CN116026293B - Laser GNSS-RTK total station coordinate conversion method and device - Google Patents
Laser GNSS-RTK total station coordinate conversion method and device Download PDFInfo
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- CN116026293B CN116026293B CN202310010761.4A CN202310010761A CN116026293B CN 116026293 B CN116026293 B CN 116026293B CN 202310010761 A CN202310010761 A CN 202310010761A CN 116026293 B CN116026293 B CN 116026293B
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
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Abstract
The invention discloses a laser GNSS-RTK total station coordinate conversion method, which comprises the following steps: s1: acquiring a three-dimensional coordinate of a phase center of the RTK antenna; s2: converting the three-dimensional coordinates of the RTK antenna phase center into three-dimensional coordinates of the laser emission point, calculating coordinate conversion parameters through a coordinate conversion equation, and replacing a rotation matrix with a Rodrig matrix in the process of calculating the coordinate conversion parameters; s3: calculating an included angle between the laser beam and the plumb line and a coordinate azimuth angle of the laser beam according to the coordinate conversion parameters; s4: and obtaining the distance from the to-be-measured point to the laser emission point by using a laser range finder, and obtaining the three-dimensional coordinate of the to-be-measured point by combining the included angle between the laser beam and the plumb line, the coordinate azimuth angle of the laser beam and the distance from the RTK antenna phase center to the laser emission point. The method solves the problem of low conversion efficiency of the GNSS-RTK model, and improves the point location precision of the point to be measured.
Description
Technical Field
The invention relates to the field of GNSS-RTK engineering measurement. More particularly, the invention relates to a laser GNSS-RTK total station coordinate conversion method and device.
Background
With the development and innovation of modern science and technology, GNSS-RTK measurement techniques have been widely used in mapping operations in engineering measurement industries. The appearance of the total station GNSS-RTK technology not only enables the instrument to acquire three-dimensional coordinate data of the target point to be measured without centering, but also can measure the target point to be measured in hidden areas such as high-steep ridges, house inflection points, bridge bottoms and the like, optimizes the working mode of engineering measurement and improves the working efficiency. The traditional three-dimensional coordinate transformation generally aims at a small angle, and the rotation matrix is simplified into a linear model, so that the solution is simpler and more convenient, in a GNSS-RTK conversion model, the coordinate conversion model is often nonlinear, the coordinate conversion parameter solution difficulty is high, the rotation matrix is difficult to determine, the GNSS-RTK model conversion efficiency is low, and the point location precision of a target point to be measured is affected. Therefore, there is a need to design a technical solution that can overcome the above-mentioned drawbacks to a certain extent.
Disclosure of Invention
The invention aims to provide a laser GNSS-RTK total station coordinate conversion method and device, which solve the problem of low conversion efficiency of a GNSS-RTK model and improve the point location precision of a to-be-measured point.
To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, there is provided a laser GNSS-RTK total station coordinate conversion method including: s1: acquiring a three-dimensional coordinate of a phase center of the RTK antenna; s2: converting the three-dimensional coordinates of the RTK antenna phase center into three-dimensional coordinates of the laser emission point, calculating coordinate conversion parameters through a coordinate conversion equation, and replacing a rotation matrix with a Rodrig matrix in the process of calculating the coordinate conversion parameters; s3: calculating an included angle between the laser beam and the plumb line and a coordinate azimuth angle of the laser beam according to the coordinate conversion parameters; s4: and obtaining the distance from the to-be-measured point to the laser emission point by using a laser range finder, and obtaining the three-dimensional coordinate of the to-be-measured point by combining the included angle between the laser beam and the plumb line, the coordinate azimuth angle of the laser beam and the distance from the RTK antenna phase center to the laser emission point.
Further, the coordinate transformation equation is:
wherein, the three-dimensional coordinate of the RTK antenna phase center is (X A ，Y A ，Z A ) The three-dimensional coordinates of the laser rangefinder were (X B ，Y B ，Z B )，R ω R is a rotation matrix ω ＝R z (ψ)R y (θ)R x Phi, theta, phi are rotation parameters, T X ,T Y ,T Z And m is a scale parameter.
