CN111780730B - GNSS three-dimensional lofting positioning method based on ellipsoid calculation - Google Patents

GNSS three-dimensional lofting positioning method based on ellipsoid calculation Download PDF

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CN111780730B
CN111780730B CN202010566206.6A CN202010566206A CN111780730B CN 111780730 B CN111780730 B CN 111780730B CN 202010566206 A CN202010566206 A CN 202010566206A CN 111780730 B CN111780730 B CN 111780730B
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ellipsoid
engineering
measured
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point
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CN111780730A (en
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金卫锋
杨兴旺
张亚东
张献州
陈铮
李超
郑旭东
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Shanghai Railway Beidou Survey Engineering Technology Co ltd
Southwest Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C15/00—Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C15/00—Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
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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
    • G01S19/38—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
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Abstract

The invention discloses a GNSS three-dimensional lofting positioning method based on ellipsoid calculation, which comprises the following steps: s1, constructing an engineering ellipsoid according to the area to be measured; s2, obtaining the geodetic coordinates of the to-be-sampled point by the Gaussian inverse calculation of the plane coordinates of the to-be-sampled point; s3, inputting the geodetic coordinates of the to-be-sampled point into a GNSS system, and positioning the position of an actual engineering point; the invention solves the problem that projection deformation cannot be avoided when a GNSS technology is used for lofting.

