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CN109459027B - A Navigation Method Based on Polarization-Geomagnetic Vector Compact Combination - Google Patents

A Navigation Method Based on Polarization-Geomagnetic Vector Compact Combination Download PDF

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CN109459027B
CN109459027B CN201811336222.5A CN201811336222A CN109459027B CN 109459027 B CN109459027 B CN 109459027B CN 201811336222 A CN201811336222 A CN 201811336222A CN 109459027 B CN109459027 B CN 109459027B
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郭雷
杨健
刘鑫
王善澎
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    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention relates to a navigation method based on a polarization-geomagnetic vector tight combination, which comprises the steps of firstly, intelligently extracting sun vector information under a carrier coordinate system by using a compound eye-imitating polarization compass; secondly, combining the solar astronomical calendar to obtain solar vector information under a geographic coordinate system, and establishing an information conversion relation of the solar vector under a body coordinate system and the geographic coordinate system; extracting the geomagnetic vectors in the body coordinate system and the geographic coordinate system, and establishing a conversion relation between the geomagnetic vectors in the body coordinate system and the geographic coordinate system; then, carrying out information fusion on the geomagnetic vector and the sun vector in a body coordinate system; and finally, establishing a combined navigation system model based on polarization/geomagnetic vector fusion. Compared with the existing method, the method realizes the deep fusion of geomagnetic information and polarization information, can improve the precision and stability of the system, and can be used in the fields of attitude determination and positioning of carriers such as ships, unmanned aerial vehicles, missiles, unmanned vehicles and the like.

Description

一种基于偏振-地磁矢量紧组合的导航方法A Navigation Method Based on the Compact Combination of Polarization-Geomagnetic Vectors

技术领域technical field

本发明涉及一种基于偏振-地磁矢量紧组合的导航方法，该方法用于无人机、舰船、导弹等载体的三维空间自主姿态确定与定位。The invention relates to a navigation method based on a tight combination of polarization-geomagnetic vectors, which is used for the determination and positioning of three-dimensional space autonomous attitudes of carriers such as unmanned aerial vehicles, ships, and missiles.

背景技术Background technique

目前无人机、舰船、导弹等载体的工作环境日趋复杂，为了弥补单一导航的不足，多传感器融合的组合导航是未来导航的发展方向。惯性/卫星组合导航系统是目前应用最为广泛的组合导航系统，但是卫星导航易受自然环境及人为干扰，在拒止、干扰、对抗等环境下无法提供准确可靠的导航信息。因此，卫星导航系统在深空探测、深海探测等领域的应用受到了极大的限制。因此亟需发展不依赖于卫星导航的组合导航系统。At present, the working environment of carriers such as unmanned aerial vehicles, ships, and missiles is becoming more and more complex. In order to make up for the insufficiency of single navigation, the combined navigation of multi-sensor fusion is the development direction of future navigation. Inertial/satellite integrated navigation system is the most widely used integrated navigation system at present, but satellite navigation is susceptible to natural environment and human interference, and cannot provide accurate and reliable navigation information in the environment of rejection, interference, and confrontation. Therefore, the application of satellite navigation systems in deep space exploration, deep sea exploration and other fields has been greatly restricted. Therefore, there is an urgent need to develop an integrated navigation system that does not rely on satellite navigation.

仿生偏振导航无源、无辐射、隐蔽性好、自主性强及不受电磁干扰影响，能够为载体提供三位姿态信息及位置信息，可于惯性导航系统进行优势互补，为提高组合导航系统的自主性、可靠性提供了新的解决途径。地磁导航系统是另一种常用的导航方式，也能够提供较高精度的姿态与位置信息，弥补惯性导航系统的姿态与位置误差。针对现有的偏振/地磁辅助的组合导航系统，都用到了卫星导航系统，如已授权的中国专利201510312112.5，“一种双模式仿生偏振/地磁辅助组合导航系统、论文“仿生偏振光/GPS/地磁组合导航方法设计及实现”、“偏振光/地磁/GPS/SINS组合导航算法研究”、“利用偏振光、地磁、GPS进行多信息源融合导航方法的研究与实现”等。另外，已申请的中国专利201310037586.4，“基于偏振光仿生导航的定位系统及其定位方法”、已申请的中国专利CN 103822629，“基于多方向偏振光导航传感器的定位系统及其定位方法”虽然没有用到卫星导航系统，但是并没有考虑到地磁信息和偏振信息的深度融合，系统可靠性有待进一步提高。Biomimetic polarization navigation is passive, non-radiative, well concealed, highly autonomous and not affected by electromagnetic interference. It can provide three-dimensional attitude information and position information for the carrier, which can complement the advantages of the inertial navigation system and improve the performance of the integrated navigation system. Autonomy and reliability provide new solutions. Geomagnetic navigation system is another commonly used navigation method, which can also provide high-precision attitude and position information to make up for the attitude and position errors of inertial navigation system. For the existing polarization/geomagnetic aided integrated navigation systems, satellite navigation systems are used, such as the authorized Chinese patent 201510312112.5, "A dual-mode bionic polarization/geomagnetic aided integrated navigation system, paper "Bionic polarized light/GPS/ Design and Implementation of Geomagnetic Integrated Navigation Method", "Research on Polarized Light/Geomagnetic/GPS/SINS Integrated Navigation Algorithm", "Research and Implementation of Multi-information Source Fusion Navigation Method Using Polarized Light, Geomagnetism and GPS", etc. The Chinese patent 201310037586.4, "Positioning system and positioning method based on polarized light bionic navigation", Chinese patent CN 103822629, "Positioning system and positioning method based on multi-directional polarized light navigation sensor", although satellite navigation is not used However, the deep fusion of geomagnetic information and polarization information is not considered, and the reliability of the system needs to be further improved.

