CN102393201B

CN102393201B - Dynamic arm compensation method for position and attitude measurement system (POS) for aerial remote sensing

Info

Publication number: CN102393201B
Application number: CN 201110220018
Authority: CN
Inventors: 钟麦英; 曹全; 房建成; 宫晓琳
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2011-08-02
Filing date: 2011-08-02
Publication date: 2013-05-15
Anticipated expiration: 2031-08-02
Also published as: CN102393201A

Abstract

A dynamic lever-arm compensation method for a position and attitude measurement system (POS) for aerial remote sensing. This method aims at the real-time change of the lever arm between the inertial measurement unit (IMU) measurement center and the GPS antenna phase center caused by the frame rotation of the three-axis inertial stabilized platform. The actual lever arm between the IMU measurement center and the GPS antenna phase center is obtained, and the real-time calculation of the initial coordinate system of the three-axis inertial stable platform relative to the local geographic coordinate system under the initial coordinate system of the three-axis inertial stable platform Angular velocity, for dynamic lever arm compensation. The invention has the characteristics of high precision, simple operation and easy realization, solves the problem that the POS lever arm is difficult to compensate accurately when the aerial remote sensing uses a three-axis inertial stable platform, and improves the accuracy of POS and aerial remote sensing imaging loads.

Description

Dynamic Lever-Arm Compensation Method for Position and Attitude Measurement System (POS) Used in Airborne Remote Sensing

技术领域 technical field

本发明涉及一种航空遥感用位置和姿态测量系统(POS)动态杆臂补偿方法，属于航空遥感领域，应用于采用三轴惯性稳定平台的航空遥感，提高了POS和航空遥感成像载荷的精度。The invention relates to a position and attitude measurement system (POS) dynamic lever arm compensation method for aerial remote sensing, belongs to the field of aerial remote sensing, is applied to aerial remote sensing using a three-axis inertial stable platform, and improves the accuracy of POS and aerial remote sensing imaging loads.

背景技术 Background technique

航空遥感是一种以飞机为载体，利用遥感载荷获取地球表面各种空间地理信息的高技术。航空遥感系统进行高分辨率成像时要求载荷在空间做匀速直线的理想运动，但飞机不可避免会受到阵风、湍流等外部扰动的影响，使载荷偏离理想运动轨迹，导致载荷成像质量下降。因此，要实现航空遥感系统的高精度成像，必须对飞行扰动进行隔离和运动补偿。三轴惯性稳定平台由三个框架组成，通过伺服控制三个框架保持成像载荷水平并指向飞机飞行方向，从而在一定程度上隔离飞行过程中的外部扰动。由于三轴惯性稳定平台负载大，自重小，响应速度有限，不可能将飞行扰动完全隔离，因此，必须使用POS精确测量未能隔离的飞行扰动，得到成像载荷相位中心的位置、速度和姿态等运动参数，并在成像过程中进行运动补偿。Aerial remote sensing is a high technology that uses aircraft as a carrier to obtain various spatial and geographical information on the earth's surface by using remote sensing payloads. When the aerial remote sensing system performs high-resolution imaging, the payload is required to move in a straight line at a constant speed in space. However, the aircraft will inevitably be affected by external disturbances such as gusts and turbulence, which will cause the payload to deviate from the ideal trajectory, resulting in a decline in the imaging quality of the payload. Therefore, to achieve high-precision imaging in aerial remote sensing systems, flight disturbance isolation and motion compensation must be performed. The three-axis inertial stabilization platform consists of three frames, which are servo-controlled to maintain the imaging load level and point to the flight direction of the aircraft, thereby isolating external disturbances during flight to a certain extent. Due to the large load of the three-axis inertial stabilized platform, the small self-weight and the limited response speed, it is impossible to completely isolate the flight disturbance. Therefore, it is necessary to use POS to accurately measure the flight disturbance that cannot be isolated, and obtain the position, velocity and attitude of the phase center of the imaging load, etc. Motion parameters, and motion compensation during imaging.

POS则由IMU、GPS接收机、POS导航计算机(PCS)和后处理软件等组成。其中IMU用于测量与其固联载体的三维角速度和三维线加速度，经捷联惯性导航解算，可得到载体的位置、速度和姿态信息，具有短时精度高，输出连续和完全自主等优点，但其导航误差随时间积累。GPS则可长时间提供高精度的位置和速度信息，但输出不连续，不能提供姿态信息，且GPS信号受到遮挡时不能实现定位。POS利用惯性导航和GPS导航天然的互补性，应用信息融合技术，将惯性量测信息同GPS量测信息进行融合，能够连续、实时地获取载体的位置、速度和姿态等全面的运动参数，且误差不随时间积累。POS is composed of IMU, GPS receiver, POS navigation computer (PCS) and post-processing software. Among them, the IMU is used to measure the three-dimensional angular velocity and three-dimensional linear acceleration of the solid-connected carrier. After the strapdown inertial navigation solution, the position, velocity and attitude information of the carrier can be obtained. It has the advantages of high short-term accuracy, continuous output and complete autonomy. But its navigation error accumulates over time. GPS can provide high-precision position and speed information for a long time, but the output is discontinuous, and attitude information cannot be provided, and positioning cannot be realized when the GPS signal is blocked. POS uses the natural complementarity of inertial navigation and GPS navigation, applies information fusion technology, and integrates inertial measurement information with GPS measurement information, and can continuously and real-time obtain comprehensive motion parameters such as the position, speed and attitude of the carrier, and Errors do not accumulate over time.

GPS量测信息同惯性量测信息进行融合时，必须进行杆臂补偿。因为GPS天线不可能同IMU安装在一起，为了接收GPS卫星信号，GPS天线一般安装在飞机顶部，而IMU则安装在机舱内部，两者之间的距离一般都在1米以上，但GPS的位置精度和速度精度可分别达到0.05m和0.005m/s，因此必须将GPS得到的位置和速度信息通过IMU量测中心与GPS天线相位中心之间的杆臂补偿到IMU量测中心。但在飞行过程中，惯性稳定平台会实时转动三个框架以保持成像载荷水平并指向飞机飞行方向，从而导致IMU量测中心与GPS天线相位中心之间的相对方位不断发生变化，使得IMU量测中心与GPS天线相位中心之间的杆臂实时变化。传统的杆臂补偿方法假设IMU和GPS天线之间没有相对方位变化，即IMU量测中心与GPS天线相位中心之间的杆臂恒定不变，利用捷联惯性导航算法解算得到的

