CN110988937A - Satellite-borne GNSS-R mirror reflection point calculation method based on quasi-circle approximate Newton iteration method - Google Patents

Satellite-borne GNSS-R mirror reflection point calculation method based on quasi-circle approximate Newton iteration method Download PDF

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CN110988937A
CN110988937A CN201911097137.2A CN201911097137A CN110988937A CN 110988937 A CN110988937 A CN 110988937A CN 201911097137 A CN201911097137 A CN 201911097137A CN 110988937 A CN110988937 A CN 110988937A
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coordinate system
reflection point
wgs
gnss
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韩星远
王延光
蒙艳松
曲博
韩琳
王登峰
边朗
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Xian Institute of Space Radio Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/35—Constructional details or hardware or software details of the signal processing chain
    • G01S19/37—Hardware or software details of the signal processing chain
    • 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

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Abstract

The invention discloses a method for calculating a satellite-borne GNSS-R mirror reflection point based on a quasi-circle approximate Newton iteration method, which comprises the following steps: (1) mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to the position R' of the unit spherical coordinate system from the WGS-84 coordinate system; (2) calculating a mirror reflection point S ' by using a Newton iteration method in a unit spherical coordinate system according to the position T ' and the position R '; (3) and mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system. The invention adopts the mirror reflection point calculation method based on the quasi-circle approximate Newton iteration method, on one hand, the Newton iteration method accelerates the iteration speed and improves the calculation efficiency, and on the other hand, the quasi-circle approximate coordinate mapping algorithm is adopted to eliminate the influence of the non-circular ellipsoid factors of the earth and improve the calculation precision of the mirror reflection point.

Description

Satellite-borne GNSS-R mirror reflection point calculation method based on quasi-circle approximate Newton iteration method
Technical Field
The invention belongs to the technical field of GNSS-R receiver reflection signal processing, and particularly relates to a satellite-borne GNSS-R mirror reflection point calculation method based on a quasi-circle approximate Newton iteration method.
Background
The global satellite navigation system transmits L-waveband microwave signals to the earth surface, and performs inversion of surface environment parameters by receiving navigation satellite signals reflected by the earth surface on an aviation or satellite platform, which is called as a GNSS-R (GNSS-reflection) remote sensing technology. Typical applications of GNSS-R techniques include sea surface wind field inversion, sea surface altimetry, sea ice detection, soil moisture detection, and the like.
The main function of the satellite-borne GNSS-R receiver is to generate a delay-Doppler (DDM) map and provide observation data for parameter inversion. The reflection point calculation is one of the important functions of the satellite-borne GNSS-R receiver, and provides time delay and Doppler forecast parameters for the open-loop correlation processing of reflection signals.
In the past, the mirror reflection point calculation mainly adopts an angular bisector iteration method, an S.C.Wu algorithm and a line segment bisection method. The calculation method of the angular bisector iteration method is simple, but the calculation efficiency is low, iteration is needed to be more than 10000 in many cases, the time cost is high, and the requirement on the real-time performance of the calculation of the reflection point is difficult to meet; the traditional S.C.Wu algorithm and the line segment bisection method have high calculation efficiency, but the influence of the earth ellipticity is not considered, and in some cases, the calculation precision of the specular reflection point reaches 10 kilometers orders of magnitude and is not high.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method for calculating the satellite-borne GNSS-R mirror reflection points based on the quasi-circle approximate Newton iteration method has the advantages that the quasi-circle approximate Newton iteration method is adopted, on one hand, the Newton iteration method accelerates the iteration speed and improves the calculation efficiency, on the other hand, the quasi-circle approximate coordinate mapping algorithm is adopted, the influence of the non-circular ellipsoid factors of the earth is eliminated, the calculation accuracy of the mirror reflection points is improved, and the method has the advantages of being high in real-time performance and high in accuracy.