为了充分利用偏振与地磁的量测信息，有效提高仿生组合导航系统的精度及可靠性，本发明对偏振与地磁矢量信息进行深度融合，首次建立了偏振/地磁矢量紧组合的导航系统模型，可在无卫星导航情况下，实现仿生偏振/地磁辅助的全自主组合导航。In order to make full use of the measurement information of polarization and geomagnetism and effectively improve the accuracy and reliability of the bionic integrated navigation system, the present invention deeply integrates the information of polarization and geomagnetism vector, and establishes a navigation system model with a tight combination of polarization and geomagnetism for the first time. In the absence of satellite navigation, fully autonomous integrated navigation with bionic polarization/geomagnetic assistance is realized.

发明内容SUMMARY OF THE INVENTION

本发明公开了一种基于偏振-地磁矢量紧组合的导航方法，首先通过设计仿复眼偏振罗盘，实时测量本体坐标系下太阳位置信息，并结合天文年历，建立太阳矢量在本体坐标下和地理坐标系下的信息转换关系，其次建立地磁矢量在本体坐标下和地理坐标系下的信息转换关系，在本体坐标系下，对地磁矢量和太阳矢量进行信息深度融合，建立基于偏振-地磁矢量紧组合的导航系统模型。The invention discloses a navigation method based on the tight combination of polarization-geomagnetic vector. First, by designing a compound eye-like polarization compass, the sun position information under the body coordinate system is measured in real time, and combined with the astronomical almanac, the sun vector under the body coordinates and the geographic coordinates are established. Next, the information conversion relationship between the geomagnetic vector under the ontology coordinate and the geographic coordinate system is established. Under the ontology coordinate system, the geomagnetic vector and the sun vector are deeply integrated to establish a tight combination based on the polarization-geomagnetic vector. model of the navigation system.

本发明的技术解决方案为：一种基于偏振-地磁矢量紧组合的导航方法，实现步骤如下：The technical solution of the present invention is: a navigation method based on the tight combination of polarization-geomagnetic vector, the implementation steps are as follows:

步骤(1)、由偏振导航传感器构成的仿复眼偏振罗盘，实时获取检测本体坐标系下的太阳矢量

Figure BDA0001859454610000021
Step (1), a compound-eye-like polarized compass composed of a polarized navigation sensor, obtains the sun vector in the real-time detection body coordinate system
Figure BDA0001859454610000021

步骤(2)、结合太阳天文年历，得到地理系下太阳矢量

Figure BDA0001859454610000022
结合步骤(1)得到的本体坐标下的太阳矢量，建立地理坐标系和本体坐标系下太阳矢量的转换关系
Figure BDA0001859454610000023
Step (2), combine the solar astronomical calendar to obtain the solar vector under the geographic system
Figure BDA0001859454610000022
Combined with the sun vector under the body coordinates obtained in step (1), establish the conversion relationship between the geographic coordinate system and the sun vector under the body coordinate system
Figure BDA0001859454610000023

步骤(3)、在本体坐标系和地理坐标系下，分别求取地磁矢量

Figure BDA0001859454610000024
及
Figure BDA0001859454610000025
建立地理坐标系和本体坐标系下地磁矢量的转换关系
Figure BDA0001859454610000026
Step (3), in the ontology coordinate system and the geographic coordinate system, obtain the geomagnetic vector respectively
Figure BDA0001859454610000024
and
Figure BDA0001859454610000025
Establish the transformation relationship between the geomagnetic vector under the geographic coordinate system and the ontology coordinate system
Figure BDA0001859454610000026

步骤(4)、在本体坐标系下，对地磁矢量和太阳矢量进行信息融合

Figure BDA0001859454610000027
Step (4), in the body coordinate system, perform information fusion on the geomagnetic vector and the sun vector
Figure BDA0001859454610000027

步骤(5)、结合步骤(4)，建立基于偏振-地磁矢量紧组合的导航系统模型。In step (5), combined with step (4), a navigation system model based on the tight combination of polarization-geomagnetic vector is established.

