A multi-scale representation method for adaptive compensation of low-frequency positioning errors in optical images

Abstract

The present invention relates to a method for adaptively compensating low-frequency positioning errors of optical images with multi-scale characterization. Compared with the prior art, it realizes the decoupling characterization of low-frequency errors from the perspectives of time, composition, etc., and is adaptive to the construction of a low-frequency error compensation model. The present invention includes the following steps: preparation for adaptive compensation of low-frequency positioning errors of optical images with multi-scale characterization; multi-time scale characterization of low-frequency positioning errors of optical images; adaptive construction of a low-frequency positioning error model of optical images considering dynamic and static error decoupling; partial least squares solution of the compensation model and application of compensation parameters using non-collinear control points. The present invention adopts a variational mode decomposition method to characterize low-frequency errors into periodic terms, trend terms, and noise terms, and adaptively constructs a low-frequency error compensation model based on the magnitude relationship between its components.

Description

Technical Field

[0001] The invention belongs to the field of ground preprocessing applications of optical remote sensing images, and specifically is a multi-scale representation optical image low-frequency positioning error adaptive compensation method. Background Art

[0002] Spaceborne optical satellite images provide high-precision ground data for the world, and their geometric positioning accuracy directly determines the quality and reliability of the images. However, due to factors such as stress release during satellite launch and changes in the orbital operating environment, the geometric imaging parameters of optical images may change, thus affecting the positioning accuracy. Traditional geometric calibration methods rely on ground control data to calibrate internal and external imaging parameters, but these methods have the problem of relying too much on ground control data and it is difficult to effectively solve the low-frequency error problem of internal and external orientation elements, resulting in difficulty in ensuring positioning accuracy in practical applications.

[0003] In recent years, variational mode decomposition technology has been widely used in remote sensing image data processing. It can effectively decompose the original error sequence into periodic terms, trend terms and noise terms, providing a new perspective for characterizing the low-frequency positioning errors of optical images. However, current research mainly focuses on the analysis of low-frequency error characteristics within the orbital period, and does not fully consider the variation patterns on multiple time scales. Satellite positioning errors usually manifest as complex time series characteristics, including daily and monthly periodic changes and long-term trend changes, which require targeted modeling methods to process and compensate for them in order to improve the geometric positioning accuracy of the image.

[0004] To address these issues, an adaptive compensation method for low-frequency positioning errors of optical images with multi-scale characterization is proposed. This method combines variational mode decomposition with grey correlation analysis technology, and identifies low-frequency trend terms and periodic terms by multi-scale decomposition of the error sequence. According to these variation characteristics, the influence of driving factors on geometric positioning accuracy at different time scales is analyzed, and the low-frequency error compensation scheme is adaptively adjusted by combining additive models, multiplicative models and hybrid models. This method can achieve accurate modeling and compensation of low-frequency errors at different time scales, such as hourly, daily and monthly, thereby significantly improving the global uncontrolled geometric positioning accuracy of satellite images. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the existing technology cannot automatically process stereo SAR images with different lifting orbits to generate available control points, and to provide a multi-scale representation optical image low-frequency positioning error adaptive estimation method to solve the above problem.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] A multi-scale representation optical image low-frequency positioning error adaptive estimation method comprises the following steps:

[0008] 11) Preparation work for adaptive compensation of low-frequency positioning errors of multi-scale optical images: obtain the star sensor angle data corresponding to the imaging time of the optical images at the hourly scale, obtain the optical image data of adjacent tracks in the area with overlapping imaging at the daily scale, and obtain the image data of multiple shots at the same location at the monthly scale.

[0009] 12) Perform multi-time scale characterization on the low-frequency positioning error of optical images: Process the star sensor data to obtain the hourly scale star sensor angle change data; match the adjacent track optical images of the overlapping imaging area to obtain the daily scale overlapping image area misalignment change data; obtain the monthly scale positioning error change data based on the image data taken multiple times at the same location; perform adaptive variational mode decomposition on the obtained three time scale change data and decompose them into trend terms , Periodic Item And the noise term .

[0010] 13) Adaptive construction of optical image low-frequency positioning error model considering dynamic and static error decoupling: Determine the driving factors of low-frequency error based on grey correlation analysis; Decouple the compensation matrix into the constant difference of satellite-ground angle and the dynamic low frequency error part ; Adaptively build compensation model according to the size of trend term, cycle term and noise term .