Further, the method for obtaining the coordinate transformation parameters comprises the following steps:
an antisymmetric matrix S is designed,wherein a, b, c are independent of each other;
establishing a Rodrig matrix R:
wherein Δ=1+a 2 +b 2 +c 2 ；
By means of (E+S) R -1 Transforming the coordinate transformation equation to obtain:
expanding the transformed coordinate conversion equation, and adding a corresponding correction to obtain a general form of an error equation, wherein k=1+m;
the error equation is calculated according to the Taylor seriesExpanding to obtain a matrix equation, wherein, a 0 ,b 0 ,c 0 ,k 0 respectively coordinate conversion parameters T X, T Y ,T Z, a, b, c, k are assumed to approximate solutions;
wherein (1)>
The solution of the matrix equation method equation is as follows:
calculating the optimal solution (T) of the coordinate transformation parameters by using a least square iteration method X ，T Y ，T Z ，a，b，c，k)。
Further, according to the corresponding relation between the Rodrign matrix and the rotation matrix, values of psi, theta and phi are obtained,
calculating an included angle i of the laser beam and the plumb line and a coordinate azimuth angle alpha of the laser beam, wherein i=arccos theta; α=arctan ((cos ψsin θcos Φ+sin ψsin Φ)/(sin ψsin θcos Φ -cos ψsin Φ).
Further, the coordinates of the point to be measured are (X, Y, Z), x=x A +L′·cosα，Y＝Y A +L′·sinα，Z＝Z A -L cosi, d is the distance between the RTK antenna phase center and the laser emission point, l=l OS +d，L OS And L is the distance between the phase center of the RTK antenna and the point to be measured.
The invention also provides a laser GNSS-RTK total station coordinate conversion device, which comprises: a processor; a memory storing executable instructions; wherein the processor is configured to execute the executable instructions to perform the laser GNSS-RTK total station coordinate conversion method.
The invention at least comprises the following beneficial effects:
the invention utilizes the Rodriger matrix to construct the rotation matrix, adopts the least square iteration method to acquire the coordinate conversion parameters, and the coordinate conversion model is nonlinear, so that the problems of high difficulty in solving the coordinate conversion parameters and difficulty in determining the rotation matrix are solved, complex trigonometric function operation in the coordinate conversion process is avoided, the problem of low efficiency of the total station laser GNSS-RTK conversion model is solved, the GNSS-RTK can acquire more accurate three-dimensional coordinates during engineering measurement, and the engineering measurement efficiency is improved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a total station laser GNSS-RTK receiver;
FIG. 3 is a diagram showing the positional relationship between a total station laser GNSS-RTK receiver and a Gaussian planar coordinate system;
fig. 4 is a diagram of the positional relationship between the total station type laser GNSS-RTK receiver and the point to be measured in the gaussian plane coordinate system.
Detailed Description
The present invention is described in further detail below with reference to the drawings to enable those skilled in the art to practice the invention by referring to the description.
It will be understood that terms, such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
As shown in fig. 2, the total station type laser GNSS-RTK apparatus includes a 1-inertial navigation RTK receiver; 2-a laser range finder; 3-centering bars; 4-a handbook; 5-antenna phase center, the laser rangefinder 2 is integrated into the inertial navigation RTK receiver 1, the antenna phase center of the inertial navigation RTK receiver 1 coincides with the line of the laser rangefinder 2 and the centering rod 3, and the distance between the two points is d, constituting a total station type laser GNSS-RTK receiver.
Since the antenna phase center 5, the laser rangefinder 2, the attitude sensor, etc. are all integrated with the RTK receiver, they can be regarded as a whole in terms of the angle between the inertial coordinate system and the gaussian coordinate system of the whole device.
As shown in fig. 3, the spatial position relationship diagram between the total station laser GNSS-RTK and the target point in the gaussian plane coordinate system is shown. Let o denote the phase center of the antenna, and the projection of the antenna phase center in the Gaussian plane coordinate system ’ S represents the laser emission point, d represents the distance from the laser emission point S to the antenna phase center, and L is used OS To indicate the distance from the laser emission point to the target point, i to indicate the angle between the laser beam and the front of the hammer headTo represent the co-ordinate azimuthal coordinates of the laser beam in a gaussian coordinate system.
