CN107367235B - Shafting error calibration method of infrared area array scanning system - Google Patents

Shafting error calibration method of infrared area array scanning system Download PDF

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CN107367235B
CN107367235B CN201610316710.4A CN201610316710A CN107367235B CN 107367235 B CN107367235 B CN 107367235B CN 201610316710 A CN201610316710 A CN 201610316710A CN 107367235 B CN107367235 B CN 107367235B
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formula
equation
axis
image
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CN107367235A (en
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唐彦琴
顾国华
费小亮
钱惟贤
陈钱
隋修宝
何伟基
任侃
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Nanjing Tech University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G01B11/03—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness by measuring coordinates of points

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Abstract

The invention provides a shafting error calibration method of an infrared area array scanning system, which comprises the steps of establishing a conversion error correction equation between a horizontal coordinate system and an image coordinate system, estimating unknown parameters in the error correction equation by nonlinear least square fitting, and reversely substituting the estimated unknown parameters into the correction equation, thereby obtaining a corrected azimuth angle and a corrected pitch angle. The invention can make the code disc reading of the infrared area array scanning system more accurate, and can be widely applied to the calibration of the axis system of the area array scanning system.

Description

Shafting error calibration method of infrared area array scanning system
Technical Field
The invention belongs to the technical field of error calibration, and particularly relates to a shafting error calibration method of an infrared area array scanning system.
Background
In the process of acquiring the target azimuth, the horizontal infrared area array scanning system mainly reads through a code disc display on the rotary table, but is limited by the limitation of machining and alignment precision in the production process of the rotary table, and the code disc reading and the actual angle of an actual target may not be consistent. Therefore, how to analyze the turntable error to obtain the correction coefficient is very important in scanning of the infrared area array scanning system, and has great influence on subsequent target detection and tracking accuracy.
Disclosure of Invention
The invention provides a shafting error calibration method of an infrared area array scanning system, which can enable the code disc reading of the infrared area array scanning system to be more accurate and can be widely applied to shafting calibration of the area array scanning system.
In order to solve the technical problem, the invention provides a shafting error calibration method of an infrared area array scanning system, which comprises the steps of establishing a conversion error correction equation between a horizontal coordinate system and an image coordinate system, estimating unknown parameters in the error correction equation by nonlinear least square fitting, and reversely substituting the estimated unknown parameters into the correction equation so as to obtain a corrected azimuth angle and a corrected pitch angle.
Further, the conversion error correction equation between the horizontal coordinate system and the image coordinate system is shown in formula (1),
in the formula (1), T (X, Y, Z) is a horizontal coordinate system, and X, Y, Z are three-axis coordinates of the horizontal coordinate system respectively;is a coordinate system of the image, and is a coordinate system of the image,andrespectively image coordinates;
in the formula (1), M (v, A)vAnd, a ', E') is a rotation matrix between the horizontal coordinate system and the turntable coordinate system, as shown in equation (2),
M＝Ml(v)Mz(A')Mx(E') (2)
in the formula (2), Ml(v) As a correction matrix M for the vertical axis inclination vl(v) It is as in formula (3):
in the formula (3), AvIn the direction of inclination of the angle v；
In the formula (2), Mz(A) Is a correction matrix for the rotation angle a' in the direction, which is as in equation (4):
in the formula (2), Mx(E ') is a correction matrix for the angle of rotation in pitch E' as in equation (5):
in the formula (1), h (c)x,cy,Fx,Fy,Tx,Ty,Tz) Representing the transformation between the coordinate system of the turntable and the coordinate system of the image, and having:
wherein, Tx、TyAnd TzRespectively the translation amount of the three-axis coordinate of the coordinate system of the turntable to the coordinate system of the camera, cxAnd cyRespectively the coordinates of the pixel points of the camera, x, y and z respectively the three-axis coordinates of the coordinate system of the turntable, FxIs the equivalent focal length of the X axis, FyAn equivalent focal length for the Y axis;
c is solved firstly by adopting LM nonlinear least square methodx、cy、Fx、Fy、Tx、TyAnd TzAccording to c, thenx、cy、Fx、Fy、Tx、TyAnd TzSubstituting the optimal value into the formula (1) to obtain v and AvA 'and E'.
Compared with the prior art, the method has the remarkable advantages that when the general conversion equation from the horizontal coordinate system to the image coordinate system corrects the reading of the code disc of the rotary table, all variables are considered, and the specific variable value is obtained by an optimization iteration method, so that the reading of the azimuth angle and the pitch angle can be well corrected, and the method has reference significance for actual engineering debugging.