所述步骤(1)由偏振导航传感器构成的仿复眼偏振罗盘，实时获取检测本体坐标系下的太阳矢量

Figure BDA0001859454610000028
具体实现如下：In the step (1), a compound eye-like polarized compass composed of a polarized navigation sensor is used to acquire and detect the sun vector in the body coordinate system in real time.
Figure BDA0001859454610000028
The specific implementation is as follows:

仿复眼偏振罗盘由三个偏振传感器组成，分别记为M1、M2、M3，其中M1观测方向为天顶方向，M2和M3分别对称安装在M1量测，安装角度都为η，以M1为基准建立坐标系Mxyz，x轴为载体体轴方向，z轴指向天顶，y轴由右手定则确定；The compound eye-like polarization compass is composed of three polarization sensors, which are marked as M 1 , M 2 and M 3 respectively . The observation direction of M 1 is the zenith direction. Be n, establish the coordinate system Mxyz with M 1 as the benchmark, the x-axis is the direction of the carrier body axis, the z-axis points to the zenith, and the y-axis is determined by the right-hand rule;

在本体坐标系下，太阳方位角

Figure BDA0001859454610000029
可以通过M1传感器测量得到的偏振方位角
Figure BDA00018594546100000210
和地磁传感器提供的方位角ψ计算得到：In the body coordinate system, the azimuth of the sun
Figure BDA0001859454610000029
Azimuth of polarization that can be measured by the M 1 sensor
Figure BDA00018594546100000210
And the azimuth angle ψ provided by the geomagnetic sensor is calculated to get:

Figure BDA00018594546100000211
Figure BDA00018594546100000211

实时获取三个偏振传感器的偏振度测量值d1，d2，d3，基于Rayleigh散射理论，观测点的偏振度与散射角有如下关系：The polarization degree measurement values d 1 , d 2 , and d 3 of the three polarization sensors are obtained in real time. Based on the Rayleigh scattering theory, the polarization degree of the observation point is related to the scattering angle as follows:

Figure BDA00018594546100000212
Figure BDA00018594546100000212

其中，dmax∈[max{d1,d2,d3},1)，θ1，θ2，θ3为M1、M2、M3观测方向与太阳矢量的夹角，Among them, d max ∈[max{d 1 ,d 2 ,d 3 },1), θ 1 , θ 2 , θ 3 are the angles between the observation directions of M 1 , M 2 , M 3 and the sun vector,

根据仿复眼偏振罗盘结构，θ1，θ2，θ3之间的关系可表示为：According to the compound eye-like polarization compass structure, the relationship between θ 1 , θ 2 , θ 3 can be expressed as:

cosθ2+cosθ3＝2cosηcosθ1 (3)cosθ 2 +cosθ 3 =2cosηcosθ 1 (3)

根据公式(2)-(3)，即可求取全天域最大偏振度dmax；According to formulas (2)-(3), the maximum polarization degree d max in the whole sky can be obtained;

在地理坐标系下，根据全空域最大偏振度dmax，得到主偏振传感器M1的偏振观测角θ1：In the geographic coordinate system, according to the maximum polarization degree d max in the whole space, the polarization observation angle θ 1 of the main polarization sensor M 1 is obtained:

Figure BDA0001859454610000031
Figure BDA0001859454610000031

其中，θ1方向可由外界附加光强传感器或者重力传感器来进行判断；Among them, the θ 1 direction can be judged by an external light intensity sensor or a gravity sensor;

根据M1传感器的安装方式以及观测太阳高度角

Figure BDA0001859454610000032
与散射角θ1之间的关系，得到本体坐标系下的观测太阳高度角
Figure BDA0001859454610000033
为：According to the installation method of the M 1 sensor and the observed sun altitude
Figure BDA0001859454610000032
The relationship between the scattering angle θ 1 and the observed solar altitude angle in the body coordinate system
Figure BDA0001859454610000033
for:

Figure BDA0001859454610000034
Figure BDA0001859454610000034

模块坐标系下，太阳矢量可表示为：In the module coordinate system, the sun vector can be expressed as:

Figure BDA0001859454610000035
Figure BDA0001859454610000035

令

Figure BDA0001859454610000036
make
Figure BDA0001859454610000036

所述步骤(2)根据太阳天文年历，得到地理系下太阳矢量

Figure BDA0001859454610000037
结合步骤(1)得到的本体坐标下的太阳矢量，建立本体坐标系和地理坐标下太阳矢量的转换关系
Figure BDA0001859454610000038
具体实现如下：The step (2) obtains the solar vector under the geographic system according to the solar astronomical almanac
Figure BDA0001859454610000037
Combined with the sun vector under the ontology coordinates obtained in step (1), establish the conversion relationship between the ontology coordinate system and the sun vector under the geographic coordinates
Figure BDA0001859454610000038
The specific implementation is as follows:

根据载体所在的地理位置及当地时间，通过太阳天文年历得到地理坐标系下的太阳方位角及太阳高度角，分别表示为：According to the geographic location and local time of the carrier, the solar azimuth angle and solar altitude angle in the geographic coordinate system are obtained through the solar astronomical almanac, which are expressed as:

Figure BDA0001859454610000039
Figure BDA0001859454610000039

Figure BDA00018594546100000310
Figure BDA00018594546100000310

其中，L为地理纬度，δ为太阳赤纬，Ω为太阳时角；Among them, L is the geographic latitude, δ is the solar declination, and Ω is the solar hour angle;

根据公式(6)，得到地理系下太阳矢量，According to formula (6), the sun vector in the geographic system is obtained,

Figure BDA00018594546100000311
Figure BDA00018594546100000311

令

Figure BDA00018594546100000312
make
Figure BDA00018594546100000312

根据本体坐标系与地理坐标系之间的姿态转换关系，建立本体坐标系和地理坐标系下太阳矢量的转换关系：According to the attitude transformation relationship between the ontology coordinate system and the geographic coordinate system, the transformation relationship between the ontology coordinate system and the sun vector in the geographic coordinate system is established:

Figure BDA00018594546100000313
Figure BDA00018594546100000313

其中，

Figure BDA0001859454610000041
为本体坐标系与地理坐标系之间的姿态转换矩阵；in,
Figure BDA0001859454610000041
is the attitude transformation matrix between the body coordinate system and the geographic coordinate system;

Figure BDA0001859454610000042
Figure BDA0001859454610000042

其中，θ，γ，ψ分别为载体俯仰角，横滚角和航向角，Among them, θ, γ, ψ are the pitch angle, roll angle and heading angle of the carrier, respectively,

定义系统的姿态误差角如下：The attitude error angle of the system is defined as follows:

φ＝[φx φy φz]T (9)φ=[φ x φ y φ z ] T (9)

则本体坐标系和地理坐标系下太阳矢量的转换关系可表示为：Then the transformation relationship of the sun vector in the ontology coordinate system and the geographic coordinate system can be expressed as:

Figure BDA0001859454610000043
Figure BDA0001859454610000043

其中

Figure BDA0001859454610000044
为名义矩阵，可由载体姿态角得到，具体表示为：in
Figure BDA0001859454610000044
is the nominal matrix, which can be obtained from the carrier attitude angle, specifically expressed as:

Figure BDA0001859454610000045
Figure BDA0001859454610000045

所述步骤(3)在本体坐标系和地理坐标系下，分别求取地磁矢量

Figure BDA0001859454610000046
及
Figure BDA0001859454610000047
建立本体坐标系和地理坐标系下地磁矢量的转换关系
Figure BDA0001859454610000048
具体实现如下：In the step (3), under the ontology coordinate system and the geographic coordinate system, the geomagnetic vector is obtained respectively
Figure BDA0001859454610000046
and
Figure BDA0001859454610000047
Establish the transformation relationship between the body coordinate system and the geomagnetic vector in the geographic coordinate system
Figure BDA0001859454610000048
The specific implementation is as follows:

对地理坐标系下的地磁矢量进行求取，得到地理坐标系下地磁矢量，表示为：Obtain the geomagnetic vector under the geographic coordinate system to obtain the geomagnetic vector under the geographic coordinate system, which is expressed as:

Figure BDA0001859454610000049
Figure BDA0001859454610000049

本体坐标系下的地磁矢量通过地磁传感器即可直接得到，表示为：The geomagnetic vector in the body coordinate system can be obtained directly through the geomagnetic sensor, which is expressed as:

Figure BDA00018594546100000410
Figure BDA00018594546100000410

建立本体坐标系和地理坐标系下地磁矢量的转换关系：Establish the transformation relationship between the body coordinate system and the geomagnetic vector in the geographic coordinate system:

Figure BDA00018594546100000411
Figure BDA00018594546100000411

所述步骤(4)在本体坐标系下，对地磁矢量

Figure BDA00018594546100000412
和太阳矢量
Figure BDA00018594546100000413
进行信息深度融合
Figure BDA00018594546100000414
具体实现如下：In the step (4), under the body coordinate system, the geomagnetic vector
Figure BDA00018594546100000412
and sun vector
Figure BDA00018594546100000413
Deep information fusion
Figure BDA00018594546100000414
The specific implementation is as follows:

根据步骤(2)和步骤(3)得到的本体坐标系太阳矢量

Figure BDA00018594546100000415
和地磁矢量
Figure BDA00018594546100000416
对公式(6)和公式(12)进行叉乘处理，得到的本体坐标系下偏振、地磁矢量融合：The sun vector of the body coordinate system obtained according to step (2) and step (3)
Figure BDA00018594546100000415
and geomagnetic vector
Figure BDA00018594546100000416
The cross product of formula (6) and formula (12) is processed to obtain the fusion of polarization and geomagnetic vector in the ontology coordinate system:

Figure BDA00018594546100000417
Figure BDA00018594546100000417

结合公式(10)和(13)，则公式(15)可表示为：Combining formulas (10) and (13), formula (15) can be expressed as:

Figure BDA0001859454610000051
Figure BDA0001859454610000051

其中：in:

Figure BDA0001859454610000052
Figure BDA0001859454610000052

所述步骤(5)，结合步骤(4)，建立基于偏振-地磁矢量紧组合的导航系统模型，具体实现如下：The step (5), combined with the step (4), establishes a navigation system model based on the tight combination of the polarization-geomagnetic vector, and the specific implementation is as follows:

通过公式(15)，得到基于偏振-地磁矢量融合的组合导航系统模型：By formula (15), the integrated navigation system model based on polarization-geomagnetic vector fusion is obtained:

Figure BDA0001859454610000053
Figure BDA0001859454610000053

本发明的原理是：通过仿复眼偏振罗盘测量太阳位置信息，并结合太阳天文年历，建立本体坐标和地理坐标系下的太阳矢量信息传递关系。根据地磁传感器在本体坐标系下得到的地磁矢量，建立本体坐标系与地理坐标系下的地磁矢量的转换关系，并在本体坐标系下，完成地磁矢量和偏振矢量的信息深度融合，建立基于偏振-地磁矢量紧组合的导航系统模型。The principle of the invention is as follows: measuring the position information of the sun by the imitation compound eye polarization compass, and combining with the solar astronomical almanac to establish the transmission relationship between the body coordinates and the sun vector information in the geographic coordinate system. According to the geomagnetic vector obtained by the geomagnetic sensor in the body coordinate system, the conversion relationship between the body coordinate system and the geomagnetic vector in the geographic coordinate system is established, and in the body coordinate system, the information depth fusion of the geomagnetic vector and the polarization vector is completed. - Navigation system model with tight combination of geomagnetic vector.

