CN113834480B - Self-positioning method of compound eye-imitating polarization sensor based on scattering angle weight distribution - Google Patents

Abstract

The invention relates to an autonomous positioning method of a compound eye-like polarization sensor based on scattering angle weight distribution. First, a compound-eye-like polarization compass with a multi-eye curved surface structure is designed to obtain the polarization information of the whole sky. Secondly, three polarization degree measurement values within the polarization degree threshold range are selected as a set of positioning calculation units. Then, using the spatial geometric relationship of the three observation points in each group of positioning and solving units and the installation matrix of the compound eye polarization sensor, the sun altitude angle under the carrier system is obtained. Select the basic polarization sensing unit with the smallest scattering angle in each group of positioning solution units, take the scattering angle that measures the accuracy of the polarization information as the weight, and use the normalized scattering angle as the weight to act on each positioning through normalization. On the solar altitude angle calculated by the solving unit, a high-precision solar altitude angle is obtained. Finally, the position of the carrier is calculated by the altitude difference method through the sun altitude angle calculated at different times.

Description

An autonomous positioning method for compound eye-like polarization sensor based on scattering angle weight distribution

technical field

The invention belongs to the field of navigation, and in particular relates to an autonomous positioning method of a compound eye-like polarization sensor based on scattering angle weight distribution.

Background technique

At present, the commonly used positioning technologies include inertial navigation, satellite navigation, visual navigation and terrain matching navigation. The position error of the inertial navigation system will accumulate over time, and it cannot meet the work requirements of long flight time. It needs to use satellite navigation for error correction; satellite navigation can provide accurate latitude and longitude information of the carrier, but the satellite signal is very vulnerable to electromagnetic interference or deception. Visual navigation and terrain matching techniques are limited by map accuracy and processor processing efficiency, and are not suitable for unfamiliar and unstructured environments.

The atmospheric polarization distribution pattern is relatively stable, which contains rich navigation information. Studies have shown that natural organisms, such as sand ants, bees, and migratory birds, can use unique polarization-sensing structures to obtain polarization information and realize long-distance foraging, homing and other activities. Inspired by the autonomous perception and navigation of living things, bionic polarization navigation has become a research hotspot. Biomimetic polarization navigation can extract and analyze polarization information by imitating biological organs, obtain the position information of the carrier, and realize the function of polarization positioning.

At present, the methods for realizing carrier positioning based on polarization information include: a positioning system based on polarized light bionic navigation and its positioning method, patent application number: CN201310037586.4, using the polarization azimuth angle information measured by a single polarization sensor at different times to solve the local longitude and latitude, In this method, when the polarization sensor is disturbed, the position cannot be calculated, and the electronic compass is required to provide heading information. Positioning system and positioning method based on multi-directional polarized light navigation sensor, patent application number: CN201410088363.5, by measuring the polarization azimuth information of multiple observation directions, using polarization vector cross product to obtain sun vector, and integrating electronic compass to provide heading information , but the system is susceptible to electromagnetic interference and does not fully utilize the polarization degree information. A real-time positioning method for polarization navigation based on polarization degree information in the whole sky, patent application number: CN201810583734.5, uses the optimal three polarization degrees in the sky area to solve the sun vector under the carrier system, and uses the attitude sensor to obtain the geographic system Under the sun vector, according to the principle of astronomical navigation, solve the longitude and latitude of the carrier. This method requires the attitude matrix information provided by the attitude sensor. A polarization navigation global autonomous positioning method based on the observation of the maximum polarization degree, patent application number: CN201811328952.0, through the relationship between the polarization degree of each observation point and the maximum polarization degree, the maximum polarization degree is solved, and then the sun altitude angle is solved. The height difference method is used to calculate the longitude and latitude information of the carrier, but this method relies on the zenith polarization sensor, and the positioning accuracy will be affected when the zenith sensor is disturbed or blocked. Compared with the existing polarization positioning method, the present invention can not rely on other auxiliary attitude sensors and zenith polarization sensors, has strong environmental adaptability, high calculation accuracy and high practicability.

