CN111504320A - Optical remote sensing satellite positioning method with swing mirror based on strict geometric imaging model - Google Patents
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Abstract
The invention provides a strict geometric imaging model-based optical remote sensing satellite positioning method with a swing mirror, which comprises the steps of resolving a transformation matrix between an object space vector and an image direction vector by utilizing an image direction vector, an object space vector and a swing angle of the swing mirror which are obtained from satellite imaging parameters; expanding an imaging relation based on a swing mirror matrix, introducing a transformation matrix of a related coordinate system in an imaging process, constructing a strict geometric relation among image points, object points and a projection center, and further constructing a strict geometric imaging model of the optical remote sensing satellite with the swing mirror; establishing an adjustment model for resolving positioning parameters on the basis of a strict geometric imaging model of the optical remote sensing satellite with the swing mirror; establishing an error equation for object space plane coordinate calculation through linearization on the basis of an adjustment model, iteratively calculating an object space coordinate correction number by using a least square optimization method, and updating coordinate values; and (5) iteratively solving the object space plane coordinates under the constraint of the reference DSM until the coordinate values tend to be stable, and obtaining a positioning result.
Description
Technical Field
The invention belongs to the field of remote sensing image processing, and relates to a pendulum mirror-containing optical remote sensing satellite positioning method based on a strict geometric imaging model.
Background
With the development of aerospace science and technology in China, the imaging mode of an optical satellite is also different day by day, an optical remote sensing satellite with a swing mirror is developed in the year, and the satellite has higher agility without rotating a load or performing whole satellite attitude maneuver by placing a rotatable swing mirror in front of a lens, so that the ground target is rapidly monitored, and the satellite is very suitable for early warning satellites needing large-scale rapid monitoring.
The strict geometric imaging model is the basis of all geometric processing of the optical satellite, the precision of the construction of the strict geometric imaging model directly influences the precision of the subsequent satellite images, and the strict geometric imaging model has an extremely important position in the processing of the satellite images. The traditional optical satellite without the swing mirror establishes a strict geometric imaging model based on the collinear relation of three points of an image point, a projection center and an object point, but for the optical remote sensing satellite with the swing mirror, the reflection of the swing mirror can cause the three points to be non-collinear, a certain included angle exists between an image direction vector and an object space vector, certain difficulty is brought to the construction of the imaging model, if the traditional collinear equation is still utilized for processing in the processing, the error of a mirror image can be introduced, and some problems in the subsequent processing are caused.
Aiming at the problem that the prior art is not suitable for the optical remote sensing satellite with the swing mirror, a new technical scheme needs to be proposed urgently in the field.
Disclosure of Invention
The invention provides a new method for positioning an optical remote sensing satellite with a swing mirror based on a strict geometric imaging model, which aims to solve the problem that the optical remote sensing satellite with the swing mirror is not applicable in the prior art.
The technical scheme of the invention provides a pendulum mirror-containing optical remote sensing satellite positioning method based on a strict geometric imaging model, which comprises the following steps,
step 1, resolving a transformation matrix between an object space vector and an image direction vector as a swing mirror matrix by using the image direction vector and the object space vector acquired from satellite imaging parameters and a swing angle of a swing mirror;
step 2, expanding based on the imaging relationship of the oscillating mirror matrix obtained in the step 1, introducing a transformation matrix of a related coordinate system in the imaging process, and constructing a strict geometric relationship among the image point, the object point and the projection center so as to construct a strict geometric imaging model of the optical remote sensing satellite with the oscillating mirror;
step 3, establishing an adjustment model for resolving positioning parameters on the basis of a strict geometric imaging model of the optical remote sensing satellite with the swing mirror;
step 4, establishing an error equation for object space plane coordinate calculation through linearization on the basis of the adjustment model, iteratively calculating an object space coordinate correction number by using a least square optimization method, and updating coordinate values;
and 5, iteratively calculating object space plane coordinates under the constraint of the reference DSM until coordinate values tend to be stable, and obtaining a positioning result.
