CN108447100B - Method for calibrating eccentricity vector and visual axis eccentricity angle of airborne three-linear array CCD camera - Google Patents
Method for calibrating eccentricity vector and visual axis eccentricity angle of airborne three-linear array CCD camera Download PDFInfo
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Abstract
The invention provides a calibration method for an eccentricity vector and a visual axis eccentricity angle of an airborne three-linear array CCD camera. Firstly, establishing a GNSS eccentricity vector calibration model and an IMU visual axis eccentricity angle calibration model of an airborne three-linear array CCD camera; secondly, designing a cyclic two-step method GNSS eccentric vector and IMU visual axis eccentric angle calibration scheme; and finally, obtaining stable and reliable calibration values of the GNSS eccentric vector and the IMU visual axis eccentric angle by implementing a cyclic two-step method calibration scheme of the GNSS eccentric vector and the IMU visual axis eccentric angle. By adopting the method, the stable calibration values of the GNSS eccentric vector and IMU visual axis eccentric angle of the airborne large-visual-field three-linear-array CCD camera can be obtained, the system error in the observation value of the GNSS/IMU of the airborne three-linear-array CCD camera is effectively removed, the uncontrolled direct positioning precision is obviously improved, and the dependence degree of aerial triangulation processing on ground control points is effectively reduced.
Description
Technical Field
The invention belongs to the technical field of photogrammetry and remote sensing mapping, and particularly relates to a method for calibrating an eccentric vector and a visual axis eccentric angle of an airborne three-linear array CCD camera.
Background
The three-linear array CCD camera has stable geometric relationship, clear image, accurate three-dimensional measurement and high surveying and mapping production efficiency, is widely applied to the aspects of aerospace remote sensing, and is the mainstream surveying and mapping camera at present. Calibrating the three-linear array CCD camera, and checking the system error is a key step for ensuring the geometric positioning precision of the data product.
The satellite-borne three-linear array CCD camera platform is stable, the system error is single, the calibration difficulty is small, and the calibration technology is mature at present. Data products of three-linear array CCD three-dimensional mapping satellites of 'Tianzhu No. one' and 'YueIII' in China are already put into the market. The airborne three-linear array CCD camera adopts an airplane as a remote sensing platform, the platform has large jitter, the system error is complex, and the calibration difficulty is large. ADS40/80/100 series cameras introduced abroad are commonly used at home, calibration and geometric processing are performed by matching ORIMA software, and processing research is limited to data products processed by the ORIMA software. The relative lag between the development of the airborne three-linear array CCD camera and the research on the geometric processing is lacked in-depth research on the calibration and the geometric error processing of the airborne three-linear array CCD camera.
GFXJ is the first airborne large-visual-field three-line array CCD camera which is self-developed under the great special support of a high-resolution earth observation system in China. The subject group initiatively develops the camera calibration technology of the autonomous property right airborne large-view-field three-line array CCD camera in China. The GFXJ camera adopts a three-line array push-broom mode for imaging, a ground target can be subjected to push-broom imaging from three different angles of forward view, downward view and backward view simultaneously in the aerial photography process, and 3-view panchromatic images and 4-wave-band multispectral (R, G, B and NIR) images are provided. Each CCD (Charge-coupled Device) line array reaches 32756 pixels, and is a single line CCD with the most pixels at present, instead of multi-chip splicing. The pixel size is 5um, and the camera focal length reaches 130 mm. Compared with ADS cameras, the camera has the advantages of longer focal length, wider CCD and wider coverage. In order to improve the image positioning precision, the following requirements are met: the requirement of 1000 scale topographic maps is met, the uncontrolled direct positioning precision level of the surveying and mapping camera is further improved, the dependence on ground control points in aerial triangulation processing is reduced, and the inherent system error source in airborne three-linear array CCD camera three-dimensional surveying and mapping needs to be calibrated. The three-dimensional surveying and mapping precision of the airborne three-linear array CCD camera is reduced, and a system error source causing geometric deformation of images mainly comprises two parts: one part is the eccentric vector of the center of the GNSS antenna and the eccentric angle of the visual axis of the IMU, and the other part is distortion errors of a camera lens, a CCD and the like.
Disclosure of Invention
The invention aims to provide a circulating two-step method for calibrating an eccentric vector and an eccentric angle of a visual axis of an airborne large-visual-field three-linear-array CCD camera, which can effectively remove system errors in GNSS and IMU observation values of the airborne three-linear-array CCD camera, remarkably improve the accuracy of uncontrolled direct positioning and effectively reduce the degree of dependence of aerial triangulation processing on ground control points.
