrix of the system noise matrix; W is (t) is the noise vector system;

[0031] 系统的状态向量为: [0031] The system state vector is:

[0032] [0032]

Figure CN101514900BD00071

[0033] 系统的白噪声向量为: [0033] White noise vector system is:

[0034] W= [ax ay ωχ COy ωζ 0 0 0 0 0]τ [0034] W = [ax ay ωχ COy ωζ 0 0 0 0 0] τ

[0035] 其中δ\、δ Vn分别表示东向、北向的速度误差;▽,、分别为IMU坐标系oxs、 oys轴加速度计零偏;ε χ、ε y、ε z分别为IMU坐标系0Xs、0ys、0zs轴陀螺的常值漂移;ax、ay 分别为IMU坐标系oxs、oys轴加速度计的白噪声误差;ωχ、coy、ωζ分别为IMU坐标系oxs、 oys、ozs轴陀螺的白噪声误差; [0035] wherein δ \, δ Vn represent the east, velocity north errors; ▽ ,, respectively IMU coordinate oxs, oys axis accelerometer zero bias; ε χ, ε y, ε z are IMU coordinate 0Xs , 0ys, 0zs axis gyro constant drift; ax, ay respectively IMU coordinate oxs, oys axis accelerometer white noise error; ωχ, coy, ωζ are white noise IMU coordinates oxs, oys, ozs axis gyroscope error;

[0036] 系统的状态转移矩阵为: [0036] The system state transition matrix is:

[0037] [0037]

[0038] [0038]

[0039] [0039]

Figure CN101514900BD00072

[0040] F2x2 二 [0040] F2x2 two

[0041] [0041]

Figure CN101514900BD00073

[0043] [0043]

Figure CN101514900BD00074

[0044] Ve, Vn分别表示东向、北向的速度;表示地球自转角速度;Rm、Rn分别表示地球子午、卯酉曲率半径;L表示当地纬度;fe、fn、4分别表示为导航坐标系下东向、北向、天向的比力。 [0044] Ve, Vn denote the east velocity north direction; represents Earth rotation angular velocity; Rm, Rn denote earth meridian, the prime vertical radius of curvature; L represents the local latitude; fe, fn, 4 are represented by the navigation coordinate system East, North, compared to the days of.

[0045] 令捷联矩阵 [0045] make strapdown matrix

Figure CN101514900BD00081

[0046] [0046]

Figure CN101514900BD00082

[0047]则 [0047] the

[0048] [0048]

Figure CN101514900BD00083

[0049] [0049]

[0050] [0050]

2)建立卡尔曼滤波的量测方程用一阶线性微分方程来描述旋转捷联惯导系统的量测方程如下 2) establishing Kalman filter measurement equation of first order linear differential equations to describe the rotation of the measurement equation below sins

[0054] H{t) [0054] H {t)

[0055] [0055]

[0056] [0056]

[0051] Z(t) = H(t)X(t)+v(t) [0051] Z (t) = H (t) X (t) + v (t)

[0052] 其中:Z(t)表示t时刻系统的量测向量;H(t)表示系统的量测矩阵;v(t)表示系统的量测噪声; [0052] wherein: Z (t) represents the time t measurement vector system; H (t) represents the measurement matrix system; V (t) represents the amount of noise measurement system;

[0053] 系统量测矩阵为: "1 00000000 0" [0053] Measurement system matrix: "1000000000"

0 10000000 0 0100000000

量测量为水平速度误差: v(t) = [ve Vn]τ Measuring the amount of horizontal velocity error: v (t) = [ve Vn] τ

[0057] (7)利用步骤(6)估计出平台失准角,并在精对准结束时用它来修正系统的捷联姿态矩阵,完成精确的初始对准。 [0057] (7) using a step (6) to estimate the misalignment angle internet, and use it to correct the strapdown system posture matrix at the end of the fine alignment, accurate initial alignment is completed.

