CN113093130A - Radar two-dimensional installation attitude calibration method and system based on global positioning system target - Google Patents

Radar two-dimensional installation attitude calibration method and system based on global positioning system target Download PDF

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CN113093130A
CN113093130A CN202110403443.5A CN202110403443A CN113093130A CN 113093130 A CN113093130 A CN 113093130A CN 202110403443 A CN202110403443 A CN 202110403443A CN 113093130 A CN113093130 A CN 113093130A
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coordinate system
radar
target
coordinates
absolute position
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吕能超
吴静成
吴超仲
王玉刚
文家强
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Wuhan University of Technology WUT
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO 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
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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    • G01S7/4004Means for monitoring or calibrating of parts of a radar system

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Abstract

The invention discloses a radar two-dimensional installation attitude calibration method based on a global positioning system target, which comprises the following steps: s1, finding out two proper characteristic points on the road side as the target placement positions; s2, acquiring absolute position coordinates of the target by the GPS measuring antenna in the target; s3, scanning triangular angle reflectors in the two targets by the radar to obtain relative position coordinates of the targets in a radar coordinate system; s4, establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target, and determining the relationship between the first coordinate system and the second coordinate system; and S5, converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data collected by the radar, and converting the position of the origin of the second coordinate system in the first coordinate system into the absolute position of the radar installation. The method realizes the accurate calibration of the radar installation attitude, determines the actual position of the point cloud data acquired by the radar, and provides convenience for the processing of the radar data in the later period.

Description

Radar two-dimensional installation attitude calibration method and system based on global positioning system target
Technical Field
The invention relates to the technical field of roadside microwave radars, in particular to a radar two-dimensional installation attitude calibration method and system based on a global positioning system target.
Background
With the continuous development of economy and the continuous progress of intelligent transportation, traffic information detection, which is one of the key parts of intelligent transportation, receives more and more attention.
At present, in the field of traffic information detection, microwave radars are widely applied to roadside traffic information detection by virtue of the advantages of multi-lane detection function, all weather, high accuracy, strong environmental impact resistance and the like. Vehicle point cloud data collected by the roadside microwave radar is relative to the radar, the actual installation position and the actual installation angle of the radar cannot be determined, and the running condition of a vehicle on an actual road cannot be further determined, so that the radar data is difficult to process in the later period, and a large error exists between the radar point cloud data and the actual condition.
Disclosure of Invention
The invention mainly aims to solve the problem that the actual installation position of a radar cannot be determined in radar collected data, and provides a method for calibrating the two-dimensional installation position of the radar by using a global positioning system target to determine the actual installation position of the radar and the running condition of a vehicle on an actual road so as to facilitate the processing and utilization of later-period radar data.
The technical scheme adopted by the invention is as follows:
the radar two-dimensional installation attitude calibration method based on the global positioning system target comprises the following steps:
s1, finding out two proper characteristic points on the road side as the target placement positions;
s2, acquiring absolute position coordinates of the target by a GPS measuring antenna in the target;
s3, scanning triangular angle reflectors in the two targets by the radar to obtain relative position coordinates of the targets in a radar coordinate system;
s4, establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target, and determining the relationship between the first coordinate system and the second coordinate system;
and S5, converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data collected by the radar, and converting the position of the origin of the second coordinate system in the first coordinate system into the absolute position of the radar installation.
In the above technical solution, the suitable feature points in step S1 are points on both sides of the road with distinct features, including diversion points of the ramp, the position of the post, and the vicinity of the position of the road sign, and the target is placed on the feature points, and the triangular corner reflector on the target is directed toward the radar direction.
In step S2, the absolute position coordinates are in the WGS-84 coordinate system.
In the above technical solution, the specific method of step S4 is as follows:
the absolute position coordinates of the target are converted into coordinates in Gaussian plane rectangular coordinates, and a first coordinate system [ X ] is established according to the coordinates1,Y1]T(ii) a The radar coordinate system with the radar as the origin is the second coordinate system [ X ]2,Y2]T
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure BDA0003021279260000021
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure BDA0003021279260000031
Wherein R isLThe rotation matrix of the second coordinate system is an orthogonal matrix with a determinant of 1; t isLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; solving the formula (1) to obtain RLAnd TLAnd obtaining the matrix relation between the two coordinate systems.