Moreover, the implementation of step 1 comprises the following sub-steps,
1) the rotation axis vector is solved, and the following is realized,
according to the coordinate of the image space vector V in the camera coordinate system as (X, y, z), and the coordinate of the object space vector V in the WGS84 coordinate system as (X)g-Xgps,Yg-Ygps,Zg-Zgps) Wherein (X)g,Yg,Zg) Representing rectangular coordinates of object points corresponding to the image points in a WGS84 coordinate system, (X)gps,Ygps,Zgps) The coordinates of the phase center of the GPS antenna under a WGS84 coordinate system are represented, and are acquired by a GPS carried on a satellite;
firstly, an image space vector V and an object space vector V are respectively transformed to a satellite body coordinate system to obtain a vector VBodyAnd VBody；
Then, the image direction quantity v under the coordinate system of the satellite body after transformation is utilizedBodySum of objects vector VBodyCalculating a unit rotation vector n by cross-multiplication of the vectors;
2) the transformation quaternion is solved, and the implementation is as follows,
for calculation from rotation angle theta and unit rotation vector nDetermining a transform quaternion Q ═ (Q) of the transform matrix0,q1,q2,q3) As follows below, the following description will be given,
3) resolving the transformation matrix to achieve
Computing a transformation matrix R from the resolved quaternionmirror，
R is to bemirrorAs a matrix of oscillating mirrors.
Moreover, the strict geometric imaging model of the optical remote sensing satellite with the swing mirror is constructed in the step 2 and is realized as follows,
where μ denotes a scaling factor, (X)g,Yg,Zg) Corresponding to the rectangular coordinates of the object point in the WGS84 coordinate system,
representing the rotation matrix of WGS84 coordinate system to J2000 coordinate system, the rotation matrix of J2000 coordinate system to satellite body coordinate system, and the rotation matrix from satellite body coordinate system to camera coordinate system, respectively.
Moreover, the adjustment model for solving the positioning parameters established in step 3 is realized as follows,
first, an intermediate variable is set
And
as follows below, the following description will be given,
then, an adjustment equation (G) for least squares adjustment solution is constructedx,Gy)，
The invention has the advantages that: the method realizes the construction of a strict geometric imaging model of the optical remote sensing satellite with the swing mirror and provides a positioning method based on the model, the constructed model considers the strict reflection relationship between the image direction quantity and the object space vector, the model has better tightness and lays a foundation for the subsequent geometric processing of the optical remote sensing satellite with the swing mirror, and in addition, the method provides the optical remote sensing satellite positioning method based on the iterative optimization on the basis of the constructed model.
Drawings
FIG. 1 is a schematic flow chart of an embodiment of the present invention,
FIG. 2 is a schematic imaging diagram of an optical remote sensing satellite with a swing mirror in the embodiment of the invention.
Detailed Description
The following detailed description of the embodiments of the present invention is provided with reference to the accompanying drawings.
The invention provides a strict geometric imaging model construction and positioning based on an optical remote sensing satellite with a swing mirror, realizes the construction of a reflection relation between an image direction vector and an object vector by constructing a strict transformation matrix between the image direction vector and the object vector, provides an optical remote sensing satellite positioning method based on iterative optimization on the basis of the constructed model, and realizes high-precision positioning calculation of the optical remote sensing satellite with the swing mirror under the constraint of reference DSM data.
Referring to fig. 1, the embodiment provides a method for positioning an optical remote sensing satellite with a swinging mirror based on a strict geometric imaging model, and the specific process includes the following steps:
step 1, constructing a swing mirror matrix, wherein a transformation matrix (swing mirror matrix) between an object direction vector and an image direction vector is solved by utilizing an image direction vector, an object direction vector and a swing angle of a swing mirror which are acquired from satellite imaging parameters (camera parameters, attitude parameters and orbit parameters);
see FIG. 2, or-xryrThe system comprises a CCD, an attitude measurement system and an orbit measurement system, wherein the CCD is used for acquiring the gray value of each pixel by converting an incoming optical signal into an electric signal, and the attitude measurement system and the orbit measurement system measure the attitude of a satellite under a J2000 coordinate system and the position of the center of a GPS antenna under a WGS84 coordinate system at certain intervals while the CCD images.
Because of the existence of the swing mirror (reflector), light rays are firstly reflected by the swing mirror before entering a pupil, an object point P, a projection center O and an image point P are not collinear, a geometric relation among the three points needs to be reestablished, an object space vector V formed by the object point P and the projection center O and an image direction quantity V formed by the projection center O and the image point P form an included angle theta, and a swing angle matrix R is established according to the included angle and the vectors V and VmirrorThe transformation relation between the image direction vector and the object direction vector is realized, and the matrix is constructed according to the Rodrigues axial angle transformation, and the transformation relation is specifically as follows:
1) resolving rotational axis vector
According to the coordinate of the image space vector V in the camera coordinate system as (X, y, z), and the coordinate of the object space vector V in the WGS84 coordinate system as (X)g-Xgps,Yg-Ygps,Zg-Zgps) Wherein (X)g,Yg,Zg) Representing rectangular coordinates of object points corresponding to the image points in a WGS84 coordinate system, (X)gps,Ygps,Zgps) Coordinates of the phase center of the GPS antenna in the WGS84 coordinate system are shown, and are acquired by a GPS mounted on a satellite.