SUMMARY OF THE INVENTION

The problems to be solved by the present invention are as follows: a method for autonomous positioning of a compound-eye-like polarization sensor based on the distribution of scattering angle weights is provided. The method can realize autonomous positioning by using polarized light in the sky, and has the advantages of strong adaptability, strong autonomy, and does not rely on other auxiliary attitude sensors and zenith polarization sensors. By designing a compound eye-like polarization compass with a multi-ocular surface structure, it is used to obtain the polarization degree information of each observation point in the sky area. The polarization degree threshold is designed, and three polarization degree measurement values within the threshold range are selected as a set of positioning calculation units. Using the spatial geometric relationship of the three observation points in each group of positioning and solving units and the installation matrix of the compound eye polarization sensor, the sun altitude angle under the carrier system is obtained. Select the basic polarization sensing unit with the smallest scattering angle in each group of positioning solution units, take the scattering angle that measures the accuracy of the polarization information as the weight, and use the normalized scattering angle as the weight to act on each positioning through normalization. On the solar altitude angle calculated by the solving unit, a high-precision solar altitude angle is obtained. According to the sun altitude angle calculated at different times, the carrier position is calculated by the altitude difference method, and the polarization positioning function is realized. The method can realize the position output of the carrier, has good environmental adaptability, can dynamically assign weights, and overcome the defects of the existing polarization positioning technology relying on other auxiliary devices and being susceptible to electromagnetic interference; at the same time, it overcomes the existing polarization positioning technology using polarization Insufficient information defect.

The technical solution of the present invention is: an autonomous positioning method of a compound eye-like polarization sensor based on scattering angle weight distribution, the implementation steps of which are as follows:

(1) Design a compound-eye-like polarization compass with a multi-eye curved surface structure, with n polarization sensors M ₁ , M ₂ , M ₃ ... M _n , which are used to obtain the polarization degree information d ₁ , d of n observation points in the sky area in real time ₂ , d ₃ … d _n ;

组；(2) Set the polarization degree threshold μ , select m polarization degree measurement values within the threshold range, where m ≤ n , and randomly select three measurement values as a set of positioning solution units, with a total of

Group;

(3) In order to improve the environmental adaptability and the calculation accuracy of the solar elevation angle, the corresponding weight of each group of positioning calculation units is established based on the scattering angle of the polarized light incident on the observation point:

θ _pi is the minimum scattering angle incident to the observation point in each group of positioning and solving units, and Wi is the _weight of each group of positioning and solving units;

(4) Taking the coordinate system of the zenith sensor in the compound-eye polarization compass as the modular system of the compound-eye polarization compass, and using the spatial geometric relationship of the three observation points in each group of positioning and solving units and the installation matrix of the compound-eye polarization sensor, the module system is obtained. Solar elevation angle. According to the weight obtained in step (3), weight the solved sets of solar altitude angles to obtain the final solar altitude angle.

(5) Calculate the longitude and latitude of the carrier by using the altitude difference method through the sun altitude angle calculated at different times, so as to realize the autonomous navigation and real-time positioning of the carrier.

Further, the specific implementation of the step (1) is as follows:

The compound-eye-like polarization compass with multi-eye curved structure is composed of n point-source polarization sensors M ₁ , M ₂ , M ₃ ... Mn , _where M _{1 is} used as the zenith polarization sensor, and M ₂ , M ₃ ... Mn are in the hemispherical structure Randomly distributed on the surface, the zenith polarization sensor M ₁ is installed in the z -axis direction of the module coordinate system, and the polarization information in the zenith direction _is observed; M ₂ , M ₃ ... Mn are randomly distributed around the zenith polarization sensor M ₁ ; The compound eye polarization compass obtains the polarization degrees d ₁ , d ₂ , d ₃ … d _n of n sky observation points in real time.

Further, the specific implementation of the step (2) is as follows:

种组合方式，每组都能够作为太阳高度角解算的输入。Under ideal conditions, the range of the sky polarization degree is 0-1, and the actual maximum polarization degree d _max is generally less than 1 due to the influence of the weather. In order to avoid abnormal data outliers in the compound-eye polarization compass measurement, the measurement values with polarization degree greater than 1 are firstly eliminated. Secondly, according to the weather conditions of the carrier, including the amount of cloud in the sky, PM2.5 content, etc., as well as the internal chip parameters of the sensor, reasonably design the polarization degree threshold μ , select m polarization degree measurement values within the threshold range, and randomly select three from them The measured values are used as a set of positioning solution units, with a total of

There are various combinations, each of which can be used as input for the calculation of the solar elevation angle.

