CN109459027B - Navigation method based on polarization-geomagnetic vector tight combination - Google Patents

Navigation method based on polarization-geomagnetic vector tight 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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coordinate system
polarization
geomagnetic
body coordinate
vector
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CN109459027A (en
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郭雷
杨健
刘鑫
王善澎
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Beihang University
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    • G—PHYSICS
    • 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
    • G01C21/04—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means
    • G01C21/08—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means involving use of the magnetic field of the earth
    • G—PHYSICS
    • 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
    • G—PHYSICS
    • 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
    • G01C21/20—Instruments for performing navigational calculations

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

Navigation method based on polarization-geomagnetic vector tight combination
Technical Field
The invention relates to a navigation method based on polarization-geomagnetic vector tight combination, which is used for determining and positioning the three-dimensional space autonomous attitude of carriers such as unmanned aerial vehicles, ships, missiles and the like.
Background
At present, the working environment of carriers such as unmanned aerial vehicles, ships, missiles and the like is increasingly complex, and in order to make up for the defect of single navigation, the combined navigation of multi-sensor fusion is the development direction of future navigation. The inertia/satellite integrated navigation system is the most widely applied integrated navigation system at present, but the satellite navigation is easily interfered by natural environment and human, and accurate and reliable navigation information cannot be provided under the environments of rejection, interference, confrontation and the like. Therefore, the application of the satellite navigation system in the fields of deep space exploration, deep sea exploration and the like is greatly limited. It is therefore desirable to develop integrated navigation systems that do not rely on satellite navigation.
The bionic polarization navigation is passive, free of radiation, good in concealment, strong in autonomy and free of influence of electromagnetic interference, can provide three-position attitude information and position information for a carrier, can perform advantage complementation on an inertial navigation system, and provides a new solution for improving the autonomy and reliability of the combined navigation system. The geomagnetic navigation system is another common navigation method, and can also provide attitude and position information with higher precision, so as to make up for attitude and position errors of the inertial navigation system. For the existing polarization/geomagnetic aided integrated navigation system, a satellite navigation system is used, such as granted chinese patent 201510312112.5, "a dual-mode bionic polarization/geomagnetic aided integrated navigation system, and papers," bionic polarized light/GPS/geomagnetic integrated navigation method design and implementation "," polarized light/geomagnetic/GPS/SINS integrated navigation algorithm research "," research and implementation of multi-information source fusion navigation method using polarized light, geomagnetic, GPS ", and the like. In addition, the applied chinese patent 201310037586.4, "positioning system and positioning method based on polarized light bionic navigation", the applied chinese patent CN 103822629, "positioning system and positioning method based on multi-directional polarized light navigation sensor", although no satellite navigation system is used, the deep fusion of geomagnetic information and polarization information is not considered, and the system reliability needs to be further improved.
In order to fully utilize the measurement information of polarization and geomagnetism and effectively improve the precision and reliability of the bionic combined navigation system, the invention carries out deep fusion on the polarization and geomagnetism vector information, establishes a navigation system model of polarization/geomagnetism vector tight combination for the first time, and can realize the bionic polarization/geomagnetism-assisted fully-autonomous combined navigation under the condition of no satellite navigation.
Disclosure of Invention
The invention discloses a navigation method based on a polarization-geomagnetic vector tight combination, which comprises the steps of firstly measuring sun position information under a body coordinate system in real time by designing a compound eye-imitating polarization compass, establishing an information conversion relation of a sun vector under the body coordinate and a geographical coordinate system by combining with an astronomical calendar, then establishing an information conversion relation of a geomagnetic vector under the body coordinate and the geographical coordinate system, carrying out information depth fusion on the geomagnetic vector and the sun vector under the body coordinate system, and establishing a navigation system model based on the polarization-geomagnetic vector tight combination.
The technical solution of the invention is as follows: a navigation method based on polarization-geomagnetic vector tight combination is realized by the following steps:
step (1), a compound eye-imitating polarization compass composed of polarization navigation sensors acquires and detects the sun vector under a body coordinate system in real time
Figure BDA0001859454610000021
Step (2) combining the solar astronomical calendar to obtain the sun vector under the geographic system
Figure BDA0001859454610000022
Combining the sun vector under the body coordinate obtained in the step (1), establishing a conversion relation between the geographic coordinate system and the sun vector under the body coordinate system
Figure BDA0001859454610000023
Step (3) respectively obtaining geomagnetic vectors under the body coordinate system and the geographic coordinate system
Figure BDA0001859454610000024
And
Figure BDA0001859454610000025
establishing a conversion relation of the magnetic vectors in the geographic coordinate system and the body coordinate system
Figure BDA0001859454610000026
And (4) carrying out information fusion on the geomagnetic vector and the sun vector under the body coordinate system
Figure BDA0001859454610000027
And (5) combining the step (4) to establish a navigation system model based on the tight combination of the polarization-geomagnetic vector.
