A Method for Modeling and Compensating the Positioning Error of the Temperature Variation Characteristics of High-Earth Orbit Satellites

Abstract

The present invention discloses a method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite, comprising the steps of: 1. According to the imaging geometric characteristics of a high-orbit remote sensing satellite, constructing an on-orbit geometric calibration model considering the temperature change characteristic error; 2. Decomposing the camera mounting angle error into a low-frequency long-period error model and a high-frequency short-period error model, solving the parameters of the low-frequency long-period error model and the parameters of the high-frequency short-period error model, and fitting an expression of the camera mounting angle error related to temperature; 3. Substituting the fitted expression of the camera mounting angle error into the on-orbit geometric calibration model of the high-orbit satellite constructed in step 1; 4. Substituting the imaging time D and the temperature T into the on-orbit geometric calibration model of the high-orbit satellite in step 3 to obtain the precise coordinate data of each position at any imaging time and temperature on the image sequence to be calibrated. The present invention can eliminate the influence of the temperature change characteristic error on the positioning accuracy of the high-orbit satellite from the model itself and achieve high-precision geometric positioning of the high-orbit satellite.

Description

Technical Field

[0001] The present invention belongs to the technical field of geometric processing of optical remote sensing satellite data, and particularly relates to a method for modeling and compensating positioning errors of the temperature change characteristics of a geostationary satellite. Background Technique

[0002] The positioning error sources in the imaging mechanism of remote sensing satellites mainly refer to the positioning error sources caused by the differences between the nominal values or measured values of satellite imaging parameters and their true values, specifically including: camera principal point error, camera principal distance error, camera distortion error, camera installation error, star sensor installation error, time measurement error, satellite orbit determination error, satellite attitude determination error, etc. Among the above errors, the camera principal point and principal distance errors, camera distortion errors, and camera and star sensor installation errors are usually systematic errors. By using the on-orbit geometric calibration method, the influence of systematic errors on positioning accuracy can be effectively eliminated.

[0003] Compared with the sun-synchronous orbit where low-earth orbit remote sensing satellites are located, the lighting conditions in the geostationary orbit where geostationary satellites are located are more complex. The drastic changes in the heat received by the satellite body often cause the systematic errors of the satellite positioning system to change with temperature, showing the temperature change error characteristics of the combination of low-frequency long-period and high-frequency short-period. This requires analyzing the variation law of its temperature change error according to the device structure and temperature control strategy of the geostationary satellite, and constructing a corresponding temperature change error model to effectively eliminate the influence of such errors. The existing optical remote sensing satellite positioning and calibration models ignore the influence of temperature changes during the geometric calibration period on positioning accuracy, and it is difficult to achieve high-precision geometric positioning of geostationary satellites. Summary of the Invention

[0004] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, and proposing a method for modeling and compensating the positioning errors of the temperature change characteristics of a geostationary satellite. On the basis of the conventional optical remote sensing satellite positioning and calibration model, the positioning errors of the temperature change characteristics of the geostationary satellite are decomposed into low-frequency long-period errors and high-frequency short-period errors, and accordingly an on-orbit geometric calibration and correction model is constructed to achieve high-precision geometric calibration and positioning of the geostationary satellite.

[0005] The technical solution adopted by the present invention is: a method for modeling and compensating the positioning errors of the temperature change characteristics of a geostationary satellite, including the following steps:

[0006] Step 1: According to the satellite attitude parameters, orbit parameters, camera parameters, and the three-dimensional coordinates of the control points on the image to be calibrated in sequence, construct an on-orbit geometric calibration model of the geostationary satellite considering the temperature change characteristics error; the on-orbit geometric calibration model of the geostationary satellite is a function of the camera installation angle error; the camera installation angle error is related to temperature;

[0007] Step 2: Decompose the camera mounting angle error into a low-frequency long-period error model and a high-frequency short-period error model, solve the parameters of the low-frequency long-period error model and the high-frequency short-period error model, and fit the camera mounting angle error expression related to the imaging time D and the temperature T from the low-frequency long-period error model and the high-frequency short-period error model;

[0008] Step 3: Substitute the camera mounting angle error expression fitted in Step 2 into the high-orbit satellite on-orbit geometric calibration model constructed in Step 1;

[0009] Step 4: Substitute the imaging time D and the temperature T into the high-orbit satellite on-orbit geometric calibration model in Step 3 to obtain the precise coordinate data of each position at any imaging time and temperature on the to-be-calibrated sequence images.