[0011] 14) The compensation model is solved by partial least squares using non-collinear control points and the compensation parameters are applied. The model parameters are then compensated to other optical images to obtain optical images with better uncontrolled positioning accuracy.

[0012] The multi-time scale characterization of the low-frequency positioning error of the optical image comprises the following steps:

[0013] 21) Process star sensor data to obtain the star sensor angle change data corresponding to the imaging time of the hour-scale optical image ,in for Moment angle, start time , the end time is , the specific steps are as follows:

[0014] 211) Extract quaternions from star sensor output data , further convert the optical axis direction vector of the star sensor in the satellite body coordinate system Calculate the viewing direction vector in the inertial coordinate system ;

[0015] 212) Calculate the inertial velocity vector of a celestial body based on the satellite's orbital data And look at the direction vector Perform aberration correction to obtain the true direction vector of the star sensor optical axis ;

[0016] 213) Combine the corrected true direction vectors of the optical axis in pairs and calculate the angle between them

[0017] ,

[0018] in, is the true direction vector of the optical axis of the i-th star sensor, is the true direction vector of the optical axis of the jth star sensor, To calculate the modulus value.

[0019] 22) Match the optical images of adjacent tracks in the overlapping imaging area to obtain the displacement change data of the overlapping image area on a daily scale ,in is the displacement of the overlapping image area at the ground coordinates of latitude lat and longitude lon along the sample column direction, To overlap the image area located at the latitude lat and longitude lon ground coordinates along the line direction, the specific steps are as follows:

[0020] 221) Select adjacent orbit image data with spatial overlap from the satellite image database and mark them as image I of orbit j. j and the whole track image I of track j+1 j+1 ;

[0021] 222) Perform point matching on the overlapping area of ​​track j and track j+1 images and extract the point pairs with the same name (x j ,y j ) and (x j+1 ,y j+1 ), x j For the image I j The column coordinates, y j For the image I j The row coordinate, x j+1 For the image I j+1 The column coordinates, y j+1 For the image I j+1 The row coordinates of

[0022] 223) Geometric model using orbital j images , the image coordinates of the same-name points are converted to ground coordinates lat and lon through model calculation, and the elevation h is interpolated at the SRTM30 data according to lat and lon, thus forming control points to verify the accuracy of the geometric model of the track j+1 image;

[0023] 224) Substitute the ground coordinates (lat, lon, h) of the control point into the image geometry model of track j+1 , through the model back calculation (x' j+1 ,y' j+1 )= (lat,lon,h), get the control point in track j+1 image I j+1 The image coordinates (x' j+1 ,y' j+1 );

[0024] 225) Compare the image coordinates of the same-name points obtained by matching on the image of track j+1 (x j+1 ,y j+1 ) and the image coordinates (x' j+1 ,y' j+1 )difference and , the specific calculation is:

[0025] x' j+1 -x j+1 , y' j+1 -y j+1 ;

[0026] 226) Process multiple adjacent track image data in chronological order, repeat the above steps, obtain positioning error data at different positions, and obtain ;

[0027] 23) Obtain monthly positioning error change data based on image data taken multiple times at the same location = ,in For The roll, pitch and yaw attitude changes at all times. The specific steps are:

[0028] 231) Select image data taken multiple times at the same location from the satellite image database to ensure that the images cover the same ground area and record the time tag t i and Image I i ;

[0029] 232) Select a fixed time moment t from multiple captured images ref The image is used as the reference image Iref , use the calibration coefficient of that moment to make all historical images consistent and unify the geometrical reference of the images;

[0030] 233) For each I i and I ref Match the images, obtain matching point pairs, and calculate the posture change of the current image relative to the reference image based on relative orientation. ;

[0031] 234) Arrange the positioning error change data of multiple shooting images in chronological order to generate positioning error change data on a monthly scale ;

[0032] 24) Perform adaptive variational mode decomposition on the acquired change data of the three time scales and decompose them into trend terms , Periodic Item And the noise term , the specific steps are:

