CN117405055B - Determination method for rotation center of navigation communication parabolic antenna - Google Patents

Determination method for rotation center of navigation communication parabolic antenna Download PDF

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Publication number
CN117405055B
CN117405055B CN202311446260.7A CN202311446260A CN117405055B CN 117405055 B CN117405055 B CN 117405055B CN 202311446260 A CN202311446260 A CN 202311446260A CN 117405055 B CN117405055 B CN 117405055B
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antenna
coordinates
phase center
point
plane
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CN117405055A (en
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胡正群
张�杰
张丽荣
张亚琨
崔君霞
马利华
庞峰
李婧华
杜晓辉
范江涛
李圣明
胡超
艾国祥
侯金爽
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National Astronomical Observatories of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • 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
    • G01S19/14—Receivers specially adapted for specific applications
    • 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
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position

Abstract

The present disclosure provides a method for determining a rotation center of a navigation communication parabolic antenna, comprising: step S1: determining the phase center coordinates of the antenna; step S2: and calculating the rotation center of the antenna by using a least square method through the fact that the distances between the phase center and the rotation center are equal. According to the measuring method for the rotation center of the navigation communication parabolic antenna, the rotation center is utilized to calculate the satellite azimuth pitching direction of the parabolic antenna of the ground station, so that the direction accuracy can be improved, and better signal quality can be obtained; meanwhile, the accuracy of calculating the space satellite-ground geometric distance can be improved by calculating the satellite-ground distance from the ground station to the satellite by using the rotation center, the effect of pseudo-range differential correction is improved in the forwarding type satellite navigation system, the precision of the virtual satellite atomic clock is improved, and then the navigation positioning precision is improved.

Description

Determination method for rotation center of navigation communication parabolic antenna
Technical Field
The disclosure relates to the technical field of satellite navigation communication, in particular to a method for measuring a rotation center of a parabolic antenna for navigation communication.
Background
The ground main control station of the satellite navigation communication system generally adopts a large-aperture parabolic antenna to transmit and receive signals with a satellite, the accuracy of the antenna in pointing the satellite greatly influences the transmitting and receiving quality of satellite signals, and the antenna pointing is usually calculated based on a certain datum point when determining the antenna pointing. For a navigation communication ground station, a large-caliber parabolic antenna is generally adopted, an electromagnetic radiation field of the parabolic antenna is not an ideal spherical wave, in order to coincide with a parabolic focus in practical application so as to obtain maximum antenna gain, an approximate phase center still needs to be determined, however, the phase center of the antenna can change at any time along with the movement of a target satellite, and the calculation of the pointing direction of the antenna and the calculation of the geometrical distance of a space satellite and earth are not facilitated.
In order to improve the accuracy of the satellite pointing precision and the space satellite-ground geometric distance of the ground station parabolic antenna, particularly in a forwarding satellite navigation system, the correction amount of the navigation uplink pseudo moment is calculated, and the accuracy of the satellite-ground geometric space moment has decisive effects on pseudo-range correction and improving positioning precision when a virtual satellite atomic clock is constructed.
In view of this, in calculating the azimuth elevation direction and the satellite-ground geometrical distance of the antenna, the rotation center of the paraboloid can be selected as the reference point of the ground station, the coordinate of the rotation center is a fixed point for the fixed ground station, the coordinate of the rotation center can be changed along with the change of the reference point for the moving ground station, however, the coordinate of the reference point and the coordinate of the rotation center are relatively fixed, but the rotation center of the paraboloid antenna is a space virtual point suspended in the air, no physical entity structure exists, the measurement is not easy to obtain by an instrument measurement mode, and the measurement can only be realized by a calculation mode.
Disclosure of Invention
First, the technical problem to be solved
In view of this, in order to improve the accuracy of the azimuth elevation pointing precision of the ground station parabolic antenna to the satellite and the accuracy of the space satellite-ground geometric distance, the present disclosure provides a measurement method of the rotation center of the navigation communication parabolic antenna accurately by providing the rotation center of the ground station large-caliber parabolic antenna as the reference for the calculation of the ground station space coordinates.
(II) technical scheme
To achieve the above object, the present disclosure provides a method for determining a rotation center of a parabolic antenna for navigation communication, the method comprising:
step S1: determining the phase center coordinates of the antenna;
step S2: and calculating the rotation center of the antenna by using a least square method through the fact that the distances between the phase center and the rotation center are equal.
In the above scheme, the determining the phase center coordinates of the antenna in step S1 includes:
step S11: calculating azimuth angle and pitch angle of the antenna;
step S12: and calculating the phase center coordinates of the antenna through the azimuth angle and the pitch angle.