Firstly, two vectors (an image space vector V and an object space vector V) are respectively transformed to a satellite body coordinate system to obtainTo vector vBodyAnd VBodyThe method comprises the following steps:
wherein the content of the first and second substances,
and
respectively representing a rotation matrix of the WGS84 coordinate system to the J2000 coordinate system, a rotation matrix of the J2000 coordinate system to the satellite body coordinate system, a rotation matrix from the camera coordinate system to the satellite body coordinate system, and a rotation matrix from the satellite body coordinate system to the camera coordinate system,
is obtained according to the ephemeris parameters at the imaging moment,
is obtained by combining star sensor and gyro for attitude determination;
determined by the three camera mounting angles between the satellite body coordinate system and the camera coordinate system.
Then, the image direction quantity v under the coordinate system of the satellite body after transformation is utilizedBodySum of objects vector VBodyCross-product the unit rotation vector n as follows:
2) resolving a transformed quaternion
Calculating a transform quaternion Q ═ (Q) for determining a transform matrix from the rotation angle θ and the unit rotation vector n0,q1,q2,q3) Each element of the quaternion is determined according to formula (3).
3) Solving transformation matrix
Computing a transformation matrix R from the resolved quaternionmirrorAnd constructing a pendulum mirror matrix:
step 2, constructing a strict geometric imaging model of the optical remote sensing satellite with the swing mirror, wherein the construction of the strict geometric imaging model of the optical remote sensing satellite with the swing mirror comprises the steps of expanding the constructed imaging relation based on a swing mirror matrix, introducing a transformation matrix of a related coordinate system in the imaging process, constructing the strict geometric relation among image points, object points and a projection center, and further constructing the strict geometric imaging model of the optical remote sensing satellite with the swing mirror;
construction-based swing mirror matrix RmirrorCan realize vector vBodyAnd VBodyThe transformation between, as follows:
vBody＝RmirrorVBody(5)
the strict geometric imaging model from the image space to the object space can be constructed by introducing the correlation transformation matrix into the formula (5), which is as follows:
where μ denotes a scaling factor, (X)g,Yg,Zg) Corresponding to the rectangular coordinates of the object point in the WGS84 coordinate system, the transformation relationship between the geographic coordinates (L at, L on, Hei) is as follows:
where N is the radius of curvature of an earth's prime, e is the first eccentricity of an earth ellipsoid (L at, L on, Hei) for (dimension, precision, elevation).
Step 3, constructing a geometric positioning adjustment model, which comprises the step of establishing an adjustment model for positioning parameter calculation on the basis of the strict geometric imaging model of the optical remote sensing satellite with the swing mirror constructed in the step 2;
the positioning based on the established model is to determine the plane coordinates of object points corresponding to image points under the constraint of reference DSM by utilizing the known image points, to iteratively approximate the optimal value of the plane coordinates of the object points by adopting a least square method, firstly, an adjustment model for calculating plane coordinate parameters is established based on a geometric positioning model, and firstly, in the formula (6):
wherein the intermediate variable
And
for representing the left and right side of the geometric imaging model (6) with equal sign, respectively. Then, an adjustment equation (G) for least squares adjustment solution can be constructedx,Gy)：
Step 4, solving the object space coordinate based on least square optimization, wherein an error equation for solving the object space plane coordinate is established through linearization on the basis of the established adjustment model, the correction number of the object space coordinate is iteratively solved by using a least square optimization method, and the coordinate value is updated;
for the plane coordinates (L at, L on) of the object space, the adjustment model constructed in the previous step is nonlinear, the model linearization process is needed to establish an error equation for parameter calculation, and the established error equation v is linearizedPThe following formula:
vP＝AX-L (10)
wherein, X ═ d L at, d L on]TAs correction vector of object space point plane coordinate, the elevation value isThe interpolated elevations from the reference DSM are taken as true values and not as unknowns; a is an error equation coefficient matrix, and is an adjustment equation (G) established according to eachx,Gy) Obtained by linearization, L is a constant vector of error equations whose element values are equal to the current values of the corresponding adjustment equations, as follows:
calculating X by using the least square adjustment, as shown in formula (10);
X＝(ATA)-1(ATL) (11)
updating the current value of the coordinates according to the resolved correction value (L at)i,Loni) The latest coordinate value (L at) can be obtainedi+1,Loni+1) The following are:
then, the updated parameters are used as input to perform the next iterative solution, and when the result of the two adjustment solutions is smaller than the preset tolerance threshold (10 is preferably taken in the embodiment)-7) When the convergence is reached, the iteration of the step is finished, and the step 5 is entered.