The purpose of the invention is realized by the following technical scheme: a satellite-borne GNSS-R mirror reflection point calculation method based on a quasi-circle approximately Newton iteration method comprises the following steps: (1) mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to the position R' of the unit spherical coordinate system from the WGS-84 coordinate system; (2) calculating a mirror reflection point S ' by using a Newton iteration method in a unit spherical coordinate system according to the position T ' and the position R '; (3) and mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system.
In the above method for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle newton's iteration method, in step (1), the position T' is:
T′＝AT；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure BDA0002268675880000021
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
In the above method for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle newton's iteration method, in step (1), the position R' is:
R′＝AR；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure BDA0002268675880000022
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
In the above method for calculating the specular reflection point S 'of the satellite-borne GNSS-R based on the quasi-circular approximately newton iteration method, in step (2), the method for calculating the specular reflection point S' by using the newton iteration method in the unit spherical coordinate system according to the position T 'and the position R' specifically includes the following steps:
a) in a unit spherical coordinate system, the coordinates of points T 'and R' are known, and the coordinates are obtained
Figure BDA0002268675880000023
Then ∠ T 'OR' is solved by using the cosine theorem;
Figure BDA0002268675880000031
b) in Δ OT 'S', ∠ S 'OT' is set to α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000032
wherein
Figure BDA0002268675880000033
Equal to the radius 1 of the unit sphere
Figure BDA0002268675880000034
Using sine theorem to obtain:
Figure BDA0002268675880000035
c) in Δ OR 'S', ∠ S 'OR' is set to β, and β is set to θ - α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000036
in the formula
Figure BDA0002268675880000037
Equal to 1, according to the principle of specular reflection
Figure BDA0002268675880000038
Using sine theorem to obtain:
Figure BDA0002268675880000039
d) combination formula
Figure BDA00022686758800000310
And
Figure BDA00022686758800000311
then there are:
Figure BDA00022686758800000312
defining a function:
Figure BDA00022686758800000313
substituting β into θ - α for f (α), and deriving f (α) as:
Figure BDA00022686758800000314
e) the newton iteration formula can be written as:
Figure BDA0002268675880000041
setting an initial value of an iteration
Figure BDA0002268675880000042
When in use
Figure BDA0002268675880000043
Or the number of iterations NαWhen the value is more than or equal to 20, the iteration is stopped, and α is made equal to αk+1；
f) The sine theorem is applied in Δ OT 'M and Δ OR' M, respectively:
Figure BDA0002268675880000044
Figure BDA0002268675880000045
order:
Figure BDA0002268675880000046
the coordinates of the M points are:
Figure BDA0002268675880000047
in the formula, T ' and R ' are coordinates of the navigation satellite and the GNSS-R receiver in a unit sphere coordinate system, respectively, the coordinates of the specular reflection point S ' on the unit sphere can be obtained:
Figure BDA0002268675880000048
in the above method for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle approximately newton iteration method, in step (3), the specular reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system is: a is-1S′。
A satellite-borne GNSS-R specular reflection point calculation system based on quasi-circle Newton's iteration method comprises the following steps: the first module is used for mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to a position R' of the unit spherical coordinate system from the WGS-84 coordinate system; the second module is used for calculating a mirror reflection point S ' in a unit spherical coordinate system by using a Newton iteration method according to the position T ' and the position R '; and the third module is used for mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system.