Further, the specific implementation of the step (3) is as follows:

The larger the scattering angle of the polarized light incident on the observation point, the smaller the influence of sunlight, and the accurate observation of polarization information. A polarization sensor with a small scattering angle will affect the calculation accuracy of each group of positioning calculation units. Therefore, in order to improve the environmental adaptability and the calculation accuracy of the solar altitude angle, the three observation points of a set of data are screened, and the smallest scattering angle incident to the observation point is selected as the allocation factor, and the corresponding positioning calculation unit of each group is established. weight, which is calculated as:

θ _pi is the minimum scattering angle incident to the observation point in each group of positioning and solving units, and Wi is the _weight of each group of positioning and solving units.

Further, the specific implementation of the step (4) is as follows:

According to the Rayleigh scattering theory, the relationship between the polarization degrees d ₁ , d ₂ , d ₃ and the maximum polarization degree d _max in the whole sky is:

，

为三个观测点偏振度的最大值，θ _n 第n个偏振传感器观测方向与太阳矢量的夹角，

；Among them, d _n is the polarization degree of the observation point measured by the nth polarization sensor, d _max is the maximum polarization degree of the whole space,

,

is the maximum value of the degree of polarization of the three observation points, θ _n is the angle between the observation direction of the nth polarization sensor and the sun vector,

;

；The corresponding observation vector is solved from the installation matrix of the compound eye polarization sensor, and the azimuth angle A _pi and height angle h _pi of each polarization sensor under the module system are solved, where

;

In the module system, the spherical triangle PSZ formed by the observed point P and the sun point S corresponding to the polarization sensor on the compound eye polarization compass and the sky vertex Z of the module system is established by the spherical triangle cosine theorem as follows:

Among them, h _p represents the height angle of the polarization sensor in the compound eye polarization compass under the module system, A _p represents the azimuth angle of the polarization sensor in the compound eye polarization compass under the module system, h _s represents the sun altitude angle under the module system, A _s represents the module system The azimuth of the sun under the system;

Taking the polarization degree of each group of observation points as the input to solve the solar altitude angle, the following equations can be established:

Among them, d ₁ , d ₂ , d ₃ represent the three polarization degrees in a set of inputs, θ ₁ , θ ₂ , θ ₃ represent the angles between the three observation vectors and the sun vector in a set of inputs, h _{p 1} , h _{p 2} , h _{p 3} represent the height angles of the three polarization sensors in a group of inputs under the module system, A _{p 1} , A _{p 2} , A _{p 3} represent the positions of the three polarization sensors in a group of inputs under the module system angle, h _s represents the sun altitude angle, A _s represents the sun azimuth angle;

In this nonlinear system of equations, there are six unknowns, the genetic algorithm is used to solve the numerical solution of the system of equations, and the range of each parameter is determined as follows:

Using the spatial geometric relationship of the three observation points in each group of positioning and solving units and the installation matrix of the compound eye polarization sensor, the solar altitude angle under the module system is obtained. According to the weight obtained in step (3), weight the solved sets of solar altitude angles to obtain the final solar altitude angle. The calculation formula of the solar altitude angle H _s is:

，

,

为第i个太阳高度角。Wi is the ith weight,

is the ith sun altitude angle.

According to the rough estimation of the carrier or the known initial latitude and longitude Lon0, Lat0, the declination Dec and the local hour angle LHA are obtained from the astronomical almanac, and the solar altitude angle H _{c 1} , H _{c 2} and the sun azimuth calculated at T ₁ and T ₂ are obtained. angles A _{c 1} and A _{c 2} ;

：The altitude angle of the same celestial body can be observed at different times, and the variation of the altitude angle under the carrier system can be obtained.

:

Use the analytical height difference method to solve. Introduce intermediate auxiliary quantities a, b, c, d, e, f;

Then the longitude and latitude λ and L of the carrier can be solved by the following formula:

The advantages of the present invention compared with the prior art are:

The invention collects the polarization degree information of multiple observation points in the sky through a compound eye-like polarization compass, randomly selects three sensor data as the solution input, can adaptively allocate weights according to the scattering angle of the polarized light incident on the observation point, and combines polarization navigation and Based on the principle of height difference method, it outputs the position of the carrier in real time, does not depend on satellite navigation and other auxiliary devices, has high autonomy, is not affected by natural or man-made electromagnetic interference, and has strong environmental adaptability. The positioning method makes full use of polarization information, has a simple structure, few steps, and has high practicability.

