CN114545348A - SVD-based radar system error calibration method - Google Patents
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- 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
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Abstract
The invention discloses a radar system error calibration method based on SVD in the technical field of radar. According to the calibration method, the radar and the total station measure for multiple times and obtain the measured value and the true value of the corner reflector under the antenna array surface coordinate system, so that the measurement error of a radar system is obtained, calibration is corrected according to the measurement error of the radar system, and system error calibration is completed, so that the detection accuracy of the radar is improved.
Description
Technical Field
The invention relates to the technical field of radars, in particular to a radar system error calibration method based on SVD.
Background
The detection precision is one of main tactical indexes of the radar, in particular to a precision tracking and guidance radar. The method for reducing errors and even eliminating certain errors can be found out by researching and mastering the reasons of error generation and the change rules of the error under various conditions, and further the radar precision is improved.
According to the nature and the characteristics of the error, the error of the radar on the target position measurement comprises a systematic error and a random error. The random error can be eliminated by data processing methods such as smoothing and filtering, and the systematic error is reduced by numerical correction.
Disclosure of Invention
The application provides a radar system error calibration method based on SVD, which is used for calibrating radar system errors, thereby improving the radar detection precision.
The embodiment of the application provides a radar system error calibration method based on SVD, which comprises the following steps:
s1, placing a measuring instrument and a radar point target in front of an antenna array of a radar, detecting the radar point target by the radar, and obtaining a measured value of the radarAnd converted into rectangular coordinate X of antenna array surfaceR(x,y,z);
S2, determining the origin position of an antenna coordinate system, selecting n mark points at the edge of the antenna array surface, and acquiring the coordinates of each mark point in the antenna array surface coordinate system, wherein the corresponding coordinate point set is P ═ P1,p2,…,pn};
S3, respectively arranging the measuring instrument reflectors on the mark points, observing and acquiring the coordinates of the mark points under the observation coordinate system of the measuring instrument by the measuring instrument, converting the spherical coordinates into rectangular coordinates, and setting the corresponding coordinate point set as Q ═ Q { (Q) } Q { (Q } Q { (Q } Q { (Q } y { (Q } y, and the coordinate system is the coordinate system1,q2,…,qn};
S4, acquiring a rotation matrix R and a transfer matrix T between the antenna array plane coordinate system and the observation coordinate system of the measuring instrument according to the corresponding coordinate point set P of each mark point in the antenna array plane coordinate system and the corresponding coordinate point set Q in the observation coordinate system of the measuring instrument;
s5, observing the radar point target by the measuring instrument to obtain an observed valueAnd converted into rectangular coordinate X of measuring instrumentETS(x,y,z);
S6, calculating the coordinates of the radar point target on the antenna array surfaceTrue value of'R(x,y,z),X'R(x,y,z)=RXETS(x,y,z)+T;;
S7, repeating the steps S1-S6k times, wherein the position of the radar point target is different every time, and obtaining a group of measured values X of the radar on the radar point targetR={XR1,XR2,…,XRkAnd a true value X 'of a group of radar point targets under the antenna array surface coordinate system'R={X'R1,X'R2,…,X'RkAcquiring a radar system measurement error err according to the measurement value and the truth valuesys(errx,erry,errz);
S8, measuring error err of the radar systemsys(errx,erry,errz) System error converted into spherical coordinate systemAnd substituting the system error of the spherical coordinate system into a detection result for calibration to finish system error calibration.
The beneficial effects of the above embodiment are as follows: the radar and the measuring instrument are used for measuring for multiple times and obtaining the measured value and the true value of the radar point target under the antenna array plane coordinate system, so that the measuring error of the radar system is obtained, the calibration is corrected according to the measuring error of the radar system, the calibration of the system error is completed, and the detection precision of the radar is improved.