The invention adopts the following technical scheme:
the method for calibrating the eccentric vector and the visual axis eccentric angle of the airborne three-linear array CCD camera is characterized by comprising the following steps of: the method comprises the following steps:
a: establishing a strict imaging model for an image of an airborne three-linear array CCD camera;
the step A comprises the following steps:
a1: converting the GNSS/IMU observation data in the strict imaging model into a UTM map projection coordinate system;
a2: establishing a strict imaging model of each scanning action center for an airborne three-linear array CCD camera image;
wherein, (X, Y, Z) is ground point coordinate, (X, Y) is image point coordinate, f is focal length of airborne three-wire array CCD camera, (X) is focal length of airborne three-wire array CCD camera
S j,Y
S j,Z
S j) The line elements are the external orientation elements of the jth scanning line, s is expressed as the projection center of the airborne three-line array CCD camera, and GNSS/IMU observation data are used as initial values;
corner element being the exterior orientation element of the jth scan line
A constructed rotation matrix;
by using
(OPK) system, with X-axis as first rotation axis, Y-axis as second rotation axis, Z-axis as third rotation axis,
the direction angles all adopt positive rotation;
the rotation matrix is then:
b: carrying out multi-route image matching based on GPU acceleration processing on the airborne three-linear array CCD image, and extracting data information of a connection point;
c: constructing a large-scale adjustment area network with multiple routes, and carrying out aerial triangulation processing;
d: establishing a GNSS eccentricity vector calibration model and an IMU visual axis eccentricity angle calibration model, respectively calibrating the GNSS eccentricity vector and the IMU visual axis eccentricity angle to obtain calibration values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)；
D1: establishing the GNSS eccentric vector calibration model of the airborne three-linear array CCD camera
According to the imaging relation, the GNSS eccentricity vector calibration model is established as follows:
wherein R is the picture attitude angle system
(OPK) the determined rotation matrix; a represents an airborne GNSS antenna, O-XYZ is a ground-assisted coordinate system, and the coordinate of the phase center of the GNSS antenna is (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is an image space coordinate system, and the coordinates of the GNSS antenna are (u, v, w);
establishing the GNSS eccentricity vector calibration model on the basis of the GNSS eccentricity vector calibration model:
wherein the content of the first and second substances,
as phase center coordinates (X) of GNSS antenna
A，Y
A，Z
A) The residual term (Δ u, Δ v, Δ w) is the correction number of the GNSS eccentricity vector, and the step C obtains an external orientation element value (X)
S,Y
S,Z
S) The initial value of (u, v, w) is the actual measurement value or zero value, R is the value of the exterior orientation element obtained in the step C4 and is calculated according to the formula (2), and then the calculation value (X) of the phase center coordinate of the antenna is calculated according to the formula (7)
A，Y
A，Z
A)
0。
D2: establishing an IMU visual axis eccentric angle calibration model of the airborne three-linear array CCD camera;
let GNSS/IMU measure attitude angle directly as (α, gamma), and its formed rotation matrix as
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
Respectively as follows:
wherein subscript b represents IMU and c represents aerial photography instrument; the IMU visual axis eccentric angle can be decomposed into angle deviations in 3 directions, namely e
x，e
y，e
z；
Then:
-inversely calculating angle values (α, γ) from said rotation matrix (2), establishing an observation equation for said attitude angle of the GNSS/IMU:
establishing an IMU collimation axis eccentric angle calibration model of the airborne three-linear array CCD camera as follows:
wherein (α, gamma) is the attitude angle (upsilon) directly measured by the GNSS/IMU
α,υ
β,υ
γ) A residual term, (Δ e) for the attitude angle (α, γ) of the GNSS/IMU direct measurement
x,Δe
y,Δe
z) Is the correction of the eccentric angle of the visual axis of the IMU, B
2Is a corresponding coefficient matrix;
calculating the value of the exterior orientation element obtained in the step C by using the formula (2);
is prepared from (e)
x,e
y，e
z) The value is calculated by the formula (2) and (e)
x，e
y，e
z) The initial value may be taken to be zero; by the formula (9)
And
multiplication to obtain
(α,β,γ)
0Is formed by
Calculating the attitude angle by using the formula (10);
d3: taking each orientation plate as sampling data, adopting the GNSS eccentricity vector calibration model and the IMU sighting axis eccentricity angle calibration model to calibrate the GNSS eccentricity vector and the IMU sighting axis eccentricity angle, and respectively obtaining the calibration values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)；
E: updating an external orientation element by utilizing the GNSS eccentricity vector and the calibration value of the IMU visual axis eccentricity angle;
f: taking the sum of the correction of the external orientation element and the correction of the GNSS eccentricity vector and the correction of the IMU visual axis eccentricity angle as a cycle parameter, and judging the difference between the cycle parameter after iteration and iteration; when the difference of the loop parameters is smaller than a threshold value, the iteration is ended, and a loop is skipped; and E, when the difference of the circulation parameters is larger than a threshold value, iterating and circulating the steps C-E on the basis of the external orientation element value updated in the step E.
Preferably, in the present invention, the step C further includes the steps of:
c1: modeling the comprehensive influence of lens distortion and CCD deformation, constructing the large-scale adjustment area network of multiple routes aiming at the comprehensive influence of the lens distortion and the CCD deformation, and setting an offset value delta x of the actual geometric position of each probe element relative to the position of a laboratory calibration value under the comprehensive influence of the lens distortion and the CCD deformation
0,Δy
0；
C2: setting each scanning line via
(OPK) taking the GNSS/IMU observation value converted by the system as an initial value, and constructing an orientation sheet adjustment model of the airborne three-linear array CCD camera image;