[0033] 241) Hourly star sensor angle change data , daily scale overlapping image area displacement change data And the positioning error change data on a monthly scale , the data is normalized: ,in is the original sequence data, and are the minimum and maximum values ​​in the original sequence data, For normalized values, the error change values ​​should be mapped to a uniform dimension range, and the box plot method should be applied to remove obvious outliers;

[0034] 242) Adaptive variational mode decomposition AVMD initialization, define the initial mode number K and penalty factor α, use grid search optimization algorithm to optimize K and α, and find the parameter configuration corresponding to the minimum value of envelope entropy;

[0035] 243) Using the optimized mode number K and penalty factor α, the variational mode decomposition of the geometric positioning error time series is performed: ,in is the original sequence, is the kth eigenmode function, is the residual noise. According to the frequency distribution and time distribution characteristics, the low-frequency trend term in IMF is distinguished , Periodic Item and high frequency noise terms .

[0036] The adaptive construction of the optical image low-frequency positioning error model considering the decoupling of dynamic and static errors includes the following steps:

[0037] 31) Determine the driving factors of low-frequency errors based on the grey correlation analysis method. The specific steps are:

[0038] 311) Define the independent variables and error sequence. First, determine the independent variables that affect the low-frequency error change of the satellite attitude, including orbital circles, distance initial geometry calibration time, and satellite solar altitude angle. The error sequence is the low-frequency trend term after variational mode decomposition. , Periodic Item and high frequency noise terms ;

[0039] 312) In order to eliminate the dimension difference and scale influence, the independent variables and error series are standardized by dividing the mean by the standard deviation;

[0040] 313) Use the grey correlation analysis method to calculate the grey correlation coefficient between the independent variable and the error sequence , is the similarity between the ith independent variable and the jth error sequence;

[0041] 314) Weighted summation to determine the correlation index ,in is the weight of the j-th independent variable;

[0042] 315) According to the correlation index, select the one with the largest correlation index As a key driver for subsequent modeling ;

[0043] 32) The compensation matrix Decoupled into the constant difference between the satellite and the ground and the dynamic low frequency error part , modeling: ,in It's the driving factor. It is the constant difference in the angle between the star and the earth;

[0044] 33) Further based on the low frequency error Trending items , Periodic Item , noise term Adaptive construction of corresponding compensation model based on the magnitude relationship between them , the specific steps are:

[0045] 331) When the trend term and the cycle term are of similar magnitude and vary independently, an additive model is used:

[0046] ;

[0047] 332) When the magnitude of the cycle term depends on the trend term, a multiplicative model is used:

[0048] ;

[0049] 333) Use polynomial models, penalized splines, Fourier series and mixed models to Modeling;

[0050] 34) For the n unknowns in the compensation matrix, the coordinates of n / 2 or more non-collinear ground control points can be used to solve the problem. The corresponding attitude low-frequency error value under the value , , , the model error equation is further constructed as follows:

[0051] ,

[0052] in Represents M observations The low-frequency error value of the pitch angle under the value, Corresponding to the model parameter matrix, partial least squares is used to solve . Beneficial Effects

[0053] Compared with the prior art, the multi-scale adaptive estimation method for characterizing the low-frequency positioning error of optical images of the present invention can realize the fusion processing of multi-time scale data, and utilize the adaptive variational mode decomposition technology to decompose the low-frequency positioning error of optical images into trend terms, periodic terms and noise terms, so as to accurately model and analyze the complex low-frequency error characteristics. Considering the dynamic and static characteristics of the optical image positioning error, the method of driving factor decoupling is adopted, and additive, multiplicative or hybrid models are constructed according to the characteristics of different error components, so as to realize adaptive low-frequency error compensation, which is applicable to a variety of satellite image platforms and imaging environments. Compared with traditional methods, it can significantly compensate for low-frequency errors and improve the uncontrolled geometric positioning accuracy of images. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a sequence diagram of the method of the present invention;

[0055] Figure 2 A flowchart for implementing the method involved in the present invention;

[0056] Figure 3 Schematic diagram of the optical axis angle of the star sensor;

[0057] Figure 4 Schematic diagram of adaptive variational mode decomposition; DETAILED DESCRIPTION

[0058] In order to have a further understanding and recognition of the structural features and the effects achieved by the present invention, a preferred embodiment and accompanying drawings are used for detailed description as follows:

[0059] like Figure 1 and Figure 2 As shown, the method for adaptively estimating low-frequency positioning errors of optical images with multi-scale representation according to the present invention comprises the following steps:

[0060] The first step is to prepare for the adaptive compensation of low-frequency positioning errors of multi-scale characterization optical images, and obtain sequence data at hourly, hourly and monthly scales: the star sensor angle data within the imaging time corresponding to the hourly optical images, the adjacent track optical image data of the area with overlapping imaging at the hourly scale, and the image data of multiple shots at the same location at the monthly scale.