On the basis of the above embodiments, the present application can be further improved, specifically as follows:
in one embodiment of the present application, the calibration method further comprises step S0 of calibrating a stabilized turntable system of the radar so that a reference plane pointed by an antenna beam is parallel to the ground; and when the radar works normally, performing static technical parameter test, and if the test result meets the technical index, performing step S1. The horizontal plane of the calibration and stabilization turntable system is parallel to the ground, so that the reference plane pointed by the antenna wave beam is parallel to the ground, and the installation of the antenna array surface is free from errors; the purpose of testing the static technical parameters is to check whether the radar has problems and prepare for subsequent system error calibration.
In one embodiment of the present application, in step S1, the radar measurement valueOrthogonal coordinate X with antenna array surfaceRThe (x, y, z) transformation relationship is as follows:
in one embodiment of the present application, in step S1, the distance between the radar point target and the antenna wavefront is not less than 10 times the far-field distance. And the measurement error of the radar system is conveniently acquired.
In one embodiment of the present application, n ≧ 4 in step S2. The accuracy of the rotation matrix R and the transfer matrix T is guaranteed.
In one embodiment of the present application, in step S3, when the measuring instrument observes and acquires the coordinates of each of the mark points in the observation coordinate system of the measuring instrument, multiple measurements are required and an average value is taken. The measurement error of the measuring instrument is reduced.
In one embodiment of the present application, in step S4, the rotation matrix R and the transition matrix T are obtained by the following method:
(1) the problem mathematical model is constructed as follows:
wherein wiRepresenting the weight before each point pair;
(2) and performing decentralization on the two point sets to obtain a new point set A ═ a1,a2,…,anB ═ B1,b2,…,bnRepresents as:
(3) calculating a covariance matrix:
(4) SVD decomposition is carried out on the covariance matrix, and a rotation matrix is solved:
[U,S,V]=SVD(H)
R=VUT
In one embodiment of the present application, in step S5, the observation value is obtained while observing the radar point target with the measuring instrumentMultiple measurements are required and averaged. The measurement error of the measuring instrument is reduced.
In one embodiment of the present application, in step S7, the radar system measures an error errsys(errx,erry,errz) The acquisition method comprises the following steps: respectively averaging the measured value and the true value according to x, y and z components, and subtracting to obtain the radar system measurement error errsys(errx,erry,errz)。
In one embodiment of the present application, the measuring instrument is a total station and the radar point target is a corner reflector. The measuring instrument is required to be capable of measuring horizontal angle, vertical angle and distance (slant distance), preferably a Total Station, namely a Total Station type Electronic distance meter (Electronic Total Station), is a high-precision measuring instrument integrating light, machine and electricity, is a surveying and mapping instrument system integrating horizontal angle, vertical angle, distance (slant distance and horizontal distance) and height difference measuring functions, and is a radar point target preferred angle reflector.
One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:
1. the measurement error of the radar system is obtained by measuring and acquiring the measurement value and the true value of the corner reflector under the antenna array surface coordinate system for many times through the radar and the total station, and the calibration is corrected according to the measurement error of the radar system, so that the system error calibration is completed, and the radar detection precision is improved.
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In order to more clearly illustrate the detailed description of the invention or the technical solutions in the prior art, the drawings that are needed in the detailed description of the invention or the prior art will be briefly described below. Throughout the drawings, like elements or portions are generally identified by like reference numerals. In the drawings, elements or portions are not necessarily drawn to scale.
FIG. 1 is a schematic diagram of an installation relationship of the present invention.
Wherein, 1 total station, 2 corner reflectors, 3 antenna array planes and 31 marking points.
Detailed Description
The present invention is further illustrated by the following detailed description, which is to be construed as merely illustrative and not limitative of the remainder of the disclosure, and modifications and variations such as those ordinarily skilled in the art are intended to be included within the scope of the present invention as defined in the appended claims.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it should also be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In describing the invention, it is not necessary for a schematic representation of the above terminology to be directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples of the invention and features of different embodiments or examples described herein may be combined and combined by those skilled in the art without contradiction.