[0058] 本发明以速度作为观测量,设计了一种新的IMU旋转式组合对准方法。 [0058] The concept of the present invention is measured as a rate, a new design of rotary IMU combination alignment method. 在精对准过程中,通过IMU的连续旋转,捷联矩阵成为一个周期变化的量。 In the fine alignment process, by continuous rotation of the IMU, strapdown matrix becomes a period varying amounts. 这种方法解决了载体静止条件下东向陀螺漂移不可观测,以及由此导致的方位失准角精度不高的问题。 This approach solves the carrier under static conditions unobservable gyro drift east, and the resulting azimuth misalignment angle accuracy is not high. 由于陀螺漂移是造成捷联惯性导航系统输出导航误差的重要因素,所以采用本发明的技术方案进行初始对准后,可以有效的提高捷联惯性导航系统的导航精度。 Since the gyro drift is an important factor strapdown inertial navigation system output error caused by navigation, the technical solution of the present invention the initial alignment, can effectively improve the accuracy of navigation strapdown inertial navigation system.

[0059] 对本发明有益的效果说明如下: [0059] The beneficial effects of the present invention will be described as follows:

[0060] 在Matlab仿真条件下,对该方法进行仿真实验: [0060] Matlab simulation under conditions of the simulation method is:

[0061] 载体初始位置:北纬45. 7796°,东经126. 6705° ; [0061] The initial position vectors: N 45. 7796 °, longitude 126. 6705 °;

[0062] 初始姿态误差角:代、φη、队分别取1°、1°、3° ; 赤道半径:Re = 6378393. Om ; 椭球度:e = 3. 367e-3 ; [0062] The initial attitude error angle: Generation, φη, team were taken 1 °, 1 °, 3 °; equatorial radius: Re = 6378393. Om; ellipsoid of: e = 3. 367e-3;

由万有引力可得的地球表面重力加速度:gQ = 9. 78049 ; 地球自转角速度(弧度/秒):7· 2921158e-5 ; 陀螺仪常值漂移:0. 01度/小时; 加速度计零偏:10_4gQ ; Gravitation available surface of the earth gravitational acceleration: gQ = 9. 78049; Earth rotation angular velocity (rad / sec): 7 · 2921158e-5; gyro constant drift: 001 degrees / hour; Accelerometer Bias:. 10_4gQ ;

8 8

[0063] [0063]

[0064] [0064]

[0065] [0065]

[0066] [0066]

[0067] [0067]

[0068][0069]常数:Ji = 3. 1415926 ; [0068] [0069] Constant: Ji = 3. 1415926;

[0070] 利用本发明所述方法得到载体东向失准角误差曲线、北向失准角误差曲线和方位失准角误差曲线分别如图4、图5、图6所示。 [0070] The method of the present invention with the carrier obtained east misalignment angle error curve, north misalignment error curve angle and azimuth angle of misalignment error curve are shown in Figure 4, 5, 6 as shown in FIG. 结果表明在载体静止且IMU连续旋转的条件下,采用本发明的方法可以获得较高的对准精度。 The results show that under the conditions of the carrier stationary and IMU continuously rotating, the present invention method can achieve high alignment accuracy.

(四)附图说明 (Iv) Brief Description of Drawings

[0071] 图1为本发明的一种单轴旋转的捷联惯导系统初始对准方法流程图; One kind of uniaxial [0071] FIG 1 the present invention rotating SINS initial alignment flowchart of a method;

[0072] 图2为初始时刻IMU坐标系与载体坐标系的初始相对位置关系; [0072] Figure 2 is an initial relative positional relationship between the initial time IMU coordinate system and the coordinate system of the carrier;

[0073] 图3为IMU转动过程中,IMU坐标系与载体坐标系的相对位置关系; [0073] FIG. 3 is a process, the relative positional relationship between the IMU coordinate system and the coordinate system IMU rotatable carrier;

[0074] 图4为本发明的基于卡尔曼滤波的旋转捷联惯导系统组合对准新方法东向失准角实验曲线。 Inertial Navigation System Kalman filter based on a combination of the rotation, Czech Republic [0074] of the present invention. FIG. 4 misalignment angle East New Method for aligning the experimental curve.

[0075] 图5为本发明的基于卡尔曼滤波的旋转捷联惯导系统组合对准新方法北向失准角实验曲线。 [0075] FIG. 5 of the present invention Kalman filtering Inertial Navigation System combination of rotational alignment of the new method based on Czech north misalignment angle experimental curve.