[0010] Further, the high-orbit satellite on-orbit geometric calibration model described in Step 1 is:

[0011]

[0012] In the above formula: (X Y Z) T WGS-84 is the three-dimensional coordinate of the control point in the WGS-84 coordinate system, [X GPS Y GPS Z GPS T is the space coordinate of the high-orbit satellite in the WGS-84 coordinate system, obtained by the on-board GNSS measurement equipment of the high-orbit satellite; m is the scale factor; is the rotation matrix from the J2000 coordinate system to the WGS-84 coordinate system, is the rotation matrix from the satellite attitude measurement coordinate system to the J2000 coordinate system, is the installation matrix of the camera in the satellite attitude measurement coordinate system; is the along-track pointing angle of the camera imaging detector in the satellite attitude measurement coordinate system, is the cross-track pointing angle of the camera imaging detector in the satellite attitude measurement coordinate system;

[0013] The origin of the satellite attitude measurement coordinate system is located at the centroid of the attitude measurement equipment on the satellite, the X-axis is the satellite flight direction, the Z-axis points to the center of the earth, and the Y-axis is perpendicular to the Z-axis and the X-axis to form a right-handed system;

[0014] In the case of the rotation sequence being the yaw direction first, then the pitch direction, and finally the roll direction, The expression form of is:

[0015]

[0016] Where: A = y cs +Δy cs,T ​, B = p cs +Δp cs,T , C = r cs +Δr cs,T ; y cs is the installation angle of the camera in the yaw direction in the satellite attitude measurement coordinate system; p cs is the installation angle of the camera in the pitch direction in the satellite attitude measurement coordinate system, r cs is the installation angle of the camera in the roll direction in the satellite attitude measurement coordinate system, Δy cs,T , Δp cs,T , Δr cs,T are respectively the installation angle errors of the camera in the yaw, pitch, and roll directions when the camera temperature is T.

[0017] Furthermore, the scale factor m is calculated according to the following ellipsoid equation:

[0018]

[0019] In the above formula, for Δy cs,T , Δp cs,T , Δr cs,T are all set to 0 for A a = a e + h, B b = b e + h, a e = 6378137.0m, b e = 6356752.3m, h is the ellipsoid height.

[0020] Furthermore, the camera installation angle error described in step 2 is decomposed into a low-frequency long-period error model and a high-frequency short-period error model as follows:

[0021]

[0022] In the above formula, Δp cs1,D , Δr cs1,D , Δy cs1,D are respectively the low-frequency long-period error models of the camera installation angle in the pitch, roll, and yaw directions with the imaging time D as the unit; Δp cs2,T , Δr cs2,T , Δy cs2,T are respectively the high-frequency short-period error models of the camera installation angle in the pitch, roll, and yaw directions with the camera temperature T as the unit; is the camera installation angle error expression related to temperature fitted by the low-frequency long-period error model and the high-frequency short-period error model.

[0023] Further, the low-frequency long-period error model is a linear model with the imaging time D as the independent variable, and its form is as follows:

[0024]

[0025] In the above formula, a0, b0, and c0 are the constant term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively, and a1, b1, and c1 are the first-order term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively; D is the imaging time, D = 1, 2, …, N, N ≥ 2, and the unit is days;

[0026] Further, the high-frequency short-period error model takes the camera temperature T as the independent variable, and its form is as follows:

[0027]

[0028] In the above formula, p A , r A , y A are the amplitudes of the harmonics of the camera installation error in the pitch, roll, and yaw directions respectively when the temperature is T; f p , f r , f y are the frequencies of the harmonics of the camera installation error in the pitch, roll, and yaw directions respectively when the temperature is T; p₀, r₀, and y₀ are the initial phases of the harmonics of the camera installation error in the pitch, roll, and yaw directions respectively when the temperature is T.