As shown in fig. 1, an embodiment of the present application provides a laser GNSS-RTK total station coordinate conversion method, including:
s1: acquiring three-dimensional coordinates of the phase center of the RTK antenna, and initializing attitude information;
s2: converting the three-dimensional coordinates of the RTK antenna phase center into three-dimensional coordinates of the laser emission point, calculating coordinate conversion parameters through a coordinate conversion equation, and replacing a rotation matrix with a Rodrig matrix in the process of calculating the coordinate conversion parameters;
s3: calculating an included angle between the laser beam and the plumb line and a coordinate azimuth angle of the laser beam according to the coordinate conversion parameters; s4: and obtaining the distance from the to-be-measured point to the laser emission point by using a laser range finder, and obtaining the three-dimensional coordinate of the to-be-measured point by combining the included angle between the laser beam and the plumb line, the coordinate azimuth angle of the laser beam and the distance from the RTK antenna phase center to the laser emission point.
Specifically, the coordinate conversion equation is:
wherein, the three-dimensional coordinate of the RTK antenna phase center is (X A ，Y A ，Z A ) The three-dimensional coordinates of the laser rangefinder were (X B ，Y B ，Z B )，R ω R is a rotation matrix ω ＝R z (ψ)R y (θ)R x Phi, theta, phi are rotation parameters, T X ,T Y ,T Z And m is a scale parameter.
Specifically, the method for obtaining the coordinate transformation parameters comprises the following steps:
an antisymmetric matrix S is designed,wherein a, b, c are independent of each other;
constructing a rodgers matrix R from the antisymmetric matrix:
wherein Δ=1+a 2 +b 2 +c 2 ；
Because the Rodriger matrix R meets the property of a rotating matrix, R is used for replacing the rotating matrix, a, b and c are used for replacing rotation parameters such as psi, theta, phi and the like, a three-dimensional conversion mathematical model is built, complex trigonometric function operation is avoided, and according to the property of an antisymmetric matrix and an orthometric matrix, the (E+S) R is multiplied simultaneously on two sides of a coordinate conversion equation -1 Transforming the coordinate transformation equation to obtain:
expanding the transformed coordinate conversion equation and adding a correction to obtain a general form of an error equation, wherein for the convenience of calculation, k=1+m:
the error equation is calculated according to the Taylor seriesExpanding to obtain a matrix equation, whichIn, a 0 ,b 0 ,c 0 ,k 0 respectively coordinate conversion parameters T X ,T Y ,T Z A, b, c, k is a hypothetical approximation solution;
wherein (1)>
The normal equation of the matrix equation is:
the solution of the matrix equation method equation is as follows:
calculating the optimal solution (T) of the coordinate transformation parameters by using a least square iteration method X ，T Y ，T Z ，a，b，c，k)。
According to the matrix R and the rotation matrix R ω Obtaining the corresponding relation of phi, theta,
θ＝arcsinR(3，1)，/>r (rows, columns) represents the values in the corresponding rows and columns of the Rodringer matrix; that is, R (3, 2) represents the value 2a-2bc of the second column of the third row inside the Rodriger matrix; r (3, 3) represents the value 1+a2-b2+c2 of the third row and the third column in the Rodringer matrix; r (2, 1) represents the value 2c-2ab of the first column of the second row inside the Rodringer matrix; r (1, 1) represents the values 1-a2-b2-c2 of the first column of the first row inside the Rodringer matrix;
calculating an included angle i of the laser beam and the plumb line and a coordinate azimuth angle alpha of the laser beam, wherein i=arccos theta; α=arctan ((cos ψsin θcos Φ+sin ψsin Φ)/(sin ψsin θcos Φ -cos ψsin Φ)).