阵、和杆臂测量值l^b进行杆臂补偿。因此，传统的杆臂补偿方法应用于采用三轴惯性稳定平台的航空遥感会产生很大的误差甚至不能使用。When fusing GPS measurements with inertial measurements, lever-arm compensation is necessary. Because the GPS antenna cannot be installed together with the IMU, in order to receive GPS satellite signals, the GPS antenna is generally installed on the top of the aircraft, while the IMU is installed inside the cabin. The distance between the two is generally more than 1 meter, but the position of GPS The accuracy and velocity accuracy can reach 0.05m and 0.005m/s respectively, so the position and velocity information obtained by GPS must be compensated to the IMU measurement center through the lever arm between the IMU measurement center and the GPS antenna phase center. However, during the flight, the inertial stabilization platform will rotate the three frames in real time to maintain the imaging load level and point to the flight direction of the aircraft, resulting in constant changes in the relative orientation between the IMU measurement center and the GPS antenna phase center, making the IMU measurement The lever arm between the center and the phase center of the GPS antenna changes in real time. The traditional lever arm compensation method assumes that there is no relative orientation change between the IMU and the GPS antenna, that is, the lever arm between the IMU measurement center and the GPS antenna phase center is constant, and the strapdown inertial navigation algorithm is used to calculate the

array and lever arm measurement value l ^b for lever arm compensation. Therefore, the traditional lever-arm compensation method applied to aerial remote sensing using a three-axis inertial stabilization platform will produce large errors and even cannot be used.

发明内容 Contents of the invention

本发明的技术解决问题是：克服现有技术的不足，提出一种航空遥感用POS动态杆臂补偿方法。该方法针对三轴惯性稳定平台框架转动导致IMU量测中心与GPS天线相位中心之间的杆臂实时变化的问题，通过实时计算三轴惯性稳定平台中心与IMU量测中心之间的动态杆臂，得到IMU量测中心与GPS天线相位中心之间的实际杆臂，并实时计算三轴惯性稳定平台初始坐标系相对当地地理坐标系在三轴惯性稳定平台初始坐标系下的角速度，进行动态杆臂补偿。本发明具有精度高、操作简单、易于实现的特点，解决了航空遥感使用三轴惯性稳定平台时POS杆臂难以精确补偿的问题，提高了POS和航空遥感成像载荷的精度。The technical problem of the present invention is: to overcome the deficiencies of the prior art, and propose a POS dynamic lever arm compensation method for aerial remote sensing. This method aims at the real-time change of the lever arm between the IMU measurement center and the GPS antenna phase center caused by the frame rotation of the three-axis inertial stabilized platform, and calculates the dynamic lever arm between the center of the three-axis inertial stabilized platform and the IMU measurement center in real time , get the actual lever arm between the IMU measurement center and the GPS antenna phase center, and calculate the angular velocity of the initial coordinate system of the three-axis inertial stable platform relative to the local geographical coordinate system in the initial coordinate system of the three-axis inertial stable platform in real time, and carry out the dynamic lever arm arm compensation. The invention has the characteristics of high precision, simple operation and easy realization, solves the problem that the POS lever arm is difficult to compensate accurately when the aerial remote sensing uses a three-axis inertial stable platform, and improves the accuracy of POS and aerial remote sensing imaging loads.

本发明的技术解决方案为：一种航空遥感用POS动态杆臂补偿方法，具体步骤如下：The technical solution of the present invention is: a POS dynamic lever arm compensation method for aerial remote sensing, the specific steps are as follows:

(1)在三轴惯性稳定平台初始坐标系下，分别测量得到三轴惯性稳定平台中心与GPS天线相位中心之间的杆臂

和三轴惯性稳定平台中心与惯性测量单元(IMU)量测中心之间的杆臂 (1) Under the initial coordinate system of the three-axis inertial stabilized platform, the lever arm between the center of the three-axis inertial stabilized platform and the phase center of the GPS antenna is measured separately

and the lever arm between the center of the three-axis inertial stabilized platform and the measurement center of the inertial measurement unit (IMU)

(2)计算GPS数据时刻三轴惯性稳定平台初始坐标系到当地地理坐标系的方向余弦阵；(2) Calculate the direction cosine array from the initial coordinate system of the three-axis inertial stabilized platform to the local geographic coordinate system at the moment of GPS data;

(3)利用步骤(1)得到的杆臂和步骤(2)得到的方向余弦阵，计算GPS数据时刻IMU量测中心与GPS天线相位中心之间的动态杆臂；(3) Utilize the lever arm that step (1) obtains and the direction cosine array that step (2) obtains, calculate the dynamic lever arm between the IMU measurement center and the GPS antenna phase center at the time of GPS data;

(4)利用步骤(2)得到的方向余弦阵，计算三轴惯性稳定平台初始坐标系相对当地地理坐标系在三轴惯性稳定平台初始坐标系下的角速度；(4) Utilize the direction cosine matrix obtained in step (2), calculate the angular velocity of the initial coordinate system of the three-axis inertial stabilized platform relative to the local geographic coordinate system under the initial coordinate system of the three-axis inertial stabilized platform;

(5)基于步骤(2)得到的方向余弦阵、步骤(3)得到的动态杆臂和步骤(4)得到的角速度，对GPS位置数据和速度数据进行动态杆臂补偿，并将补偿后的GPS数据与惯性数据进行融合，得到最优的运动参数；(5) Based on the direction cosine matrix obtained in step (2), the dynamic lever arm obtained in step (3) and the angular velocity obtained in step (4), the dynamic lever arm compensation is performed on the GPS position data and velocity data, and the compensated The GPS data and inertial data are fused to obtain the optimal motion parameters;

(6)重复步骤(2)至步骤(5)，直至POS系统数据处理结束。(6) Steps (2) to (5) are repeated until the POS system data processing ends.

本发明的原理：针对三轴惯性稳定平台框架转动导致IMU量测中心与GPS天线相位中心之间的杆臂实时变化的问题，本发明在三轴惯性稳定平台初始坐标系下，将IMU量测中心与GPS天线相位中心之间的动态杆臂l分解为两个杆臂的差，如说明书附图2所示，计算杆臂l₁与杆臂l₂的差，即可得到动态杆臂l。其中杆臂l₁为三轴惯性稳定平台中心与GPS天线相位中心之间的杆臂，杆臂l₂为三轴惯性稳定平台中心与IMU量测中心之间的动态杆臂。通过对比说明书附图2a和说明书附图2b可知，l₁为固定杆臂，不随着惯性稳定平台的框架转动而变化；l₂为动态杆臂，随着惯性稳定平台的框架转动而改变。通过测量得到三轴惯性稳定平台中心与GPS天线相位中心之间的固定杆臂l₁，并实时计算三轴惯性稳定平台中心与IMU量测中心之间的动态杆臂l₂，从而可准确获得由于三轴惯性稳定平台框架转动导致的IMU量测中心与GPS天线相位中心之间实时变化的杆臂l，再利用捷联惯性导航算法和三轴惯性稳定平台三轴转动关系解算出的