Drawings
Fig. 1 is a schematic view of a turntable measurement coordinate system.
FIG. 2 is a schematic diagram of an LM non-linear least squares iteration curve.
Detailed Description
It is easily understood that, according to the technical solution of the present invention, a person skilled in the art can imagine various embodiments of the shafting error calibration method of the infrared area array scanning system of the present invention without changing the spirit of the present invention. Therefore, the following detailed description and the accompanying drawings are merely illustrative of the technical aspects of the present invention, and should not be construed as all of the present invention or as limitations or limitations on the technical aspects of the present invention.
The invention relates to a shafting error calibration method of an infrared area array scanning system, which comprises the following steps of in-situ flattening a coordinate system to a turntable coordinate system and then to an image coordinate system of a thermal imager, providing a conversion error correction equation between the coordinate systems, estimating an unknown parameter value by nonlinear least square fitting, and reversely bringing the unknown parameter value into the correction equation, thereby obtaining a corrected azimuth angle and a corrected pitch angle, and improving the reading precision of a code disc, wherein the method comprises the following specific implementation steps:
step one, deriving a rotation matrix M between a horizontal coordinate system O-XYZ and a turntable coordinate system O-XYZ;
deducing a conversion relation between a turntable coordinate system o-xyz and an image coordinate system (x-, y-);
step three, establishing a total conversion matrix between the horizontal coordinate system O-XYZ and the image coordinates (x-, y-), and solving unknown parameters (v, A) in the total conversion matrix by using the original azimuth and pitch angle parameters through an LM nonlinear least square methodv,A',E',Cx,Cy,Fx,Fy,Tx,Ty,Tz) An estimated value of (d);
step four, the obtained parameters (v, A)v,A',E',Cx,Cy,Fx,Fy,Tx,Ty,Tz) Is inversely substituted into the horizontal coordinate system O-XYZ to the figureAnd obtaining the corrected azimuth angle and the corrected pitch angle in the general conversion equation of the image coordinates (x to y) so as to finish the shafting error calibration.
And step one, setting a horizontal coordinate system to be O-XYZ, and setting an origin O of the horizontal coordinate system to be an intersection point of three axes of the turntable coordinate system. Where the Z axis is perpendicular to the turntable horizontal plane, the X, Y axis is in the horizontal plane, and the Y axis points to big north, the three axes are orthogonal and satisfy the right hand coordinate system. In fact, the direction of each axis of the horizontal coordinate system is respectively the direction of a horizontal axis, a sighting axis and a vertical axis of the turntable at the theoretical zero position, the coordinate system of the turntable is O-XYZ, the y axis is the direction of a rear visual axis of the alignment target, the z axis is orthogonal to the y axis and points to the zenith, the x axis and the y axis are orthogonal at the same time, the right-hand coordinate system is formed, and the two coordinates are converted and are shown in figure 1.
Under the ideal condition without shafting errors, the turntable needs to rotate an angle A in the azimuth and rotate an angle E in the pitching from the zero position to the target, so that the horizontal coordinate system O-XYZ firstly rotates the angle A around the vertical axis X and then rotates the angle E around the horizontal axis Y, and finally the turntable coordinate system O-XYZ is obtained, namely the conversion relation between the horizontal coordinate system O-XYZ and the turntable coordinate system O-XYZ is shown as the formula (1):
wherein M isz(A) Is a conversion matrix of rotating an angle A in the azimuth of the horizontal coordinate system
Mx(E) Is a transformation matrix of the horizon coordinate system rotated by E degrees in pitch, an
In fact, since the rotating platform has axis system errors during the target detection process, the transformation matrix is affected by each inclination angle, the transformation between the horizontal coordinate system and the rotating platform coordinate system can be expressed by formula (4),
wherein M is a total rotation matrix between a horizontal coordinate system and a rotary table coordinate system, and is mainly determined by a vertical axis inclination angle v, an azimuth rotation angle A 'and a pitching rotation angle E', and the azimuth rotation angle A 'and the pitching rotation angle E' are both real readings of an instrument code disc.
Correction matrix M for vertical axis tilt angle vl(v) As in equation (5):
wherein A isvIs the direction of inclination of the angle v.
Correction matrix M for the rotation angle A' in the directionz(A) As in equation (6):
correction matrix M for pitch upper rotation angle Ex(E') is as in formula (7):
finally, according to the sequence of rotation, M is addedl(v)、Mz(A')、Mx(E') successively multiplying to obtain a total rotation matrix M between the horizontal coordinate system and the turntable coordinate system, as shown in equation (8),
M＝Ml(v)Mz(A')Mx(E') (8)