The step (1) is to obtain and detect the sun vector under the body coordinate system in real time by a compound eye-imitating polarization compass formed by a polarization navigation sensor
Figure BDA0001859454610000028
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 zenith direction, M2And M3Are respectively symmetrically arranged at M1Measuring and mounting angle is 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 BDA0001859454610000029
Can pass through M1Polarization azimuth angle measured by sensor
Figure BDA00018594546100000210
And the azimuth angle psi provided by the geomagnetic sensor is calculated to obtain:
Figure BDA00018594546100000211
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 BDA00018594546100000212
wherein d ismax∈[max{d1,d2,d3},1)，θ1，θ2，θ3Is M1、M2、M3The angle between the observation direction and the sun vector,
according to the structure of a compound eye-imitating polarizing compass1，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 M1Angle of polarization observation theta1：
Figure BDA0001859454610000031
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 BDA0001859454610000032
Angle of scattering theta1The relation between the solar altitude and the solar altitude is obtained under the body coordinate system
Figure BDA0001859454610000033
Comprises the following steps:
Figure BDA0001859454610000034
in the module coordinate system, the sun vector can be expressed as:
Figure BDA0001859454610000035
order to
Figure BDA0001859454610000036
The step (2) obtains the sun vector under the geographic system according to the solar astronomical calendar
Figure BDA0001859454610000037
Combining stepEstablishing a conversion relation between the body coordinate system and the sun vector under the geographic coordinate by the sun vector under the body coordinate obtained in the step (1)
Figure BDA0001859454610000038
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 BDA0001859454610000039
Figure BDA00018594546100000310
Wherein, L is the geographical latitude, delta is the solar declination, and omega is the solar hour angle;
obtaining the sun vector under the geographic system according to the formula (6),
Figure BDA00018594546100000311
order to
Figure BDA00018594546100000312
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 BDA00018594546100000313
wherein the content of the first and second substances,
Figure BDA0001859454610000041
a posture conversion matrix between the body coordinate system and the geographic coordinate system;
Figure BDA0001859454610000042
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 BDA0001859454610000043
wherein
Figure BDA0001859454610000044
The nominal matrix can be obtained by carrier attitude angles, and is specifically represented as:
Figure BDA0001859454610000045
the step (3) is to respectively obtain the geomagnetic vector under the body coordinate system and the geographic coordinate system
Figure BDA0001859454610000046
And
Figure BDA0001859454610000047
establishing a conversion relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system
Figure BDA0001859454610000048
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 BDA0001859454610000049
the geomagnetic vector under the body coordinate system can be directly obtained through the geomagnetic sensor, and is represented as:
Figure BDA00018594546100000410
establishing a transformation relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system:
Figure BDA00018594546100000411
The step (4) is to earth magnetism vector under the body coordinate system
Figure BDA00018594546100000412
Sun vector sum
Figure BDA00018594546100000413
Performing information depth fusion
Figure BDA00018594546100000414
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 BDA00018594546100000415
And geomagnetic vector
Figure BDA00018594546100000416
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 BDA00018594546100000417
combining equations (10) and (13), equation (15) can be expressed as:
Figure BDA0001859454610000051
wherein:
Figure BDA0001859454610000052
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 BDA0001859454610000053
the principle of the invention is as follows: the sun position information is measured by the compound eye-imitating polarization compass, and the sun astronomical calendar is combined to establish the sun vector information transmission relation under the body coordinate and the geographic coordinate system. According to the geomagnetic vector obtained by the geomagnetic sensor in the body coordinate system, the conversion relation between the body coordinate system and the geomagnetic vector in the geographic coordinate system is established, in addition, the information depth fusion of the geomagnetic vector and the polarization vector is completed in the body coordinate system, and a navigation system model based on the close combination of the polarization-geomagnetic vector is established.
Compared with the prior art, the invention has the advantages that:
(1) the invention does not depend on satellite navigation signals, can carry out information fusion of the polarization vector and the geomagnetic vector by observing the atmospheric polarization field and the geomagnetic field, and jointly make up attitude and position measurement errors of inertial navigation, and has strong autonomy, robustness and reliability;
(2) the invention adopts the idea of tightly combining the polarization navigation system and the terrestrial magnetism navigation system, establishes a combined navigation system model based on polarization-terrestrial magnetism by introducing the attitude measurement error of inertial navigation, and can improve the observability of the system model.