Description of drawings

Fig. 1 is a kind of self-positioning method of imitation compound eye polarization sensor based on scattering angle weight distribution of the present invention;

Fig. 2 is the schematic diagram of the imitation compound eye polarization compass involved in the present invention;

FIG. 3 is a schematic diagram of the geometric relationship between the sun vector and the observation vector in the carrier coordinate system involved in the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in Figure 1, the concrete realization steps of the present invention are as follows:

1. As shown in FIG. 2 , which is a schematic diagram of the imitation compound eye polarization compass involved in the present invention, the imitation compound eye polarization compass with a multi-eye curved surface structure _is composed of n point source polarization sensors M ₁ , M ₂ , M ₃ . . . Mn , Among them, M _{1 is} used as a zenith polarization sensor, M ₂ , M ₃ ... Mn are randomly distributed on the surface of the hemispherical structure, and the zenith polarization sensor M ₁ is installed in the z -axis direction of the module coordinate system to observe the polarization information in the zenith direction; M ₂ , M ₃ ... Mn are randomly distributed around the zenith polarization sensor M ₁ ; the polarization degrees d ₁ , d ₂ , d ₃ ... d _n of n sky observation points are obtained in real time by using the compound eye _- like polarization compass;

种组合方式，每组都能够作为太阳高度角解算的输入。2. Under ideal conditions, the range of the sky polarization degree is 0-1, and the actual maximum polarization degree d _max is generally less than 1 due to the influence of the weather. In order to avoid outliers in the compound-eye polarization compass measurement, the measurement values with polarization degree greater than 1 are firstly eliminated. Secondly, according to the weather conditions of the carrier, including the amount of cloud in the sky, PM2.5 content, etc., as well as the internal chip parameters of the sensor, reasonably design the polarization degree threshold μ , select m polarization degree measurement values within the threshold range, and randomly select three from them The measured values are used as a set of positioning solution units, with a total of

There are various combinations, each of which can be used as input for the calculation of the solar elevation angle.

3. The larger the scattering angle of the polarized light incident on the observation point, the smaller the influence of sunlight, and the accurate observation of polarization information. A polarization sensor with a small scattering angle will affect the calculation accuracy of each group of positioning calculation units. Therefore, in order to improve the environmental adaptability and the calculation accuracy of the solar altitude angle, the three observation points of a set of data are screened, and the smallest scattering angle incident to the observation point is selected as the weight, and the corresponding weight of each group of positioning calculation units is established. , the calculation result is:

θ _pi is the minimum scattering angle incident to the observation point in each group of positioning and solving units, and Wi is the _weight of each group of positioning and solving units;

4. According to the Rayleigh scattering theory, the relationship between the polarization degrees d ₁ , d ₂ , d ₃ and the maximum polarization degree d _max in the whole sky is:

，

为三个观测点偏振度的最大值，θ _n 第n个偏振传感器观测方向与太阳矢量的夹角，

；Among them, d _n is the polarization degree of the observation point measured by the nth polarization sensor, d _max is the maximum polarization degree of the whole space,

,

is the maximum value of the degree of polarization of the three observation points, θ _n is the angle between the observation direction of the nth polarization sensor and the sun vector,

;

；The corresponding observation vector is solved from the installation matrix of the compound eye polarization sensor, and the azimuth angle A _pi and height angle h _pi of each polarization sensor under the module system are solved, where

;

3 is a schematic diagram of the geometric relationship between the sun vector and the observation vector in the carrier coordinate system involved in the present invention. In the module coordinate system, the observed point P , the sun point S corresponding to the polarization sensor on the compound eye polarization compass and the module system sky vertex Z are formed The spherical triangle PSZ of , is established by the spherical triangle cosine theorem as follows:

Among them, h _p represents the height angle of the polarization sensor in the compound eye polarization compass under the module system, A _p represents the azimuth angle of the polarization sensor in the compound eye polarization compass under the module system, h _s represents the sun altitude angle under the module system, A _s represents the module system The azimuth of the sun under the system;