In the above technical solution, the specific method of step S5 is as follows:
when the microwave radar detects the point cloud coordinates (x) of the vehicle2,y2) And (3) substituting the absolute position coordinates into the formula (1) to obtain the absolute position coordinates of the vehicle in the first coordinate system, and simultaneously, taking the translation matrix of the second coordinate system as the actual installation position coordinates of the radar.
The invention also provides a radar two-dimensional installation attitude calibration system based on the global positioning system target, which comprises the following steps:
the target position determining module is used for finding out two proper characteristic points on the road side as the places where the targets are placed;
the target absolute position acquisition module is used for acquiring the absolute position coordinates of the target through a GPS measurement antenna in the target;
the target relative position acquisition module is used for scanning triangular angle reflectors in the two targets through a radar to obtain relative position coordinates of the targets in a radar coordinate system;
the coordinate system establishing module is used for establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target and determining the relationship between the first coordinate system and the second coordinate system;
and the data conversion module is used for converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, and the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
In connection with the above technical solution, the coordinate system establishing module is specifically configured to:
the absolute position coordinates of the target are converted into coordinates in Gaussian plane rectangular coordinates, and a first coordinate system [ X ] is established according to the coordinates1,Y1]T(ii) a The radar coordinate system with the radar as the origin is the second coordinate system [ X ]2,Y2]T
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure BDA0003021279260000041
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure BDA0003021279260000042
Wherein R isLThe rotation matrix of the second coordinate system is an orthogonal matrix with a determinant of 1; t isLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; solving the formula (1) to obtain RLAnd TLA matrix relationship between the two coordinate systems is obtained.
In connection with the above technical solution, the data conversion module is specifically configured to:
when the microwave radar detects the point cloud coordinates (x) of the vehicle2,y2) And (3) substituting the absolute position coordinates of the vehicle into the formula (1) to obtain the absolute position coordinates of the vehicle in the first coordinate system, wherein the translation matrix of the second coordinate system is the actual installation position coordinates of the radar, and the rotation angle determined by the rotation matrix of the second coordinate system is the actual installation angle of the radar.
The invention also provides a radar two-dimensional installation attitude calibration system based on the global positioning system target, which comprises a data acquisition module, a data transmission module and a data processing module; wherein:
the data acquisition module comprises a microwave radar and a target, wherein the surface of the target is a triangular corner reflector, and a GPS measurement antenna and a communication module are embedded in the target;
the data transmission module transmits the GPS position information acquired by the target and the position information of the target scanned by the microwave radar to the data processing module;
the data processing module establishes a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target and determines the relationship between the first coordinate system and the second coordinate system; and converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, wherein the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
The invention further provides a storage medium, which can be executed by a processor, and in which a computer program is stored, and the computer program executes the method for calibrating the two-dimensional installation attitude of the global positioning system target-based radar according to the above technical solution.
The invention has the following beneficial effects: the method comprises the steps of arranging two targets with a GPS positioning function at feature points on the road side, obtaining absolute position information of the two targets, scanning the targets through an installed microwave radar, obtaining relative position information of the targets in a radar coordinate system, and establishing corresponding coordinate systems through the absolute position information and the relative position information respectively, so that the relationship between the two coordinate systems is determined, and the actual installation position of the radar is further determined. The method realizes the accurate calibration of the radar installation position, and simultaneously determines the actual position of the point cloud data collected by the radar, thereby providing convenience for the processing of the radar data in the later period.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method for calibrating a two-dimensional installation attitude of a radar based on a target of a global positioning system according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a two-dimensional radar installation attitude calibration system based on a GPS target according to an embodiment of the present invention;
FIG. 3 is a transformation diagram of a first coordinate system and a second coordinate system;
fig. 4 is a schematic structural diagram of a two-dimensional installation attitude calibration system of a radar based on a global positioning system target according to another embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, the radar two-dimensional installation attitude calibration method based on the global positioning system target in the embodiment of the present invention includes the following steps:
s101, finding out two appropriate characteristic points on the road side as places for placing targets;
s102, a GPS measuring antenna in the target acquires absolute position coordinates of the target;
s103, scanning triangular angle reflectors in the two targets by the radar to obtain relative position coordinates of the targets in a radar coordinate system;
s104, establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target, and determining the relationship between the first coordinate system and the second coordinate system;
and S105, converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, wherein the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
The specific method of step S101 is: two proper characteristic points are found at the road side, the characteristic points are points with distinct characteristics at two sides of the road, including diversion points of ramps, marker posts, sides of road signboards and the like, the target is placed on the characteristic points, and the triangular corner reflector faces the radar direction.