[0076] 图6为本发明的基于卡尔曼滤波的旋转捷联惯导系统组合对准新方法方位失准角实验曲线。 [0076] FIG. 6 of the present invention Kalman filtering Inertial Navigation System Czech combination of rotational alignment of the new method based on the azimuth angle of misalignment experimental curve.

(五)具体实施方式 (E) Detailed Description

[0077] 下面结合附图对本发明的具体实施方式进行详细地描述: [0077] described in detail below in conjunction with the accompanying drawings of specific embodiments of the present invention:

[0078] (1)利用全球定位系统GPS确定载体的初始位置参数,将它们装订至导航计算机中; [0078] (1) using the global positioning system GPS parameters determine the initial position of the carrier, the stapling them to the navigation computer;

[0079] (2)光纤陀螺捷联惯性导航系统进行预热,然后采集光纤陀螺仪和石英加速度计输出的数据; [0079] (2) FOG strapdown inertial navigation system for preheating, and then collect data quartz fiber optic gyroscope and accelerometer output;

[0080] (3)对采集到的光纤陀螺仪和石英加速度计的数据进行处理,采用解析法来完成系统的粗对准,初步确定载体的姿态信息; [0080] (3) on the basis of data collected and quartz fiber optic gyroscope acceleration process, using an analytical method to complete the coarse alignment system, initially identified posture information carrier;

[0081] 根据加速度计的输出的重力矢量i以及陀螺仪输出与地球自转角速率^的测量值初步确定此时载体的姿态信息完成系统的粗对准,建立载体坐标系b和计算地理坐标系η'之间的转换矩阵Tbn': [0081] At this time, the initial coarse alignment determined posture vector information to complete the system in accordance with the gravity vector i and the output of the gyroscope and accelerometer earth output from the angular rate measurements ^, and to establish a bearer b coordinates calculated geographic coordinate system η 'between the conversion matrix Tbn':

[0082] 对于某一纬度树炉< 90°),有: [0082] For a certain latitude tree oven <90 °), are:

[0083] ? [0083]? = [0 0-g]T (1) = [0 0-g] T (1)

[0084] [0084]

ω,β = [O ωΙ(, cos φ ωΙ(ί sin φ]' (2) ω, β = [O ωΙ (, cos φ ωΙ (ί sin φ] '(2)

[0085] 用S和、可以构成一个新的矢量I,即忑=SX^,再根据导航系与载体系之间的方向余弦矩阵可以得: [0085] with S and may constitute a new vector I, i.e. nervous = SX ^, then in accordance with the direction cosine matrix between the navigation system and the carrier system can be obtained:

—b 8 =Tnb7' —b ω,. =T^ ω,β ' (3)— E = T:. E -b 8 = Tnb7 '-b ω ,. = T ^ ω, β' (3) - E = T :. E

[0087] 考虑捷联矩阵的正交性,即: [0087] Consider strapdown orthogonal matrix, namely:

[0088] (TX= (Τ:,)1'=Th"' (4) [0088] (TX = (Τ:,) 1 ​​'= Th "' (4)

Figure CN101514900BD00101

[0090] 其中gb、ω 用陀螺和加速度的输出近似代替。 [0090] wherein the output gb, ω gyro and accelerometer approximation instead.

[0091] (4)惯性测量单元绕载体坐标系oyb轴正向旋转45度(如附图2),确定IMU坐标系与载体坐标系之间的初始相对位置; [0091] (4) an inertial measurement unit vector normal rotation axis coordinate system oyb initial relative position between the IMU coordinate system and coordinate vector (e.g., Fig. 2), it is determined about 45 degrees;

[0092] 载体坐标系与IMU坐标系具有同一坐标原点O,oys轴与oyb轴相重合,oxs轴、ozs 轴、OXb轴和OZb轴位于同一平面内,但OZs轴与OZb轴的夹角为45°,OZs轴与oxb轴的夹角为90° -45° = 45°。 [0092] The IMU support coordinate system and a coordinate system with the same coordinate origin O, oys oyb axis coincides with the axis, the axis OXS, ozs axis, and the axis OXB OZb axis in the same plane, the angle between the axis and OZs axis is OZb 45 °, the angle OZs oxb shaft axis is 90 ° -45 ° = 45 °.