[0061] The second step is to characterize the low-frequency positioning error of optical images at multiple time scales: process the star sensor data and extract the hourly star sensor angle change data; match the adjacent track optical images of the overlapping imaging area to obtain the daily scale overlapping image area misalignment change data; obtain the monthly scale positioning error change data based on the image data taken multiple times at the same location; perform adaptive variational mode decomposition on the obtained three time scale change data and decompose them into trend terms , Periodic Item And the noise term The specific steps are as follows:

[0062] (1) Process star sensor data to obtain the star sensor angle change data corresponding to the imaging time of the hour-scale optical image ,in for Moment angle, start time , the end time is , the specific steps are as follows:

[0063] (1-1) Extracting quaternions from star sensor output data , further convert the optical axis direction vector of the star sensor in the satellite body coordinate system Calculate the viewing direction vector in the inertial coordinate system ;

[0064] (1-2) Calculate the inertial velocity vector of the celestial body based on the satellite's orbital data And look at the direction vector Perform aberration correction to obtain the true direction vector of the star sensor optical axis ;

[0065] (1-3) Combine the corrected true direction vectors of the optical axis in pairs and calculate the angle between them

[0066] ,

[0067] in, is the true direction vector of the optical axis of the i-th star sensor, is the true direction vector of the optical axis of the jth star sensor, To calculate the modulus value;

[0068] (1-4) Select the less maneuverable remote sensing satellites such as ZY-3, GF-1, and GF-6 to obtain the data on the change of the star-sensing optical axis angle of the multi-circle satellite in the sunlit area. ;

[0069] (2) Match the optical images of adjacent tracks in the overlapping imaging area to obtain the displacement change data of the overlapping image area on a daily scale ,in is the displacement of the overlapping image area at the ground coordinates of latitude lat and longitude lon along the sample column direction, To overlap the image area located at the latitude lat and longitude lon ground coordinates along the line direction, the specific steps are as follows:

[0070] (2-1) Select adjacent orbit image data with spatial overlap from the satellite image database and mark them as image I of orbit j. j and the whole track image I of track j+1 j+1 ;

[0071] (2-2) Perform point matching on the overlapping areas of track j and track j+1 images and extract the point pairs with the same name (x j ,y j ) and (x j+1 ,y j+1 ), x j For the image I j The column coordinates, y j For the image I j The row coordinate, x j+1 For the image I j+1 The column coordinates, y j+1 For the image I j+1 The row coordinates of

[0072] (2-3) Geometric model using orbital j images , the image coordinates of the same-name points are converted to ground coordinates lat and lon through model calculation, and the elevation h is interpolated at the SRTM30 data according to lat and lon, thus forming control points to verify the accuracy of the geometric model of the track j+1 image;

[0073] (2-4) Substitute the ground coordinates (lat, lon, h) of the control point into the image geometry model of track j+1 , through the model back calculation (x' j+1 ,y' j+1 )= (lat,lon,h), get the control point in track j+1 image I j+1 The image coordinates (x' j+1 ,y' j+1 );

[0074] (2-5) Compare the image coordinates of the same-name points obtained by matching on the image of track j+1 (x j+1 ,y j+1 ) and the image coordinates (x' j+1 ,y' j+1 )difference and , the specific calculation is:

[0075] x' j+1 -x j+1 , y' j+1 -y j+1 ;

[0076] (2-6) Process multiple adjacent track image data in chronological order, repeat steps (2-1) to (2-5) to obtain positioning error data at different positions, and thus obtain ;

[0077] (3) Obtaining monthly positioning error change data based on image data taken multiple times at the same location = ,in For The roll, pitch and yaw attitude changes at all times. The specific steps are:

[0078] (3-1) Select image data taken multiple times at the same location from the satellite image database to ensure that the images cover the same ground area and record the time tag t i and Image I i ;