阵、

和杆臂计算值l^b′进行实时动态杆臂补偿。Principle of the present invention: Aiming at the problem that the frame rotation of the three-axis inertial stable platform causes the real-time change of the lever arm between the IMU measurement center and the GPS antenna phase center, the present invention measures the IMU in the initial coordinate system of the three-axis inertial stable platform. The dynamic lever arm l between the center and the GPS antenna phase center is decomposed into the difference between the two lever arms, as shown in Figure 2 of the specification, the difference between the lever arm l ₁ and the lever arm l ₂ can be calculated to obtain the dynamic lever arm l . The lever arm _l1 is the lever arm between the center of the three-axis inertial stabilized platform and the phase center of the GPS antenna, and the lever arm _l2 is the dynamic lever arm between the center of the three-axis inertial stabilized platform and the IMU measurement center. By comparing the accompanying drawings 2a and 2b of the description, it can be seen that l ₁ is a fixed lever arm, which does not change with the frame rotation of the inertial stable platform; l ₂ is a dynamic lever arm, which changes with the frame rotation of the inertial stable platform. By measuring the fixed lever arm l ₁ between the center of the three-axis inertial stabilized platform and the phase center of the GPS antenna, and calculating the dynamic lever arm l ₂ between the center of the three-axis inertial stabilized platform and the IMU measurement center in real time, it can be accurately obtained The lever arm l that changes in real time between the IMU measurement center and the GPS antenna phase center due to the frame rotation of the three-axis inertial stabilized platform is calculated by using the strapdown inertial navigation algorithm and the three-axis rotation relationship of the three-axis inertial stabilized platform

array

Real-time dynamic lever arm compensation is performed with the calculated value l ^b ′ of the lever arm.

本发明与现有技术相比的优点在于：本发明通过实时计算IMU量测中心与GPS天线相位中心之间的动态杆臂l^b′和

进行精确的动态杆臂补偿，相对现有技术具有精度高的特点，解决了航空遥感使用三轴惯性稳定平台时POS杆臂难以精确补偿的问题，提高了POS和航空遥感成像载荷的精度。Compared with the prior art, the present invention has the advantages that: the present invention calculates in real time the dynamic lever arm l ^b ' between the IMU measurement center and the GPS antenna phase center

Accurate dynamic lever arm compensation has the characteristics of high precision compared with the existing technology, which solves the problem that the POS lever arm is difficult to accurately compensate when the aerial remote sensing uses a three-axis inertial stabilization platform, and improves the accuracy of POS and aerial remote sensing imaging loads.

附图说明 Description of drawings

图1为本发明的POS动态杆臂补偿方法流程图；Fig. 1 is the flow chart of POS dynamic lever arm compensation method of the present invention;

图2为本发明的航空遥感各子系统相对方位示意图，图中，ox_b′y_b′z_b′坐标系为三轴惯性稳定平台初始坐标系，ox_by_bz_b坐标系为三轴惯性稳定平台内框架坐标系，O_P为三轴惯性稳定平台中心，O_I为IMU量测中心，O_G为GPS天线相位中心。其中，图2a为三轴惯性稳定平台内框架坐标系ox_by_bz_b和三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′重合时的相对方位示意图；图2b为三轴惯性稳定平台内框架坐标系ox_by_bz_b和三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′不重合时的相对方位示意图。Fig. 2 is a schematic diagram of the relative orientation of each subsystem of aerial remote sensing of the present invention, in the figure, the ox _b' y _b' z _b' coordinate system is the initial coordinate system of the three-axis inertial stabilization platform, and the ox _by y _b z _b coordinate system is the three-axis The internal frame coordinate system of the inertial stabilized platform, O _P is the center of the three-axis inertial stabilized platform, O _I is the IMU measurement center, O _G is the GPS antenna phase center. Among them, Figure 2a is a schematic diagram of the relative orientation when the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilized platform and the initial coordinate system ox _b' y _b' z _b' of the three-axis inertial stabilized platform coincide; Figure 2b is the three-axis Schematic diagram of the relative orientation when the internal frame coordinate system ox _b y _b z _{b of} the inertial stabilized platform and the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stabilized platform do not coincide.

具体实施方式 Detailed ways

如说明书附图1所示，本发明的具体实施包括以下步骤：As shown in Figure 1 of the description, the specific implementation of the present invention comprises the following steps:

1、将三轴惯性稳定平台设置为调平模式，三轴惯性稳定平台控制三轴框架，使惯性稳定平台三轴的电编码器输出为零，设此时三轴惯性稳定平台内框架坐标系为三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′，以b′表示；设三轴惯性稳定平台实时的内框架坐标系ox_by_bz_b以b表示；设当地地理坐标系ox_ny_nz_n以n表示。在三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′下，使用经纬仪测量三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的杆臂和三轴惯性稳定平台中心O_P与IMU量测中心之间O_I的杆臂，得到三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的杆臂为

三轴惯性稳定平台中心O_P与IMU量测中心O_I之间的杆臂为

然后将三轴惯性稳定平台设置为遥控模式，跟踪POS输出，进行实时控制。成像载荷、三轴惯性稳定平台和IMU间的方位关系见说明书附图2，其中三轴惯性稳定平台安装在飞机机体上，成像载荷则安装在三轴惯性稳定平台上，与三轴惯性稳定平台的内框架固联，IMU则与成像载荷固联，测量成像载荷实时的运动参数。1. Set the three-axis inertial stabilized platform to the leveling mode, the three-axis inertial stabilized platform controls the three-axis frame, so that the output of the three-axis electric encoder of the inertial stabilized platform is zero, and set the internal frame coordinate system of the three-axis inertial stabilized platform at this time is the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stabilized platform, denoted by b′; let the real-time internal frame coordinate system ox _b y _b z _b of the three-axis inertial stabilized platform be denoted by b; let the local geographic coordinates The system ox _ny _nz _n is represented by n. Under the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stabilized platform, use theodolite to measure the center of the lever arm and the center of the three-axis inertial stabilized platform between the center O _P of the three-axis inertial stabilized platform and the phase center O _G of the GPS antenna The lever arm of O _I between O _P and the IMU measurement center, the lever arm between the three-axis inertial stable platform center O _P and the GPS antenna phase center O _G is obtained as

The lever arm between the center O _P of the three-axis inertial stabilized platform and the IMU measurement center O _I is

Then set the three-axis inertial stabilization platform to remote control mode, track the POS output, and perform real-time control. The orientation relationship between the imaging load, the three-axis inertial stabilized platform and the IMU is shown in Figure 2 of the instruction manual. The three-axis inertial stabilized platform is installed on the aircraft body, and the imaging load is installed on the three-axis inertial stabilized platform. The inner frame is fixedly connected, and the IMU is fixedly connected with the imaging load to measure the real-time motion parameters of the imaging load.