In the above scheme, the calculating the azimuth angle and the elevation angle of the antenna in step S11 includes:
step S111: determining a position coordinate P (a) of a ground station antenna calibration point in a geocentric and geodetic fixed coordinate system by a GNSS navigation system 0 ，b 0 ，c 0 ) And the longitude in the geographic coordinate system is lambda, and the latitude isWherein the ground station comprises a fixed station and a mobile station;
step S112: will beThe geocentric fixed coordinate system translates and rotates to point coordinates P (a) 0 ，b 0 ，c 0 ) A horizon coordinate system that is the origin of coordinates;
step S113: the azimuth axis of the parabolic antenna is coincident with the Z axis in the constructed rectangular coordinate system, the plane where the foundation of the antenna is connected with the antenna is horizontal, and when the antenna works in the northern hemisphere and is communicated with the orbit determination satellite, the rotation range of the antenna is used as a reference in the direction of the positive south;
step S114: coordinates S (x) 0 ，y 0 ，z 0 ) Is converted into a calibration point P (a 0 ，b 0 ，c 0 ) The coordinates in the north Tiandong local coordinate system which is the center of a circle are as follows:
step S115: calculating azimuth angle theta of antenna under horizontal coordinate system with calibration point as origin of coordinates AZ And pitch angle theta EL ；
θ AZ ＝arctan(z‘’ 0 /x‘’ 0 ) (2)
Wherein, (x' 0 y‘’ 0 z‘’ 0 ) At the calibration point P (a) for the target satellite 0 ，b 0 ，c 0 ) Coordinates in a north-east local coordinate system with the center of a circle and azimuth angle theta AZ The physical meaning of (2) is the clockwise included angle between the orthographic projection line of the calibration point and the target satellite connecting line on the horizontal plane and the orthonorth direction, and the pitch angle theta EL The physical meaning of (2) is the included angle between the calibration point and the target satellite line and the horizontal line.
In the above scheme, the geocentric fixed coordinate system is translated and rotated to the calibrated point position coordinate P (a) 0 ，b 0 ，c 0 ) In a horizontal coordinate system with the origin of coordinates, the south is rightThe horizontal direction is the X-axis direction, the forward direction is the Y-axis direction, the vertical upward direction is the Z-direction, a rectangular coordinate system is established, and a new local coordinate system is established, and the method comprises the following steps:
step S1121: translating the geocenter to the calibration point according to the geocenter geofixed coordinates of the calibration point, and at the moment, translating the origin of coordinates from the geocenter to the calibration point;
step S1122: the coordinate system rotates by lambda+90 degrees anticlockwise around the Z axis;
step S1123: the coordinate system rotates anticlockwise around the X-axisThus, the calibration point P (a) 0 ，b 0 ，c 0 ) The northeast and north day coordinate system is the origin;
step S1124: the northeast coordinate system rotates 90 degrees counterclockwise around the Z axis;
step S1125: the coordinate system rotates 90 degrees anticlockwise around the X axis; thus, the calibration point P (a) 0 ，b 0 ，c 0 ) Is a north-east coordinate system of (a) to obtain a calibration point P (a) 0 ，b 0 ，c 0 ) A local coordinate system at.
In the above scheme, in step S12, the calculating the phase center coordinates of the antenna through the azimuth angle and the pitch angle includes:
step S121: according to the design structure of the antenna, the projection of the pitching axis of the antenna on the horizontal plane is obtained to P (x) 0 ，y 0 ，z 0 ) The distance between the points is L 1 The vector is expressed asProjection in vertical direction to P (x 0 ，y 0 ，z 0 ) The distance between the points is L 2 The vector is denoted +.>The distance from the antenna phase center to the antenna pitching axis is L 3 The vector is denoted +.>The expression of which is given by formula (4);
wherein,in terms of position coordinates P (a 0 ，b 0 ，c 0 ) The unit vector of the antenna phase center to be solved in the xyz direction is in the north-east local horizon coordinate system of the origin.
Step S122: according to the vector definition, the position coordinate P (a 0 ，b 0 ，c 0 ) The coordinates of the phase center of the antenna are in a north-east local horizon coordinate system of an origin;
wherein L is 1 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the horizontal plane, L 2 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the vertical plane, L 3 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) Distance of point to antenna pitch axis, θ AZ Azimuth angle, θ, of the antenna EL Is the pitch angle of the antenna.
In the above scheme, the determining the phase center coordinates of the antenna in step S1 includes:
step S101: measuring the coordinates of M points on the paraboloid to obtain the polar coordinates of the M points;
step S102: calculating a normal vector of the M point according to the included angle between the phase center and the M point relative to the connecting line between the phase center and the origin;
step S103: calculating projection coordinates of the phase center in an xz plane, a zy plane and an xy plane according to the M point coordinates and the normal vector; and
step S104: and obtaining the phase center coordinates of the antenna according to least square surface fitting.