the orientation piece adjustment model adopts an improved Lagrange linear interpolation model to describe track and attitude changes of the airborne three-linear array CCD camera and is provided with a lower image point P of a ground point P
NImaging on the jth scan line, the lower image point p
NThe outer orientation element of the scanning line j is obtained by interpolation of the outer orientation elements of the k directional slice and the k +1 directional slice;
the outer square element model of the directional slice is as follows:
wherein (ω)
j，
κ
j) Is the corner element of the exterior orientation element of the jth scan line, (X)
S k,Y
S k,Z
S k,ω
S k,
κ
S k) An exterior orientation element of the k-th oriented piece, (X)
S k+1,Y
S k+1,Z
S k+1,ω
S k+1,
κ
S k+1) The outer orientation element of the k +1 th oriented piece;
is a weight coefficient calculated from the imaging time of the kth directional slice and the kth +1 directional slice, t
jIs imaging of the jth scan lineTime, t
kIs the imaging time of the k-th orientation plate, t
k+1Is the imaging time of the (k + 1) th oriented slice; then δ X
j,δY
j,δZ
j,δω
j,
δκ
jTo correct the item:
(X
GNSS k,Y
GNSS k,Z
GNSS k,ω
IMU k,
κ
IMU k) (X) GNSS/IMU observations for the kth orientation piece
GNSS k+1,Y
GNSS k+1,Z
GNSS k+1,ω
IMU k+1,
κ
IMU k+1) GNSS/IMU observations for the (k + 1) th directional slice, (X)
GNSS j，Y
GNSS j，Z
GNSS j，ω
IMU j，
κ
IMU j) A GNSS/IMU observation for the jth scan line;
introducing the offset value Deltax of the probe position
0,Δy
0Substituting the formula (3) into the formula (1) to obtain the alignment sheet adjustment model of the airborne three-linear array CCD camera image:
c3: constructing the adjustment area network according to the sequence of the multiple routes, and implementing adjustment of the area network;
linearizing the formula (5) to obtain an adjustment equation based on the orientation sheet:
wherein (dX)
S k,dY
S k,dZ
S k,dω
S k,
dκ
S k) The correction number of the outer orientation element for the k-th oriented piece; (dX)
S k+1,dY
S k+1,dZ
S k+1,dω
S k+1,
dκ
S k+1) The correction number of the exterior orientation element oriented for the k +1 th piece; v. of
x，v
yIs a residual term; l
x，l
yIs a constant term; dX, dY and dZ are correction numbers of the coordinates of the control points; c. C
ja
11,c
ja
12,c
ja
13,c
ja
14,c
ja
15,c
ja
16Is the correction dX in the first equation in the above equation set
S k,dY
S k,dZ
S k,dω
k,
dκ
kThe coefficient of (a); (1-c)
j)a
11,(1-c
j)a
12,(1-c
j)a
13,(1-c
j)a
14,(1-c
j)a
15,(1-c
j)a
16Is the correction dX in the first equation in the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a); c. C
ja
21,c
ja
22,c
ja
23,c
ja
24,c
ja
25,c
ja
26Is the correction dX in the second equation of the above equation set
S k,dY
S k,dZ
S k,dω
k,
dκ
kThe coefficient of (a). (1-c)
j)a
21,(1-c
j)a
22,(1-c
j)a
23,(1-c
j)a
24,(1-c
j)a
25,(1-c
j)a
26Is the correction dX in the second equation of the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a).
According to the sequence of the multiple routes and the formula (6), establishing the structure of the adjustment area network, performing adjustment of the area network, and performing aerial triangulation processing to obtain an external orientation element value of the orientation sheet;
c4: interpolating and updating the exterior orientation element of each scan line by using the exterior orientation element value of the orientation patch obtained by the block adjustment according to the exterior orientation element model of the orientation patch;
c5: calibrating the offset value Deltax
0,Δy
0And updating the geometric position calibration value of each probe element on the front-view CCD, the lower-view CCD and the rear-view CCD.
Preferably, in the present invention, the step E includes the steps of:
e1: updating the line elements of the external orientation with the calibration values (Δ u, Δ v, Δ w):
r is the attitude angle system of the photo
(OPK) the determined rotation matrix; a represents an airborne GNSS antenna, O-XYZ is a ground-assisted coordinate system, and the coordinate of the phase center of the GNSS antenna is (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is an image space coordinate system, and the coordinates of the phase center of the GNSS antenna in the image space coordinate system are (u, v, w), namely the GNSS eccentricity vector.
E2: using a calibration value (Δ e)
x，Δe
y，Δe
z) Updating the corner elements of the external orientation:
let the attitude angle directly measured by the GNSS/IMU be (α, gamma), and the formed rotation matrix be
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
The invention aims to provide a method for calibrating an eccentric vector and an eccentric angle of a visual axis of an airborne large-visual-field three-linear-array CCD camera by a cyclic two-step method, wherein the algorithm core is to establish a GNSS eccentric vector calibration model and an IMU visual axis eccentric angle calibration model of the airborne three-linear-array CCD camera; by designing a cyclic two-step method GNSS eccentric vector and IMU visual axis eccentric angle calibration scheme, the GNSS eccentric vector and IMU visual axis eccentric angle calibration value of the airborne three-linear array CCD camera can be stably and reliably calibrated, system errors in the GNSS and IMU observation values of the airborne three-linear array CCD camera are effectively removed, uncontrolled direct positioning precision is remarkably improved, and the degree of dependence of aerial triangulation processing on ground control points is effectively reduced.
Drawings
FIG. 1 is a schematic view of an alignment sheet model according to the present invention;
FIG. 2 is a schematic view of an eccentricity vector of a GNSS antenna relative to a perspective center S according to the present invention;
FIG. 3 is a schematic diagram of the relative geometry between the IMU and the aerial camera of the present invention;
FIG. 4 is a schematic view of the apparent axis eccentricity angle between the IMU and the aerial camera;
FIG. 5 is a graph of distribution of experimental zones and control points in accordance with an embodiment of the present invention;
FIG. 6 is a schematic diagram of geometric residuals directly located according to experimental data in an embodiment of the present invention;
FIG. 7 is a schematic illustration of the geometric residual error after adjustment and calibration based on experimental data in an embodiment of the present invention;
FIG. 8 is a schematic diagram of the geometric residuals after 2 nd direct positioning according to the experimental data in an embodiment of the present invention;
FIG. 9 is a schematic diagram of the geometric residuals after 3 rd direct positioning according to the experimental data in an embodiment of the present invention.