Taking the polarization degree of each group of observation points as the input to solve the solar altitude angle, the following equations can be established:

Among them, d ₁ , d ₂ , d ₃ represent the three polarization degrees in a set of inputs, θ ₁ , θ ₂ , θ ₃ represent the angles between the three observation vectors and the sun vector in a set of inputs, h _{p 1} , h _{p 2} , h _{p 3} represent the height angles of the three polarization sensors in a group of inputs under the module system, A _{p 1} , A _{p 2} , A _{p 3} represent the three polarization sensors in a group of inputs under the module system The azimuth angle of , h _s represents the sun altitude angle, A _s represents the sun azimuth angle;

In this nonlinear equation system, there are six unknowns, and the genetic algorithm can be used to solve the numerical solution of the equation system, and the range of each parameter is determined as follows:

Inputting a set of polarization data can obtain a solar altitude angle, the corresponding weight of the solar altitude angle is W _i , and fully utilizing the k sets of data, the solar altitude angle H _s under the module system can be calculated;

，

,

为第i个太阳高度角。 Wi is the _ith weight,

is the ith sun altitude angle.

5. According to the rough estimation of the carrier or the known initial longitude and latitude Lon0, Lat0, the declination Dec and the local hour angle LHA are obtained from the astronomical almanac, and the solar altitude angles H _{c 1} , H _{c 2} and calculated at T 1 and T ₂ are obtained. Sun azimuths A _{c 1} and A _{c 2} .

。The altitude angle of the same celestial body can be observed at different times, and the variation of the altitude angle under the carrier system can be obtained.

.

Use the analytical height difference method to solve. Introduce intermediate auxiliary quantities a, b, c, d, e, f;

Then the longitude and latitude λ of the carrier, L can be solved by the following formula:

。

.

Although illustrative specific embodiments of the present invention have been described above to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited in scope to the specific embodiments, to those skilled in the art, As long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the inventive concept are included in the protection list.

Claims (4)

1. An automatic positioning method of a compound eye-imitating polarization sensor based on scattering angle weight distribution is characterized by comprising the following implementation steps:

(1) a compound eye-imitating polarization compass with multi-view curved surface structure is providednPolarization sensorM ₁,M ₂,M ₃…M _n For real-time acquisition of sky regionsnPolarization degree information of individual observation pointd ₁,d ₂, d ₃…d _n ；

(2) Setting a polarization degree threshold value according to the weather conditions of the carrier, including the cloud cover in the sky, the PM2.5 content and the chip parameters in the sensorμWithin a selected threshold rangemA measure of the degree of polarization, whereinm≤nRandomly selecting three measured values from the three measured values as a group of positioning solution units, and sharing

Group (d); the step (2) is specifically realized as follows:

the range of sky polarization degree is 0-1, actual maximum degree of polarization affected by weatherd _maxLess than 1, in order to avoid abnormal data situation in the measurement of the compound eye-imitating polarization compass, firstly, the measured value with the polarization degree greater than 1 is rejected, and secondly, the polarization degree threshold value is designed according to the weather conditions of the carrier, including the cloud cover in the sky, the PM2.5 content, and the chip parameters in the sensorμWithin a selected threshold rangemThree polarization degree measured values are randomly selected from the three measured values to be used as a group of positioning resolving units, and the total number is

Each group can be used as input for resolving the solar altitude angle;

(3) in order to improve the environmental adaptability and the calculation accuracy of the solar altitude angle, the weight corresponding to each group of positioning calculation units is established according to the scattering angle of the polarized light incident to the observation point;

the step (3) is specifically realized as follows:

screening three observation points of a group of data, selecting the minimum scattering angle incident to the observation points as a distribution factor, and establishing the weight corresponding to each group of positioning resolving units, wherein the calculation result is as follows:

wherein,θ _pi the minimum scatter angle incident on the observation point in each set of localization solution units,W _i weights for each set of positioning calculation units;

(4) taking a zenith sensor coordinate system in the compound eye polarization compass as a module system of the compound eye polarization compass, and obtaining a solar altitude angle under the module system by utilizing the space geometric relationship of three observation points in each group of positioning resolving units and the installation matrix of the compound eye polarization sensor; weighting the plurality of groups of solved solar altitude angles according to the weight obtained in the step (3) to obtain a final solar altitude angle;

(5) and calculating the longitude and latitude of the carrier by using a height difference method through the solar altitude calculated at different moments, so as to realize autonomous navigation and real-time positioning of the carrier.