In the above solution, in step S101, the measuring the coordinates of the M point on the paraboloid to obtain the polar coordinates of the M point includes:
step S1011: taking the vertex of a parabolic surface of an antenna reflector as an origin, taking the east-west direction of the parabolic surface antenna as an X axis, taking the north-north direction as a Y axis, and taking the upward direction as a Z axis, and constructing a local coordinate system;
step S1012: determining the coordinate of a reflection point M on a paraboloid, converting the coordinate into the coordinate under a local coordinate system, wherein the distance between the M point and the phase center is r f Expressed as:
the polar coordinates of the paraboloid are expressed as (r f ，θ f )，θ f And f is the focal length of the parabolic antenna, and is the included angle between the phase center and the M point and the connecting line between the phase center and the origin.
In the above scheme, in step S102, calculating the normal vector of M point according to the included angle between the phase center and the M point with respect to the line connecting the phase center and the origin, includes:
step S1021: in the local coordinate system constructed in step S1011, the reflection lines of the radiation of the phase center reflected by the M points are all parallel to the parabolic axis, and the incident angle α of the M points can be expressed on the xz plane s And reflection angle alpha r ：
Step S1022: according to the M-point incidence angle alpha s And reflection angle alpha r Normal vector after normalization of cosine and M points relative to phase centerPolar parameter representing M point:
step S1023: according to the normalized definition, solving the normal vector of the M point unit:
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The physical meaning of which can be expressed as the reflection of an electromagnetic wave by a phase center by a paraboloid, all of the emitted waves being parallel to the axis of the paraboloid, with the M point being in the negative direction of the polar axis.
In the above scheme, in step S103, calculating the projection coordinates of the phase center in the xz plane, the zy plane and the xy plane according to the M-point coordinates and the normal vector includes:
according to the unit normal vector, solving a vector of the M point to the phase center, and according to the projection of the coordinate of the M point on the xz plane, the zy plane and the xy plane, solving the projection coordinate of the phase center on the xz plane, the zy plane and the xy plane;
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The phase center is in the negative direction of the polar axis.
In the above scheme, the step S104 of obtaining the phase center coordinates of the antenna according to the least square surface fitting includes:
a. collecting projection point coordinates of M points on an xz plane and a zy plane;
b. fitting phase center coordinates to the xz plane according to equation (14)
c. Fitting phase center coordinates to the zy plane according to equation (14)
d. Calculating estimated coordinates of phase center
e. Repeating the steps a-d on the xz plane, the xy plane, the zy plane and the xy plane respectively, calculating the coordinates of the phase center, obtaining three calculated estimated coordinates of the phase center, and taking the average value as the final calculated coordinates of the phase center.
In the above scheme, in the step S2, the distance between the phase center and the rotation center is equal, and the calculating the rotation center of the antenna by using the least square method includes:
step S21: in the process of tracking a satellite, the phase center of the ground station parabolic antenna is consistent with the track of the satellite, and is in an 8 shape, n (n is more than or equal to 3) points are arbitrarily taken on the phase center track, and an equation set (6) is listed according to the fact that the distances from coordinate points on the phase center track to the rotation center of the antenna are equal;
wherein (a) xn ，a yn ，a zn )，(b xn ，b yn ，b zn ) Coordinates of the phase center of the antenna;
step S22: solving the equation set (6) according to the least square method to obtain a position coordinate P (a 0 ，b 0 ，c 0 ) And the position coordinates (x, y, z) of the rotation center of the antenna are in a north-east local horizon coordinate system with the origin.
In the above scheme, in step S22, the solution to the equation set (6) according to the least square method is obtained to obtain the position coordinate P (a 0 ，b 0 ，c 0 ) The position coordinates (x, y, z) of the rotation center of the antenna in the north-east local horizon coordinate system, which is the origin, include:
step S221: simplifying and arranging the equation set (6) to obtain an equation set (7);
step S222: writing equation set (7) into a matrix form:
A*W＝D (8)
wherein,
step S223: carrying out least square method solution on the formula (8), and finally obtaining coordinates (x, y, z) of the rotation center of the antenna through the solution;
W＝(A T A) -1 A T D (9)
wherein A is T Is the transposed matrix of array a.
(III) beneficial effects
From the above technical solution, the method for measuring the rotation center of the navigation communication parabolic antenna provided by the present disclosure has the following beneficial effects:
1. according to the measuring method for the rotation center of the navigation communication parabolic antenna, the rotation center is used for calculating the satellite azimuth pitching direction of the parabolic antenna of the ground station, the direction accuracy can be improved, and better signal quality can be obtained.
2. According to the measuring method for the rotation center of the navigation communication parabolic antenna, the accuracy of calculating the space satellite-ground geometric distance can be improved by calculating the satellite-ground distance from the ground station to the satellite by using the rotation center, the effect of pseudo range differential correction is improved in the forwarding type satellite navigation system, the precision of a virtual satellite atomic clock is improved, and then the navigation positioning precision is improved.