[0029] Further, the method for solving the parameters of the low-frequency long-period error model is as follows:

[0030] T1. According to the change of the camera mounting base temperature at different times within a day, obtain the camera mounting angle errors at different temperatures, and respectively count the error means of Δp cs , Δr cs and Δy cs every day to obtain the low-frequency long-period errors Δp cs1,D , Δr cs1,D , Δy cs1,D , D = 1, 2, …, N, and establish a low-frequency long-period error model;

[0031] T2. According to the low-frequency long-period error model, construct the residual function models F p,D , F r,D , F y,D in the pitch, roll, and yaw directions:

[0032]

[0033] T3. For the low-frequency long-period errors Δp of N, N ≥ 2 dayscs1,D , Δr cs1,D , Δy cs1,D , D = 1, 2, …, N, construct the standard error equation:

[0034] V D = A D X D - L D

[0035] In the above formula: is the residual vector of the low-frequency long-period error term;

[0036] A D is a 3N×6-dimensional design matrix composed of partial derivatives of unknowns, and its representation is as follows:

[0037]

[0038] X D is the unknown matrix, and iterative calculation is performed according to the least squares adjustment principle. The expression form is: X D = [a0 a1 b0 b1 c0 c1] T ;

[0039] L D is obtained by substituting the current calculated value of the unknown matrix X D into F p,D , F r,D , F y,D , F D = [F p,1 F r,1 F y,1 … F p,N F r,N F y,N T ;

[0040] T4. According to the least squares adjustment principle, solve a0, a1, b0, b1, c0, c1 when the iteration stops.

[0041] Furthermore, in step T1, when solving the camera mounting angle error at each temperature, the following steps are included:

[0042] S1. Establish a detector pointing angle residual function model based on the on-orbit geometric calibration model of high-orbit satellites:

[0043]

[0044] In the formula: F x is the detector pointing angle residual function model along the satellite track direction, F y ​It is the model of the residual function of the detector pointing angle in the satellite vertical orbit direction; define R is an orthogonal matrix;

[0045] S2. Use the three-dimensional coordinates of M, M≥3 control points on the undetermined calibration sequence image to construct the standard error equation:

[0046] V i =A i X-L i

[0047] In the above formula: V i =[v Fx,1 v Fy,1 …v Fx,M v Fy,M T is the normalized residual vector of the detector pointing angle;

[0048] A i is the 2M×3-dimensional design matrix composed of the partial derivatives of the unknowns, and the representation form is as follows;

[0049]

[0050] X is the unknown matrix, and iterative calculation is performed according to the least squares adjustment principle. The expression form is: X=[Δp cs,T ,Δr cs,T ,Δy cs,T T ;

[0051] L i is the constant term matrix obtained by substituting the current calculated value of the unknown matrix X into g1, d1, e1, g3, d3, e3 in the F x expression and g2, d2, e2, g3, d3, e3 in the F y expression. The representation form is as follows:

[0052] L i =[F x,1 F y,1 …F x,M F y,M T ;

[0053] S3. According to the least squares adjustment principle, solve the camera installation angle errors Δp cs,T ,Δr cs,T ,Δy cs,T ; The condition for judging the iteration stop is: the differences of Δp cs,T ,Δr cs,T ,Δy cs,T obtained from the previous and current calculations are all within the preset threshold, which is regarded as iteration convergence and the iteration is stopped.​​​

[0054] Further, the method for solving the parameters of the high-frequency short-period error model is as follows:

[0055] Step1. Subtract the low-frequency long-period errors Δp cs,T , Δr cs,T , Δy cs,T obtained when establishing the low-frequency long-period error model from the camera mounting angle errors Δp cs1,D , Δr cs1,D , Δy cs1,D respectively to obtain the corresponding groups of high-frequency short-period errors Δp cs2,T , Δr cs2,T , Δy cs2,T and establish a high-frequency short-period error model;

[0056] Step2. According to the high-frequency short-period error model, construct the residual function models F p,T , F r,T , F y,T in the pitch, roll, and yaw directions:

[0057]

[0058] Step3. For the high-frequency short-period errors at K, K≥3 different temperatures, construct the standard error equation:

[0059] V T =A T X T -L T

[0060] In the above formula: is the residual vector of the low-frequency long-period error term;

[0061] A T is a 3K×9-dimensional design matrix composed of the partial derivatives of the unknowns, and the representation form is as follows:

[0062]

[0063] Among them:

[0064] Q 11 =p0 + 2πT1f p , Q 12 =r0 + 2πT1f r , Q 13 =y0 + 2πT1f y

[0065] Q K1 =p0 + 2πT K f p , QK2 = r0 + 2πT K f r , Q K3 = y0 + 2πT K f y

[0066] X T is an unknown matrix, and iterative calculations are performed according to the least squares adjustment principle. The expression form is:

[0067] X T = [p A f p p0 r A f r r0 y A f y y0] T ;

[0068] L T is the constant term matrix obtained by substituting the current calculated value of the unknown matrix X T into F p,T , F r,T , F y,T . The representation form is as follows:

[0069] Step 4. According to the least squares adjustment principle, solve p A , r A , y A , f p , f r , f y , p0, r0, y0 when the iteration stops.