thus, the rotation matrix M of the horizontal coordinate system O-XYZ obtains the turntable coordinate system O-XYZ, wherein the parameters to be used include: azimuth rotation angle A 'and pitch rotation angle E' actually read from the code wheel, and inclination angle v and inclination direction A of the vertical axisv. However, the three parameters need to be corrected due to errors, so that the actual code disc is usedThe readings are also put in the unknown parameters of the subsequent algorithm and iterated together.
For the second step, in order to complete the conversion between the turntable coordinate system o-xyz and the image coordinate (x-, y-), firstly, a central projection model is utilized to obtain the coordinate conversion relationship between the image coordinate system (x-, y-) and the turntable coordinate system o-xyz. The method is divided into two parts, namely a turntable coordinate system o-xyz to a camera coordinate system K-XkYkZkThe conversion relation of (II), the camera coordinate system K-XkYkZkAnd (4) conversion relation with an image coordinate system (x-, y-).
From the turntable coordinate system o-xyz to the camera coordinate system K-XkYkZkThe conversion relationship of (c) can be expressed by the amount of translation, which is shown in equation (9):
wherein T ═ T (T)x,Ty,Tz) The translation vector is the coordinate of the origin of the rotating table coordinate system in the camera coordinate system, that is, the translation amount for moving the origin of the rotating table coordinate system to the origin of the camera coordinate system.
For the camera coordinate system K-XkYkZkAnd the image coordinate systemBased on the basic relationship of the central perspective projection model, the image coordinates can be obtainedAnd a camera coordinate system K-XkYkZkIs shown in equation (10):
wherein (c)x,cy) The image coordinate is the pixel point coordinate of the image, namely the image coordinate of the intersection point of the optical axis and the image plane; zkFrom object point to optical centreProjection of the distance in the direction of the optical axis, so ZkNot equal to 0; equivalent focal length F of X axisxIs the focal length f and the transverse and longitudinal dimension d of the pixelxThe ratio of (A) to (B); equivalent focal length F of Y axisyIs the focal length f and the transverse and longitudinal dimension d of the pixelyThe ratio of.
Through the transformation of the coordinate systems of the formula (9) and the formula (10) twice, the turntable coordinate system o-xyz is finally transformed into the image coordinate systemIs shown in formula (11),
for step three, first, the unknown parameters in the formula are considered, and the horizon coordinate system represented by the formula (4) is subjected to
The conversion relationship between O-XYZ and the turntable coordinate system O-XYZ can be further expressed by equation (12):
T(X,Y,Z)＝M(v,Av,A',E')R(x,y,z) (12)
wherein, M (v, A)vThe function A ', E') represents the conversion relation between the horizontal coordinate system O-XYZ and the turntable coordinate system O-XYZ, and although the angles A 'and E' have readings on the code disc, the angles A 'and E' need to be corrected, so that the angles A 'and E' are processed by unknown parameters, M (v, A) isvA ', E') have a total of 4 unknown parameters, v, AvA ', E'; t (X, Y, Z) and R (X, Y, Z) represent the horizon coordinate system and the turntable coordinate system, respectively.
Furthermore, for the turntable coordinate system o-xyz and image coordinatesThe formula (11) may further use the symbol h (c)x,cy,Fx,Fy,Tx,Ty,Tz) Expressed, as in equation (13):
wherein, h (c)x,cy,Fx,Fy,Tx,Ty,Tz) There are 7 unknown parameters, each cx,cy,Fx,Fy,Tx,Ty,Tz；And R (x, y, z) represent the image coordinate system and the turntable coordinate system, respectively.
For the third step, the first step and the second step are integrated, so that a total conversion equation of the horizontal coordinate system and the image coordinate system can be obtained:
in order to obtain the above 11 unknown parameters, the invention adopts LM nonlinear least square method to solve (c)x,cy,Fx,Fy,Tx,Ty,Tz) Then according to (c)x,cy,Fx,Fy,Tx,Ty,Tz) Substituting the optimal value into formula (13) to obtain v, AvAnd A ', E', obtaining the correction value.
Equation of parametersWherein the horizon coordinate (X, Y, Z) is obtained by a global positioning system such as GPS, and the image coordinate is obtained correspondinglyThus through what is knownTo solve for the unknown parameter (c)x,cy,Fx,Fy,Tx,Ty,Tz,v,AvA ', E'). The above solution problem is thus transformed into an optimization algorithm as shown in equation (15):
11 unknown parameters (c) were selectedx,cy,Fx,Fy,Tx,Ty,Tz,v,AvInitial point of A ', E'), parameter beta, damping coefficient mu and amplification coefficient v, and obtaining final iterative optimization values of 11 unknown parameters through iterative algorithm, thereby being capable of being substituted into a final conversion formulaAnd correcting the azimuth value A 'and the pitch value v' obtained by each turn table.
The invention adopts MATLAB to carry out simulation optimization to obtain a specific parameter optimization value, and the specific process is as follows:
firstly, constructing W ═ x; y; z is a radical of]-M; m is a coordinate system obtained by matrix rotation, [ x; y; z is a radical of]Is the GPS initial check point value, the initial value X0＝[1 1 1 1 1 1](ii) a Calling a min LM function:
x＝min LM(W,X0,0.4,2,1.5,[cx cy Fx Fy Tx Ty Tz v Av])
wherein, the iteration curve is shown in fig. 2, and when the last iteration is approximately carried out to 100 times, min tends to be flat, so that each internal optimization value c is obtained according to the x vectorx、cy、Fx、Fy、Tx、Ty、Tz、v、Av。