2、计算GPS数据时刻三轴惯性稳定平台初始坐标系到当地地理坐标系的方向余弦阵

2. Calculate the direction cosine array from the initial coordinate system of the three-axis inertial stable platform to the local geographic coordinate system at the moment of GPS data

(1)计算GPS数据时刻三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′到三轴惯性稳定平台内框架坐标系ox_by_bz_b的方向余弦阵

(1) Calculate the direction cosine matrix from the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stable platform to the internal frame coordinate system ox _b y _b z _b of the three-axis inertial stable platform at the moment of GPS data

由于三轴惯性稳定平台最外框为横滚框，中框为俯仰框，内框为航向框，故可得Since the outermost frame of the three-axis inertial stabilized platform is a roll frame, the middle frame is a pitch frame, and the inner frame is a heading frame, it can be obtained

${C C}_{{b b}^{' '}}^{b b} = = [\begin{matrix} cos cos (({ψ ψ}_{11})) & sin sin (({ψ ψ}_{11})) & 00 \\ - - sin sin (({ψ ψ}_{11})) & cos cos (({ψ ψ}_{11})) & 00 \\ 00 & 00 & 11 \end{matrix}] [\begin{matrix} 11 & 00 & 00 \\ 00 & cos cos (({θ θ}_{11})) & sin sin (({θ θ}_{11})) \\ 00 & - - sin sin (({θ θ}_{11})) & cos cos (({θ θ}_{11})) \end{matrix}] [\begin{matrix} cos cos (({γ γ}_{11})) & 00 & - - sin sin (({γ γ}_{11})) \\ 00 & 11 & 00 \\ sin sin (({γ γ}_{11})) & 00 & cos cos (({γ γ}_{11})) \end{matrix}]$

其中，γ₁角为GPS数据时刻三轴惯性稳定平台外框相对于惯性稳定平台初始外框旋转的角度，θ₁角为GPS数据时刻三轴惯性稳定平台中框相对于三轴惯性稳定平台初始中框旋转的角度，ψ₁角为GPS数据时刻三轴惯性稳定平台内框相对于三轴惯性稳定平台初始内框旋转的角度。Among them, γ ₁ angle is the rotation angle of the outer frame of the three-axis inertial stable platform relative to the initial outer frame of the inertial stable platform at the time of GPS data, and θ ₁ is the rotation angle of the middle frame of the three-axis inertial stable platform relative to the initial frame of the three-axis inertial stable platform at the time of GPS data. The rotation angle of the middle frame, ψ ₁ angle is the rotation angle of the inner frame of the three-axis inertial stabilized platform relative to the initial inner frame of the three-axis inertial stabilized platform at the moment of GPS data.

由于三轴惯性稳定平台与GPS各自具有独立的时钟系统，三轴惯性稳定平台输出的电编码器数据与GPS数据难以完全同步，设在GPS数据时刻前采样得到的惯性稳定平台三轴的电编码器数据分别为

和

在GPS数据时刻后采样得到的惯性稳定平台三轴的电编码器数据分别为

和由于三轴惯性稳定平台各框架惯量都较大，可假设在每个采样间隔下三轴惯性稳定平台框架角速度不变，可得Since the three-axis inertial stable platform and GPS have independent clock systems, it is difficult to completely synchronize the electrical encoder data output by the three-axis inertial stable platform with the GPS data. device data are

and

The three-axis electric encoder data of the inertial stable platform obtained by sampling after the GPS data time are respectively

and Since the inertia of each frame of the three-axis inertial stabilized platform is relatively large, it can be assumed that the frame angular velocity of the three-axis inertial stabilized platform remains unchanged at each sampling interval, and it can be obtained

$[\begin{matrix} {γ γ}_{11} \\ {θ θ}_{11} \\ {ψ ψ}_{11} \end{matrix}] = = [\begin{matrix} (({P P}_{Ay Ay}^{+ +} - - {P P}_{Ay Ay}^{- -})) (({T T}_{GPS GPS} - - {T T}_{A A}^{- -})) / / (({T T}_{A A}^{+ +} - - {T T}_{A A}^{- -})) + + {P P}_{Ay Ay}^{- -} \\ (({P P}_{Ax Ax}^{+ +} - - {P P}_{Ax Ax}^{- -})) (({T T}_{GPS GPS} - - {T T}_{A A}^{- -})) / / (({T T}_{A A}^{+ +} - - {T T}_{A A}^{- -})) + + {P P}_{Ax Ax}^{- -} \\ (({P P}_{Az Az}^{+ +} - - {P P}_{Az Az}^{- -})) (({T T}_{GPS GPS} - - {T T}_{A A}^{- -})) / / (({T T}_{A A}^{+ +} - - {T T}_{A A}^{- -})) + + {P P}_{Az Az}^{- -} \end{matrix}]$

其中，T_GPS为GPS数据时刻的UTC时间，

为

和

数据采样时刻的UTC时间，

为

和

数据采样时刻的UTC时间。Among them, T _GPS is the UTC time of the GPS data moment,

for

and

The UTC time of the data sampling moment,

for

and

The UTC time of the data sampling moment.

(2)计算GPS数据时刻三轴惯性稳定平台内框架坐标系ox_by_bz_b到当地地理坐标系ox_ny_nz_n的方向余弦阵

(2) Calculate the direction cosine matrix from the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilization platform to the local geographic coordinate system ox _n y _n z _n at the moment of GPS data

${C C}_{b b}^{n no} = = [\begin{matrix} cos cos {γ γ}_{22} cos cos {ψ ψ}_{22} + + sin sin {γ γ}_{22} sin sin {θ θ}_{22} sin sin {ψ ψ}_{22} & cos cos {θ θ}_{22} sin sin {ψ ψ}_{22} & sin sin {γ γ}_{22} cos cos {ψ ψ}_{22} - - cos cos {γ γ}_{22} sin sin {θ θ}_{22} sin sin {ψ ψ}_{22} \\ - - cos cos {γ γ}_{22} sin sin {ψ ψ}_{22} + + sin sin {γ γ}_{22} sin sin {θ θ}_{22} cos cos {ψ ψ}_{22} & cos cos {θ θ}_{22} cos cos {ψ ψ}_{22} & - - sin sin {γ γ}_{22} sin sin {ψ ψ}_{22} - - cos cos {γ γ}_{22} sin sin {θ θ}_{22} cos cos {ψ ψ}_{22} \\ - - sin sin {γ γ}_{22} cos cos {θ θ}_{22} & sin sin {θ θ}_{22} & cos cos {γ γ}_{22} cos cos {θ θ}_{22} \end{matrix}]$

其中，γ₂、θ₂、ψ₂分别是三轴惯性稳定平台内框架坐标系ox_by_bz_b相对当地地理坐标系ox_ny_nz_n的横滚角、俯仰角和航向角。Among them, γ ₂ , θ ₂ , and ψ ₂ are the roll angle, pitch angle and heading angle of the internal frame coordinate system ox _by y _b z _b of the three-axis inertial stabilized platform relative to the local geographic coordinate system ox _ny _nz _n , respectively.