Further, the absolute position coordinates of the targets obtained in step S102 are converted into gaussian plane rectangular coordinates by the data processing module using WGS-84 coordinate system, and the coordinate system defined by the absolute position coordinates of the two targets is defined as a first coordinate system [ X [ ]1,Y1]TDefining a radar coordinate system as a second coordinate system [ X ]2,Y2]T
Step S104 specifically includes:
converting the target position coordinate which is obtained in the step S102 and adopts the WGS-84 coordinate system into a coordinate in a Gaussian plane rectangular coordinate, and establishing a first coordinate system according to the coordinate; the radar coordinate system with the radar as the origin is a second coordinate system.
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure BDA0003021279260000071
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure BDA0003021279260000072
Wherein R isLRotating the matrix for the second coordinate system, the rotating matrix being an orthogonal matrix with a determinant 1, TLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; r solved according to formula (1)LAnd TL
Further, the specific method of step S105 of the present invention is:
the rotation matrix R solved according to S104LAnd translation matrix TLObtaining a matrix relation between two coordinate systems, and detecting a vehicle point cloud coordinate (X) by using a microwave radar2,Y2) And (3) substituting the coordinate into the formula (1) to obtain the coordinate of the vehicle in the first coordinate system, namely the absolute position coordinate of the vehicle, wherein the translation matrix of the second coordinate system is the actual installation position coordinate of the radar, and the rotation angle determined by the rotation matrix of the second coordinate system is the actual installation angle of the radar.
The method can determine the actual position and the azimuth of radar installation through the collected data, can obtain the actual point cloud coordinates and the running track of the vehicle, and can further determine which lane the vehicle runs in by combining with a map. The problem that the installation position of the radar and the running condition of a vehicle on an actual road cannot be determined only relative to the radar when the current radar acquires data is solved.
As shown in fig. 2, the radar two-dimensional installation attitude calibration system device based on the global positioning system target in the embodiment of the present invention includes a data acquisition module, a data transmission module and a data processing module; the data acquisition module comprises a microwave radar 1 and a target 2, wherein the surface of the target is a triangular corner reflector, and a GPS measurement antenna and a communication device are embedded in the target. 4 and 5 are support means, and the support means 4 may be a traffic light bar, an electric traffic light bar, or the like, for fixing the radar position. The data transmission module comprises transmission between a communication device in the target and the PC terminal 3 and transmission between a communication device in the radar and the PC terminal 3, wherein the former adopts wireless communication, and the latter adopts wired communication. The data processing module is positioned at the PC end 3 and is used for processing data transmitted by the radar and the target.
In the embodiment, a microwave radar is adopted, the detection distance is 200m, the scanning interval is 50ms, the distance resolution is 0.25m, and the triangular corner reflector is a regular triangle with the side length of 30 cm.
The calibration method of the radar two-dimensional installation attitude calibration device based on the global positioning system target comprises the following steps:
s1, firstly, finding out two proper characteristic points on the road side as the target placement positions;
before this, the radar 1 is installed, the feature points are in the radar scanning range, the target 2 is placed on the feature points, and the triangular angular reflector surface on the target faces the radar direction.
S2, the GPS measuring antenna in the target acquires the absolute coordinate position of the target and transmits the position data to the data processing module through the communication device;
the PC terminal 3 receives the target absolute coordinate position information transmitted by the target communication device.