Detailed Description
The invention relates to a circulating two-step method for calibrating an eccentric vector and an eccentric angle of a visual axis of a domestic airborne large-visual-field three-line array CCD camera, which comprises the following steps:
a: establishing a strict imaging model for an image of an airborne three-linear array CCD camera;
wherein the step A comprises the following steps:
a1: converting GNSS/IMU observation data of the airborne three-linear array CCD camera image into a UTM map projection coordinate system; it should be noted that the GNSS/IMU observation data can be converted not only to the UTM map projection coordinate system, but also to a local ground assistance coordinate system or a geocentric space rectangular coordinate system;
a2: establishing a strict imaging model of each scanning action center for an airborne three-linear array CCD camera image;
wherein, (X, Y, Z) is ground point coordinate, (X, Y) is image point coordinate, f is focal length of airborne three-wire array CCD camera, (X) is focal length of airborne three-wire array CCD camera
S j,Y
S j,Z
S j) The line elements are the external orientation elements of the jth scanning line, s is expressed as the projection center of the airborne three-line array CCD camera, and GNSS/IMU observation data are used as initial values;
corner element being the exterior orientation element of the jth scan line
A constructed rotation matrix;
by using
(OPK) system, with X-axis as first rotation axis, Y-axis as second rotation axis, Z-axis as third rotation axis,
the direction angles all adopt positive rotation;
there are two main types of photogrammetric angle element systems commonly used internationally:
(OPK) System and
provided is a system.
The (OPK) system is a corner element system recommended by ISPRS (International society for photogrammetry and remote sensing), takes an X axis as a first rotating axis,
the angle is rotated in the positive direction.
The rotation matrix is then:
the invention can adopt two photogrammetric angle element systems for rotation, and the invention adopts
The (OPK) system is illustrated.
B: carrying out multi-route image matching based on GPU acceleration processing on the airborne three-linear array CCD image, and extracting data information of a connection point; it is prior art in the field of the present invention, and will not be described repeatedly herein.
C: constructing a large-scale adjustment area network with multiple routes, and carrying out aerial triangulation processing;
the step C also comprises the following steps:
c1: modeling the comprehensive influence of lens distortion and CCD deformation, constructing the multi-route adjustment area network aiming at the comprehensive influence of the lens distortion and the CCD deformation, and setting an offset value delta x of the actual geometric position of each probe element relative to the position of a laboratory calibration value under the comprehensive influence of the lens distortion and the CCD deformation
0,Δy
0；
C2: setting each scanning line via
(OPK) taking the GNSS/IMU observation value converted by the system as an initial value, and constructing an orientation sheet adjustment model of the airborne three-linear array CCD camera image;
the directional slice adjustment model adopts an improved Lagrange linear interpolation model to describe track and attitude changes of the airborne three-linear array CCD camera, and a lower image point P of a ground point P is set as shown in figure 1
NImaging on the jth scan line, the lower image point p
NThe outer orientation element of the scanning line j is obtained by interpolation of the outer orientation elements of the k directional slice and the k +1 directional slice;
the outer square element model of the directional slice is as follows:
wherein (ω)
j，
κ
j) Is the corner element of the exterior orientation element of the jth scan line, (X)
S k,Y
S k,Z
S k,ω
S k,
κ
S k) An exterior orientation element for the kth oriented piece, the exterior orientation element having an initial value of
GNSS/IMU Observations of (OPK) systems, (X)
S k+1,Y
S k+1,Z
S k+1,ω
S k+1,
κ
S k+1) The outer orientation element of the k +1 th oriented piece;
is a weight coefficient calculated from the imaging time of the kth directional slice and the kth +1 directional slice, t
jIs the imaging time of the jth scan line, t
kIs the imaging time of the k-th orientation plate, t
k+1Is the imaging time of the (k + 1) th oriented slice; then δ X
j,δY
j,δZ
j,δω
j,
δκ
jTo correct the item:
(X
GNSS k,Y
GNSS k,Z
GNSS k,ω
IMU k,
κ
IMU k) (X) GNSS/IMU observations for the kth orientation piece
GNSS k+1,Y
GNSS k+1,Z
GNSS k+1,ω
IMU k+1,
κ
IMU k+1) GNSS/IMU observations for the (k + 1) th directional slice, (X)
GNSS j，Y
GNSS j，Z
GNSS j，ω
IMU j，
κ
IMU j) A GNSS/IMU observation for the jth scan line;
introducing the offset value Deltax of the probe position
0,Δy
0Substituting the formula (3) into the formula (1) to obtain the airborne IIIThe alignment film adjustment model of the linear array CCD camera image is as follows:
c3: constructing the adjustment area network according to the sequence of the multiple routes, and implementing adjustment of the area network;
linearizing the formula (5) to obtain an adjustment equation based on the orientation sheet:
wherein (dX)
S k,dY
S k,dZ
S k,dω
S k,
dκ
S k) The correction number of the outer orientation element for the k-th oriented piece; (dX)
S k+1,dY
S k+1,dZ
S k+1,dω
S k+1,
dκ
S k+1) The correction number of the exterior orientation element oriented for the k +1 th piece; v. of
x，v
yIs a residual term; l
x，l
yIs a constant term; dX, dY and dZ are correction numbers of the coordinates of the control points; c. C
ja
11,c
ja
12,c
ja
13,c
ja
14,c
ja
15,c
ja
16Is the correction dX in the first equation in the above equation set
S k,dY
Sk,dZ
S k,dω
k,
dκ
kThe coefficient of (a); (1-c)
j)a
11,(1-c
j)a
12,(1-c
j)a
13,(1-c
j)a
14,(1-c
j)a
15,(1-c
j)a
16Is the correction dX in the first equation in the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a); c. C
ja
21,c
ja
22,c
ja
23,c
ja
24,c
ja
25,c
ja
26Is the correction dX in the second equation of the above equation set
S k,dY
S k,dZ
S k,dω
k,
dκ
kThe coefficient of (a). (1-c)
j)a
21,(1-c
j)a
22,(1-c
j)a
23,(1-c
j)a
24,(1-c
j)a
25,(1-c
j)a
26Is the correction dX in the second equation of the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a).