[0093] (5)确定两坐标系相对初始位置关系后,惯性测量单元绕载体坐标系方位轴OZb正向以角速度ω =6° /s连续转动(如附图3); After [0093] (5) determining an initial relative positional relationship between the two coordinate systems, inertial measurement unit around the carrier axis orientation coordinates OZb forward at an angular velocity ω = 6 ° / s continuous rotation (e.g., Figure 3);

[0094] IMU转动过程中,IMU坐标系到载体坐标系的转换矩阵为: [0094] IMU during rotation, IMU coordinate system to coordinate transformation matrix as a carrier:

[0095] [0095]

Figure CN101514900BD00102

[0096] (6)建立以速度误差为状态变量的卡尔曼滤波状态方程及速度误差为量测量的量测方程; [0096] (6) establishing the Kalman filter state equations the speed error and speed error of the state variable measured quantity measurement equation;

[0097] 1)建立卡尔曼滤波的状态方程: [0097] 1) established Kalman filter state equations:

[0098] 用一阶线性微分方程来描述旋转捷联惯导系统的状态误差: [0098] with a first order linear differential equation that describes the rotation strapdown inertial navigation system error state:

[0099] X{t) = A{t)X{t) + B{t)W{t) (7) [0099] X {t) = A {t) X {t) + B {t) W {t) (7)

[0100] 其中X(t)为t时刻系统的状态向量;A(t)和B(t)分别为系统的状态矩阵和噪声矩阵;W(t)为系统噪声向量; State vector [0100] wherein X (t) of the system at time t; A (t) and B (t) respectively and the state matrix of the system noise matrix; W is (t) is the noise vector system;

[0101] 系统的状态向量为: [0101] The system state vector is:

[0102] [0102]

Z=[代Wn cpe φη φΜ V, Vy εχ sy EzJ (8) Z = [Generation Wn cpe φη φΜ V, Vy εχ sy EzJ (8)

[0103] 系统的白噪声向量为: [0103] White noise vector system is:

[0104] W= [ax zy ωχ COy ωζ OOOO 0]τ (9) [0104] W = [ax zy ωχ COy ωζ OOOO 0] τ (9)

[0105] 其中δ\、δ Vn分别表示东向、北向的速度误差;▽,、分别为IMU坐标系oxs、 oys轴加速度计零偏;ε χ、ε y、ε z分别为IMU坐标系0Xs、0ys、0zs轴陀螺的常值漂移;ax、ay 分别为IMU坐标系oxs、oys轴加速度计的白噪声误差;ωχ、coy、ωζ分别为IMU坐标系oxs、 oys、ozs轴陀螺的白噪声误差; [0105] wherein δ \, δ Vn represent the east, velocity north errors; ▽ ,, respectively IMU coordinate oxs, oys axis accelerometer zero bias; ε χ, ε y, ε z are IMU coordinate 0Xs , 0ys, 0zs axis gyro constant drift; ax, ay respectively IMU coordinate oxs, oys axis accelerometer white noise error; ωχ, coy, ωζ are white noise IMU coordinates oxs, oys, ozs axis gyroscope error;

[0106] 系统的状态转移矩阵为: [0106] The system state transition matrix is:

10 10

Figure CN101514900BD00111
Figure CN101514900BD00112

[0114] Ve, Vn分别表示东向、北向的速度;ω 表示地球自转角速度;Rm、Rn分别表示地球子午、卯酉曲率半径;L表示当地纬度;fe、fn、4分别表示为导航坐标系下东向、北向、天向的比力。 [0114] Ve, Vn denote the speed east, north direction; [omega] represents the Earth's rotation angular velocity; Rm, Rn denote earth meridian, the prime vertical radius of curvature; L represents the local latitude; fe, fn, 4 are represented by navigational coordinate system under east, north, compared to the days of.