Specifically, as shown in fig. 4, on the gaussian plane, the coordinates of the antenna phase center o are (X A ，Y A ，Z A ) The coordinate azimuth angle of the laser beam is i, d is the distance between the phase center o of the RTK antenna and the laser emitting point S, and L=L OS +d，L OS For the distance from the point to be measured O to the laser emission point S, L is the distance between the phase center of the RTK antenna and the point to be measured, so that the flat distance L' =L.sin (i) between the two points is used for calculating the plane coordinate of the point to be measured by adopting a polar coordinate method; the coordinates of the point to be measured are (X, Y, Z);
X＝X A +L′·cosα
Y＝Y A +L′·sinα
as shown in fig. 4, the elevation of the antenna phase center o is Z o The included angle between the laser beam and the plumb line is i, and the elevation of the target point to be measured can be obtained according to the geometric relation:
Z＝Z A -L·cosi。
the embodiment of the application also provides a laser GNSS-RTK total station coordinate conversion device, which comprises: a processor; a memory storing executable instructions; wherein the processor is configured to execute the executable instructions to perform the laser GNSS-RTK total station coordinate conversion method; the device of the present embodiment may be disposed in a local server, a cloud server, a terminal, or the like, and the method of each embodiment described above is implemented by executing predetermined program instructions.
The number of equipment and the scale of processing described herein are intended to simplify the description of the present invention. Applications, modifications and variations of the laser GNSS-RTK total station coordinate conversion method and apparatus of the present invention will be apparent to those skilled in the art.
Although embodiments of the present invention have been disclosed above, it is not limited to the details and embodiments shown and described, it is well suited to various fields of use for which the invention would be readily apparent to those skilled in the art, and accordingly, the invention is not limited to the specific details and illustrations shown and described herein, without departing from the general concepts defined in the claims and their equivalents.
Claims (2)
1. The laser GNSS-RTK total station coordinate conversion method is characterized by comprising the following steps of:
s1: acquiring a three-dimensional coordinate of a phase center of the RTK antenna;
s2: converting the three-dimensional coordinates of the RTK antenna phase center into three-dimensional coordinates of the laser emission point, calculating coordinate conversion parameters through a coordinate conversion equation, and replacing a rotation matrix with a Rodrig matrix in the process of calculating the coordinate conversion parameters;
s3: calculating an included angle between the laser beam and the plumb line and a coordinate azimuth angle of the laser beam according to the coordinate conversion parameters;
s4: obtaining a distance from a to-be-measured point to a laser emission point by using a laser range finder, and obtaining a three-dimensional coordinate of the to-be-measured point by combining an included angle of a laser beam and a plumb line, a coordinate azimuth angle of the laser beam and a distance from a phase center of an RTK antenna to the laser emission point;
the coordinate conversion equation is:
；
wherein, the three-dimensional coordinate of the phase center of the RTK antenna isThe three-dimensional coordinates of the laser range finder are，R ω For rotating matrix +.>Phi, theta, phi are rotation parameters, T X, T Y , T Z The translation parameter is m, and the scale parameter is m;
the method for obtaining the coordinate transformation parameters comprises the following steps:
an antisymmetric matrix S is designed,wherein a, b, c are independent of each other;
establishing a Rodrig matrix R:wherein, the method comprises the steps of, wherein,；
by means ofTransforming the coordinate transformation equation to obtain:
；
and developing the transformed coordinate conversion equation, adding a corresponding correction to obtain a general form of an error equation, wherein k=1+m:
；
the error equation is calculated according to the Taylor seriesExpanding to obtain a matrix equation, wherein +.>, , />, a 0 , b 0 , c 0 , k 0 Respectively coordinate conversion parameters T X, T Y , T Z, a, b, c, k are assumed to approximate solutions;
wherein->，
The solution of the matrix equation method equation is as follows:
；
calculating the optimal solution of the coordinate transformation parameters by using a least square iteration method；
According to the matrix R and the rotation matrix R ω Obtaining the corresponding relation of phi, theta,
；
calculating the included angle i between the laser beam and the plumb line and the coordinate azimuth angle alpha of the laser beam,；
；
the coordinates of the point to be measured are (X, Y, Z),，/>，/>d is the distance between the phase center of the RTK antenna and the laser emission point, < >>，L OS L is the distance between the phase center of the RTK antenna and the point to be measured, which is the distance between the point to be measured and the laser emission point, and +.>。
2. Laser GNSS-RTK total powerstation coordinate conversion equipment, its characterized in that includes:
a processor;
a memory storing executable instructions;
wherein the processor is configured to execute the executable instructions to perform the laser GNSS-RTK total station coordinate conversion method of claim 1.
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