(3)由上述分析可进一步求得：GPS数据时刻三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′到当地地理坐标系ox_ny_nz_n的方向余弦阵可以由GPS数据时刻三轴惯性稳定平台内框架坐标系ox_by_bz_b到当地地理坐标系ox_ny_nz_n的方向余弦阵和GPS数据时刻三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′到三轴惯性稳定平台内框架坐标系ox_by_bz_b的方向余弦阵

点积得到，即

C_{b^{'}}^{n} = C_{b}^{n} C_{b^{'}}^{b}

(3) From the above analysis, it can be further obtained: the direction cosine matrix from the initial coordinate system ox _b′ y _b′ z _b′ to the local geographic coordinate system ox _n y _n z _n of the three-axis inertial stabilization platform at the time of GPS data The direction cosine matrix from the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilization platform to the local geographic coordinate system ox _n y _n z _n at the moment of GPS data and the direction cosine matrix from the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stable platform to the internal frame coordinate system ox _b y _b z _b of the three-axis inertial stable platform at the moment of GPS data

dot product, that is,

C_{b^{'}}^{no} = C_{b}^{no} C_{b^{'}}^{b}

3、计算GPS数据时刻IMU量测中心与GPS天线相位中心之间的动态杆臂l^b′3. Calculate the dynamic lever arm l ^b ′ between the IMU measurement center and the GPS antenna phase center at the time of GPS data

(1)计算GPS数据时刻三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的杆臂

(1) Calculating the lever arm between the center O _P of the three-axis inertial stable platform and the phase center O _G of the GPS antenna at the time of calculation of GPS data

在三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′下，惯性稳定平台在控制三轴框架转动过程中，三轴惯性稳定平台中心O_P与飞机之间没有相对方位变化，因此三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的相对方位关系不变，由步骤1得到的三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的杆臂与相等，即Under the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stabilized platform, when the inertial stabilized platform controls the rotation of the three-axis frame, there is no relative orientation change between the center _OP of the three-axis inertial stabilized platform and the aircraft, so The relative orientation relationship between the three-axis inertial stabilized platform center O _P and the GPS antenna phase center O _G remains unchanged, and the lever arm between the three-axis inertial stabilized platform center _OP and the GPS antenna phase center O _G obtained from step 1 and equal, ie

${l l}_{11}^{{b b}^{' '}} = = {l l}_{0101}^{{b b}^{' '}}$

(2)计算GPS数据时刻三轴惯性稳定平台中心O_P与IMU量测中心O_I之间的杆臂

(2) Calculate the lever arm between the three-axis inertial stable platform center O _P and the IMU measurement center O _I at the time of calculation of GPS data

由于三轴惯性稳定平台实时控制框架转动以保持成像载荷水平并指向飞机飞行方向，使得

实时变化，但由于IMU与三轴惯性稳定平台内框架固联，因此IMU量测中心O_I在三轴惯性稳定平台内框架坐标系ox_by_bz_b的位置坐标与IMU量测中心在三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′的位置坐标相同，可得Since the three-axis inertial stabilization platform controls the rotation of the frame in real time to keep the imaging load level and point to the flight direction of the aircraft, so that

changes in real time, but because the IMU is fixedly connected to the inner frame of the three-axis inertial stable platform, the position coordinates of the IMU measurement center O _I in the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stable platform are in the three The position coordinates of the initial coordinate system ox _b′ y _b′ z _b′ of the axial inertial stable platform are the same, and it can be obtained

${l l}_{22}^{b b} = = {l l}_{0202}^{{b b}^{' '}}$

由步骤2中得到的GPS数据时刻三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′到三轴惯性稳定平台内框架坐标系ox_by_bz_b的方向余弦阵通过转置可得GPS数据时刻三轴惯性稳定平台内框架坐标系ox_by_bz_b到三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′的方向余弦阵

The direction cosine matrix from the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stable platform to the internal frame coordinate system ox _b y _b z _b of the three-axis inertial stable platform at the moment of GPS data obtained in step 2 The direction cosine matrix from the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stable platform to the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stable platform can be obtained by transposing the GPS data

${C C}_{b b}^{{b b}^{' '}} = = {C C}_{{b b}^{' '}}^{bT bT}$

从而可得GPS数据时刻三轴惯性稳定平台中心O_P与IMU量测中心O_I之间的杆臂

Thus, the lever arm between the center O _P of the three-axis inertial stabilized platform and the IMU measurement center O _I at the moment of GPS data can be obtained

${l l}_{22}^{{b b}^{' '}} = = {C C}_{b b}^{{b b}^{' '}} {l l}_{22}^{b b}$

(3)由上述分析可进一步求得：GPS数据时刻IMU量测中心O_I与GPS天线相位中心O_G之间的动态杆臂l^b′可由GPS数据时刻三轴惯性稳定平台中心O_P与GPS天线相位中心O_G之间的杆臂

和GPS数据时刻三轴惯性稳定平台中心O_P与IMU量测中心O_I之间的杆臂

之差得到，即(3) From the above analysis, it can be further obtained: the dynamic lever arm l ^b ′ between the IMU measurement center O _I and the GPS antenna phase center O _G at the time of GPS data can be determined by the center O _P of the three-axis inertial stable platform at the time of GPS data and GPS Lever arm between antenna phase center O _G

and the lever arm between the three-axis inertial stabilized platform center O _P and the IMU measurement center O _I at the moment of GPS data

The difference is obtained, that is

${l l}^{{b b}^{' '}} = = {l l}_{11}^{{b b}^{' '}} - - {l l}_{22}^{{b b}^{' '}}$

4、计算三轴惯性稳定平台初始坐标系相对当地地理坐标系在三轴惯性稳定平台初始坐标系下的角速度

4. Calculate the angular velocity of the initial coordinate system of the three-axis inertial stabilized platform relative to the local geographic coordinate system in the initial coordinate system of the three-axis inertial stabilized platform

(1)计算三轴惯性稳定平台内框架坐标系ox_by_bz_b相对三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′在三轴惯性稳定平台内框架坐标系ox_by_bz_b下的角速度

(1) Calculate the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilized platform relative to the initial coordinate system ox _{b′ y} b _{′ z} _b′ of the three-axis inertial stabilized platform in the inner frame coordinate system ox _b y of the three-axis inertial stabilized platform Angular velocity at _b z _b

由步骤2可知，GPS数据时刻前采样得到的惯性稳定平台三轴的电编码器数据分别为

GPS数据时刻后采样得到的惯性稳定平台三轴的电编码器数据分别为

和

三轴惯性稳定平台输出的电编码器数据周期为0.01秒。由于三轴惯性稳定平台各框架惯量较大，可假设相邻两个采样时刻之间，三轴惯性稳定平台框架角速度不变，可得三个框架角速度为：It can be seen from step 2 that the three-axis electrical encoder data of the inertial stable platform obtained by sampling before the GPS data time are respectively

and

The data period of the electric encoder output by the three-axis inertial stabilization platform is 0.01 second. Since the frame inertia of the three-axis inertial stabilized platform is relatively large, it can be assumed that the frame angular velocity of the three-axis inertial stabilized platform remains unchanged between two adjacent sampling moments, and the angular velocity of the three frames can be obtained as:

${w w}_{{b b}^{' '} b b}^{b b} = = [\begin{matrix} {w w}_{x x} \\ {w w}_{y the y} \\ {w w}_{z z} \end{matrix}] = = [\begin{matrix} (({P P}_{Ax Ax}^{+ +} - - {P P}_{Ax Ax}^{- -})) / / 0.01 0.01 \\ (({P P}_{Ay Ay}^{+ +} - - {P P}_{Ay Ay}^{- -})) / / 0.01 0.01 \\ (({P P}_{Az Az}^{+ +} - - {P P}_{Az Az}^{- -})) / / 0.01 0.01 \end{matrix}]$

当三轴惯性稳定平台输出的电编码器数据噪声较大时，需要先对电编码器数据进行滤波，然后采用插值的方法得到惯性稳定平台三轴角位置随时间变化的函数，通过在GPS数据时刻对函数进行微分运算得到惯性稳定平台三轴的角速度。When the electrical encoder data output by the three-axis inertial stable platform is noisy, it is necessary to filter the electrical encoder data first, and then use the interpolation method to obtain the function of the three-axis angular position of the inertial stable platform with time, through the GPS data Differentiate the function at all times to obtain the angular velocity of the three axes of the inertial stable platform.

(2)计算三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′相对当地地理坐标系ox_ny_nz_n在三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′下的角速度

(2) Calculate the initial coordinate system of the three-axis inertial stabilized platform ox _b′ y _b′ _{z b′} relative to the local geographic coordinate system ox _n y _n z _n in the initial coordinate system of the three-axis inertial stabilized platform ox _b′ y _b′ z _b′ Angular velocity under

由于because

${w w}_{in in}^{n no} = = {w w}_{ie ie}^{n no} + + {w w}_{en en}^{n no}$

其中，为当地地理坐标系ox_ny_nz_n相对惯性坐标系在当地地理坐标系ox_ny_nz_n下的角速度，为地球坐标系相对惯性坐标系在当地地理坐标系ox_ny_nz_n下的角速度，

为当地地理坐标系ox_ny_nz_n相对地球坐标系在当地地理坐标系ox_ny_nz_n下的角速度，且in, is the angular velocity of the local geographic coordinate system ox _n y _n z _n relative to the inertial coordinate system in the local geographic coordinate system ox _n y _n z _n , is the angular velocity of the earth coordinate system relative to the inertial coordinate system in the local geographic coordinate system ox _n y _n z _n ,

is the angular velocity of the local geographic coordinate system ox _n y _n z _n relative to the earth coordinate system in the local geographic coordinate system ox _n y _n z _n , and

${w w}_{ie ie}^{n no} = = [\begin{matrix} 00 \\ cos cos ((Lat Lat)) \\ sin sin ((Lat Lat)) \end{matrix}]$

${w w}_{en en}^{n no} = = [\begin{matrix} - - {V V}_{N N}^{n no} / / {R R}_{M m} \\ {V V}_{E E.}^{n no} / / {R R}_{N N} \\ {V V}_{E E.}^{n no} tan the tan ((Lat Lat)) / / {R R}_{N N} \end{matrix}]$

其中，Lat为当地纬度，为飞行载体在当地地理坐标系ox_ny_nz_n下的东向速度，

为飞行载体在当地地理坐标系ox_ny_nz_n下的北向速度，R_M和R_N分别为当地子午圈主曲率半径和当地卯酉圈主曲率半径。Among them, Lat is the local latitude, is the eastward velocity of the flight carrier in the local geographic coordinate system ox _n y _n z _n ,

is the northward velocity of the flight carrier in the local geographic coordinate system ox _ny _nz _n , and R _M and R _N are the principal curvature radii of the local meridian circle and the local maoyou circle principal curvature radii, respectively.

可得Available

${w w}_{in in}^{b b} = = {C C}_{n no}^{b b} {w w}_{in in}^{n no}$

由于because

${w w}_{{ib ib}^{' '}}^{b b} = = {w w}_{ib ib}^{b b} - - {w w}_{{b b}^{' '} b b}^{b b}$

其中，

为陀螺仪输出的三轴惯性稳定平台内框架坐标系ox_by_bz_b相对惯性坐标系在三轴惯性稳定平台内框架坐标系ox_by_bz_b下的角速度，

为三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′相对惯性坐标系在三轴惯性稳定平台内框架坐标系ox_by_bz_b下的角速度。in,

is the angular velocity of the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilized platform relative to the inertial coordinate system output by the gyroscope under the inner frame coordinate system ox _b y _b z _b of the three-axis inertial stabilized platform,

is the angular velocity of the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stable platform relative to the inertial coordinate system in the internal frame coordinate system ox _by y _b z _b of the three-axis inertial stable platform.

因此可得Therefore available

${w w}_{{nb nb}^{' '}}^{{b b}^{' '}} = = {C C}_{b b}^{{b b}^{' '}} (({w w}_{{ib ib}^{' '}}^{b b} - - {w w}_{in in}^{b b}))$

5、对GPS位置数据和速度数据进行动态杆臂补偿5. Dynamic lever arm compensation for GPS position data and speed data

(1)对GPS位置数据进行动态杆臂补偿(1) Dynamic lever arm compensation for GPS position data

GPS数据时刻IMU量测中心O_I与GPS天线相位中心O_G之间的杆臂lⁿ The lever arm l ⁿ between the IMU measurement center O _I and the GPS antenna phase center O _G at the time of GPS data

${l l}^{n no} = = {C C}_{{b b}^{' '}}^{n no} {l l}^{{b b}^{' '}} = = [\begin{matrix} {l l}_{E E.}^{n no} \\ {l l}_{N N}^{n no} \\ {l l}_{U u}^{n no} \end{matrix}]$

其中，

为杆臂lⁿ在当地地理坐标系ox_ny_nz_n下的东向分量，

为杆臂lⁿ在当地地理坐标系ox_ny_nz_n下的北向分量，

为杆臂lⁿ在当地地理坐标系ox_ny_nz_n下的天向分量。in,

is the east component of the lever arm l ⁿ in the local geographic coordinate system ox _n y _n z _n ,

is the north component of the lever arm l ⁿ in the local geographic coordinate system ox _n y _n z _n ,

is the celestial component of the lever arm l ⁿ in the local geographic coordinate system ox _{ny nz} _n _.

GPS天线相位中心O_G的位置数据

通过杆臂补偿得到的IMU量测中心O_I的位置数据

为Position data of GPS antenna phase center O _G

The position data of the IMU measurement center O _I obtained by lever arm compensation

for

${P P}_{IMU IMU}^{n no} = = {P P}_{GPS GPS}^{n no} - - {l l}^{n no} = = [\begin{matrix} Lat Lat - - {l l}_{N N}^{n no} / / {R R}_{M m} \\ Lon Lon - - {l l}_{E E.}^{n no} / / {R R}_{N N} / / cos cos ((Lat Lat)) \\ H h - - {l l}_{U u}^{n no} \end{matrix}]$

其中，Lat、Lon、H分别为GPS输出的纬度、经度和高度。Among them, Lat, Lon, H are the latitude, longitude and height output by GPS respectively.