Description

GNSS three-dimensional lofting positioning method based on ellipsoid calculation
Technical Field
The invention belongs to the field of measurement, and particularly relates to a GNSS three-dimensional lofting positioning method based on ellipsoid calculation.
Background
With the development of the country, the engineering construction of China is more and more, and the total station or GNSS is adopted for the work of the engineering construction. The step of lofting by using the total station comprises the steps of erecting the total station on a control point, then setting another control point for orientation, inputting coordinates of feature points of the ground object to be measured into the total station, automatically calculating related data by the total station, and lofting the point positions by an observer according to a command prism person. However, the method needs to see through between the station and the sampling point, the Gaussian coordinate has the problem of projection deformation, the working intensity is high, and the efficiency is not high. And the GNSS technology is used for lofting, the perspective between point positions is not needed, the lofting speed is high, the efficiency is high, and the problem of projection deformation cannot be avoided by the technology.
Disclosure of Invention
Aiming at the defects in the prior art, the GNSS three-dimensional lofting positioning method based on ellipsoidal computation solves the problem that projection deformation cannot be avoided when lofting is performed by using a GNSS technology.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a GNSS three-dimensional lofting positioning method based on ellipsoid calculation comprises the following steps:
s1, constructing an engineering ellipsoid according to the area to be measured;
s2, obtaining the geodetic coordinates of the to-be-sampled point by the Gaussian inverse calculation of the plane coordinates of the to-be-sampled point;
and S3, inputting the geodetic coordinates of the to-be-sampled point into the GNSS system, and positioning the position of the actual engineering point.
Further, the step S1 includes the following steps:
s11, calculating the average curvature radius of the region to be measured according to the latitude of the region to be measured;
s12, averaging the geodetic heights of all to-be-sampled points of the region to be measured to serve as the average geodetic height of the region to be measured;
s13, calculating the major-semiaxis and the oblateness of the engineering ellipsoid according to the average curvature radius and the average height of the area to be measured;
and S14, constructing the engineering ellipsoid according to the major semiaxis and the oblateness of the engineering ellipsoid.
Further, the calculation formula of the major-semiaxis of the engineering ellipsoid in the step S13 is as follows:
Figure BDA0002547924990000021
the oblateness of the engineering ellipsoid is as follows:
alpha＝1-a(1-e2)(2)
wherein a is a long semi-axis of an engineering ellipsoid, RmFor national referenceMean radius of curvature of a point of an ellipsoid, HmAverage ground height of region to be measured, BmThe average latitude of the area to be measured, e is the eccentricity of the engineering ellipsoid, and alpha is the oblateness of the engineering ellipsoid.
Further, the formula for calculating the geodetic coordinates of the to-be-sampled point in step S2 is as follows:
Figure BDA0002547924990000022
Figure BDA0002547924990000023
tf＝tanBf (5)
ηf 2＝e2cos2Bf (6)
Figure BDA0002547924990000024
Figure BDA0002547924990000025
wherein y is the ordinate of the to-be-sampled point in the area to be measured, B is the abscissa of the geodetic coordinate of the to-be-sampled point, L is the ordinate of the geodetic coordinate of the to-be-sampled point, tfIs a value of the derivative of the time angle, MfIs a curvature radius derivative value of the fourth prime circle, NfIs the derivative value of the radius of curvature of the meridian, BfLatitude, η, at the base pointfAs a component of the deviation of the perpendicular to the unit circle, L0The central meridian accuracy.
Further, the bottom point latitude BfThe calculation method comprises the following steps:
a1, iteration bottom point latitude
Figure BDA0002547924990000031
Initial value of (2)
Figure BDA0002547924990000032
Is arranged as
Figure BDA0002547924990000033
Wherein i is the number of iterations, X is the meridian arc length measured from the equator, a0Is an intermediate variable;
a2, iteration bottom point latitude
Figure BDA0002547924990000034
Iterating through an iteration formula until:
Figure BDA0002547924990000035
where ε is a minimum threshold;
a3, obtaining the iteration bottom point latitude finally obtained in the step A2
Figure BDA0002547924990000036
Assigning to the bottom point latitude Bf。
Further, the intermediate variable a in the step A10The calculation formula of (2) is as follows:
Figure BDA0002547924990000037
further, the iterative formula in step a2 is:
Figure BDA0002547924990000038
Figure BDA0002547924990000039
wherein F is an iterative latitude function, a2,a4,a6,a8Are all intermediate variables.
Further, the intermediate variable a2,a4,a6,a8The calculation formula of (2) is as follows:
Figure BDA00025479249900000310
Figure BDA00025479249900000311
Figure BDA00025479249900000312
Figure BDA00025479249900000313
the invention has the beneficial effects that:
(1) and constructing a proper ellipsoid according to the area to be measured of the actual engineering, accurately obtaining the geodetic coordinates of the to-be-sampled point through inverse Gaussian calculation, and accurately calculating the latitude through an iteration mode, thereby avoiding the problem of projection deformation.
(2) The invention can obtain results on various projection surfaces according to various projection rules, so that the calculated data has reusability and universality.
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Fig. 1 is a flowchart of a GNSS three-dimensional lofting positioning method based on ellipsoid calculation.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, a GNSS three-dimensional lofting positioning method based on ellipsoid calculation includes the following steps:
s1, constructing an engineering ellipsoid according to the area to be measured;
the step S1 includes the steps of:
s11, calculating the average curvature radius of the region to be measured according to the latitude of the region to be measured;
s12, averaging the geodetic heights of all to-be-sampled points of the region to be measured to serve as the average geodetic height of the region to be measured;
s13, calculating the major-semiaxis and the oblateness of the engineering ellipsoid according to the average curvature radius and the average height of the area to be measured;
the calculation formula of the major-semiaxis of the engineering ellipsoid in the step S13 is as follows:
Figure BDA0002547924990000041
the oblateness of the engineering ellipsoid is as follows:
alpha＝1-a(1-e2)(2)
wherein a is a long semi-axis of an engineering ellipsoid, RmIs the average radius of curvature of one point of a national reference ellipsoid, HmAverage ground height of region to be measured, BmThe average latitude of the area to be measured, e is the eccentricity of the engineering ellipsoid, and alpha is the oblateness of the engineering ellipsoid.
And S14, constructing the engineering ellipsoid according to the major semiaxis and the oblateness of the engineering ellipsoid.
S2, obtaining the geodetic coordinates of the to-be-sampled point by the Gaussian inverse calculation of the plane coordinates of the to-be-sampled point;
the formula for calculating the geodetic coordinates of the to-be-sampled point in step S2 is:
Figure BDA0002547924990000051
Figure BDA0002547924990000052
tf＝tanBf (5)
ηf 2＝e2cos2Bf (6)
Figure BDA0002547924990000053
Figure BDA0002547924990000054
wherein y is the ordinate of the to-be-sampled point in the area to be measured, B is the abscissa of the geodetic coordinate of the to-be-sampled point, L is the ordinate of the geodetic coordinate of the to-be-sampled point, tfIs a value of the derivative of the time angle, MfIs a curvature radius derivative value of the fourth prime circle, NfIs the derivative value of the radius of curvature of the meridian, BfLatitude, η, at the base pointfAs a component of the deviation of the perpendicular to the unit circle, L0The central meridian accuracy.
The bottom point latitude BfThe calculation method comprises the following steps:
a1, iteration bottom point latitude
Figure BDA0002547924990000055
Initial value of (2)
Figure BDA0002547924990000056
Is arranged as
Figure BDA0002547924990000057
Wherein i is the number of iterations, X is the meridian arc length measured from the equator, a0Is an intermediate variable;
intermediate variable a in step A10The calculation formula of (2) is as follows:
Figure BDA0002547924990000058
a2, iteration bottom point latitude
Figure BDA0002547924990000059
Iterating through an iteration formula until:
Figure BDA00025479249900000510
where ε is a minimum threshold;
the iterative formula in the step a2 is:
Figure BDA00025479249900000511
Figure BDA0002547924990000061
wherein F is an iterative latitude function, a2,a4,a6,a8Are all intermediate variables.
The intermediate variable a2,a4,a6,a8The calculation formula of (2) is as follows:
Figure BDA0002547924990000062
Figure BDA0002547924990000063
Figure BDA0002547924990000064
Figure BDA0002547924990000065
a3, obtaining the iteration bottom point latitude finally obtained in the step A2
Figure BDA0002547924990000066
Assigning to the bottom point latitude Bf。
And S3, inputting the geodetic coordinates of the to-be-sampled point into the GNSS system, and positioning the position of the actual engineering point.
The invention has the beneficial effects that:
(1) and constructing a proper ellipsoid according to the area to be measured of the actual engineering, accurately obtaining the geodetic coordinates of the to-be-sampled point through inverse Gaussian calculation, and accurately calculating the latitude through an iteration mode, thereby avoiding the problem of projection deformation.
(2) The invention can obtain results on various projection surfaces according to various projection rules, so that the calculated data has reusability and universality.