[0079] (3-2) Select a fixed time t from multiple captured images refThe image is used as the reference image I ref , use the calibration coefficient of that moment to make all historical images consistent and unify the geometrical reference of the images;

[0080] (3-3) For each I i and I ref Match the images, obtain matching point pairs, and calculate the posture change of the current image relative to the reference image based on relative orientation. ;

[0081] (3-4) Arrange the positioning error change data of multiple images in chronological order to generate positioning error change data on a monthly scale ;

[0082] (4) If Figure 4 As shown in the figure, the acquired change data of three time scales are processed by adaptive variational mode decomposition and decomposed into trend terms. , Periodic Item And the noise term , the specific steps are:

[0083] (4-1) The hourly star sensor angle change data , daily scale overlapping image area displacement change data And the positioning error change data on a monthly scale , the data is normalized: ,in is the original sequence data, and are the minimum and maximum values ​​in the original sequence data, For normalized values, the error change values ​​should be mapped to a uniform dimension range, and the box plot method should be applied to remove obvious outliers;

[0084] (4-2) Initialize the adaptive variational mode decomposition AVMD, define the initial mode number K and penalty factor α, use the grid search optimization algorithm to optimize the combination of K and α, and find the parameter configuration corresponding to the minimum value of the envelope entropy;

[0085] (4-3) Using the optimized mode number K and penalty factor α, the geometric positioning error time series is subjected to variational mode decomposition: ,in is the original sequence, is the kth eigenmode function, is the residual noise. According to the frequency distribution and time distribution characteristics, the low-frequency trend term in IMF is distinguished , Periodic Item and high frequency noise terms .

[0086] The third step is to adaptively construct an optical image low-frequency positioning error model that considers the decoupling of dynamic and static errors: Figure 3 As shown in the figure, the optical image low-frequency positioning error model first needs to perform grey correlation analysis on the influencing factors to determine the driving factors of the low-frequency error; decouple the compensation matrix of the optical image low-frequency positioning error model into the satellite-ground angle constant difference part and the dynamic low frequency error part ; Adaptively build compensation model according to the size of trend term, cycle term and noise term ; The specific steps are as follows:

[0087] (1) Determine the driving factors of low-frequency errors based on the grey correlation analysis method. The specific steps are as follows:

[0088] (1-1) Define independent variables and error sequences. First, determine the independent variables that affect the low-frequency error of satellite attitude, including orbital cycles, distance initial geometry calibration time, and satellite solar altitude angle. The error sequence is the low-frequency trend term after variational mode decomposition. , Periodic Item and high frequency noise terms ;

[0089] (1-2) In order to eliminate the dimension difference and scale influence, the independent variables and error series are standardized by dividing the mean by the standard deviation;

[0090] (1-3) Use the grey correlation analysis method to calculate the grey correlation coefficient between the independent variable and the error sequence , is the similarity between the ith independent variable and the jth error sequence;

[0091] (1-4) Weighted summation to determine the correlation index ,in is the weight of the j-th independent variable;

[0092] (1-5) According to the correlation index, select the one with the largest correlation index As a key driver for subsequent modeling ;

[0093] (2) The compensation matrix Decoupled into the constant difference between the satellite and the ground angle and the dynamic low frequency error part , the decoupling process can be expressed as: ,in It's the driving factor. It is the constant difference in angle between the star and the earth;

[0094] (3) Further based on the low-frequency error Trending items , Periodic Item , noise term Adaptive construction of corresponding compensation model based on the magnitude relationship between them , the specific steps are:

[0095] (3-1) When the trend term and the cycle term are of similar magnitude and change independently, the additive model is used:

[0096] ;

[0097] (3-2) When the magnitude of the cycle term depends on the trend term, a multiplicative model is used:

[0098] ;

[0099] (3-3) Using polynomial models, penalized splines, Fourier series and mixed models Modeling;

[0100] (4) For the n unknowns in the compensation matrix, the coordinates of n / 2 or more non-collinear ground control points can be used to solve the problem. The corresponding attitude low-frequency error value under the value , , , the model error equation is further constructed as follows:

[0101] ,

[0102] in Represents M observations The low-frequency error value of the pitch angle under the value, Corresponding to the model parameter matrix, partial least squares is used to solve .