S3, scanning triangular angle reflectors in the two targets by the radar to obtain the relative coordinate positions of the targets in a radar coordinate system, and outputting position data to the data processing module;
and the PC terminal 3 receives the relative coordinate position information of the target transmitted by the radar communication device.
S4, the data processing module establishes a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target respectively, and determines the relationship between the first coordinate system and the second coordinate system;
a data processing module in the PC end converts the obtained target position coordinate adopting the WGS-84 coordinate system into a coordinate in a Gaussian plane rectangular coordinate, and establishes a first coordinate system; the radar coordinate system with the radar as the origin is a second coordinate system. The coordinate conversion relationship as shown in fig. 3 is established.
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure BDA0003021279260000091
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure BDA0003021279260000092
Wherein R isLRotating the matrix for the second coordinate system, the rotating matrix being an orthogonal matrix with a determinant 1, TLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; r solved according to formula (1)LAnd TL
And S5, converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data collected by the radar, and converting the position of the origin of the second coordinate system in the first coordinate system into the absolute position of the radar installation.
Solved rotation matrix RLAnd translation TLObtaining a matrix relation between two coordinate systems, and detecting a vehicle point cloud coordinate (X) by using a microwave radar2,Y2) Then, the coordinate of the vehicle in the first coordinate system is obtained by substituting the formula (1)And obtaining the absolute position coordinates of the vehicle, wherein the translation matrix is the actual installation position coordinates of the radar, and the rotation angle determined by the rotation matrix of the second coordinate system is the actual installation angle of the radar.
As shown in fig. 4, the radar two-dimensional installation attitude calibration system based on the global positioning system target according to the embodiment of the present invention is mainly used for implementing the radar two-dimensional installation attitude calibration method based on the global positioning system target according to the embodiment, and the system mainly includes:
the target position determining module is used for finding out two proper characteristic points on the road side as the places where the targets are placed;
the target absolute position acquisition module is used for acquiring the absolute position coordinates of the target through a GPS measurement antenna in the target;
the target relative position acquisition module is used for scanning triangular angle reflectors in the two targets through a radar to obtain relative position coordinates of the targets in a radar coordinate system;
the coordinate system establishing module is used for establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target and determining the relationship between the first coordinate system and the second coordinate system;
and the data conversion module is used for converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, and the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
The present invention further provides a storage medium, which can be executed by a processor, and in which a computer program is stored, where the computer program executes the method for calibrating a two-dimensional installation attitude of a gps-based radar according to the foregoing embodiments.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.

Claims (10)

1. A radar two-dimensional installation attitude calibration method based on a global positioning system target is characterized by comprising the following steps:
s1, finding out two proper characteristic points on the road side as the target placement positions;
s2, acquiring absolute position coordinates of the target by a GPS measuring antenna in the target;
s3, scanning triangular angle reflectors in the two targets by the radar to obtain relative position coordinates of the targets in a radar coordinate system;
s4, establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target, and determining the relationship between the first coordinate system and the second coordinate system;
and S5, converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data collected by the radar, and converting the position of the origin of the second coordinate system in the first coordinate system into the absolute position of the radar installation.
2. The method for calibrating the two-dimensional installation attitude of the gps-based radar according to claim 1, wherein the suitable feature points in step S1 are points on both sides of the road with distinct features, including a diversion point of a ramp, a post position, and a vicinity of a road sign position, the target is placed on the feature points, and triangular corner reflectors on the target are directed toward the radar.
3. The method for calibrating the two-dimensional installation attitude of the global positioning system target-based radar according to claim 1, wherein the absolute position coordinates in step S2 are in WGS-84 coordinate system.
4. The method for calibrating the two-dimensional installation attitude of the global positioning system target-based radar according to claim 1, wherein the specific method in step S4 is as follows:
the absolute position coordinates of the target are converted into coordinates in Gaussian plane rectangular coordinates, and a first coordinate system [ X ] is established according to the coordinates1,Y1]T(ii) a The radar coordinate system with the radar as the origin is the second coordinate system [ X ]2,Y2]T
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure FDA0003021279250000021
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure FDA0003021279250000022
Wherein R isLThe rotation matrix of the second coordinate system is an orthogonal matrix with a determinant of 1; t isLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; solving the formula (1) to obtain RLAnd TLAnd obtaining the matrix relation between the two coordinate systems.