In the above system for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle newton's iteration method, the position T' is:
T′＝AT；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure BDA0002268675880000051
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
In the above system for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle newton's iteration method, the position R' is:
R′＝AR；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure BDA0002268675880000052
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
In the above system for calculating a specular reflection point S 'of a satellite-borne GNSS-R based on the quasi-circular near-newton iteration method, the following steps are specifically included in calculating the specular reflection point S' in a unit spherical coordinate system by using the newton iteration method according to the position T 'and the position R':
a) in a unit spherical coordinate system, the coordinates of points T 'and R' are known, and the coordinates are obtained
Figure BDA0002268675880000053
Then ∠ T 'OR' is solved by using the cosine theorem;
Figure BDA0002268675880000054
b) in Δ OT 'S', ∠ S 'OT' is set to α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000061
wherein
Figure BDA0002268675880000062
Equal to the radius 1 of the unit sphere
Figure BDA0002268675880000063
Using sine theorem to obtain:
Figure BDA0002268675880000064
c) in Δ OR 'S', ∠ S 'OR' is set to β, and β is set to θ - α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000065
in the formula
Figure BDA0002268675880000066
Equal to 1, according to the principle of specular reflection
Figure BDA0002268675880000067
Using sine theorem to obtain:
Figure BDA0002268675880000068
d) combination formula
Figure BDA0002268675880000069
And
Figure BDA00022686758800000610
then there are:
Figure BDA00022686758800000611
defining a function:
Figure BDA00022686758800000612
substituting β into θ - α for f (α), and deriving f (α) as:
Figure BDA00022686758800000613
e) the newton iteration formula can be written as:
Figure BDA00022686758800000614
setting an initial value of an iteration
Figure BDA00022686758800000615
When in use
Figure BDA00022686758800000616
Or the number of iterations NαWhen the value is more than or equal to 20, the iteration is stopped, and α is made equal to αk+1；
f) The sine theorem is applied in Δ OT 'M and Δ OR' M, respectively:
Figure BDA0002268675880000071
Figure BDA0002268675880000072
order:
Figure BDA0002268675880000073
the coordinates of the M points are:
Figure BDA0002268675880000074
in the formula, T ' and R ' are coordinates of the navigation satellite and the GNSS-R receiver in a unit sphere coordinate system, respectively, the coordinates of the specular reflection point S ' on the unit sphere can be obtained:
Figure BDA0002268675880000075
in the above system for calculating the specular reflection point of the satellite-borne GNSS-R based on the quasi-circle approximately newton iteration method, the coordinate S of the specular reflection point in the WGS-84 earth ellipsoid coordinate system is as follows: a is-1S′。
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the method, when the satellite-borne GNSS-R mirror reflection point is calculated, the Newton iteration method-based mirror reflection point calculation method is adopted, so that the convergence rate of iterative calculation is increased, the calculation efficiency is improved, the time consumption is low, and the method is suitable for satellite-borne application of the GNSS-R technology;
(2) the invention adopts the quasi-circular approximate coordinate mapping algorithm to convert the WGS-84 earth ellipsoid coordinate system into the unit sphere coordinate system, basically eliminates the influence of the non-circular ellipsoid of the earth on the calculation of the mirror reflection point, and improves the calculation precision of the mirror reflection point.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a graphical representation of the geometric relationship of the specular reflection points calculated in a unit sphere coordinate system;
FIG. 2 is a calculation accuracy analysis of mirror reflection points by a quasi-circle approximation Newton iteration method;
FIG. 3 is a diagram illustrating the main steps of a quasi-circular approximate coordinate mapping method;
FIG. 4 is a flow chart of the calculation of the specular reflection point by the quasi-circular Newton's iteration method.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
As shown in fig. 3, a method for calculating a satellite-borne GNSS-R specular reflection point based on a quasi-circular near newton iteration method mainly includes three steps of quasi-circular approximate coordinate mapping, newton iteration method calculation of specular reflection point, and specular reflection point ellipsoid coordinate mapping.