(2)对GPS速度数据进行动态杆臂补偿(2) Dynamic lever arm compensation for GPS speed data

GPS天线相位中心O_G的速度数据

通过杆臂补偿得到的IMU量测中心O_I的速度数据

为Velocity data of GPS antenna phase center O _G

Velocity data of the IMU measurement center O _I obtained through lever arm compensation

for

${V V}_{IMU IMU}^{n no} = = {V V}_{GPS GPS}^{n no} - - {C C}_{{b b}^{' '}}^{n no} {V V}_{l l}^{{b b}^{' '}}$

其中

为GPS速度数据在三轴惯性稳定平台初始坐标系ox_b′y_b′z_b′下的速度杆臂误差，由下式计算得到in

is the speed lever arm error of the GPS speed data in the initial coordinate system ox _b′ y _b′ z _b′ of the three-axis inertial stabilized platform, which is calculated by the following formula

${V V}_{l l}^{{b b}^{' '}} = = {w w}_{{nb nb}^{' '}}^{{b b}^{' '}} \times \times {l l}^{{b b}^{' '}}$

将补偿后的GPS位置数据和速度数据与惯性数据进行融合，得到最优的运动参数。The compensated GPS position data and velocity data are fused with the inertial data to obtain the optimal motion parameters.

6、重复步骤2至步骤5，直至POS系统数据处理结束。6. Repeat step 2 to step 5 until the POS system data processing ends.

本发明说明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A dynamic lever arm compensation method of a position and attitude measurement system (POS) for aerial remote sensing is characterized by comprising the following steps:

step (1), respectively measuring and obtaining a lever arm between the center of the triaxial inertially stabilized platform and the phase center of the GPS antenna under the initial coordinate system of the triaxial inertially stabilized platform

And a lever arm between the center of the three-axis inertially stabilized platform and the measurement center of an Inertial Measurement Unit (IMU)The initial coordinate system ox of the three-axis inertially stabilized platform_b'y_b′z_b'The inner frame coordinate system, ox, when the output of the electrical encoder of the triaxial inertially stabilized platform is zero_b'y_b′z_b'The coordinate system is denoted by b';

step (2), calculating a direction cosine array from the initial coordinate system of the triaxial inertial stabilization platform to a local geographical coordinate system at the moment of GPS data; the calculation process of the direction cosine array from the initial coordinate system of the triaxial inertial stabilization platform to the local geographic coordinate system at the time of the GPS data is as follows:

1) initial coordinate system ox of triaxial inertial stabilization platform for calculating GPS data time_b'y_b′z_b′To the internal frame coordinate system ox of the triaxial inertially stabilized platform_by_bz_bDirectional cosine array of

[\begin{matrix} γ_{1} \\ θ_{1} \\ ψ_{1} \end{matrix}] = [\begin{matrix} (P_{Ay}^{+} - P_{Ay}^{-}) (T_{GPS} - T_{A}^{-}) / (T_{A}^{+} - T_{A}^{-}) + P_{Ay}^{-} \\ (P_{Ax}^{+} - P_{Ax}^{-}) (T_{GPS} - T_{A}^{-}) / (T_{A}^{+} - T_{A}^{-}) + P_{Ax}^{-} \\ (P_{Az}^{+} - P_{Az}^{-}) (T_{GPS} - T_{A}^{-}) / (T_{A}^{+} - T_{A}^{-}) + P_{Az}^{-} \end{matrix}]

C_{b^{'}}^{b} = [\begin{matrix} \cos (ψ_{1}) & \sin (ψ_{1}) & 0 \\ - \sin (ψ_{1}) & \cos (ψ_{1}) & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos (θ_{1}) & \sin (θ_{1}) \\ 0 & - \sin (θ_{1}) & \cos (θ_{1}) \end{matrix}] [\begin{matrix} \cos (γ_{1}) & 0 & - \sin (γ_{1}) \\ 0 & 1 & 0 \\ \sin (γ_{1}) & 0 & \cos (γ_{1}) \end{matrix}]

Wherein, γ₁The angle is the angle of the outer frame of the triaxial inertially stabilized platform rotating relative to the initial outer frame of the triaxial inertially stabilized platform at the time of GPS data, theta₁The angle is the angle psi of the rotation of the middle frame of the triaxial inertially stabilized platform relative to the initial middle frame of the triaxial inertially stabilized platform at the time of GPS data₁The angle is the rotation angle of the inner frame of the triaxial inertial stabilization platform relative to the initial inner frame of the triaxial inertial stabilization platform at the moment of GPS data,

and

is the three-axis electrical encoder data of the inertially stabilized platform sampled before the GPS data moment,

and

three-axis electrical encoder data, T, of an inertially stabilized platform sampled after the time of GPS data_GPSThe UTC time at the time of the GPS data,

is composed of

And

the UTC time of the data sample time,

is composed of

And

UTC time of data sampling time;

2) inner frame coordinate system ox of triaxial inertial stabilization platform for calculating GPS data time_by_bz_bTo the local geographical coordinate system ox_ny_nz_nDirectional cosine array of

C_{b}^{n} = [\begin{matrix} {\cos γ}_{2} \cos ψ_{2} + {\sin γ}_{2} \sin θ_{2} {\sin ψ}_{2} & \cos θ_{2} {\sin ψ}_{2} & {\sin γ}_{2} {\cos ψ}_{2} - {\cos γ}_{2} {\sin θ}_{2} {\sin ψ}_{2} \\ {- \cos γ}_{2} {\sin ψ}_{2} + {\sin γ}_{2} {\sin θ}_{2} {\cos ψ}_{2} & {\cos θ}_{2} {\cos ψ}_{2} & - {\sin γ}_{2} {\sin ψ}_{2} - {\cos γ}_{2} {\sin θ}_{2} {\cos ψ}_{2} \\ - {\sin γ}_{2} {\cos θ}_{2} & {\sin θ}_{2} & {\cos γ}_{2} {\cos θ}_{2} \end{matrix}]

Wherein, γ₂、θ₂、ψ₂Respectively, the coordinate system ox of the inner frame of the three-axis inertially stabilized platform_by_bz_bRelative local geographical coordinate system ox_ny_nz_nRoll angle, pitch angle and course angle;

3) initial coordinate system ox of triaxial inertial stabilization platform for calculating GPS data time_b'y_b′z_b′To the local geographical coordinate system ox_ny_nz_nDirectional cosine array of

C_{b^{'}}^{n} = C_{b}^{n} C_{b^{'}}^{b};

Step (3) utilizing the lever arm obtained in the step (1)