And 5, iteratively solving the object space plane coordinates under the constraint of the reference DSM until the coordinate values tend to be stable. In an embodiment, based on the new object plane coordinates, the elevation value is interpolated from the reference DSM, and this is used as input, and step 4 is repeated until the result of the two adjustment calculations is less than the preset tolerance (e.g., threshold 10)-7) And when the positioning calculation is finished, a positioning result is obtained.
In specific implementation, the above processes can be automatically operated by adopting a computer software technology, and a system device of the operation method is also within the protection scope of the invention.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (4)
1. A method for positioning an optical remote sensing satellite with a swing mirror based on a strict geometric imaging model is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
step 1, resolving a transformation matrix between an object space vector and an image direction vector as a swing mirror matrix by using the image direction vector and the object space vector acquired from satellite imaging parameters and a swing angle of a swing mirror;
step 2, expanding based on the imaging relationship of the oscillating mirror matrix obtained in the step 1, introducing a transformation matrix of a related coordinate system in the imaging process, and constructing a strict geometric relationship among the image point, the object point and the projection center so as to construct a strict geometric imaging model of the optical remote sensing satellite with the oscillating mirror;
step 3, establishing an adjustment model for resolving positioning parameters on the basis of a strict geometric imaging model of the optical remote sensing satellite with the swing mirror;
step 4, establishing an error equation for object space plane coordinate calculation through linearization on the basis of the adjustment model, iteratively calculating an object space coordinate correction number by using a least square optimization method, and updating coordinate values;
and 5, iteratively calculating object space plane coordinates under the constraint of the reference DSM until coordinate values tend to be stable, and obtaining a positioning result.
2. The method for aggregating irregular angular direction costs based on dominant line constraint according to claim 1, wherein: the implementation of step 1 comprises the following sub-steps,
1) the rotation axis vector is solved, and the following is realized,
according to the coordinate of the image space vector V in the camera coordinate system as (X, y, z), and the coordinate of the object space vector V in the WGS84 coordinate system as (X)g-Xgps,Yg-Ygps,Zg-Zgps) Wherein (X)g,Yg,Zg) Representing object space corresponding to image pointRectangular coordinates of the point in WGS84 coordinate system, (X)gps,Ygps,Zgps) The coordinates of the phase center of the GPS antenna under a WGS84 coordinate system are represented, and are acquired by a GPS carried on a satellite;
firstly, an image space vector V and an object space vector V are respectively transformed to a satellite body coordinate system to obtain a vector VBodyAnd VBody；
Then, the image direction quantity v under the coordinate system of the satellite body after transformation is utilizedBodySum of objects vector VBodyCalculating a unit rotation vector n by cross-multiplication of the vectors;
2) the transformation quaternion is solved, and the implementation is as follows,
calculating a transform quaternion Q ═ (Q) for determining a transform matrix from the rotation angle θ and the unit rotation vector n0,q1,q2,q3) As follows below, the following description will be given,
3) resolving the transformation matrix to achieve
Computing a transformation matrix R from the resolved quaternionmirror，
R is to bemirrorAs a matrix of oscillating mirrors.
3. The method for aggregating irregular angular direction costs based on dominant line constraint according to claim 2, wherein: the strict geometric imaging model of the optical remote sensing satellite with the swing mirror is constructed in the step 2 and is realized as follows,
where μ denotes a scaling factor, (X)g,Yg,Zg) Corresponding to the rectangular coordinates of the object point in the WGS84 coordinate system,
representing the rotation matrix of WGS84 coordinate system to J2000 coordinate system, the rotation matrix of J2000 coordinate system to satellite body coordinate system, and the rotation matrix from satellite body coordinate system to camera coordinate system, respectively.
4. The method for aggregation of irregular angular direction costs based on mainline constraint according to claim 3, wherein: the establishment of the adjustment model for positioning parameter solution in step 3 is realized as follows,
first, an intermediate variable is set
And
as follows below, the following description will be given,
then, an adjustment equation (G) for least squares adjustment solution is constructedx,Gy)，
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