(1) Quasi-circular approximate coordinate mapping refers to mapping the position of a navigation satellite and the position of a GNSS-R receiver to a unit spherical coordinate system, and because the earth is an ellipsoid and the calculation of a mirror reflection point in the ellipsoid is more complicated, the WGS-84 earth elliptical coordinate system needs to be converted to the unit spherical coordinate system;
(2) the step of calculating the mirror reflection point by a Newton iteration method is to iteratively calculate the mirror reflection point S' in a unit spherical coordinate system, list a function expression f (α) of a geocentric included angle α formed by the mirror reflection point and a navigation satellite by utilizing a cosine law and a sine law according to a geometric relation among the position of the navigation satellite, the position of a GNSS-R receiver and the geocentric, and calculate by utilizing the Newton iteration method;
(3) the mirror reflection point ellipsoid coordinate mapping refers to mapping a mirror reflection point S' calculated in a unit spherical coordinate system into a WGS-84 global elliptical coordinate system to obtain a mirror reflection point S in the WGS-84 global elliptical coordinate system.
As shown in fig. 4, a method for calculating a satellite-borne GNSS-R specular reflection point based on a quasi-circular near newton iteration method mainly includes three steps of quasi-circular approximate coordinate mapping, newton iteration method calculation of a specular reflection point, and specular reflection point ellipsoid coordinate mapping, and a mapping matrix from a WGS-84 earth ellipsoid coordinate system to a unit sphere coordinate system can be expressed as:
Figure BDA0002268675880000091
in the formula (10), a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model. As shown in fig. 1, the specific calculation process of the coordinate mapping is as follows:
(1) navigation satellite position T, GNSS-R receiver position R is mapped from the WGS-84 coordinate system to a unit spherical coordinate system:
T′＝AT
R′＝AR
(2) calculating a mirror reflection point S 'in a unit spherical coordinate system by using a Newton iteration method, wherein the S' is a mirror reflection point coordinate in the unit spherical coordinate system, and a specific process is attached;
(3) and mapping a mirror reflection point S' from a unit spherical coordinate system to a WGS-84 earth elliptical coordinate system:
S＝A-1S′
then S is the mirror reflection point coordinate in the WGS-84 earth ellipsoid coordinate system.
Calculating the specular reflection point in a unit spherical coordinate system:
as shown in fig. 1, in the earth WGS-84 elliptical coordinate system, the navigation satellite position is T, GNSS-R, the receiver position is R, the mapping matrix from the earth WGS-84 coordinate system to the unit circular coordinate system is a, and after coordinate mapping, the navigation satellite position in the unit circular coordinate system is T 'and the GNSS-R receiver position is R'.
Calculating a specular reflection point S ' in a unit spherical coordinate system, wherein O is the geocenter, an included angle formed by T ' and R ' relative to the geocenter O is theta, an included angle formed by T ' and S ' relative to the geocenter O is α, an included angle formed by S ' and R ' relative to the geocenter O is β, and
Figure BDA0002268675880000092
an extension line and
Figure BDA0002268675880000093
the intersection point of (A) is M, and the principle of specular reflection is utilized according to sine and cosine theorems
Figure BDA00022686758800001015
An objective function f (α) may be defined and Newton iterations appliedThe method obtains the specular reflection point S'.
The mapping matrix from the unit spherical coordinate system to the earth WGS-84 coordinate system is A-1The specular reflection point S' of the unit circular coordinate system may be inversely mapped to the specular reflection point S of the WGS-84 coordinate system of the earth.