本发明与现有技术相比的优点在于：The advantages of the present invention compared with the prior art are:

(1)本发明不依赖于卫星导航信号，可通过对大气偏振场、地磁场的观测，进行偏振矢量和地磁矢量的信息融合，共同弥补惯性导航的姿态和位置测量误差，具有强自主性、鲁棒性及可靠性；(1) The present invention does not rely on satellite navigation signals, and can perform information fusion of the polarization vector and the geomagnetic vector through the observation of the atmospheric polarization field and the geomagnetic field to jointly compensate for the attitude and position measurement errors of inertial navigation, and has strong autonomy, Robustness and reliability;

(2)本发明采用偏振导航系统和地磁导航系统紧组合的思想，通过引入惯性导航的姿态测量误差，建立基于偏振-地磁的组合导航系统模型，可提高系统模型的可观测性。(2) The present invention adopts the idea of tightly combining the polarization navigation system and the geomagnetic navigation system, and establishes a polarization-geomagnetic integrated navigation system model by introducing the attitude measurement error of inertial navigation, which can improve the observability of the system model.

(3)本发明采用偏振度信息确定太阳的方位，相比较于传统方法，本方法不受偏振方位角误差传递的影响，可提高太阳高度观测的精度，进而提高基于偏振-地磁的紧组合的导航系统性能。(3) The present invention uses polarization degree information to determine the orientation of the sun. Compared with the traditional method, this method is not affected by the transmission of the polarization azimuth angle error, which can improve the accuracy of the solar height observation, and then improve the accuracy of the sun height observation based on the tight combination of polarization and geomagnetism. Navigation system performance.

附图说明Description of drawings

图1为本发明一种基于偏振-地磁矢量紧组合的导航方法的流程图；Fig. 1 is the flow chart of a kind of navigation method based on polarization-geomagnetic vector tight combination of the present invention;

图2为本发明涉及仿复眼偏振罗盘结构示意图。FIG. 2 is a schematic diagram of the structure of the imitation compound eye polarized compass according to the present invention.

具体实施方式Detailed ways

下面结合附图以及具体实施方式进一步说明本发明。The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

如图1所示，本发明一种基于偏振-地磁矢量紧组合的导航方法的具体实现步骤如下：As shown in Figure 1, the concrete realization steps of a kind of navigation method based on the tight combination of polarization-geomagnetic vector of the present invention are as follows:

1、由偏振导航传感器构成的仿复眼偏振罗盘，实时获取检测模块坐标系下的太阳矢量

Figure BDA0001859454610000061
仿复眼偏振罗盘结构示意图如图2所示，仿复眼偏振罗盘由三个偏振传感器组成，分别记为M1、M2、M3，其中M1观测方向为天顶方向，M2和M3分别对称安装在M1量测，安装角度都为η，以M1为基准建立坐标系Mxyz，x轴为载体体轴方向，z轴指向天顶，y轴由右手定则确定，1. The compound-eye-like polarization compass composed of polarization navigation sensors can obtain the sun vector in the coordinate system of the detection module in real time
Figure BDA0001859454610000061
The schematic diagram of the structure of the imitation compound eye polarization compass is shown in Figure 2. The imitation compound eye polarization compass consists of three polarization sensors, which are denoted as M 1 , M 2 , and M 3 respectively. The observation direction of M 1 is the zenith direction, and the observation direction of M 2 and M 3 Symmetrically installed at M1 for measurement, the installation angles are all η, the coordinate system Mxyz is established based on M1, the x - axis is the direction of the carrier body axis, the z-axis points to the zenith, and the y-axis is determined by the right-hand rule.

在本体坐标系下，太阳方位角

Figure BDA0001859454610000062
可以通过M1传感器测量得到的偏振方位角
Figure BDA0001859454610000063
和地磁传感器提供的方位角ψ计算得到：In the body coordinate system, the azimuth of the sun
Figure BDA0001859454610000062
Azimuth of polarization that can be measured by the M 1 sensor
Figure BDA0001859454610000063
And the azimuth angle ψ provided by the geomagnetic sensor is calculated to get:

Figure BDA0001859454610000064
Figure BDA0001859454610000064

实时获取三个偏振传感器的偏振度测量值d1，d2，d3，基于Rayleigh散射理论，观测点的偏振度与散射角有如下关系：The polarization degree measurement values d 1 , d 2 , and d 3 of the three polarization sensors are obtained in real time. Based on the Rayleigh scattering theory, the polarization degree of the observation point is related to the scattering angle as follows:

Figure BDA0001859454610000065
Figure BDA0001859454610000065

其中，dmax∈[max{d1,d2,d3},1)，θ1，θ2，θ3为M1、M2、M3观测方向与太阳矢量的夹角；Wherein, d max ∈[max{d 1 ,d 2 ,d 3 },1), θ 1 , θ 2 , θ 3 are the angles between the observation directions of M 1 , M 2 , M 3 and the sun vector;

根据仿复眼偏振罗盘结构，θ1，θ2，θ3之间的关系可表示为：According to the compound eye-like polarization compass structure, the relationship between θ 1 , θ 2 , θ 3 can be expressed as:

cosθ2+cosθ3＝2cosηcosθ1 (3)cosθ 2 +cosθ 3 =2cosηcosθ 1 (3)

根据公式(2)-(3)，即可求取全天域最大偏振度dmax；According to formulas (2)-(3), the maximum polarization degree d max in the whole sky can be obtained;

在地理坐标系下，根据全空域最大偏振度dmax，得到主偏振传感器M1的观测角θ1：In the geographic coordinate system, according to the maximum polarization degree d max in the whole space, the observation angle θ 1 of the main polarization sensor M 1 is obtained:

Figure BDA0001859454610000066
Figure BDA0001859454610000066

其中，θ1方向可由外界附加光强传感器或者重力传感器来进行判断；Among them, the θ 1 direction can be judged by an external light intensity sensor or a gravity sensor;

根据M1传感器的安装方式以及观测太阳高度角

Figure BDA0001859454610000067
与散射角θ1之间的关系，得到本体坐标系下的观测太阳高度角
Figure BDA0001859454610000068
为：According to the installation method of the M 1 sensor and the observed sun altitude
Figure BDA0001859454610000067
The relationship between the scattering angle θ 1 and the observed solar altitude angle in the body coordinate system
Figure BDA0001859454610000068
for:

Figure BDA0001859454610000069
Figure BDA0001859454610000069

本体坐标系下，太阳矢量可表示为，In the ontology coordinate system, the sun vector can be expressed as,

Figure BDA0001859454610000071
Figure BDA0001859454610000071

令

Figure BDA0001859454610000072
make
Figure BDA0001859454610000072

2、结合太阳天文年历，得到地理系下太阳矢量

Figure BDA0001859454610000073
建立地理坐标系和本体坐标下太阳矢量的转换关系
Figure BDA0001859454610000074
根据载体所在的地理位置及当地时间，通过太阳天文年历得到地理坐标系下的太阳方位角及太阳高度角，分别表示为：2. Combine the solar astronomical calendar to get the sun vector in the geographic system
Figure BDA0001859454610000073
Establish the conversion relationship between the geographic coordinate system and the sun vector in the ontology coordinate
Figure BDA0001859454610000074
According to the geographic location and local time of the carrier, the solar azimuth angle and solar altitude angle in the geographic coordinate system are obtained through the solar astronomical almanac, which are expressed as:

Figure BDA0001859454610000075
Figure BDA0001859454610000075

Figure BDA0001859454610000076
Figure BDA0001859454610000076

其中，L为地理纬度，δ为太阳赤纬，Ω为太阳时角；Among them, L is the geographic latitude, δ is the solar declination, and Ω is the solar hour angle;

根据公式(6)，得到地理系下太阳矢量，According to formula (6), the sun vector in the geographic system is obtained,

Figure BDA0001859454610000077
Figure BDA0001859454610000077

令

Figure BDA0001859454610000078
make
Figure BDA0001859454610000078

根据本体坐标系与地理坐标系之间的姿态转换关系，建立本体坐标系和地理坐标系下太阳矢量的转换关系：According to the attitude transformation relationship between the ontology coordinate system and the geographic coordinate system, the transformation relationship between the ontology coordinate system and the sun vector in the geographic coordinate system is established:

Figure BDA0001859454610000079
Figure BDA0001859454610000079

其中，

Figure BDA00018594546100000710
为本体坐标系与地理坐标系之间的姿态转换矩阵，in,
Figure BDA00018594546100000710
is the attitude transformation matrix between the body coordinate system and the geographic coordinate system,

Figure BDA00018594546100000711
Figure BDA00018594546100000711

其中，θ，γ，ψ分别为载体俯仰角，横滚角和航向角，Among them, θ, γ, ψ are the pitch angle, roll angle and heading angle of the carrier, respectively,

定义系统的姿态误差角如下：The attitude error angle of the system is defined as follows:

φ＝[φx φy φz]T (9)φ=[φ x φ y φ z ] T (9)

则本体坐标系和地理坐标系下太阳矢量的转换关系可表示为：Then the transformation relationship of the sun vector in the ontology coordinate system and the geographic coordinate system can be expressed as:

Figure BDA00018594546100000712
Figure BDA00018594546100000712

其中

Figure BDA00018594546100000713
为名义矩阵，可由载体姿态角得到，具体表示为：in
Figure BDA00018594546100000713
is the nominal matrix, which can be obtained from the carrier attitude angle, specifically expressed as:

Figure BDA00018594546100000714
Figure BDA00018594546100000714

3、在本体坐标系和地理坐标系下，分别求取地磁矢量

Figure BDA00018594546100000715
及
Figure BDA00018594546100000716
建立本体坐标系和地理坐标系下地磁矢量的转换关系：3. In the ontology coordinate system and the geographic coordinate system, respectively obtain the geomagnetic vector
Figure BDA00018594546100000715
and
Figure BDA00018594546100000716
Establish the transformation relationship between the body coordinate system and the geomagnetic vector in the geographic coordinate system:

对地理坐标系下的地磁矢量进行求取，得到地理坐标系下地磁矢量，表示为：Obtain the geomagnetic vector under the geographic coordinate system to obtain the geomagnetic vector under the geographic coordinate system, which is expressed as:

Figure BDA0001859454610000081
Figure BDA0001859454610000081

本体坐标系下的地磁矢量通过地磁传感器即可直接得到，表示为：The geomagnetic vector in the body coordinate system can be obtained directly through the geomagnetic sensor, which is expressed as:

Figure BDA0001859454610000082
Figure BDA0001859454610000082

建立本体坐标系和地理坐标系下地磁矢量的转换关系：Establish the transformation relationship between the body coordinate system and the geomagnetic vector in the geographic coordinate system:

Figure BDA0001859454610000083
Figure BDA0001859454610000083

4、在本体坐标系下，对地磁矢量

Figure BDA0001859454610000084
和太阳矢量
Figure BDA0001859454610000085
进行信息深度融合
Figure BDA0001859454610000086
4. In the body coordinate system, the geomagnetic vector
Figure BDA0001859454610000084
and sun vector
Figure BDA0001859454610000085
Deep information fusion
Figure BDA0001859454610000086

根据步骤(2)和步骤(3)得到的本体坐标系太阳矢量

Figure BDA0001859454610000087
和地磁矢量
Figure BDA0001859454610000088
对公式(6)和公式(12)进行叉乘处理，得到的本体坐标系下偏振、地磁矢量融合：The sun vector of the body coordinate system obtained according to step (2) and step (3)
Figure BDA0001859454610000087
and geomagnetic vector
Figure BDA0001859454610000088
The cross product of formula (6) and formula (12) is processed to obtain the fusion of polarization and geomagnetic vector in the ontology coordinate system:

Figure BDA0001859454610000089
Figure BDA0001859454610000089

结合公式(10)和(13)，则公式(15)可表示为：Combining formulas (10) and (13), formula (15) can be expressed as:

Figure BDA00018594546100000810
Figure BDA00018594546100000810

其中in

Figure BDA00018594546100000811
Figure BDA00018594546100000811

5、结合步骤(4)，建立基于偏振/地磁矢量紧组合的导航系统模型：5. Combined with step (4), a navigation system model based on the tight combination of polarization/geomagnetic vector is established:

通过公式(15)，得到基于偏振/地磁矢量融合的组合导航系统模型：By formula (15), the integrated navigation system model based on polarization/geomagnetic vector fusion is obtained:

Figure BDA00018594546100000812
Figure BDA00018594546100000812

Claims (5)