Drawings
For a more complete understanding of the present disclosure and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a flow chart of a method of determining a center of rotation of a navigation communication parabolic antenna provided by the present disclosure;
FIG. 2 schematically illustrates a flow chart of a method of determining a center of rotation of a navigation communication parabolic antenna according to a first embodiment of the present disclosure;
FIG. 3 schematically illustrates a flow chart of a method of constructing a local coordinate system referenced to calibration points in the embodiment illustrated in FIG. 2;
fig. 4 schematically illustrates a flow chart of a method of determining a center of rotation of a navigation communication parabolic antenna according to a second embodiment of the present disclosure.
Detailed Description
Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. It should be understood that the description is only exemplary and is not intended to limit the scope of the present disclosure. In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the embodiments of the present disclosure. It may be evident, however, that one or more embodiments may be practiced without these specific details. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the concepts of the present disclosure.
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, fig. 1 is a flowchart of a method for determining a rotation center of a navigation communication parabolic antenna provided by the present disclosure, the method comprising the steps of:
step S1: determining the phase center coordinates of the antenna;
in this step, determining the phase center coordinates of the antenna may take any of two ways:
mode one: calculating azimuth angle and pitch angle of the antenna; and calculating the phase center coordinates of the antenna through the azimuth angle and the pitch angle.
Mode two: measuring the coordinates of M points on the paraboloid to obtain the polar coordinates of the M points; calculating a normal vector of the M point according to the included angle between the phase center and the M point relative to the connecting line between the phase center and the origin; calculating projection coordinates of the M points on an xz plane, a zy plane and an xy plane according to the M point coordinates and the normal vector; and obtaining the phase center coordinates of the antenna according to least square surface fitting.
Step S2: and calculating the rotation center of the antenna by using a least square method through the fact that the distances between the phase center and the rotation center are equal.
The method for determining the rotation center of the navigation communication parabolic antenna provided by the present disclosure will be described in detail below in one and the other ways as one embodiment, with respect to two ways of determining the phase center coordinates of the antenna in step S1.
In an exemplary embodiment of the present disclosure, a method for determining a rotation center of a parabolic antenna for navigation communication is provided, in which a phase center coordinate of the antenna is determined in the above-mentioned manner, and in particular, as shown in fig. 2, the method includes the steps of:
step S1: the method for determining the phase center coordinates of the antenna specifically comprises the following steps:
step S11: the method for calculating the azimuth angle and the pitch angle of the antenna specifically comprises the following steps:
step S111: determining a position coordinate P (a) of a ground station antenna calibration point in a geocentric and geodetic fixed coordinate system by a GNSS navigation system 0 ，b 0 ，c 0 ) And the longitude in the geographic coordinate system is lambda, and the latitude isWherein the ground station comprises a fixed station and a mobile station;
step S112: translating and rotating the geocentric geodetic coordinate system to a calibrated point position coordinate P (a 0 ，b 0 ，c 0 ) A horizon coordinate system that is the origin of coordinates;
wherein, the geocentric fixed coordinate system is translated and rotated to the position coordinate P (a) 0 ，b 0 ，c 0 ) In a coordinate origin horizontal coordinate system, the forward south horizontal direction is the X-axis direction, the forward east direction is the Y-axis direction, the vertical upward direction is the Z-axis direction, a rectangular coordinate system is established, and a new local coordinate system is constructed, specifically as shown in fig. 3, the method comprises the following steps:
step S1121: translating the geocenter to the calibration point according to the geocenter geofixed coordinates of the calibration point, and at the moment, translating the origin of coordinates from the geocenter to the calibration point;
step S1122: the coordinate system rotates by lambda+90 degrees anticlockwise around the Z axis;
step S1123: the coordinate system rotates anticlockwise around the X-axisThus, the calibration point P (a) 0 ，b 0 ，c 0 ) The northeast and north day coordinate system is the origin;
step S1124: the northeast coordinate system rotates 90 degrees counterclockwise around the Z axis;
step S1125: the coordinate system rotates 90 degrees anticlockwise around the X axis; thus, the calibration point P (a) 0 ，b 0 ，c 0 ) Is a north-east coordinate system of (a) to obtain a calibration point P (a) 0 ，b 0 ，c 0 ) A local coordinate system at.