[0103] The fourth step is to solve the model parameters: use the non-collinear control points to perform partial least squares to solve the compensation model. The compensation parameters are applied and the model parameters are compensated to other optical images to obtain optical images with better uncontrolled positioning accuracy.

[0104] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-scale representation method for adaptive compensation of low-frequency positioning errors of optical images, characterized in that: The following steps are involved: 11) Preparation work for adaptive compensation of low-frequency positioning errors of multi-scale characterization optical images: obtain the star sensor angle data corresponding to the imaging time of the optical images at the hourly scale, obtain the optical image data of adjacent tracks in the area with overlapping imaging at the daily scale, and obtain the image data of multiple shots of the same location at the monthly scale; 12) Perform multi-time scale characterization on the low-frequency positioning error of optical images: Process the star sensor data to obtain the hourly scale star sensor angle change data; match the adjacent track optical images of the overlapping imaging area to obtain the daily scale overlapping image area misalignment change data; obtain the monthly scale positioning error change data based on the image data taken multiple times at the same location; perform adaptive variational mode decomposition on the obtained three time scale change data and decompose them into trend terms , Periodic Item And the noise term ; 13) Adaptive construction of low-frequency positioning error model of optical image considering decoupling of dynamic and static errors: Determine the driving factors of low-frequency error based on grey correlation analysis; Decouple the compensation matrix into the satellite-to-ground angle constant difference part and the dynamic low frequency error part ; Adaptively build compensation model according to the size of trend term, cycle term and noise term ; 14) The compensation model is solved by partial least squares using non-collinear control points and the compensation parameters are applied. The model parameters are then compensated to other optical images to obtain optical images with better uncontrolled positioning accuracy.

2. The method for adaptively compensating low-frequency positioning errors of optical images with multi-scale representation according to claim 1, characterized in that: The multi-time scale characterization of the low-frequency positioning error of the optical image comprises the following steps: 21) Process the star sensor data to obtain the star sensor angle change data corresponding to the imaging time of the hour-scale optical image ,in for Moment angle, start time , the end time is , the specific steps are as follows: 211) Extract quaternions from star sensor output data , further convert the optical axis direction vector of the star sensor in the satellite body coordinate system Calculate the viewing direction vector in the inertial coordinate system ; 212) Calculate the inertial velocity vector of a celestial body based on the satellite's orbital data And look at the direction vector Perform aberration correction to obtain the true direction vector of the star sensor optical axis ; 213) Combine the corrected true direction vectors of the optical axis in pairs and calculate the angle between them ， in, is the true direction vector of the optical axis of the i-th star sensor, is the true direction vector of the optical axis of the jth star sensor, To calculate the modulus value; 214) Select the less maneuverable remote sensing satellites such as ZY-3, GF-1 and GF-6 to obtain the data on the change of the angle of the star-sensing optical axis of the multi-circle satellite in the sunlit area. ; 22) Match the optical images of adjacent tracks in the overlapping imaging area to obtain the displacement change data of the overlapping image area on a daily scale ,in is the displacement of the overlapping image area at the ground coordinates of latitude lat and longitude lon along the sample column direction, To overlap the image area located at the latitude lat and longitude lon ground coordinates along the line direction, the specific steps are as follows: 221) Select adjacent orbit image data with spatial overlap from the satellite image database and mark them as image I of orbit j. j and the whole track image I of track j+1 j+1 ; 222) Perform point matching on the overlapping area of ​​track j and track j+1 images and extract the point pairs with the same name (x j ,y j ) and (x j+1 ,y j+1 ), x j For the image I j The column coordinates, y j For the image I j The row coordinate, x j+1 For the image I j+1 The column coordinates, y j+1 For the image I j+1 The row coordinates of 223) Geometric model using orbital j images , the image coordinates of the same-name points are converted to ground coordinates lat and lon through model calculation, and the elevation h is interpolated at the SRTM30 data according to lat and lon, thus forming control points to verify the accuracy of the geometric model of the track j+1 image; 224) Substitute the ground coordinates (lat, lon, h) of the control point into the image geometry model of track j+1 , through the model back calculation (x' j+1 ,y' j+1 )= (lat,lon,h), get the control point in track j+1 image I j+1 The image coordinates (x' j+1 ,y' j+1 ); 225) Compare the image coordinates of the same-name points obtained by matching on the image of track j+1 (x j+1 ,y j+1 ) and the image coordinates (x' j+1 ,y' j+1 )difference and , the specific calculation is: x' j+1 - x j+1 , and' j+1 - and j+1 ; 226) Process multiple adjacent track image data in chronological order, repeat the above steps, obtain positioning error data at different positions, and obtain ; 23) Obtain monthly positioning error change data based on image data taken multiple times at the same location = ,in For The roll, pitch and yaw attitude changes at all times. The specific steps are: 231) Select image data taken multiple times at the same location from the satellite image database to ensure that the images cover the same ground area and record the time tag t i and Image I i ; 232) Select a fixed time moment t from multiple captured images ref The image is used as the reference image I ref , use the calibration coefficient of that moment to make all historical images consistent and unify the geometrical reference of the images; 233) For each I i and I ref Match the images, obtain matching point pairs, and calculate the posture change of the current image relative to the reference image based on relative orientation. ; 234) Arrange the positioning error change data of multiple shooting images in chronological order to generate positioning error change data on a monthly scale ; 24) Perform adaptive variational mode decomposition on the acquired change data of the three time scales and decompose them into trend terms , Periodic Item And the noise term , the specific steps are: 241) Hourly star sensor angle change data , daily scale overlapping image area displacement change data And the positioning error change data on a monthly scale , the data is normalized: ,in is the original sequence data, and are the minimum and maximum values ​​in the original sequence data, For normalized values, the error change values ​​should be mapped to a uniform dimension range, and the box plot method should be applied to remove obvious outliers; 242) Adaptive variational mode decomposition AVMD initialization, define the initial mode number K and penalty factor α, use grid search optimization algorithm to optimize K and α, and find the parameter configuration corresponding to the minimum value of envelope entropy; 243) Using the optimized mode number K and penalty factor α, the variational mode decomposition of the geometric positioning error time series is performed: ,in is the original sequence, is the kth eigenmode function, is the residual noise. According to the frequency distribution and time distribution characteristics, the low-frequency trend term in IMF is distinguished , Periodic Item and high frequency noise terms .