Claims (6)

1. A GNSS three-dimensional lofting positioning method based on ellipsoid calculation is characterized by comprising the following steps:
s1, constructing an engineering ellipsoid according to the area to be measured;
s2, obtaining the geodetic coordinates of the to-be-sampled point by the Gaussian inverse calculation of the plane coordinates of the to-be-sampled point;
s3, inputting the geodetic coordinates of the to-be-sampled point into a GNSS system, and positioning the position of an actual engineering point;
step S1 includes the following steps:
s11, calculating the average curvature radius of the region to be measured according to the latitude of the region to be measured;
s12, averaging the geodetic heights of all to-be-sampled points of the region to be measured to serve as the average geodetic height of the region to be measured;
s13, calculating the major-semiaxis and the oblateness of the engineering ellipsoid according to the average curvature radius and the average height of the area to be measured;
s14, constructing an engineering ellipsoid according to the major semi-axis and the oblateness of the engineering ellipsoid;
the calculation formula of the major-semiaxis of the engineering ellipsoid in the step S13 is as follows:
Figure FDA0003007942440000011
the oblateness of the engineering ellipsoid is as follows:
alpha＝1-a(1-e2) (2)
wherein a is a long semi-axis of an engineering ellipsoid, RmIs the average radius of curvature of one point of a national reference ellipsoid, HmAverage ground height of region to be measured, BmThe average latitude of the area to be measured, e is the eccentricity of the engineering ellipsoid, and alpha is the oblateness of the engineering ellipsoid.
2. The GNSS three-dimensional lofting positioning method based on ellipsoid calculation according to claim 1, wherein the formula for calculating the geodetic coordinates of the to-be-lofted point in the step S2 is as follows:
Figure FDA0003007942440000012
Figure FDA0003007942440000021
tf＝tanBf (5)ηf 2＝e2cos2Bf (6)
Figure FDA0003007942440000022
Figure FDA0003007942440000023
wherein y is the ordinate of the to-be-sampled point in the area to be measured, B is the abscissa of the geodetic coordinate of the to-be-sampled point, L is the ordinate of the geodetic coordinate of the to-be-sampled point, tfIs a value of the derivative of the time angle, MfIs a curvature radius derivative value of the fourth prime circle, NfIs the derivative value of the radius of curvature of the meridian, BfLatitude, η, at the base pointfAs a component of the deviation of the perpendicular to the unit circle, L0The central meridian accuracy.
3. According to the claimsSolving 2 the GNSS three-dimensional lofting positioning method based on ellipsoid calculation is characterized in that the base point latitude BfThe calculation method comprises the following steps:
a1, iteration bottom point latitude
Figure FDA0003007942440000024
Initial value of (2)
Figure FDA0003007942440000025
Is arranged as
Figure FDA0003007942440000026
Wherein i is the number of iterations, X is the meridian arc length measured from the equator, a0Is an intermediate variable;
a2, iteration bottom point latitude
Figure FDA0003007942440000027
Iterating through an iteration formula until:
Figure FDA0003007942440000028
where ε is a minimum threshold;
a3, obtaining the iteration bottom point latitude finally obtained in the step A2
Figure FDA0003007942440000029
Assigning to the bottom point latitude Bf。
4. The GNSS three-dimensional lofting positioning method based on ellipsoid calculation of claim 3, wherein the intermediate variable a in step A10The calculation formula of (2) is as follows:
Figure FDA00030079424400000210
5. the GNSS three-dimensional lofting positioning method based on ellipsoid calculation of claim 3, wherein the iterative formula in the step A2 is as follows:
Figure FDA00030079424400000211
Figure FDA0003007942440000031
wherein F is an iterative latitude function, a2,a4,a6,a8Are all intermediate variables.
6. The GNSS three-dimensional lofting positioning method based on ellipsoid calculation of claim 5, wherein the intermediate variable a2,a4,a6,a8The calculation formula of (2) is as follows:
Figure FDA0003007942440000032
Figure FDA0003007942440000033
Figure FDA0003007942440000034
Figure FDA0003007942440000035
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