(16) (16)

Figure CN101514900BD00113
Figure CN101514900BD00114
Figure CN101514900BD00115
Figure CN101514900BD00116
Figure CN101514900BD00117
Figure CN101514900BD00118

2)建立卡尔曼滤波的量测方程 2) to establish the measurement equation Kalman Filter

(17) (17)

用一阶线性微分方程来描述旋转捷联惯导系统的量测方程如下 With a first order linear differential equation that describes the rotation of the sins measurement equation as follows

11[0121] Z(t) = H(t)X(t)+v(t) (18) 11 [0121] Z (t) = H (t) X (t) + v (t) (18)

[0122] 其中:Z(t)表示t时刻系统的量测向量;H(t)表示系统的量测矩阵;v(t)表示系统的量测噪声; [0122] wherein: Z (t) represents the time t measurement vector system; H (t) represents the measurement matrix system; V (t) represents the amount of noise measurement system;

[0123] 系统量测矩阵为: [0123] Measurement system matrix:

「1 0 0 0 0 0 0 0 0 0. 一 "100 million 0.5 a

[0124] H(t)= (19) [0124] H (t) = (19)

w 010000000 0 w 010000000 0

[0125] 量测量为水平速度误差: [0125] measurement of the horizontal velocity error:

[0126] v(t) = [ve vn]τ (20) [0126] v (t) = [ve vn] τ (20)

[0127] (7)利用步骤(6)估计出平台失准角,并在精对准结束时用它来修正系统的捷联姿态矩阵,完成精确的初始对准。 [0127] (7) using a step (6) to estimate the misalignment angle internet, and use it to correct the strapdown system posture matrix at the end of the fine alignment, accurate initial alignment is completed.

12 12

Claims (3)