Claims (1)

1. A shafting error calibration method of an infrared area array scanning system is characterized in that a conversion error correction equation between a horizontal coordinate system and an image coordinate system is established, then unknown parameters in the error correction equation are estimated by nonlinear least square fitting, and the estimated unknown parameters are back-introduced into the correction equation, so that corrected azimuth angles and pitch angles are obtained;
the conversion error correction equation between the horizontal coordinate system and the image coordinate system is shown in formula (1),
in the formula (1), T (X, Y, Z) is a horizontal coordinate system, and X, Y, Z are three-axis coordinates of the horizontal coordinate system respectively;is a coordinate system of the image, and is a coordinate system of the image,andrespectively image coordinates;
in the formula (1), M (v, A)vAnd, a ', E') is a rotation matrix between the horizontal coordinate system and the turntable coordinate system, as shown in equation (2),
M＝Ml(v)Mz(A')Mx(E') (2)
in the formula (2), Ml(v) As a correction matrix M for the vertical axis inclination vl(v) It is as in formula (3):
in the formula (3), AvAn inclination direction at an inclination angle v;
in the formula (2), Mz(A) Is a correction matrix for the rotation angle a' in the direction, which is as in equation (4):
in the formula (2), Mx(E ') is a correction matrix for the angle of rotation in pitch E' as in equation (5):
in the formula (1), h (c)x,cy,Fx，Fy，Tx，Ty，Tz) Representing the transformation between the coordinate system of the turntable and the coordinate system of the image, and having:
wherein, Tx、TyAnd TzRespectively the translation amount of the three-axis coordinate of the coordinate system of the turntable to the coordinate system of the camera, cxAnd cyRespectively the coordinates of the pixel points of the camera, x, y and z respectively the three-axis coordinates of the coordinate system of the turntable, FxIs the equivalent focal length of the X axis, FyAn equivalent focal length for the Y axis;
c is solved firstly by adopting LM nonlinear least square methodx、cy、Fx、Fy、Tx、TyAnd TzAccording to c, thenx、cy、Fx、Fy、Tx、TyAnd TzSubstituting the optimal value into the formula (1) to obtain v and AvA 'and E'.
CN201610316710.4A 2016-05-13 2016-05-13 Shafting error calibration method of infrared area array scanning system Expired - Fee Related CN107367235B (en)

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