[0070] Furthermore, the on-orbit geometric calibration model of the geostationary satellite in step 3 updates the low-frequency long-period error model parameters and high-frequency short-period error model parameters in the camera mounting angle error expression at time intervals of 1 month to 3 months, so that the on-orbit geometric calibration model of the geostationary satellite is applicable in the long term.

[0071] The beneficial effects of the present invention compared with the prior art are:

[0072] (1) Based on the traditional calibration model, the present invention expands the positioning error model of the temperature change characteristics of the geostationary satellite, which can eliminate the influence of temperature change on the positioning accuracy of the geostationary satellite from the model itself and achieve high-precision geometric positioning of the geostationary satellite.

[0073] (2) The present invention adopts a method for modeling and solving the satellite temperature change characteristic error. By using the imaging time as the independent variable to construct a low-frequency long-period error model and the satellite body temperature as the independent variable to construct a high-frequency short-period error model, the unified modeling and compensation of the temperature change error of high-orbit satellites under different temperature control strategies are realized, solving the problems of non-universal models and complex error compensation processes caused by taking the imaging time or solar altitude angle as the independent variable in the conventional models, and ensuring the high-precision positioning requirements of high-orbit satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a flowchart for implementing the embodiment of the present invention DETAILED DESCRIPTION OF THE EMBODIMENTS

[0075] The present invention will be further described below with reference to the accompanying drawings.

[0076] As Figure 1 shown, it is a flowchart for implementing the method of the present invention, specifically including steps 1 to 4:

[0077] Step 1: According to the satellite attitude parameters, orbital parameters, camera parameters, and three-dimensional coordinates of the control points on the to-be-calibrated sequence images, construct a geometric calibration model for high-orbit satellites in orbit considering the temperature change characteristic error. The geometric calibration model for high-orbit satellites in orbit is a function of the camera mounting angle error, and its form is as follows:

[0078]

[0079] In the above formula: (X Y Z) T WGS-84 is the three-dimensional coordinate of the control point in the WGS-84 coordinate system, obtained by manual measurement or automatic matching; [X GPS Y GPS Z GPS T is the space coordinate of the high-orbit satellite in the WGS-84 coordinate system, obtained by the on-board GNSS measurement equipment of the high-orbit satellite; m is the scale factor; is the rotation matrix from the J2000 coordinate system to the WGS-84 coordinate system, is the rotation matrix from the satellite attitude measurement coordinate system to the J2000 coordinate system, is the installation matrix of the camera in the satellite attitude measurement coordinate system; is the along-track pointing angle of the camera imaging element in the satellite attitude measurement coordinate system, is the cross-track pointing angle of the camera imaging element in the satellite attitude measurement coordinate system.

[0080] The origin of the satellite attitude measurement coordinate system is located at the centroid of the on-board attitude measurement equipment, the X-axis is the satellite flight direction, the Z-axis points to the earth's center, and the Y-axis is perpendicular to the Z-axis and the X-axis to form a right-handed system.​

[0081] In the case where the sequence of rotation is first the yaw direction, then the pitch direction, and finally the roll direction, the expression form is:

[0082]

[0083] where: A = y cs + Δy cs，T , B = p cs + Δp cs，T , C = r cs + Δr cs，T ; y cs is the installation angle of the camera in the yaw direction in the satellite attitude measurement coordinate system; p cs is the installation angle of the camera in the pitch direction in the satellite attitude measurement coordinate system, r cs is the installation angle of the camera in the roll direction in the satellite attitude measurement coordinate system, Δy cs，T , Δp cs，T , Δr cs，T are respectively the angular errors of the camera installation angle in the yaw, pitch, and roll directions when the camera temperature is T.