Step S113: the azimuth axis of the parabolic antenna is coincident with the Z axis in the constructed rectangular coordinate system, the plane where the foundation of the antenna is connected with the antenna is horizontal, and when the antenna works in the northern hemisphere and is communicated with the orbit determination satellite, the rotation range of the antenna is the reference of the direction of the right south;
step S114: coordinates S (x) 0 ，y 0 ，z 0 ) Is converted into a calibration point P (a 0 ，b 0 ，c 0 ) The coordinates in the north Tiandong local coordinate system which is the center of a circle are as follows:
step S115: calculating azimuth angle theta of antenna under coordinate system with calibration point as origin AZ And pitch angle theta EL ；
θ AZ ＝arctan(z‘’ 0 /x‘’ 0 ) (2)
Wherein, (x' 0 y‘’ 0 z‘’ 0 ) At the calibration point P (a) for the target satellite 0 ，b 0 ，c 0 ) Coordinates in a north-east local coordinate system with the center of a circle and azimuth angle theta AZ The physical meaning of the method is expressed as the clockwise included angle between the orthographic projection line of the calibration point and the target satellite connecting line on the horizontal plane and the orthonorth direction, and the pitch angle theta EL The physical meaning of the method is expressed as an included angle between a calibration point and a connecting line of a target satellite and a horizontal line.
Step S12: the phase center coordinates of the antenna are calculated through the azimuth angle and the pitch angle, and the method specifically comprises the following steps:
step S121: according to the design structure of the antenna, the projection of the pitching axis of the antenna on the horizontal plane is obtained to P (x) 0 ，y 0 ，z 0 ) The distance between the points is L 1 The vector is expressed asProjection in vertical direction to P (x 0 ，y 0 ，z 0 ) The distance between the points is L 2 The vector is denoted +.>The distance from the antenna phase center to the antenna pitching axis is L 3 The vector is denoted +.>The expression of which is given by formula (4);
wherein,in terms of position coordinates P (a 0 ，b 0 ，c 0 ) The unit vector of the antenna phase center to be solved in the xyz direction is in the north-east local horizon coordinate system of the origin.
Step S122: according to the vector definition, the position coordinate P (a 0 ，b 0 ，c 0 ) The coordinates of the phase center of the antenna are in a north-east local horizon coordinate system of an origin;
wherein L is 1 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the horizontal plane, L 2 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the vertical plane, L 3 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) Distance of point to antenna pitch axis, θ AZ Azimuth angle, θ, of the antenna EL Is the pitch angle of the antenna.
Step S2: the rotation center of the antenna is calculated by a least square method through the fact that the distances between the phase center and the rotation center are equal, and the method specifically comprises the following steps:
step S21: in the process of tracking a satellite, the phase center of the ground station parabolic antenna is consistent with the track of the satellite, and is in an 8 shape, n (n is more than or equal to 3) points are arbitrarily taken on the phase center track, and an equation set (6) is listed according to the fact that the distances from coordinate points on the phase center track to the rotation center of the antenna are equal;
step S22: solving the equation set (6) according to the least square method to obtain a position coordinate P (a 0 ，b 0 ，c 0 ) The position coordinates (x, y, z) of the rotation center of the antenna in the north-east local horizon coordinate system which is the origin;
wherein (a) xn ，a yn ，a zn )，(b xn ，b yn ，b zn ) Is the coordinates of the phase center of the antenna.
In step S22, the equation set (6) is solved according to the least square method to obtain the position coordinates P (a 0 ，b 0 ，c 0 ) The position coordinates (x, y, z) of the rotation center of the antenna in the north-east local horizon coordinate system, which is the origin, include:
step S221: simplifying and arranging the equation set (6) to obtain an equation set (7);
step S222: writing equation set (7) into a matrix form:
A*W＝D (8)
wherein,
step S223: carrying out least square method solution on the formula (8), and finally obtaining coordinates (x, y, z) of the rotation center of the antenna through the solution;
W＝(，A T A) -1 A T D (9)
wherein A is T Is the transposed matrix of array a.
The rotation center coordinates of the ground station parabolic antenna calculated by the above steps in the embodiments shown in fig. 2 and 3 are calculated as the position coordinates P (a 0 ，b 0 ，c 0 ) And (3) taking the coordinates of the rotation center as the coordinates of the origin under the north-east local horizon coordinate system, and carrying out multiple iterations until the difference value of the coordinates of the rotation center of the front and back two times reaches a preset threshold value, so as to finally obtain the accurate coordinates of the rotation center of the antenna.
In another exemplary embodiment of the present invention, a method for determining a rotation center of a navigation communication parabolic antenna may also be implemented, in which the phase center coordinates of the antenna are determined in the second manner, as shown in fig. 4, and fig. 4 schematically illustrates a method flowchart for determining a rotation center of a navigation communication parabolic antenna according to a second embodiment of the present disclosure, where the method includes the following steps:
step S1: the method for determining the phase center coordinates of the antenna specifically comprises the following steps:
step S101: measuring the coordinates of M points on the paraboloid to obtain the polar coordinates of the M points;
in this step, the measuring the coordinates of the M points on the paraboloid to obtain the polar coordinates of the M points includes:
step S1011: taking the vertex of a parabolic surface of an antenna reflector as an origin, taking the east-west direction of the parabolic surface antenna as an X axis, taking the north-north direction as a Y axis, and taking the upward direction as a Z axis, and constructing a local coordinate system;
step S1012: determining the coordinate of a reflection point M on a paraboloid, converting the coordinate into the coordinate under a local coordinate system, wherein the distance between the M point and the phase center is r f Expressed as:
the paraboloid is represented by polar coordinates (r f ，θ f )，θ f And f is the focal length of the parabolic antenna, and is the included angle between the phase center and the M point and the connecting line between the phase center and the origin.