  1. 一种单轴旋转的捷联惯导系统初始对准方法,其特征在于包括以下步骤:(1)利用全球定位系统GPS确定载体的初始位置参数,并装订至导航计算机中;(2)采集光纤陀螺捷联惯性导航系统的光纤陀螺仪和石英加速度计输出的数据;(3)对采集到的光纤陀螺仪和石英加速度计的数据进行处理,采用解析法来完成系统的粗对准,初步确定载体的姿态信息;具体方法为:根据加速度计输出的重力矢量 以及陀螺仪输出与地球自转角速率 的测量值初步确定此时载体的姿态信息完成系统的粗对准,建立载体坐标系b和计算地理坐标系n′之间的转换矩阵 对于某一小于纬度为90°的角度 有:用 和 构成一个新的矢量 即: 再根据导航系与载体系之间的方向余弦矩阵得:考虑捷联矩阵的正交性,即:其中gb、 用陀螺和加速度的输出近似代替;(4)惯性测量单元绕载体坐标系oyb SINS initial alignment method for a single axis, characterized by comprising the steps of: (1) the use of a global positioning system GPS parameters determine the initial position of the carrier, and the binding to the navigation computer; (2) acquiring the optical fiber data and quartz fiber optic gyroscope gyroscopic accelerometer output strapdown inertial navigation system; (3) a fiber optic gyroscope data and quartz accelerometer collected for processing to complete the analytical method using coarse alignment system, initially determined posture information carrier; specific methods of: determining the initial attitude of the carrier case coarse alignment information to complete the system in accordance with the gravity vector and the accelerometer output the gyro output angle from the earth rate measurements, to establish a bearer and b coordinates calculated conversion matrix between the geographic coordinate system n 'is less than the latitude for a certain angle of 90 ° are: with and form a new vector that is: then according to a direction between the navigation system and the carrier system obtained cosine matrix: matrix consider strapdown orthogonality, namely: wherein gb, gyro and accelerometer output approximate place; (4) an inertial measurement unit around the carrier coordinate system oyb 正向旋转45度,确定惯性测量单元坐标系与载体坐标系之间的初始相对位置;(5)确定两坐标系相对初始位置关系后,惯性测量单元绕载体坐标系方位轴ozb正向以角速度ω=6°/s连续转动;(6)建立以速度误差为状态变量的卡尔曼滤波状态方程及速度误差为量测量的量测方程;1)建立卡尔曼滤波的状态方程:用一阶线性微分方程来描述旋转捷联惯导系统的状态误差:其中X(t)为t时刻系统的状态向量;A(t)和B(t)分别为系统的状态矩阵和噪声矩阵;W(t)为系统噪声向量;系统的状态向量为:系统的白噪声向量为:W=[axayωxωyωz00000]T其中δVe、δVn分别表示东向、北向的速度误差;▽x、▽y分别为惯性测量单元坐标系oxs、oys轴加速度计零偏;εx、εy、δz分别为惯性测量单元坐标系oxs、oys、ozs轴陀螺的常值漂移;ax、ay分别为惯性测量单元坐标系oxs、oys轴加速度计的白 Forward rotation of 45 degrees, to determine an initial relative position between the inertial measurement unit coordinate system and the coordinate system of the carrier; (5) determining an initial relative positional relationship between the two coordinate systems, inertial measurement unit around the carrier axis coordinate position to a forward angular velocity ozb ω = 6 ° / s continuous rotation; (6) establish a speed error of the Kalman filter state equations of the state variables and the speed of the measurement equation error of measurement; 1) established Kalman filter state equations: first order linear Equations to describe the state of the rotary strapdown inertial navigation system error: wherein X (t) is the system state vector at time t; a (t) and B (t) respectively and the state matrix of the system noise matrix; W is (t) system noise vector; state vector system is: a white noise vector system is: W = [axayωxωyωz00000] T wherein δVe, δVn respectively represent the east, velocity north errors; ▽ x, ▽ y respectively inertial measurement unit coordinate system oxs, oys axis accelerometer zero bias; εx, εy, δz are the inertial measurement unit coordinates oxs, oys, ozs axis gyro constant drift; ax, ay respectively of the inertial measurement unit coordinates oxs, oys axis accelerometer White 声误差;ωx、ωy、ωz分别为惯性测量单元坐标系oxs、oys、ozs轴陀螺的白噪声误差;系统的状态转移矩阵为:其中: Ve、Vn分别表示东向、北向的速度;ωie表示地球自转角速度;Rm、Rn分别表示地球子午、卯酉曲率半径;L表示当地纬度;fe、fn、fu分别表示为导航坐标系下东向、北向、天向的比力;令捷联矩阵 为:则2)建立卡尔曼滤波的量测方程: 用一阶线性微分方程来描述旋转捷联惯导系统的量测方程如下:Z(t)=H(t)X(t)+v(t)其中:Z(t)表示t时刻系统的量测向量;H(t)表示系统的量测矩阵;v(t)表示系统的量测噪声;系统量测矩阵为:量测量为水平速度误差:v(t)=[vevn]T;(7)利用步骤(6)估计出平台失准角,并在精对准结束时用它来修正系统的捷联姿态矩阵,完成精确的初始对准。 