[0084] Furthermore, the calculation method is as follows:

[0085]

[0086] In the above formula, (s, l) are the coordinates of the control points on the calibration sequence image in the image coordinate system, s is the column number, and l is the row number; h0 is the constant term in the direction of the satellite along-track pointing angle direction, h1, h2, h3, h4, h5, h6, h7, h8, h9 respectively correspond to s, l, sl, s direction of the satellite along-track pointing angle 2 , l 2 , s 2 l, sl 2 , s 3 , l 3 coefficients, k0 is the constant term in the direction of the satellite cross-track pointing angle direction, k1, k2, k3, k4, k5, k6, k7, k8, k9 respectively correspond to s, l, sl, s direction of the satellite cross-track pointing angle 2 , l 2 , s 2 l, sl 2 , s 3 , l 3 coefficients.

[0087] Further, the scale factor m is calculated according to the following ellipsoid equation:

[0088]

[0089] In the above formula, is Δy cs，T , Δp cs，T , Δr cs，T are all set to 0 when A a = a e + h, B b = b e + h, a e = 6378137.0 m, b e = 6356752.3 m, and h is the ellipsoid height.

[0090] Step 2: Decompose the camera mounting angle error into a low-frequency long-period error model and a high-frequency short-period error model, solve the parameters of the low-frequency long-period error model and the high-frequency short-period error model, and fit an expression of the camera mounting angle error related to the imaging time D and the temperature T from the low-frequency long-period error model and the high-frequency short-period error model.

[0091] First, the forms of the decomposed low-frequency long-period error model and high-frequency short-period error model are as follows:

[0092]

[0093] In the above formula, Δp cs1,D , Δr cs1,D , Δy cs1,D are respectively the low-frequency long-period error models of the camera mounting angle in the pitch, roll, and yaw directions with the imaging time D as the unit; Δp cs2,T , Δr cs2,T , Δy cs2,T are respectively the high-frequency short-period error models of the camera mounting angle in the pitch, roll, and yaw directions with the camera temperature T as the unit; is the expression of the camera mounting angle error fitted from the low-frequency long-period error model and the high-frequency short-period error model.

[0094] The low-frequency long-period error model is a linear model with the imaging time D as the independent variable, and its form is as follows:

[0095]

[0096] In the above formula, a0, b0, and c0 are the constant term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively, and a1, b1, and c1 are the first-order term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively; D is the imaging time, with the unit of day.

[0097] When establishing the low-frequency long-period error model, it is necessary to solve the camera installation angle error at different temperatures. When solving the camera installation angle error under each temperature condition, the following steps are included:

[0098] S1. Definition: R is an orthogonal matrix, R -1 =R T ;

[0099] Perform the following transformation on the on-orbit geometric calibration model of the high-orbit satellite to obtain:

[0100]

[0101] Multiply both sides of the above equation on the left by R -1 , and through four arithmetic operations, the following formula can be obtained:

[0102]

[0103] In the formula: F x is the detector pointing angle residual function model in the along-track direction of the satellite, and F y is the detector pointing angle residual function model in the cross-track direction of the satellite;

[0104] S2. For each control point coordinate on the sequence of images to be calibrated, construct a standard error equation. In this embodiment, the number of control points M selected is 9, and the constructed standard error equation is:

[0105] V i =A i X - L i

[0106] In the above formula: In the above formula: V i =[v Fx,1 v Fy,1 …v Fx,M v Fy,M T is the normalized residual vector of the detector pointing angle;

[0107] A i is a 2M×3-dimensional design matrix composed of the partial derivatives of the unknowns, and the representation form is as follows;

[0108]

[0109] X is the unknown matrix, and the expression form is: X = [Δp cs,T ​, Δr cs,T , Δy cs,T T ; X is iteratively calculated according to the least squares adjustment principle, and the calculation formula is:

[0110] X = (A T PA) -1 (A T PL)

[0111] In this embodiment, the initial value of X is set to [0 0 0].

[0112] L i is the constant term matrix obtained by substituting the current calculated value of the unknown matrix X into g1, d1, e1, g3, d3, e3 in the F x expression, and g2, d2, e2, g3, d3, e3 in the F y expression, and the representation form is as follows:

[0113] L i = [F x,1 F y,1 …F x,M F y,M T ;

[0114] P is the observation weight of the target particle coordinates and is the identity matrix.