According to the sequence of the multiple routes and the formula (6), establishing the structure of the adjustment area network, performing adjustment of the area network, and performing aerial triangulation processing to obtain an external orientation element value of the orientation sheet;
c4: interpolating and updating the exterior orientation element of each scan line by using the exterior orientation element value of the orientation patch obtained by the block adjustment according to the exterior orientation element model of the orientation patch;
c5: calibrating the offset value Deltax
0,Δy
0And updating the geometric position calibration value of each probe element on the front-view CCD, the lower-view CCD and the rear-view CCD.
D: establishingRespectively calibrating the GNSS eccentricity vector and the IMU visual axis eccentricity angle to obtain calibrated values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)；
D1: establishing the GNSS eccentric vector calibration model of the airborne three-linear array CCD camera
In the GNSS/IMU combined system, the GNSS relative dynamic positioning determines the spatial position of the phase center of the onboard GNSS antenna, and the photogrammetry requires the spatial coordinates of the rear node of the camera, i.e. the perspective center. The vector of eccentricity of the GNSS antenna with respect to the perspective center S is shown in fig. 2.
According to the imaging relation, the GNSS eccentricity vector calibration model is established as follows:
wherein R is the picture attitude angle system
(OPK) the determined rotation matrix; a represents an airborne GNSS antenna, O-XYZ is a ground-assisted coordinate system, and the coordinate of the phase center of the GNSS antenna is (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is like a space coordinate system, and the GNSS antenna has coordinates of (u, v, w).
In view of strong correlation and complexity of external orientation elements of an airborne three-linear array CCD camera, the invention provides a cyclic two-step calibration scheme, the external orientation element solution and the GNSS eccentricity vector calibration are separately and circularly solved, and the external orientation elements are known fixed values in the GNSS eccentricity vector calibration process.
Establishing the GNSS eccentricity vector calibration model on the basis of the GNSS eccentricity vector calibration model:
wherein the content of the first and second substances,
as phase center coordinates (X) of GNSS antenna
A，Y
A，Z
A) The residual term (Δ u, Δ v, Δ w) is the correction number of the GNSS eccentricity vector, and the step C obtains an external orientation element value (X)
S,Y
S,Z
S) The initial value of (u, v, w) is the actual measurement value or zero value, R is the value of the exterior orientation element obtained in the step C4 and is calculated according to the formula (2), and then the calculation value (X) of the phase center coordinate of the antenna is calculated according to the formula (7)
A，Y
A，Z
A)
0；
D2: establishing an IMU visual axis eccentric angle calibration model of the airborne three-linear array CCD camera
The GNSS/IMU provides position, attitude, velocity, acceleration, etc. information of the IMU in the local horizontal coordinate system, but the photogrammetric positioning requires the position and attitude of the aerial camera in the object coordinate system. The angular difference between the two corresponding axes is called the IMU boresight eccentricity angle, and the relative relationship is shown in FIG. 3.
Let the attitude angle directly measured by the GNSS/IMU be (α, gamma), and the formed rotation matrix be
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
Respectively as follows:
wherein subscript b represents IMU and c represents aerial photography instrument; the IMU visual axis eccentric angle can be decomposed into angle deviations in 3 directions, namely e
x，e
y，e
zAs shown in fig. 4.
Then:
from the rotation matrix (2) or a second kind
The rotation matrix in the system performs an inverse calculation of the angle values (α, γ), establishing an observation equation for the attitude angle of the GNSS/IMU:
according to the cyclic two-step calibration scheme provided by the invention, in the calibration process of the IMU visual axis eccentric angle, the external orientation element is fixed to be a constant, and the IMU visual axis eccentric angle calibration model of the airborne three-linear array CCD camera is provided and established as follows:
wherein (α, gamma) is the attitude angle directly measured by the GNSS/IMU, and (v)
α,v
β,v
γ) A residual term for an attitude angle (α, gamma) directly measured by the GNSS/IMU, ([ delta ] e)
x，Δe
y，Δe
z) Is the correction of the eccentric angle of the visual axis of the IMU, B
2Is a corresponding coefficient matrix;
calculating the value of the exterior orientation element obtained in the step C by using the formula (2);
is prepared from (e)
x，e
y，e
z) The value is calculated by the formula (2) and (e)
x，e
y，e
z) The initial value may be taken to be zero; by the formula (9)
And
multiplication to obtain
(α,β,γ)
0Is formed by
Calculating the attitude angle by using the formula (10);
d3: taking each orientation plate as sampling data, adopting the GNSS eccentricity vector calibration model and the IMU sighting axis eccentricity angle calibration model to calibrate the GNSS eccentricity vector and the IMU sighting axis eccentricity angle, and respectively obtaining the calibration values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)。
E: updating an external orientation element by utilizing the GNSS eccentricity vector and the calibration value of the IMU visual axis eccentricity angle;
the step E comprises the following steps:
e1: updating the line elements of the external orientation with the calibration values (Δ u, Δ v, Δ w):
r is the attitude angle system of the photo
(OPK) the determined rotation matrix; a represents an airborne GNSS antenna, and O-XYZ is groundThe auxiliary coordinate system has the GNSS antenna phase center with the coordinate of (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is like a space coordinate system, and the GNSS antenna has coordinates of (u, v, w).
E2: using a calibration value (Δ e)
x，Δe
y，Δe
z) Updating the corner elements of the external orientation:
let the attitude angle directly measured by the GNSS/IMU be (α, gamma), and the formed rotation matrix be
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
F: taking the sum of the correction of the external orientation element and the correction of the GNSS eccentricity vector and the correction of the IMU visual axis eccentricity angle as a cycle parameter, and judging the difference between the cycle parameter after iteration and iteration; when the difference of the loop parameters is smaller than a threshold value, the iteration is ended, and a loop is skipped; and E, when the difference of the circulation parameters is larger than a threshold value, iterating and circulating the steps C-E on the basis of the external orientation element value updated in the step E.