Step S102: calculating a normal vector of the M point according to the included angle between the phase center and the M point relative to the connecting line between the phase center and the origin;
in this step, the calculating the normal vector of the M point according to the included angle between the phase center and the M point relative to the line connecting the phase center and the origin includes:
step S1021: in the local coordinate system constructed in step S1011, the reflection lines of the radiation of the phase center reflected by the M points are all parallel to the parabolic axis, and the incident angle α of the M points can be expressed on the xz plane s And reflection angle alpha r ：
Step S1022: according to the M-point incidence angle alpha s And reflection angle alpha r Normal vector after normalization of cosine and M points relative to phase centerPolar parameter representing M point:
step S1023: according to the normalized definition, solving the normal vector of the M point unit:
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The physical meaning is that after electromagnetic waves emitted by the phase center are reflected by the paraboloid, all emitted waves are parallel to the axis of the paraboloid, wherein the M point is in the negative direction of the polar axis.
Step S103: calculating projection coordinates of the phase center in an xz plane, a zy plane and an xy plane according to the M point coordinates and the normal vector;
in this step, the calculating the projection coordinates of the phase center in the xz plane, the zy plane and the xy plane according to the M-point coordinates and the normal vector includes: according to the unit normal vector, solving a vector of the M point to the phase center, and according to the projection of the coordinate of the M point on the xz plane, the zy plane and the xy plane, solving the projection coordinate of the phase center on the xz plane, the zy plane and the xy plane;
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The phase center is in the negative direction of the polar axis.
Step S104: and obtaining the phase center coordinates of the antenna according to least square surface fitting.
In this step, the obtaining the phase center coordinates of the antenna according to the least square surface fitting includes:
1. collecting projection point coordinates of M points on an xz plane and a zy plane;
2. fitting phase center coordinates to the xz plane according to equation (14)
3. Fitting phase center coordinates to the zy plane according to equation (14)
4. Calculating estimated coordinates of phase center
5. Repeating the steps 1-4 on the xz plane, the xy plane, the zy plane and the xy plane respectively, calculating the coordinates of the phase center, obtaining the estimated coordinates of the phase center calculated for three times, and taking the average value as the final calculated coordinates of the phase center.
Step S2: calculating the rotation center of the antenna by using a least square method through the fact that the distances between the phase center and the rotation center are equal; step S2 in the present embodiment is the same as step S2 in the embodiment shown in fig. 2 and fig. 3, and the technical solutions adopted by both are the same, and will not be described here again.
By the method of the embodiment, the method for measuring the rotation center of the navigation communication parabolic antenna can improve the pointing precision and obtain better signal quality by calculating the opposite star azimuth pitching pointing of the ground station parabolic antenna by using the rotation center; meanwhile, the accuracy of calculating the space satellite-ground geometric distance can be improved by calculating the satellite-ground distance from the ground station to the satellite by using the rotation center, the effect of pseudo-range differential correction is improved in the forwarding type satellite navigation system, the precision of the virtual satellite atomic clock is improved, and then the navigation positioning precision is improved.
Thus far, the disclosure has been described in detail with reference to the accompanying drawings. From the foregoing description, those skilled in the art will readily appreciate the present disclosure.
It should be noted that, in the drawings or the text of the specification, implementations not shown or described are all forms known to those of ordinary skill in the art, and not described in detail. Furthermore, the above definitions of the elements are not limited to the specific structures, shapes or modes mentioned in the embodiments, and may be simply modified or replaced by those of ordinary skill in the art.
While the present disclosure has been shown and described with reference to certain exemplary embodiments thereof, various changes in form and details may be made therein without departing from the spirit and scope of the present disclosure as defined by the appended claims and their equivalents. The scope of the disclosure should, therefore, not be limited to the above-described embodiments, but should be determined not only by the following claims, but also by the equivalents of the following claims.

Claims (11)

1. A method for determining the center of rotation of a parabolic antenna for navigational communication, comprising:
step S1: determining the phase center coordinates of the antenna;
step S2: calculating the rotation center of the antenna by using a least square method through the fact that the distances between the phase center and the rotation center are equal;
in step S2, the distance between the phase center and the rotation center is equal, and the calculation of the rotation center of the antenna by using the least square method includes:
step S21: the phase center of the ground station parabolic antenna is consistent with the track of the satellite in the process of tracking the satellite, and is in an 8 shape, n points are arbitrarily taken on the track of the phase center, n is more than or equal to 3, and an equation set (6) is listed according to the fact that the distances from coordinate points on the track of the phase center to the rotation center of the antenna are equal;
wherein (a) xn ，a yn ，a zn )，(b xn ，b yn ，b zn ) Coordinates of the phase center of the antenna;
step S22: solving the equation set (6) according to the least square method to obtain a position coordinate P (a 0 ，b 0 ，c 0 ) And the position coordinates (x, y, z) of the rotation center of the antenna are in a north-east local horizon coordinate system with the origin.
2. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 1, wherein determining the phase center coordinates of the antenna in step S1 comprises:
step S11: calculating azimuth angle and pitch angle of the antenna;
step S12: and calculating the phase center coordinates of the antenna through the azimuth angle and the pitch angle.
3. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 2, wherein the calculating the azimuth angle and the pitch angle of the antenna in step S11 comprises:
step S111: determining a position coordinate P (a) of a ground station antenna calibration point in a geocentric and geodetic fixed coordinate system by a GNSS navigation system 0 ，b 0 ，c 0 ) And the longitude in the geographic coordinate system is lambda, and the latitude isWherein the ground station comprises a fixed station and a mobile station;
step S112: translating and rotating the geocentric geodetic coordinate system to a calibrated point position coordinate P (a 0 ，b 0 ，c 0 ) A horizon coordinate system that is the origin of coordinates;
step S113: the azimuth axis of the parabolic antenna is coincident with the Z axis in the constructed rectangular coordinate system, the plane where the foundation of the antenna is connected with the antenna is horizontal, and when the antenna works in the northern hemisphere and is communicated with the orbit determination satellite, the rotation range of the antenna is used as a reference in the direction of the positive south;
step S114: coordinates S (x) 0 ，y 0 ，z 0 ) Is converted into a calibration point P (a 0 ，b 0 ，c 0 ) The coordinates in the north Tiandong local coordinate system which is the center of a circle are as follows:
step S115: calculating azimuth angle theta of antenna under horizontal coordinate system with calibration point as origin of coordinates AZ And pitch angle theta EL ；
θ AZ ＝arctan(z‘’ 0 /x‘’ 0 ) (2)
Wherein, (x' 0 ，y‘’ 0 ，z‘’ 0 ) At the calibration point P (a) for the target satellite 0 ，b 0 ，c 0 ) Coordinates in a north-east local coordinate system with the center of a circle and azimuth angle theta AZ The physical meaning of (2) is the clockwise included angle between the orthographic projection line of the calibration point and the target satellite connecting line on the horizontal plane and the orthonorth direction, and the pitch angle theta EL The physical meaning of (2) is the included angle between the calibration point and the target satellite line and the horizontal line.
4. A method according to claim 3, wherein in step S112, the geodetic fixed coordinate system is translated and rotated to the calibration point position coordinates P (a 0 ，b 0 ，c 0 ) In a horizontal coordinate system which is a coordinate origin, the forward south horizontal direction is the X-axis direction, the forward east direction is the Y-axis direction, the vertical upward direction is the Z-direction, a rectangular coordinate system is established, and a new local coordinate system is constructed, and the method comprises the following steps:
step S1121: translating the geocenter to the calibration point according to the geocenter geofixed coordinates of the calibration point, and at the moment, translating the origin of coordinates from the geocenter to the calibration point;
step S1122: the coordinate system rotates by lambda+90 degrees anticlockwise around the Z axis;
step S1123: the coordinate system rotates anticlockwise around the X-axisThus, the calibration point P (a) 0 ，b 0 ，c 0 ) The northeast and north day coordinate system is the origin;
step S1124: the northeast coordinate system rotates 90 degrees counterclockwise around the Z axis;
step S1125: the coordinate system rotates 90 degrees anticlockwise around the X axis; thus, the calibration point P (a) 0 ，b 0 ，c 0 ) Is a north-east coordinate system of (a) to obtain a calibration point P (a) 0 ，b 0 ，c 0 ) A local coordinate system at.
5. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 2, wherein the calculating the phase center coordinates of the antenna by the azimuth angle and the pitch angle in step S12 comprises:
step S121: according to the design structure of the antenna, the projection of the pitching axis of the antenna on the horizontal plane is obtained to P (x) 0 ，y 0 ，z 0 ) The distance between the points is L 1 The vector is expressed asProjection in vertical direction to P (x 0 ，y 0 ，z 0 ) The distance between the points is L 2 The vector is expressed asThe distance from the antenna phase center to the antenna pitching axis is L 3 The vector is denoted +.>The expression of which is given by formula (4);
wherein,in terms of position coordinates P (a 0 ，b 0 ，c 0 ) Under the north-east local horizon coordinate system with the origin, the unit vector of the antenna phase center to be solved in the xyz direction;
step S122: according to the vector definition, the position coordinate P (a 0 ，b 0 ，c 0 ) The coordinates of the phase center of the antenna are in a north-east local horizon coordinate system of an origin;
wherein L is 1 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the horizontal plane, L 2 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) The distance from the point to the projection line of the antenna pitch axis on the vertical plane, L 3 Expressed as position origin coordinates P (a 0 ，b 0 ，c 0 ) Distance of point to antenna pitch axis, θ AZ Azimuth angle, θ, of the antenna EL Is the pitch angle of the antenna.
6. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 1, wherein determining the phase center coordinates of the antenna in step S1 comprises:
step S101: measuring the coordinates of M points on the paraboloid to obtain the polar coordinates of the M points;
step S102: calculating a normal vector of the M point according to the included angle between the phase center and the M point relative to the connecting line between the phase center and the origin;
step S103: calculating projection coordinates of the phase center in an xz plane, a zy plane and an xy plane according to the M point coordinates and the normal vector; and
step S104: and obtaining the phase center coordinates of the antenna according to least square surface fitting.
7. The method according to claim 6, wherein the measuring M-point coordinates on the paraboloid in step S101, obtaining the polar coordinates of the M-point, comprises:
step S1011: taking the vertex of a parabolic surface of an antenna reflector as an origin, taking the east-west direction of the parabolic surface antenna as an X axis, taking the north-north direction as a Y axis, and taking the upward direction as a Z axis, and constructing a local coordinate system;
step S1012: determining the coordinate of a reflection point M on a paraboloid, converting the coordinate into the coordinate under a local coordinate system, wherein the distance between the M point and the phase center is r f Expressed as:
the polar coordinates of the paraboloid are expressed as (r f ，θ f )，θ f And f is the focal length of the parabolic antenna, and is the included angle between the phase center and the M point and the connecting line between the phase center and the origin.
8. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 7, wherein in step S102, calculating the normal vector of M point according to the angle between the phase center and M point and the line connecting the phase center and the origin comprises:
step S1021: in the local coordinate system constructed in step S1011, the reflection lines of the radiation of the phase center reflected by the M points are all parallel to the parabolic axis, and the incident angle α of the M points can be expressed on the xz plane s And reflection angle alpha r ：
Step S1022: according to the M-point incidence angle alpha s And reflection angle alpha r Normal vector after normalization of cosine and M points relative to phase centerPolar parameter representing M point:
step S1023: according to the normalized definition, solving the normal vector of the M point unit:
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The physical meaning of which can be expressed as the reflection of an electromagnetic wave by a phase center by a paraboloid, all of the emitted waves being parallel to the axis of the paraboloid, with the M point being in the negative direction of the polar axis.
9. The method for determining a rotation center of a navigation communication parabolic antenna according to claim 8, wherein in step S103, the calculating projection coordinates of the phase center in the xz plane, the zy plane and the xy plane according to the M-point coordinates and the normal vector includes:
according to the unit normal vector, solving a vector of the M point to the phase center, and according to the projection of the coordinate of the M point on the xz plane, the zy plane and the xy plane, solving the projection coordinate of the phase center on the xz plane, the zy plane and the xy plane;
wherein θ f The size of the polar diameter is as follows, and the included angle between the phase center and the M point is relative to the connecting line between the phase center and the originThe polar angle is +.>The phase center is in the negative direction of the polar axis.
10. The method for determining the rotation center of a navigation communication parabolic antenna according to claim 9, wherein the obtaining the phase center coordinates of the antenna according to the least square surface fitting in step S104 comprises:
a. collecting projection point coordinates of M points on an xz plane and a zy plane;
b. fitting phase center coordinates to the xz plane according to equation (14)
c. Fitting phase center coordinates to the zy plane according to equation (14)
d. Calculating estimated coordinates of phase center
e. Repeating the steps a-d on the xz plane, the xy plane, the zy plane and the xy plane respectively, calculating the coordinates of the phase center, obtaining three calculated estimated coordinates of the phase center, and taking the average value as the final calculated coordinates of the phase center.
11. The method for determining the center of rotation of a navigation communication parabolic antenna according to claim 1, wherein in step S22, the equation set (6) is solved according to a least square method to obtain the position coordinate P (a 0 ，b 0 ，c 0 ) The position coordinates (x, y, z) of the rotation center of the antenna in the north-east local horizon coordinate system, which is the origin, include:
step S221: simplifying and arranging the equation set (6) to obtain an equation set (7);
step S222: writing equation set (7) into a matrix form:
A*W＝D (8)
wherein,
step S223: carrying out least square method solution on the formula (8), and finally obtaining coordinates (x, y, z) of the rotation center of the antenna through the solution;
W＝(A T A) -1 A T D (9)
wherein A is T Is the transposed matrix of matrix a.
CN202311446260.7A 2023-11-02 2023-11-02 Determination method for rotation center of navigation communication parabolic antenna Active CN117405055B (en)

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