And

and (3) calculating a dynamic lever arm between the IMU measurement center and the GPS antenna phase center at the GPS data moment by the direction cosine array obtained in the step (2), and calculatingThe process is as follows:

1) triaxial inertial stabilization platform center O for calculating GPS data time_PAnd IMU measurement center O_ILever arm between

l_{2}^{b} = l_{02}^{b^{'}}

C_{b}^{b^{'}} = C_{b^{'}}^{bT}

l_{2}^{b^{'}} = C_{b}^{b^{'}} l_{2}^{b}

WhereinFor the purpose of stabilizing the frame coordinate system ox in the three-axis inertially_by_bz_bCenter O of lower triaxial inertially stabilized platform_PAnd IMU measurement center O_IThe lever arm in between, and the lever arm,is composed of

Transposing;

2) IMU measuring center O for calculating GPS data time_IAnd GPS antenna phase center O_GDynamic lever arm l between^b'

l_{1}^{b^{'}} = l_{01}^{b^{'}}

l^{b^{'}} = l_{1}^{b^{'}} - l_{2}^{b^{'}};

And (4) calculating the angular velocity of the initial coordinate system of the triaxial inertial stabilization platform relative to the local geographic coordinate system under the initial coordinate system of the triaxial inertial stabilization platform by using the direction cosine array obtained in the step (2), wherein the calculation process is as follows:

1) calculating frame coordinate system ox in three-axis inertially stabilized platform_by_bz_bRelative triaxial initial coordinate system ox of inertially stabilized platform_b'y_b′z_b'Frame coordinate system ox in three-axis inertially stabilized platform_by_bz_bAngular velocity of

w_{b^{'} b}^{b} = [\begin{matrix} w_{x} \\ w_{y} \\ w_{z} \end{matrix}] = [\begin{matrix} (P_{Ax}^{+} - P_{Ax}^{-}) / T_{s} \\ (P_{Ay}^{+} - P_{Ay}^{-}) / T_{s} \\ (P_{Az}^{+} - P_{Az}^{-}) / T_{s} \end{matrix}]

Wherein T is_sSampling period of an electrical encoder of the triaxial inertially stabilized platform;

2) calculating initial coordinate system ox of three-axis inertially stabilized platform_b'y_b′z_b'Relative local geographical coordinate system ox_ny_nz_nIn the initial coordinate system ox of the three-axis inertially stabilized platform_b'y_b′z_b'Angular velocity of

w_{{ib}^{'}}^{b} = w_{ib}^{b} - w_{b^{'} b}^{b}

w_{ie}^{n} = [\begin{matrix} 0 \\ \cos (Lat) \\ \sin (Lat) \end{matrix}]

w_{en}^{n} = [\begin{matrix} - V_{N}^{n} / R_{M} \\ V_{E}^{n} / R_{N} \\ V_{E}^{n} \tan (Lat) / R_{N} \end{matrix}]

w_{in}^{n} = w_{ie}^{n} + w_{en}^{n}

w_{in}^{b} = C_{n}^{b} w_{in}^{n}

w_{{nb}^{'}}^{b^{'}} = C_{b}^{b^{'}} (w_{{ib}^{'}}^{b} - w_{in}^{b})

Wherein,frame coordinate system ox in three-axis inertially stabilized platform for gyroscope output_by_bz_bRelative inertial coordinate system ox of inner frame coordinate system of three-axis inertial stabilization platform_by_bz_bThe angular velocity of the lower part of the body,

for three-axis inertially stabilized platform initial coordinate system ox_b'y_b′z_b'Relative inertial coordinate system ox of inner frame coordinate system of three-axis inertial stabilization platform_by_bz_bThe angular velocity of the lower part of the body,

for a terrestrial coordinate system relative to an inertial coordinate system in a local geographical coordinate system ox_ny_nz_nThe angular velocity of the lower part of the body,

for the local geographical coordinate system ox_ny_nz_nLocal geographical coordinate system ox relative to the earth coordinate system_ny_nz_nThe angular velocity of the lower, Lat, is the local latitude,

for flying carriers in the local geographical coordinate system ox_ny_nz_nThe speed of the east direction of the downward direction,

for flying carriers in the local geographical coordinate system ox_ny_nz_nLower north velocity, R_MAnd R_NRespectively is a local meridian main curvature radius and a local unitary fourth-element main curvature radius,

for the local geographical coordinate system ox_ny_nz_nRelative inertial frame to local geographic frame ox_ny_nz_nThe angular velocity of the lower part of the body,

for the local geographical coordinate system ox_ny_nz_nRelative inertial coordinate systemFrame coordinate system ox in stable platform_by_bz_bAngular velocity of the rotor;

step (5), based on the direction cosine array obtained in the step (2), the dynamic lever arm obtained in the step (3) and the angular velocity obtained in the step (4), performing dynamic lever arm compensation on GPS position data and velocity data, and fusing the compensated GPS data and inertial data to obtain optimal motion parameters; the calculation process for performing dynamic lever arm compensation on the GPS position data and the speed data comprises the following steps:

1) dynamic lever arm compensation for GPS position data

l^{n} = C_{b^{'}}^{n} l^{b^{'}} = [\begin{matrix} l_{E}^{n} \\ l_{N}^{n} \\ l_{U}^{n} \end{matrix}]

P_{IMU}^{n} = P_{GPS}^{n} - l^{n} = [\begin{matrix} Lat - l_{N}^{n} / R_{M} \\ Lon - l_{E}^{n} / R_{N} / \cos (Lat) \\ H - l_{U}^{n} \end{matrix}]

Wherein,

is a lever arm lⁿIn the local geographical coordinate system ox_ny_nz_nThe east-directional component of the downward direction,

is a lever arm lⁿIn the local geographical coordinate system ox_ny_nz_nThe north-going component of the lower direction,

is a lever arm lⁿIn the local geographical coordinate system ox_ny_nz_nComponent of the downward direction,/ⁿIMU measurement center O for GPS data time_IAnd GPS (global positioning system) antennaLine phase center O_GThe arms in between, Lat, Lon, H are latitude, longitude and altitude of GPS output respectively,

GPS antenna phase center O for GPS output_GThe position data of (a) of (b),

for IMU measurement center O obtained by lever arm compensation_IPosition data of

2) Dynamic lever arm compensation for GPS velocity data

V_{l}^{b^{'}} = w_{n b^{'}}^{b^{'}} \times l^{b^{'}}

V_{IMU}^{n} = V_{GPS}^{n} - C_{b^{'}}^{n} V_{l}^{b^{'}}

Wherein,

initial coordinate system ox of three-axis inertially stabilized platform for GPS speed data_b′y_b′z_b′The lower velocity lever arm error, x is the cross product,

GPS antenna phase center O for GPS output_GThe speed data of (a) is stored,

for IMU measurement center O obtained by lever arm compensation_ISpeed data of (2);

and (6) repeating the steps (2) to (5) until the data processing of the POS system is finished.