The threshold value can be set artificially according to actual conditions.
Example 1
In the embodiment, a GFXJ camera is adopted to perform the adjustment and calibration experiment of the area network in 1 group of data. 214 permanent high-precision control points are distributed in a grading mode in the control points in a buried stone mode.
Fig. 5 shows the distribution diagram of the experimental area and the control points, and the flight heights of the two experiments are 2000 meters. The solid line frame represents the acquired four crossed route data, 70 control points are distributed in the image coverage area, wherein 21 control points are located in the overlapping range of a plurality of routes, and the data are experimental data A.
The coordinates of the image points of the control points are manually measured, and the precision is about 0.3 pixel. The experimental data A four routes adopt an SIFT feature matching algorithm, a GPU acceleration calculation and RANSAC matching gross error point elimination strategy are utilized to implement interactive block image matching among multiple routes, 63088 feature connection points are extracted in total, 63088 feature connection points are subjected to gross error point elimination and screening processing again according to the theoretical basis that the same-name image points on the front/lower/rear three-view CCD images of the GFXJ camera are intersected with the same point on the ground, and finally 14157 points are reserved for area network adjustment and calibration processing. And (3) extracting 21389 feature connection points from the two routes of the experimental data B after SIFT feature matching, performing gross error point elimination and screening treatment, and finally reserving 8802 points for block adjustment and calibration treatment.
The experimental data A is subjected to four groups of experiments, wherein ① direct positioning experiments are carried out, GNSS/IMU measurement values and laboratory measurement values of positions of front/lower/rear view CCD detector elements are used as initial values to carry out direct positioning, initial positioning precision of a camera is checked, error sources are analyzed, ② regional net adjustment and GNSS/IMU calibration experiments are carried out to carry out circulating two-step calibration, calibration values, GNSS eccentric vectors and IMU visual axis eccentric angles of each detector element geometric position of the front/lower/rear view CCD are obtained, positioning precision after regional net adjustment and calibration processing is obtained, ③ 2 nd direct positioning experiment is carried out, the GNSS/IMU measurement values are corrected by using the front/lower/rear view CCD element positioning calibration values and the GNSS/IMU measurement values as external position elements to carry out direct positioning, the precision level of direct positioning of the camera after regional net adjustment is checked, ④ rd direct positioning experiment is carried out, GNSS visual axis eccentric vectors and IMU axial angle calibration values are used to carry out correction, and the GNSS/IMU correction value is obtained by using the GNSS/IMU correction, the GNSS/IMU correction value, the forward/lower/rear view position correction, the GNSS and the positioning precision of the GNSS/IMU correction value is verified, the positioning precision of the positioning accuracy of.
The experimental data A and the experimental results are shown in Table 1, the second row of Table 1 lists the direct positioning experimental results, the third row lists the adjustment of the area network and the positioning precision after calibration, the fourth row shows the 2 nd direct positioning precision, and the fifth row shows the 3 rd direct positioning precision. The positioning accuracy indexes of the three directions X, Y and Z of each group of experiments are counted respectively in the 2 nd column, the 3 rd column and the 4 th column. In table 1, the second, fourth and fifth rows of statistics are accuracy indexes of all control points, and the second row of statistics is accuracy indexes of 20 remaining check points after 50 control points are used for adjustment and calibration.
TABLE 1 direct localization, block adjustment and calibration results for Experimental data A
It can be seen from the second row of table 1 that the image direct positioning accuracy has a large systematic error by using the raw parameters of the GFXJ camera and the GNSS/IMU measurement values. From the third row of table 1, it can be seen that after adjustment and calibration processing of the local area network, the positioning error caused by the deformation of the camera lens and the CCD, the GNSS eccentric vector, and the IMU view axis eccentric angle is effectively eliminated. From the 2 nd direct positioning experiment result, it can be seen that the positioning error caused by geometric deformation such as lens distortion, CCD rotation and scaling can be effectively improved by using the front/down/back vision CCD probe position calibration value, and especially the elevation positioning error is improved remarkably, but the plane precision improvement effect is not significant. The 3 rd direct positioning result shows that the positioning precision in X, Y and Z directions is remarkably improved by utilizing the front/lower/rear view CCD probe position calibration value and the GNSS/IMU correction value for direct positioning, the precision level is close to the positioning precision after adjustment and calibration of a regional net, and the result proves that the GNSS eccentricity vector and the IMU visual axis eccentricity angle are a main error source influencing the geometric positioning precision of the GFXJ camera and must be considered in the geometric calibration of the airborne trilinear array CCD camera.
The experimental results in table 1 are plotted, and fig. 6 shows the distribution of positioning residuals of 70 control points after the experimental data a is directly geometrically positioned, the left graph shows the distribution of residuals in the planar direction (X, Y direction), and the right graph shows the distribution of residuals in the elevation direction. Fig. 7 lists the distribution of the residuals for the zonal net adjustment and 70 post calibration control points, and fig. 8 and 9 lists the distributions of the residuals for the 2 nd and 3 rd direct fixes, respectively. Where the residual coordinates shown in fig. 6-9 are in a local coordinate system.