5. The method for calibrating the two-dimensional installation attitude of the global positioning system target-based radar according to claim 4, wherein the specific method in step S5 is as follows:
when the microwave radar detects the point cloud coordinates (x) of the vehicle2,y2) And (3) substituting the absolute position coordinates of the vehicle into the formula (1) to obtain the absolute position coordinates of the vehicle in the first coordinate system, wherein the translation matrix of the second coordinate system is the actual installation position coordinates of the radar, and the rotation angle determined by the rotation matrix of the second coordinate system is the actual installation angle of the radar.
6. The utility model provides a radar two-dimentional installation gesture calibration system based on global positioning system target which characterized in that includes:
the target position determining module is used for finding out two proper characteristic points on the road side as the places where the targets are placed;
the target absolute position acquisition module is used for acquiring the absolute position coordinates of the target through a GPS measurement antenna in the target;
the target relative position acquisition module is used for scanning triangular angle reflectors in the two targets through a radar to obtain relative position coordinates of the targets in a radar coordinate system;
the coordinate system establishing module is used for establishing a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target and determining the relationship between the first coordinate system and the second coordinate system;
and the data conversion module is used for converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, and the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
7. The global positioning system target-based radar two-dimensional mounting attitude calibration system according to claim 6, wherein the coordinate system establishing module is specifically configured to:
the absolute position coordinates of the target are converted into coordinates in Gaussian plane rectangular coordinates, and a first coordinate system [ X ] is established according to the coordinates1,Y1]T(ii) a The radar coordinate system with the radar as the origin is the second coordinate system [ X ]2,Y2]T
Establishing a relation matrix equation of a first coordinate system and a second coordinate system:
Figure FDA0003021279250000031
the coordinates of the two targets in the first coordinate system are respectively (x)11,y11),(x12,y12);
The coordinates of the two targets in the second coordinate system are respectively (x)21,y21),(x22,y22);
Then
Figure FDA0003021279250000032
Wherein R isLThe rotation matrix of the second coordinate system is an orthogonal matrix with a determinant of 1; t isLIs a second coordinate system translation matrix, and RLIs a 2 × 2 matrix, TLIs a 2 x 1 matrix; solving the formula (1) to obtain RLAnd TLA matrix relationship between the two coordinate systems is obtained.
8. The system of claim 7, wherein the data conversion module is specifically configured to:
when the microwave radar detects the point cloud coordinates (x) of the vehicle2,y2) And (3) substituting the absolute position coordinates of the vehicle into the formula (1) to obtain the absolute position coordinates of the vehicle in the first coordinate system, wherein the translation matrix of the second coordinate system is the actual installation position coordinates of the radar, and the rotation angle determined by the rotation matrix of the second coordinate system is the actual installation angle of the radar.
9. A radar two-dimensional installation attitude calibration system based on a global positioning system target is characterized by comprising a data acquisition module, a data transmission module and a data processing module; wherein:
the data acquisition module comprises a microwave radar and a target, wherein the surface of the target is a triangular corner reflector, and a GPS measurement antenna and a communication module are embedded in the target;
the data transmission module transmits the GPS position information acquired by the target and the position information of the target scanned by the microwave radar to the data processing module;
the data processing module establishes a first coordinate system and a second coordinate system according to the obtained absolute position coordinates and relative position coordinates of the target and determines the relationship between the first coordinate system and the second coordinate system; and converting the data in the second coordinate system into the data in the first coordinate system so as to obtain the absolute position of the point cloud data acquired by the radar, wherein the position of the origin of the second coordinate system converted in the first coordinate system is the absolute position of the radar installation.
10. A storage medium, executable by a processor, having stored therein a computer program for performing the method for two-dimensional attitude calibration of a gps-based radar, according to any one of claims 1 to 5.
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