[0115] S3. According to the least squares adjustment principle, solve the camera installation angle error Δp cs,T , Δr cs,T , Δy cs,T at the end of iteration; where the condition for judging the end of iteration is: the difference between the Δp cs,T , Δr cs,T , Δy cs,T calculated in the previous and current iterations is within 10 -6 , which is regarded as iterative convergence and the iteration stops.

[0116] After obtaining the camera installation angle errors at different temperatures, the parameters of the low-frequency long-period error model are obtained by the following method:

[0117] T1. According to the camera installation angle errors at different temperatures obtained at different times within a day, respectively count the error means of Δp cs , Δr cs and Δy cs for each day, and obtain the low-frequency long-period errors Δp cs1,D , Δr cs1,D , Δy cs1,D , D = 1, 2,..., N, and establish a low-frequency long-period error model; in this embodiment, N = 7 is selected. ​​

[0118] T2. Based on the low-frequency long-period error model, construct the residual function model F of the low-frequency long-period error in the pitch, roll, and yaw directions p,D , F r,D , F y,D :

[0119]

[0120] T3, low-frequency long-period error Δp for N days cs1,D , Δr cs1,D , Δy cs1,D ,D=1,2,…,N, construct the standard error equation:

[0121] V D =A D X D -L D

[0122] In the above formula: is the residual vector of the low-frequency long-period error term;

[0123] A D is a 3N×6 dimensional design matrix consisting of partial derivatives of unknown numbers, expressed as follows:

[0124]

[0125] X D Is the unknown matrix, expressed as: X D =[a0 a1 b0 b1 c0 c1] T ;X D Iterative calculation is performed based on the least squares adjustment principle. The calculation formula is:

[0126] X D =(A D T P D A D ) -1 (A D T P D L D )

[0127] In this embodiment, set X D The initial value of is [0 0 0 0 0 0].

[0128] L D The unknown matrix X D Substitute the current calculated value of F into p,D , F r,D , F y,D The constant term matrix obtained by the expression is expressed as follows: LD = [F p,1 F r,1 F y,1 …F p,N F r,N F y,N T ;

[0129] T4. Solve for a0, a1, b0, b1, c0, c1 at the end of iteration according to the least squares adjustment principle.

[0130] Furthermore, the high-frequency short-period error model takes the camera temperature T as the independent variable and has the following form:

[0131]

[0132] In the above formula, p A , r A , y A are the amplitudes of the harmonics of the camera mounting error in the pitch, roll, and yaw directions at temperature T, respectively; f p , f r , f y are the frequencies of the harmonics of the camera mounting error in the pitch, roll, and yaw directions at temperature T, respectively; p0, r0, y0 are the initial phases of the harmonics of the camera mounting error in the pitch, roll, and yaw directions at temperature T.

[0133] Furthermore, the solution methods for the parameters p A , r A , y A , f p , f r , f y , p0, r0, y0 are as follows:

[0134] Step1. Subtract the low-frequency long-period errors Δp cs,T , Δr cs,T , Δy cs,T from the camera mounting angle errors Δp cs1,D , Δr cs1,D , Δy cs1,D obtained at different temperatures when establishing the low-frequency long-period error model, respectively, to obtain the corresponding groups of high-frequency short-period errors Δp cs2,T , Δr cs2,T , Δy cs2,T , and establish a high-frequency short-period error model;

[0135] Step2. According to the high-frequency short-period error model, construct the residual function models F p,T , F r,T , F​y,T :

[0136]

[0137] Step 3. Construct a standard error equation for the high-frequency short-period errors at K different temperatures; in this embodiment, K = 10, and the standard error equation is:

[0138] V T = A T X T - L T

[0139] In the above formula: is the residual vector of the low-frequency long-period error term;

[0140] A T is a 3K×9 design matrix composed of partial derivatives of unknowns, and its representation form is as follows:

[0141]

[0142] Where:

[0143] Q 11 = p0 + 2πT1f p , Q 12 = r0 + 2πT1f r , Q 13 = y0 + 2πT1f y

[0144] Q K1 = p0 + 2πT K f p , Q K2 = r0 + 2πT K f r , Q K3 = y0 + 2πT K f y

[0145] X T is the unknown matrix, and its expression form is: X T = [p A f p p0 r A f r r0 y A f y y0] T ; X T Perform iterative calculation according to the least squares adjustment principle, and the calculation formula is:

[0146] X T = (A T TP T A T ) -1 (A T T P T L T )

[0147] In this embodiment, the initial value of X is set to [0 0 0 0 0 0 0 0 0]. T T .