The step of calculating the specular reflection point S' in the unit sphere coordinate system is as follows:
a) in a unit spherical coordinate system, the coordinates of points T 'and R' are known, and the coordinates are obtained
Figure BDA0002268675880000101
Then ∠ T 'OR' is solved by using the cosine theorem;
Figure BDA0002268675880000102
b) in Δ OT 'S', ∠ S 'OT' is set to α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000103
wherein
Figure BDA0002268675880000104
Equal to the radius 1 of the unit sphere
Figure BDA0002268675880000105
Using sine theorem to obtain:
Figure BDA0002268675880000106
c) in Δ OR 'S', ∠ S 'OR' is set to β, and β is set to θ - α, which can be obtained by the cosine theorem:
Figure BDA0002268675880000107
in the formula
Figure BDA0002268675880000108
Equal to 1, according to the principle of specular reflection
Figure BDA0002268675880000109
Using sine theorem to obtain:
Figure BDA00022686758800001010
d) combination formula
Figure BDA00022686758800001011
And
Figure BDA00022686758800001012
then there are:
Figure BDA00022686758800001013
defining a function:
Figure BDA00022686758800001014
substituting β into θ - α for f (α), and deriving f (α) as:
Figure BDA0002268675880000111
e) the newton iteration formula can be written as:
Figure BDA0002268675880000112
setting an initial value of an iteration
Figure BDA0002268675880000113
When in use
Figure BDA0002268675880000114
Or the number of iterations NαStopping iteration when the number of the iteration is more than or equal to 20,
let α be αk+1。
f) The sine theorem is applied in Δ OT 'M and Δ OR' M, respectively:
Figure BDA0002268675880000115
Figure BDA0002268675880000116
order:
Figure BDA0002268675880000117
the coordinates of the M points are:
Figure BDA0002268675880000118
in the formula, T ' and R ' are coordinates of the navigation satellite and the GNSS-R receiver in a unit sphere coordinate system, respectively, the coordinates of the specular reflection point S ' on the unit sphere can be obtained:
Figure BDA0002268675880000119
the embodiment also compares the calculation efficiency and the calculation precision of 4 methods, namely a diagonal bisector method, a quasi-circle approximate line bisector method, a Newton iteration method and a quasi-circle approximate Newton iteration method, wherein the coordinate of the navigation satellite is T (-14849242.405,14849242.405,36373066.959), the coordinate of the GNSS-R receiver is R (-4207851.668,4207851.668,3435696.500), the specular reflection point calculation of all methods is performed in matlab, the numerical calculation results of the 4 algorithms are shown in table 1, the coordinate of the specular reflection point calculated by the quasi-circle approximation newton iteration method is S (-3284497.912,3949634.542,3767944.885), the position accuracy is-2 km, and the accuracy of the spatial transmission distance is 1.448m, since the accuracy of the spatial transmission distance has a greater influence on the estimation of the loop parameters of the reflected signal processing, especially on the estimation of the delay of the reflected path, the calculation accuracy is more critical, so the quasi-circle approximation Newton iteration method is a mirror reflection point calculation method with high accuracy.
TABLE 1 Performance comparison of different algorithms
Figure BDA0002268675880000121
As can be seen from Table 1, the quasi-circle approximate Newton iteration method has high calculation efficiency and calculation accuracy, the calculation time is 0.003664s, which is obviously lower than the calculation time of the angular bisector method 0.073176 s; FIG. 2 analyzes the calculation accuracy of the mirror reflection point of the quasi-circle approximate Newton iteration method, the calculation accuracy is superior to the accuracy level of the Newton iteration method to 6km, the comprehensive performance of the quasi-circle approximate Newton iteration method is equivalent to that of the quasi-circle approximate line segment dichotomy, the method is the satellite-borne GNSS-R mirror reflection point calculation method with excellent performance, and a new calculation scheme is provided for the satellite-borne GNSS-R mirror reflection point calculation.
The embodiment also provides a system for calculating the satellite-borne GNSS-R specular reflection point based on the quasi-circle approximately newton iteration method, which includes: the first module is used for mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to a position R' of the unit spherical coordinate system from the WGS-84 coordinate system; the second module is used for calculating a mirror reflection point S ' in a unit spherical coordinate system by using a Newton iteration method according to the position T ' and the position R '; and the third module is used for mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system.
Compared with the prior art, the method has the advantages that on one hand, a Newton iteration method is introduced into the calculation of the satellite-borne GNSS-R mirror reflection point for the first time, the Newton iteration method has the characteristics of high iteration efficiency, high convergence speed and the like, the calculation efficiency of the mirror reflection point is improved, and the time consumption is low; on the other hand, the method adopts a quasi-circular approximate coordinate mapping algorithm to eliminate the influence of the non-circular ellipsoid factors of the earth and improve the calculation precision of the specular reflection point.