1. a navigation method based on polarization-geomagnetic vector tight combination is characterized in that: the method comprises the following implementation steps:
Step (1), a compound eye-imitating polarization compass formed by polarization navigation sensors acquires and detects the sun vector under a body coordinate system in real time
Figure FDA0003535118760000011
Step (2) obtaining sun vectors under the geographic system according to the solar almanac
Figure FDA0003535118760000012
Combining the sun vector under the body coordinate obtained in the step (1) to establish a conversion relation between the body coordinate system and the sun vector under the geographic coordinate system
Figure FDA0003535118760000013
Wherein,
Figure FDA0003535118760000014
converting a matrix for the posture between the body coordinate system and the geographic coordinate system;
step (3) respectively obtaining geomagnetic vectors under the body coordinate system and the geographic coordinate system
Figure FDA0003535118760000015
And
Figure FDA0003535118760000016
establishing a conversion relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system
Figure FDA0003535118760000017
Step (4) under the body coordinate system, geomagnetic vector is aligned
Figure FDA0003535118760000018
And sun vector
Figure FDA0003535118760000019
Performing information depth fusion
Figure FDA00035351187600000110
S is the fusion of polarization and geomagnetic vectors under a body coordinate system;
step (5), combining with the step (4), establishing a navigation system model based on the tight combination of the polarization-geomagnetic vector;
the step (1) is to obtain the compound eye-imitating polarization compass formed by the polarization navigation sensor in real timeDetecting sun vector under body coordinate system
Figure FDA00035351187600000111
The concrete implementation is as follows:
the compound eye-imitating polarization compass consists of three polarization sensors, which are respectively marked as M1、M2、M3Wherein M is1The observation direction is the zenith direction, M 2And M3Are respectively symmetrically arranged at M1Measuring and mounting angle of eta, in M1Establishing a coordinate system Mxyz for the reference, wherein the x axis is the body axis direction of the carrier, the z axis points to the zenith, and the y axis is determined by a right-hand rule;
in the body coordinate system, the sun azimuth angle
Figure FDA00035351187600000112
Can pass through M1Polarization azimuth angle measured by sensor
Figure FDA00035351187600000115
And the azimuth angle psi provided by the geomagnetic sensor is calculated to obtain:
Figure FDA00035351187600000113
real-time obtaining polarization degree measured values d of three polarization sensors1，d2，d3Based on Rayleigh scattering theory, the polarization degree of an observation point has the following relation with a scattering angle:
Figure FDA00035351187600000114
wherein d ismax∈[max{d1,d2,d3},1)，θ1，θ2，θ3Is M1、M2、M3Observing an included angle between the direction and the sun vector;
based on the structure of the compound eye-imitating polarization compass，θ1，θ2，θ3The relationship between can be expressed as:
cosθ2+cosθ3＝2cosηcosθ1 (3)
according to the formulas (2) to (3), the maximum polarization degree d of the whole day domain can be obtainedmax，
According to the maximum polarization degree d of the full airspace under the geographic coordinate systemmaxObtaining the main polarization sensor M1Observation angle of (theta)1：
Figure FDA0003535118760000021
Wherein, theta1The direction can be judged by an external light intensity sensor or a gravity sensor;
according to M1Sensor mounting method and sun altitude observation angle
Figure FDA0003535118760000022
And scattering angle theta1The relation between the solar altitude and the solar altitude is obtained under the body coordinate system
Figure FDA0003535118760000023
Comprises the following steps:
Figure FDA0003535118760000024
in the body coordinate system, the sun vector can be expressed as:
Figure FDA0003535118760000025
Order to
Figure FDA0003535118760000026
2. The navigation method according to claim 1, wherein the navigation method based on the close combination of polarization-geomagnetic vectors is characterized in that: the step (2) obtains the sun vector under the geographic system according to the solar astronomical calendar
Figure FDA0003535118760000027
Combining the sun vector under the body coordinate obtained in the step (1), establishing a conversion relation between the body coordinate system and the sun vector under the geographic coordinate
Figure FDA0003535118760000028
The concrete implementation is as follows:
according to the geographical position of the carrier and the local time, the solar azimuth angle and the solar altitude angle under the geographical coordinate system are obtained through the solar almanac and are respectively expressed as follows:
Figure FDA0003535118760000029
Figure FDA00035351187600000210
wherein L is geographical latitude, delta is solar declination, omega is solar hour angle,
obtaining the sun vector under the geographic system according to the formula (6),
Figure FDA00035351187600000211
order to
Figure FDA00035351187600000212
According to the attitude transformation relation between the body coordinate system and the geographic coordinate system, establishing the transformation relation of the sun vectors under the body coordinate system and the geographic coordinate system:
Figure FDA0003535118760000031
wherein,
Figure FDA0003535118760000032
is the attitude transformation matrix between the body coordinate system and the geographic coordinate system,
Figure FDA0003535118760000033
wherein, theta, gamma and psi are carrier pitch angle, roll angle and course angle respectively;
the attitude error angle of the system is defined as follows:
φ＝[φx φy φz]T (9)
the conversion relationship between the body coordinate system and the sun vector under the geographic coordinate system can be expressed as:
Figure FDA0003535118760000034
Wherein
Figure FDA0003535118760000035
The nominal matrix can be obtained by carrier attitude angles, and is specifically represented as:
Figure FDA0003535118760000036
3. the navigation method according to claim 1, wherein the navigation method based on the close combination of polarization-geomagnetic vectors is characterized in that: the step (3) is to respectively obtain the geomagnetic vector under the body coordinate system and the geographic coordinate system
Figure FDA0003535118760000037
And
Figure FDA0003535118760000038
establishing a conversion relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system
Figure FDA0003535118760000039
The concrete implementation is as follows:
solving the geomagnetic vector under the geographic coordinate system to obtain the geomagnetic vector under the geographic coordinate system, which is expressed as:
Figure FDA00035351187600000310
the geomagnetic vector under the body coordinate system can be directly obtained through the geomagnetic sensor, and is represented as:
Figure FDA00035351187600000311
establishing a transformation relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system:
Figure FDA00035351187600000312
4. the method according to claim 2, wherein the navigation method based on the close combination of polarization-geomagnetic vectors comprises: the step (4) is to measure the geomagnetic vector under the body coordinate system
Figure FDA00035351187600000313
And sun vector
Figure FDA00035351187600000314
Performing information depth fusion
Figure FDA00035351187600000315
The concrete implementation is as follows:
the sun vector of the body coordinate system obtained according to the step (2) and the step (3)
Figure FDA00035351187600000316
And geomagnetic vector
Figure FDA00035351187600000317
And (3) performing cross multiplication processing on the formula (6) and the formula (12) to obtain polarization and geomagnetic vector fusion under a body coordinate system:
Figure FDA0003535118760000041
Combining equations (10) and (13), equation (15) can be expressed as:
Figure FDA0003535118760000042
wherein:
Figure FDA0003535118760000043
5. the navigation method according to claim 1, wherein the navigation method based on the close combination of polarization-geomagnetic vectors is characterized in that: the step (5) is combined with the step (4) to establish a navigation system model based on the tight combination of polarization-geomagnetic vectors, and the method is specifically realized as follows:
obtaining a combined navigation system model based on polarization-geomagnetic vector fusion through formula (15):
Figure FDA0003535118760000044
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