Example (b):
a radar system error calibration method based on SVD comprises the following steps:
s1, placing the total station 1 and the corner reflector 2 in front of the antenna array surface 3 of the radar, as shown in figure 1, detecting the corner reflector by the radar, recording data, detecting, settling to obtain the distance, azimuth angle and pitch angle of the corner reflector, namely obtaining the measured valueAnd converted into rectangular coordinate X of antenna array surfaceR(x,y,z)。
Wherein the distance between the corner reflector and the antenna array surface is not less than 10 times the far field distance. The total station, the corner reflector and the antenna array surface are not collinear. Radar measurementOrthogonal coordinate X with antenna array surfaceRThe (x, y, z) transformation relationship is as follows:
s2, determining the origin position of the antenna coordinate system, selecting n mark points 31 at the edge of the antenna array surface, wherein n is more than or equal to 4, respectively measuring the coordinates of each mark point in the antenna array surface coordinate system as shown in figure 1, and the corresponding coordinate point set of the mark points in the antenna array surface coordinate system is P ═ P { (P) }1,p2,…,pn}。
S3, respectively arranging total station reflectors at the positions of the mark points, respectively measuring and recording the coordinates of the mark points in the observation coordinate system of the total station by the total station, converting the spherical coordinates into rectangular coordinates, and setting the coordinate set of the mark points in the observation coordinate system of the total station as Q ═ Q { (Q) } Q1,q2,…,qn}。
When the total station observes and acquires the coordinates of each mark point under the total station observation coordinate system, multiple times of measurement are needed and an average value is obtained.
And S4, acquiring a rotation matrix R and a transfer matrix T between the antenna array surface coordinate system and the total station observation coordinate system according to the corresponding coordinate point set P of each mark point in the antenna array surface coordinate system and the corresponding coordinate point set Q in the total station observation coordinate system.
The method for acquiring the rotation matrix R and the transfer matrix T comprises the following steps:
(1) the problem mathematical model is constructed as follows:
wherein wiRepresenting the weight before each point pair;
(2) and performing decentralization on the two point sets to obtain a new point set A ═ a1,a2,…,anB ═ B1,b2,…,bnRepresents as:
(3) calculating a covariance matrix:
(4) SVD decomposition is carried out on the covariance matrix, and a rotation matrix is solved:
[U,S,V]=SVD(H)
R=VUT
S5 obtaining observation value by observing corner reflector with total stationAnd converted into rectangular coordinate X of total stationETS(x,y,z)。
Wherein, the observation angle reflector of the total station is used for obtaining the observation valueMultiple measurements are required and averaged.
S6 calculating true value X 'of corner reflector under radar antenna array surface coordinate system'R(x,y,z),X'R(x,y,z)=RXETS(x,y,z)+T;。
S7, repeating the steps S1-S6k times, and obtaining a group of measured values X of the radar diagonal reflector each time the positions of the diagonal reflectors are differentR={XR1,XR2,…,XRkAnd true value X 'of a set of corner reflectors under an antenna array plane coordinate system'R={X'R1,X'R2,…,X'RkAcquiring a radar system measurement error err according to the measurement value and the truth valuesys(errx,erry,errz)。
Wherein the radar system measures the error errsys(errx,erry,errz) The acquisition method comprises the following steps: respectively averaging the measured value and the true value according to x, y and z components, and subtracting to obtain the radar system measurement error errsys(errx,erry,errz). Namely:
XRi(x) Representing the X-coordinate component, X ', in the ith radar measurement'Ri(x) And the x coordinate component in the truth value obtained by the coordinate conversion calculation of the ith radar measured value is represented. The y-coordinate component and the z-coordinate component are the same as above.
S8 measuring error err of radar systemsys(errx,erry,errz) System error converted into spherical coordinate systemAnd substituting the system error of the spherical coordinate system into the detection result for calibration to finish the calibration of the system error.