The method is applied to the development of the satellite-borne GNSS-R receiver, can meet the requirement of on-orbit real-time calculation of the mirror reflection point of the satellite-borne GNSS-R receiver, provides a new high-instantaneity and high-precision calculation method for the calculation of the mirror reflection point of the satellite-borne GNSS-R receiver, and has wide market application prospect.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.

Claims (10)

1. A satellite-borne GNSS-R mirror reflection point calculation method based on a quasi-circle approximately Newton iteration method is characterized by comprising the following steps:
(1) mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to the position R' of the unit spherical coordinate system from the WGS-84 coordinate system;
(2) calculating a mirror reflection point S ' by using a Newton iteration method in a unit spherical coordinate system according to the position T ' and the position R ';
(3) and mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system.
2. The method for calculating the GNSS-R specular reflection point on the satellite based on quasi-circular Newtonian iteration method according to claim 1, wherein: in step (1), position T' is:
T′＝AT；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure FDA0002268675870000011
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
3. The method for calculating the GNSS-R specular reflection point on the satellite based on quasi-circular Newtonian iteration method according to claim 1, wherein: in step (1), position R' is:
R′＝AR；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure FDA0002268675870000012
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
4. The method for calculating the GNSS-R specular reflection point on the satellite based on quasi-circular Newtonian iteration method according to claim 1, wherein: in the step (2), calculating the specular reflection point S ' by using a newton iteration method in the unit spherical coordinate system according to the position T ' and the position R ' specifically includes the following steps:
a) in a unit spherical coordinate system, the coordinates of points T 'and R' are known, and the coordinates are obtained
Figure FDA0002268675870000021
Then ∠ T 'OR' is solved by using the cosine theorem;
Figure FDA0002268675870000022
b) in Δ OT 'S', ∠ S 'OT' is set to α, which can be obtained by the cosine theorem:
Figure FDA0002268675870000023
wherein
Figure FDA0002268675870000024
Equal to the radius 1 of the unit sphere
Figure FDA0002268675870000025
Using sine theorem to obtain:
Figure FDA0002268675870000026
c) in Δ OR 'S', ∠ S 'OR' is set to β, and β is set to θ - α, which can be obtained by the cosine theorem:
Figure FDA0002268675870000027
in the formula
Figure FDA0002268675870000028
Equal to 1, according to the principle of specular reflection
Figure FDA0002268675870000029
Using sine theorem to obtain:
Figure FDA00022686758700000210
d) combination formula
Figure FDA00022686758700000211
And
Figure FDA00022686758700000212
then there are:
Figure FDA00022686758700000213
defining a function:
Figure FDA00022686758700000214
substituting β into θ - α for f (α), and deriving f (α) as:
Figure FDA0002268675870000031
e) the newton iteration formula can be written as:
Figure FDA0002268675870000032
setting an initial value of an iteration
Figure FDA0002268675870000033
When in use
Figure FDA0002268675870000034
Or the number of iterations NαWhen the value is more than or equal to 20, the iteration is stopped, and α is made equal to αk+1；
f) The sine theorem is applied in Δ OT 'M and Δ OR' M, respectively:
Figure FDA0002268675870000035
Figure FDA0002268675870000036
order:
Figure FDA0002268675870000037
the coordinates of the M points are:
Figure FDA0002268675870000038
where T 'and R' are the coordinates of the navigation satellite and GNSS-R receiver respectively in a unit spherical coordinate system,
the coordinates of the specular reflection point S' on the unit sphere can be found:
Figure FDA0002268675870000039
5. the method for calculating the GNSS-R specular reflection point on the satellite based on quasi-circular Newtonian iteration method according to claim 2, wherein: in the step (3), the mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system is: a is-1S′。
6. A satellite-borne GNSS-R mirror reflection point calculation system based on quasi-circle Newton's iteration method is characterized by comprising:
the first module is used for mapping the position T of the navigation satellite to a unit spherical coordinate system from a WGS-84 coordinate system to obtain a position T ', and mapping the position R of the GNSS-R receiver to a position R' of the unit spherical coordinate system from the WGS-84 coordinate system;
the second module is used for calculating a mirror reflection point S ' in a unit spherical coordinate system by using a Newton iteration method according to the position T ' and the position R ';
and the third module is used for mapping the mirror reflection point S' to a WGS-84 earth ellipsoid coordinate system from a unit sphere coordinate system to obtain a mirror reflection point coordinate S in the WGS-84 earth ellipsoid coordinate system.