2. The method for autonomously positioning the simulated compound eye polarization sensor based on scattering angle weight distribution of claim 1, wherein the method comprises the following steps: the step (1) is specifically realized as follows:

compound eye-imitating polarization compass with multi-eye curved surface structurenPoint source type polarization sensorM ₁,M ₂,M ₃…M _n Is composed of (a) whereinM ₁As a result of the zenith polarization sensor,M ₂,M ₃ …M _n randomly distributed zenith polarization sensors on surface of hemispherical structureM ₁Mounted in a modular systemzObserving polarization information in the zenith direction in the axial direction;M ₂,M ₃…M _n polarization sensor randomly distributed on zenithM ₁Four weeks; real-time acquisition using compound eye-like polarizing compassnPolarization degree information of sky observation pointd ₁,d ₂,d ₃…d _n 。

3. The method for autonomously positioning the simulated compound eye polarization sensor based on scattering angle weight distribution of claim 1, wherein the method comprises the following steps: the step (4) is specifically realized as follows:

the information of the degree of polarization can be known from Rayleigh scattering theoryd ₁,d ₂,d ₃And maximum degree of polarization of all-sky domaind _maxThe relationship between:

wherein,d _j is as followsjThe polarization degree of an observation point measured by each polarization sensor,d _maxis the maximum polarization degree in a full spatial domain,

，

is the maximum of the degrees of polarization for the three observation points,θ _j is as followsjThe angle between the observation direction of each polarization sensor and the sun vector,

；

solving the corresponding observation vector by the installation matrix of the compound eye polarization sensor, and solving the azimuth angle of each polarization sensor under the module systemA _pi And angle of elevationh _pi Wherein

；

In the module system, observed points corresponding to the polarization sensors on the compound eye polarization compassPSun pointSBeing module is zenithZFormed spherical trianglePSZThe following relationship is established by the cosine theorem of spherical triangle:

wherein,h _p the height angle of the polarization sensor under the module system in the compound eye polarization compass is shown,A _p shows the azimuth angle of the polarization sensor under the module system in the compound eye polarization compass,h _s the indication module is a lower solar altitude angle,A _s representing the solar azimuth angle of the module system;

and (3) taking the polarization degree of each group of observation points as resolving input of the solar altitude angle, and establishing the following equation set:

wherein,d ₁,d ₂ ,d ₃representing three degrees of polarization in a set of inputs,θ ₁,θ ₂ ,θ ₃representing the angle of three observation vectors in a set of inputs with respect to the sun vector,h _p1,h _p2 ,h _p3representing the elevation angles of three polarization sensors in a set of inputs under the module system,A _p1,A _p2 ,A _p3representing the azimuth angle of the three polarization sensors in a set of inputs under the module system,h _s which represents the altitude of the sun,A _s representing the sun azimuth;

the nonlinear equation set contains six unknowns, a genetic algorithm is adopted to solve the numerical solution of the equation set, and the range of each parameter is determined as follows:

obtaining the solar altitude angle under the module system by utilizing the space geometric relationship of three observation points in each group of positioning resolving units and the installation matrix of the compound eye polarization sensor; weighting the solved multiple groups of solar altitude angles according to the weight obtained in the step (3) to obtain the final solar altitude angle and the solar altitude angleH _s The calculation formula is as follows:

，

W _i is the (i) th weight, and is,

is the ith solar altitude.

4. The method for autonomously positioning the simulated compound eye polarization sensor based on scattering angle weight distribution of claim 1, wherein the method comprises the following steps: the step (5) is specifically realized as follows:

declination from almanac according to estimated or known initial latitude and longitude Lon0, Lat0 of the vectorDecAnd local time angleLHATo obtainT ₁AndT ₂solar altitude angle calculated at any momentH _c1，H _c2And azimuth of the sunA _c1AndA _c2；

observing the altitude angles of the same celestial body at different moments to obtain the change amount of the altitude angles under the carrier system

；

Resolving by using an analytic height difference method, and introducing intermediate auxiliary quantities a, b, c, d, e and f;

the longitude and latitude of the vectorλ、LSolving by:

Images