(3) Compared with the traditional method, the method is not influenced by the error transmission of the polarization azimuth angle, can improve the precision of sun altitude observation, and further improves the performance of a navigation system based on the tight combination of polarization-geomagnetism.
Drawings
FIG. 1 is a flowchart illustrating a navigation method based on a combination of polarization-geomagnetic vector closeness according to the present invention;
fig. 2 is a schematic structural diagram of an imitation compound eye polarization compass according to the invention.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1, the navigation method based on the combination of the polarization-geomagnetic vector includes the following steps:
1. A compound eye-imitating polarization compass formed by polarization navigation sensors acquires the sun vector under the coordinate system of a detection module in real time
Figure BDA0001859454610000061
The schematic structural diagram of the compound eye-imitating polarization compass is shown in fig. 2, and the compound eye-imitating polarization compass is composed of three polarization sensors which are respectively marked as M1、M2、M3Wherein M is1The observation direction is the zenith direction, M2And M3Are respectively symmetrically arranged at M1Measuring and mounting angle is 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, the y axis is determined by a right-hand rule,
in the body coordinate system, the sun azimuth angle
Figure BDA0001859454610000062
Can pass through M1Polarization azimuth angle measured by sensor
Figure BDA0001859454610000063
And the azimuth angle psi provided by the geomagnetic sensor is calculated to obtain:
Figure BDA0001859454610000064
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 BDA0001859454610000065
wherein d ismax∈[max{d1,d2,d3},1)，θ1，θ2，θ3Is M1、M2、M3Observing an included angle between the direction and the sun vector;
according to the structure of a compound eye-imitating polarizing compass1，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 BDA0001859454610000066
Wherein, theta 1The 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 BDA0001859454610000067
And scattering angle theta1The relation between the solar altitude and the solar altitude is obtained under the body coordinate system
Figure BDA0001859454610000068
Comprises the following steps:
Figure BDA0001859454610000069
in the body coordinate system, the sun vector can be expressed as,
Figure BDA0001859454610000071
order to
Figure BDA0001859454610000072
2. Combining with solar astronomical calendar to obtain sun vector under geographic system
Figure BDA0001859454610000073
Establishing conversion relation between the sun vector under the geographic coordinate system and the body coordinate
Figure BDA0001859454610000074
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 BDA0001859454610000075
Figure BDA0001859454610000076
wherein, L is the geographical latitude, delta is the solar declination, and omega is the solar hour angle;
obtaining the sun vector under the geographic system according to the formula (6),
Figure BDA0001859454610000077
order to
Figure BDA0001859454610000078
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 BDA0001859454610000079
wherein the content of the first and second substances,
Figure BDA00018594546100000710
is the attitude transformation matrix between the body coordinate system and the geographic coordinate system,
Figure BDA00018594546100000711
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 BDA00018594546100000712
Wherein
Figure BDA00018594546100000713
The nominal matrix can be obtained by carrier attitude angles, and is specifically represented as:
Figure BDA00018594546100000714
3. respectively obtaining geomagnetic vectors under a body coordinate system and a geographic coordinate system
Figure BDA00018594546100000715
And
Figure BDA00018594546100000716
establishing a transformation relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system:
solving the geomagnetic vector under the geographic coordinate system to obtain the geomagnetic vector under the geographic coordinate system, which is expressed as:
Figure BDA0001859454610000081
the geomagnetic vector under the body coordinate system can be directly obtained through the geomagnetic sensor, and is represented as:
Figure BDA0001859454610000082
establishing a transformation relation of the geomagnetic vectors in the body coordinate system and the geographic coordinate system:
Figure BDA0001859454610000083
4. under the body coordinate system, for the geomagnetic vector
Figure BDA0001859454610000084
And sun vector
Figure BDA0001859454610000085
Performing information depth fusion
Figure BDA0001859454610000086
The sun vector of the body coordinate system obtained according to the step (2) and the step (3)
Figure BDA0001859454610000087
And geomagnetic vector
Figure BDA0001859454610000088
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 BDA0001859454610000089
combining equations (10) and (13), equation (15) can be expressed as:
Figure BDA00018594546100000810
wherein
Figure BDA00018594546100000811
5. And (4) establishing a navigation system model based on the tight combination of the polarization/geomagnetic vectors by combining the steps of:
obtaining a combined navigation system model based on polarization/geomagnetic vector fusion through formula (15):
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, the first and the second end of the pipe are connected with each other,
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 the content of the first and second substances,
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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