7. The system according to claim 6, wherein the GNSS-R specular reflection point calculation system is based on quasi-circular Newtonian iteration method, and comprises: position T' is:
T′＝AT；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure FDA0002268675870000041
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
8. The system according to claim 6, wherein the GNSS-R specular reflection point calculation system is based on quasi-circular Newtonian iteration method, and comprises: position R' is:
R′＝AR；
wherein, A is a mapping matrix from WGS-84 earth ellipsoid coordinate system to unit sphere coordinate system, and is expressed as:
Figure FDA0002268675870000042
wherein, a and b are respectively the semimajor axis and the semiminor axis of the WGS-84 earth ellipsoid model.
9. The system according to claim 6, wherein the GNSS-R specular reflection point calculation system is based on quasi-circular Newtonian iteration method, and comprises: the method for calculating the specular reflection point S ' by using the Newton iteration method in the unit spherical coordinate system according to the position T ' and the position R ' specifically comprises the following steps:
a) in a unit spherical coordinate system, the coordinates of points T 'and R' are known, and the coordinates are obtained
Figure FDA0002268675870000051
Then ∠ T 'OR' is solved by using the cosine theorem;
Figure FDA0002268675870000052
b) in Δ OT 'S', ∠ S 'OT' is set to α, which can be obtained by the cosine theorem:
Figure FDA0002268675870000053
wherein
Figure FDA0002268675870000054
Is equal to a unitThe radius of the sphere 1 is
Figure FDA0002268675870000055
Using sine theorem to obtain:
Figure FDA0002268675870000056
c) in Δ OR 'S', ∠ S 'OR' is set to β, and β is set to θ - α, which can be obtained by the cosine theorem:
Figure FDA0002268675870000057
in the formula
Figure FDA0002268675870000058
Equal to 1, according to the principle of specular reflection
Figure FDA0002268675870000059
Using sine theorem to obtain:
Figure FDA00022686758700000510
d) combination formula
Figure FDA00022686758700000511
And
Figure FDA00022686758700000512
then there are:
Figure FDA00022686758700000513
defining a function:
Figure FDA00022686758700000514
substituting β into θ - α for f (α), and deriving f (α) as:
Figure FDA0002268675870000061
e) the newton iteration formula can be written as:
Figure FDA0002268675870000062
setting an initial value of an iteration
Figure FDA0002268675870000063
When in use
Figure FDA0002268675870000064
Or the number of iterations NαWhen the value is more than or equal to 20, the iteration is stopped, and α is made equal to αk+1；
f) The sine theorem is applied in Δ OT 'M and Δ OR' M, respectively:
Figure FDA0002268675870000065
Figure FDA0002268675870000066
order:
Figure FDA0002268675870000067
the coordinates of the M points are:
Figure FDA0002268675870000068
where T 'and R' are the coordinates of the navigation satellite and GNSS-R receiver respectively in a unit spherical coordinate system,
the coordinates of the specular reflection point S' on the unit sphere can be found:
Figure FDA0002268675870000069
10. the system according to claim 7, wherein the computing system comprises: the coordinate S of the specular reflection point in the WGS-84 earth ellipsoid coordinate system is as follows: a is-1S′。
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