Acoustic error; ωx, ωy, ωz are the inertial measurement unit coordinates oxs, oys, ozs axis gyro white noise error; system state transition matrix is: wherein: Ve, Vn denote the speed east, north direction; ωie represents Earth rotation angular velocity; Rm, Rn denote earth meridian, the prime vertical radius of curvature; L represents the local latitude; fe, fn, fu denoted as east, north, than the days of the next navigation coordinates; order strapdown matrix : the 2) established Kalman filter measurement equation: using a first order linear differential equation that describes the measurement equation rotation strapdown inertial navigation system as follows: Z (t) = H (t) X (t) + v (t ) wherein: the Z (t) represents the measurement vector at time t system; H (t) represents the system of the measurement matrix; V (t) represents the system of measurement noise; system measurement matrix: measuring the amount of horizontal velocity error : v (t) = [vevn] T; (7) using a step (6) to estimate the misalignment angle internet, and use it to correct the strapdown system posture matrix at the end of the fine alignment, accurate initial alignment of complete . dest_path_FSB00000195101700011.tif,dest_path_FSB00000195101700012.tif,dest_path_FSB00000195101700013.tif,dest_path_FSB00000195101700014.tif,dest_path_FSB00000195101700015.tif,dest_path_FSB00000195101700016.tif,dest_path_FSB00000195101700017.tif,dest_path_FSB00000195101700018.tif,dest_path_FSB00000195101700019.tif,dest_path_FSB000001951017000110.tif,dest_path_FSB000001951017000111.tif,dest_path_FSB000001951017000112.tif,dest_path_FSB000001951017000113.tif,dest_path_FSB00000195101700021.tif,dest_path_FSB00000195101700022.tif,dest_path_FSB00000195101700023.tif,dest_path_FSB00000195101700024.tif,dest_path_FSB00000195101700031.tif,dest_path_FSB00000195101700032.tif,dest_path_FSB00000195101700033.tif,dest_path_FSB00000195101700034.tif,dest_path_FSB00000195101700035.tif,dest_path_FSB00000195101700036.tif,dest_path_FSB00000195101700037.tif,dest_path_FSB00000195101700038.tif,dest_path_FSB00000195101700041.tif dest_path_FSB00000195101700011.tif, dest_path_FSB00000195101700012.tif, dest_path_FSB00000195101700013.tif, dest_path_FSB00000195101700014.tif, dest_path_FSB00000195101700015.tif, dest_path_FSB00000195101700016.tif, dest_path_FSB00000195101700017.tif, dest_path_FSB00000195101700018.tif, dest_path_FSB00000195101700019.tif, dest_path_FSB000001951017000110.tif, dest_path_FSB000001951017000111.tif, dest_path_FSB000001951017000112.tif, dest_path_FSB000001951017000113. tif, dest_path_FSB00000195101700021.tif, dest_path_FSB00000195101700022.tif, dest_path_FSB00000195101700023.tif, dest_path_FSB00000195101700024.tif, dest_path_FSB00000195101700031.tif, dest_path_FSB00000195101700032.tif, dest_path_FSB00000195101700033.tif, dest_path_FSB00000195101700034.tif, dest_path_FSB00000195101700035.tif, dest_path_FSB00000195101700036.tif, dest_path_FSB00000195101700037.tif, dest_path_FSB00000195101700038.tif, dest_path_FSB00000195101700041.tif
  2. 2.根据权利要求1所述的一种单轴旋转的捷联惯导系统初始对准方法,其特征在于所述的惯性测量单元绕载体坐标系oyb轴正向旋转45度是:载体坐标系与惯性测量单元坐标系具有同一坐标原点O,oys轴与oyb轴相重合,OXs轴、ozs轴、oxb轴和ozb轴位于同一平面内,但Ozs轴与Ozb轴的夹角为45°,Ozs轴与Oxb轴的夹角为90° -45° =45°。 The initial alignment of the strapdown inertial navigation system 1. A method as claimed in claim single axis, wherein said inertial measurement unit around the carrier oyb coordinate axes are rotated by 45 degrees forward: vector coordinates and an inertial measurement unit having the same coordinate system the coordinate origin O, oys oyb axis coincides with the axis, the axis OXs, ozs axis, and the axis OXB ozb axis in the same plane, the angle between the axis and Ozb ozs axis is 45 °, ozs Oxb axis angle with the axis of 90 ° -45 ° = 45 °.
  3. 3.根据权利要求2所述的一种单轴旋转的捷联惯导系统初始对准方法,其特征在于所述的确定两坐标系相对初始位置关系后,惯性测量单元绕载体坐标系方位轴OZb正向以角速度ω =6° /s连续转动的惯性测量单元转动过程中,惯性测量单元坐标系到载体坐标系的转换矩阵为: COSOJt -sincX 0" cos 45° 0 sin45° cosioi cos 45° -sinfflf cosiaf sin 45° Tt = sin ^ COSCOt 0 0 1 0 = sine* cos 45° cosiaf sin<afsin45° O 0 0 1 -sin45° 0 cos 45° -sin45° 0 cos 45° 3. The method of claim 2 Initial alignment of one kind of a single axis of strapdown inertial navigation system as claimed in claim, wherein said determining an initial relative positional relationship between the two coordinate systems, inertial measurement unit about the azimuth axis coordinate vector OZb forward at an angular velocity ω = 6 ° / s continuously rotating during the rotation of an inertial measurement unit, an inertial measurement unit to the coordinate transformation matrix for the vector coordinates: COSOJt -sincX 0 "cos 45 ° 0 sin45 ° cosioi cos 45 ° -sinfflf cosiaf sin 45 ° Tt = sin ^ COSCOt 0 0 1 0 = sine * cos 45 ° cosiaf sin <afsin45 ° O 0 0 1 -sin45 ° 0 cos 45 ° -sin45 ° 0 cos 45 °
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CN102435206A (en) * 2011-09-01 2012-05-02 中国航空工业第六一八研究所 Automatic calibrating and compensating method of onboard mounting deflection angle of strapdown inertial navigation system

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