Further, the calibration method comprises step S0, calibrating a stable turntable system of the radar to make the reference plane pointed by the antenna beam parallel to the ground; and when the radar works normally, performing static technical parameter test, and if the test result meets the technical index, performing step S1.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (10)
1. A radar system error calibration method based on SVD is characterized by comprising the following steps:
s1, placing a measuring instrument and a radar point target in front of an antenna array of a radar, detecting the radar point target by the radar, and obtaining a measured value of the radarAnd converted into rectangular coordinate X of antenna array surfaceR(x,y,z);
S2, determining the origin position of an antenna coordinate system, selecting n mark points at the edge of the antenna array surface, and acquiring the coordinates of each mark point in the antenna array surface coordinate system, wherein the corresponding coordinate point set is P ═ P1,p2,…,pn};
S3, respectively arranging the reflection sheet of the measuring instrument on each mark point, observing and acquiring the coordinates of each mark point under the observation coordinate system of the measuring instrument by using the measuring instrument, converting the spherical coordinates into rectangular coordinates, and setting the corresponding coordinate point set as Q ═ Q { (Q) } Q1,q2,…,qn};
S4, acquiring a rotation matrix R and a transfer matrix T between the antenna array plane coordinate system and the observation coordinate system of the measuring instrument according to the corresponding coordinate point set P of each mark point in the antenna array plane coordinate system and the corresponding coordinate point set Q in the observation coordinate system of the measuring instrument;
s5, observing the radar point target by the measuring instrument to obtain an observed valueAnd converted into rectangular coordinate X of measuring instrumentETS(x,y,z);
S6, calculating a true value X 'of the radar point target under the antenna array surface coordinate system'R(x,y,z),X'R(x,y,z)=RXETS(x,y,z)+T;;
S7, repeating the steps S1-S6k times, wherein the position of the radar point target is different every time, and obtaining a group of measured values X of the radar on the radar point targetR={XR1,XR2,…,XRkAnd a true value X 'of a group of radar point targets under the antenna array surface coordinate system'R={X'R1,X'R2,…,X'RkAcquiring a radar system measurement error err according to the measurement value and the truth valuesys(errx,erry,errz);
2. The calibration method according to claim 1, characterized in that: the calibration method further comprises step S0, calibrating the stabilizing turntable system of the radar to make the reference plane pointed by the antenna beam parallel to the ground; and when the radar works normally, performing static technical parameter test, and if the test result meets the technical index, performing step S1.
4. the calibration method according to claim 1, characterized in that: in step S1, the distance between the radar point target and the antenna wavefront is not less than 10 times the far-field distance.
5. The calibration method according to claim 1, characterized in that: in step S2, n.gtoreq.4.
6. The calibration method according to claim 1, characterized in that: in step S3, when the measuring instrument observes and acquires the coordinates of each of the mark points in the observation coordinate system of the measuring instrument, multiple measurements are required and an average value is obtained.
7. The calibration method according to claim 1, characterized in that: in step S4, the rotation matrix R and the transition matrix T are obtained as follows:
(1) the problem mathematical model is constructed as follows:
wherein wiRepresenting the weight before each point pair;
(2) decentralizing the two point sets to obtain a new point set A ═ a1,a2,…,anB ═ B1,b2,…,bnRepresents as:
(3) calculating a covariance matrix:
(4) SVD decomposition is carried out on the covariance matrix, and a rotation matrix is solved:
[U,S,V]=SVD(H)
R=VUT
9. The calibration method according to claim 1, characterized in that: in step S7, the radar system measures an error errsys(errx,erry,errz) The acquisition method comprises the following steps: respectively averaging the measured value and the true value according to x, y and z components, and subtracting to obtain the radar system measurement error errsys(errx,erry,errz)。
10. The calibration method according to claim 1, characterized in that: the measuring instrument is a total station, and the radar point target is a corner reflector.
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