As can be seen from FIG. 7, the laboratory measurement values and the GNSS/IMU measurement values of the positions of the front/down/back vision CCD probe elements are directly positioned, the experimental result has obvious system errors, the plane residual errors of different routes have obvious directionality, and the elevation residual errors are very consistent. Fig. 7 shows that after adjustment and calibration processing of the local area network, systematic errors caused by GNSS eccentricity vectors, IMU visual axis eccentricity angles, lens distortion, CCD distortion, and the like are effectively eliminated, residual errors on control points no longer appear systematic, and residual errors should be mainly accidental errors. And calibrating the geometric position of each probe element on the front/lower/rear-view CCD by using the calibrated lens distortion and CCD deformation parameters to obtain a probe element position calibration value of the front/lower/rear-view CCD, and performing 2 nd direct positioning together with the GNSS/IMU measurement value, wherein the elevation precision is obviously improved, but the plane precision is not obviously improved as shown in FIG. 8. Correcting the GNSS/IMU correction value by utilizing the GNSS eccentricity vector and the IMU visual axis eccentricity angle calibration value, and performing 3 rd time direct positioning by utilizing the front/down/back vision CCD detection element position calibration value and the GNSS/IMU correction value, wherein the plane and elevation precision is obviously improved, and the precision is close to the adjustment of a regional network and the precision level of the calibrated geometric positioning.
The above embodiments are only for illustrating the invention and are not to be construed as limiting the invention, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention, therefore, all equivalent technical solutions also belong to the scope of the invention, and the scope of the invention is defined by the claims.
Claims (3)
1. The method for calibrating the eccentric vector and the visual axis eccentric angle of the airborne three-linear array CCD camera is characterized by comprising the following steps of: the method comprises the following steps:
a: establishing a strict imaging model for an image of an airborne three-linear array CCD camera;
the step A comprises the following steps:
a1: converting the GNSS/IMU observation data in the strict imaging model into a UTM map projection coordinate system;
a2: establishing a strict imaging model of each scanning action center for an airborne three-linear array CCD camera image;
wherein, (X, Y, Z) is ground point coordinate, (X, Y) is image point coordinate, f is focal length of airborne three-wire array CCD camera, (X) is focal length of airborne three-wire array CCD camera
S j,Y
S j,Z
S j) The line elements are the external orientation elements of the jth scanning line, s is expressed as the projection center of the airborne three-line array CCD camera, and GNSS/IMU observation data are used as initial values;
corner element being the exterior orientation element of the jth scan line
A constructed rotation matrix;
by using
The system takes an X axis as a first rotating shaft, a Y axis as a second rotating shaft, a Z axis as a third rotating shaft, omega,
the kappa direction angles all adopt positive rotation;
the rotation matrix is then:
b: carrying out multi-route image matching based on GPU acceleration processing on the airborne three-linear array CCD image, and extracting data information of a connection point;
c: constructing a large-scale adjustment area network with multiple routes, and carrying out aerial triangulation processing;
d: establishing a GNSS eccentricity vector calibration model and an IMU visual axis eccentricity angle calibration model, respectively calibrating the GNSS eccentricity vector and the IMU visual axis eccentricity angle to obtain calibration values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)；
D1: establishing the GNSS eccentric vector calibration model of the airborne three-linear array CCD camera
According to the imaging relation, the GNSS eccentricity vector calibration model is established as follows:
wherein R is the picture attitude angle system
A determined rotation matrix; a represents an airborne GNSS antenna, O-XYZ is a ground-assisted coordinate system, and the coordinate of the phase center of the GNSS antenna is (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is an image space coordinate system, and the coordinates of the GNSS antenna are (u, v, w);
establishing the GNSS eccentricity vector calibration model on the basis of the GNSS eccentricity vector calibration model:
wherein the content of the first and second substances,
as phase center coordinates (X) of GNSS antenna
A，Y
A，Z
A) The residual term (Δ u, Δ v, Δ w) is the correction number of the GNSS eccentricity vector, and the step C obtains an external orientation element value (X)
S,Y
S,Z
S) The initial value of (u, v, w) is the actual measurement value or zero value, R is the value of the exterior orientation element obtained in the step C4 and is calculated according to the formula (2), and then the calculation value (X) of the phase center coordinate of the antenna is calculated according to the formula (7)
A，Y
A，Z
A)
0；
D2: establishing an IMU visual axis eccentric angle calibration model of the airborne three-linear array CCD camera;
let GNSS/IMU measure attitude angle directly as (α, gamma), and its formed rotation matrix as
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
Respectively as follows:
wherein subscript b represents IMU and c represents aerial photography instrument; the IMU visual axis eccentric angle can be decomposed into angle deviations in 3 directions, namely e
x，e
y，e
z；
Then:
-inversely calculating angle values (α, γ) from said rotation matrix (2), establishing an observation equation for said attitude angle of the GNSS/IMU:
establishing an IMU collimation axis eccentric angle calibration model of the airborne three-linear array CCD camera as follows:
wherein (α, gamma) is the attitude angle of the IMU directly measured, (v)
α,v
β,v
γ) A residual term for an attitude angle (α, gamma) directly measured by the GNSS/IMU, ([ delta ] e)
x，Δe
y，Δe
z) Is the correction of the eccentric angle of the visual axis of the IMU, B
2Is a corresponding coefficient matrix;
calculating the value of the exterior orientation element obtained in the step C by using the formula (2);
is prepared from (e)
x，e
y，e
z) The value is calculated by the formula (2) and (e)
x，e
y，e
z) The initial value may be taken to be zero; by the formula (9)
And
multiplication to obtain
(α,β,γ)
0Is formed by
Calculating the attitude angle by using the formula (10);
d3: taking each orientation plate as sampling data, adopting the GNSS eccentricity vector calibration model and the IMU sighting axis eccentricity angle calibration model to calibrate the GNSS eccentricity vector and the IMU sighting axis eccentricity angle, and respectively obtaining the calibration values (delta u, delta v, delta w) and (delta e)
x，Δe
y，Δe
z)；
E: updating an external orientation element by utilizing the GNSS eccentricity vector and the calibration value of the IMU visual axis eccentricity angle;
f: taking the sum of the correction of the external orientation element and the correction of the GNSS eccentricity vector and the correction of the IMU visual axis eccentricity angle as a cycle parameter, and judging the difference between the cycle parameter after iteration and iteration; when the difference of the loop parameters is smaller than a threshold value, the iteration is ended, and a loop is skipped; and E, when the difference of the circulation parameters is larger than a threshold value, iterating and circulating the steps C-E on the basis of the external orientation element value updated in the step E.