3. The method for adaptively compensating low-frequency positioning errors of optical images with multi-scale representation according to claim 1, characterized in that: The adaptive construction of the optical image low-frequency positioning error model considering the decoupling of dynamic and static errors includes the following steps: 31) Determine the driving factors of low-frequency errors based on the grey correlation analysis method. The specific steps are: 311) Define the independent variables and error sequence. First, determine the independent variables that affect the low-frequency error change of the satellite attitude, including orbital circles, distance initial geometry calibration time, and satellite solar altitude angle. The error sequence is the low-frequency trend term after variational mode decomposition. , Periodic Item and high frequency noise terms ; 312) In order to eliminate the dimension difference and scale influence, the independent variables and error series are standardized by dividing the mean by the standard deviation; 313) Use the grey correlation analysis method to calculate the grey correlation coefficient between the independent variable and the error sequence , is the similarity between the ith independent variable and the jth error sequence; 314) Weighted summation to determine the correlation index ,in is the weight of the j-th independent variable; 315) According to the correlation index, select the one with the largest correlation index As a key driver for subsequent modeling ; 32) The compensation matrix Decoupled into the constant difference between the satellite and the ground and the dynamic low frequency error part , modeling: ,in It's the driving factor. It is the constant difference in the angle between the star and the earth; 33) Further based on the low frequency error Trending items , Periodic Item , noise term Adaptive construction of corresponding compensation model based on the magnitude relationship between them , the specific steps are: 331) When the trend term and the cycle term are of similar magnitude and vary independently, an additive model is used: ； 332) When the magnitude of the cycle term depends on the trend term, a multiplicative model is used: ； 333) Use polynomial models, penalized splines, Fourier series and mixed models to Modeling; 34) For the n unknowns in the compensation matrix, the coordinates of n / 2 or more non-collinear ground control points can be used to solve the problem. The corresponding attitude low-frequency error value under the value , , , the model error equation is further constructed as follows: ， in Represents M observations The low-frequency error value of the pitch angle under the value, Corresponding to the model parameter matrix, partial least squares is used to solve .

Images