2. The method for calibrating the eccentricity vector and the eccentricity angle of the visual axis of the airborne three-line array CCD camera according to claim 1, is characterized in that: the step C also comprises the following steps:
c1: modeling the comprehensive influence of lens distortion and CCD deformation, constructing the large-scale adjustment area network of multiple routes aiming at the comprehensive influence of the lens distortion and the CCD deformation, and setting an offset value delta x of the actual geometric position of each probe element relative to the position of a laboratory calibration value under the comprehensive influence of the lens distortion and the CCD deformation
0,Δy
0；
C2: setting each scanning line via
(OPK) system converted GNSS/IMU observation value is an initial value, and airborne three-linear array CCD camera image is constructedAn alignment sheet adjustment model;
the orientation piece adjustment model adopts an improved Lagrange linear interpolation model to describe track and attitude changes of the airborne three-linear array CCD camera and is provided with a lower image point P of a ground point P
NImaging on the jth scan line, the lower image point p
NThe outer orientation element of the scanning line j is obtained by interpolation of the outer orientation elements of the k directional slice and the k +1 directional slice;
the outer square element model of the directional slice is as follows:
wherein the content of the first and second substances,
the corner element which is the outer orientation element of the jth scan line,
an outer orientation element for the k-th oriented piece,
the outer orientation element of the k +1 th oriented piece;
is a weight coefficient calculated from the imaging time of the kth directional slice and the kth +1 directional slice, t
jIs the imaging time of the jth scan line, t
kIs the imaging time of the k-th orientation plate, t
k+1Is the imaging time of the (k + 1) th oriented slice; then δ X
j,δY
j,δZ
j,δω
j,
δκ
jTo correct the item:
introducing the offset value Deltax of the probe position
0,Δy
0Substituting the formula (3) into the formula (1) to obtain the alignment sheet adjustment model of the airborne three-linear array CCD camera image:
c3: constructing the adjustment area network according to the sequence of the multiple routes, and implementing adjustment of the area network;
linearizing the formula (5) to obtain an adjustment equation based on the orientation sheet:
wherein the content of the first and second substances,
the correction number of the outer orientation element for the k-th oriented piece;
is the firstThe number of corrections of k +1 pieces of the oriented exterior orientation element; v. of
x，v
yIs a residual term; l
x，l
yIs a constant term; dX, dY and dZ are correction numbers of the coordinates of the control points; c. C
ja
11,c
ja
12,c
ja
13,c
ja
14,c
ja
15,c
ja
16Respectively the correction dX in the first equation in the above equation set
S k,dY
S k,dZ
S k,dω
k,
dκ
kThe coefficient of (a); (1-c)
j)a
11,(1-c
j)a
12,(1-c
j)a
13,(1-c
j)a
14,(1-c
j)a
15,(1-c
j)a
16Is the correction dX in the first equation in the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a); c. C
ja
21,c
ja
22,c
ja
23,c
ja
24,c
ja
25,c
ja
26Is the correction dX in the second equation of the above equation set
S k,dY
S k,dZ
S k,dω
k,
dκ
kThe coefficient of (a); (1-c)
j)a
21,(1-c
j)a
22,(1-c
j)a
23,(1-c
j)a
24,(1-c
j)a
25,(1-c
j)a
26Is the correction dX in the second equation of the above equation set
S k+1,dY
S k+1,dZ
S k+1,dω
k+1,
dκ
k+1The coefficient of (a);
according to the sequence of the multiple routes and the formula (6), establishing the structure of the adjustment area network, performing adjustment of the area network, and performing aerial triangulation processing to obtain an external orientation element value of the orientation sheet;
c4: interpolating and updating the exterior orientation element of each scan line by using the exterior orientation element value of the orientation patch obtained by the block adjustment according to the exterior orientation element model of the orientation patch;
c5: calibrating the offset value Deltax
0,Δy
0And updating the geometric position calibration value of each probe element on the front-view CCD, the lower-view CCD and the rear-view CCD.
3. The method for calibrating the eccentricity vector and the eccentricity angle of the visual axis of the airborne three-line array CCD camera according to claim 1, is characterized in that: the step E comprises the following steps:
e1: updating the line elements of the external orientation with the calibration values (Δ u, Δ v, Δ w):
r is the attitude angle system of the photo
A determined rotation matrix; a represents an airborne GNSS antenna, O-XYZ is a ground-assisted coordinate system, and the coordinate of the phase center of the GNSS antenna is (X)
A，Y
A，Z
A) S represents the rear node of the camera, i.e. the perspective center, the coordinate of which is (X)
S，Y
S，Z
S) (ii) a S-xyz is an image space coordinate system, and the coordinates of the GNSS antenna are (u, v, w);
e2: using a calibration value (Δ e)
x，Δe
y，Δe
z) Updating the corner elements of the external orientation:
let the attitude angle directly measured by the GNSS/IMU be (α, gamma), and the formed rotation matrix be
The exterior orientation angle element is
Form a rotation matrix of
Eccentric angle of visual axis (e)
x，e
y，e
z) Form a rotation matrix of
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