[0148] L T is a constant term matrix obtained by substituting the current calculated value of the unknown matrix X into the expressions of F, F, F, and has the following representation: T p,T r,T y,T A A A p

[0149] Step 4. According to the least squares adjustment principle, solve p, r, y, f, f, f, f, p0, r0, y0 when the iteration stops. In step 3, substitute the camera installation angle error expression fitted in step 2 into the high-orbit satellite on-orbit geometric calibration model constructed in step 1. r y

[0150] In step 4, substitute the imaging time D and temperature T into the high-orbit satellite on-orbit geometric calibration model in step 3 to obtain the accurate coordinate data of each position at any imaging time and temperature on the to-be-calibrated sequence of images.

[0151] After the high-orbit satellite on-orbit geometric calibration model of the present invention is established once, the applicable period is 1 to 3 months; at intervals of 1 to 3 months, regularly update the low-frequency long-period error model parameters and high-frequency short-period error model parameters in the camera installation error, so that the high-orbit satellite on-orbit geometric calibration model described in step 3 is applicable in the long term.

[0152] Although the present invention has been disclosed above with preferred embodiments, it is not used to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention all belong to the protection scope of the technical solution of the present invention.​​​​​​​​​​​

Claims

1. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite, characterized in that, It includes the following steps: Step 1: Construct a geometric calibration model for high-orbit satellites in orbit considering temperature-variation characteristic errors based on satellite attitude parameters, orbital parameters, camera parameters, and the three-dimensional coordinates of control points on the to-be-calibrated sequential images; the geometric calibration model for high-orbit satellites in orbit is a function of the camera mounting angle error; the camera mounting angle error is related to temperature; Step 2: Decompose the camera mounting angle error into a low-frequency long-period error model and a high-frequency short-period error model, solve the parameters of the low-frequency long-period error model and the high-frequency short-period error model, and fit an expression for the camera mounting angle error related to the imaging time D and temperature T from the low-frequency long-period error model and the high-frequency short-period error model; Step 3: Substitute the expression for the camera mounting angle error fitted in Step 2 into the geometric calibration model for high-orbit satellites in orbit constructed in Step 1; Step 4: Substitute the imaging time D and temperature T into the geometric calibration model for high-orbit satellites in orbit in Step 3 to obtain the accurate coordinate data of each position at any imaging time and temperature on the to-be-calibrated sequential images.

2. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 1, characterized in that The geometric calibration model for high-orbit satellites in orbit described in Step 1 is: In the above formula: (X Y Z) T WGS-84 is the three-dimensional coordinates of the control point in the WGS-84 coordinate system, [X GPS Y GPS Z GPS T is the space coordinates of the high-orbit satellite in the WGS-84 coordinate system, obtained by the on-board GNSS measurement equipment of the high-orbit satellite; m is the scale factor; is the rotation matrix from the J2000 coordinate system to the WGS-84 coordinate system, is the rotation matrix from the satellite attitude measurement coordinate system to the J2000 coordinate system, is the installation matrix of the camera in the satellite attitude measurement coordinate system; is the along-track pointing angle of the camera imaging element in the satellite attitude measurement coordinate system, is the cross-track pointing angle of the camera imaging element in the satellite attitude measurement coordinate system;​ The origin of the satellite attitude measurement coordinate system is located at the centroid of the attitude measurement device on the satellite, the X-axis is the satellite flight direction, the Z-axis points to the center of the earth, and the Y-axis is perpendicular to the Z-axis and the X-axis to form a right-handed system; In the case where the order of rotation is first the yaw direction, then the pitch direction, and finally the roll direction, The expression form is: Where: A = y cs + Δy cs,T , B = p cs + Δp cs,T , C = r cs + Δr cs,T ; y cs is the installation angle of the camera in the yaw direction in the satellite attitude measurement coordinate system; p cs is the installation angle of the camera in the pitch direction in the satellite attitude measurement coordinate system, r cs is the installation angle of the camera in the roll direction in the satellite attitude measurement coordinate system, Δy cs,T , Δp cs,T , Δr cs,T are respectively the installation angle errors of the camera in the yaw, pitch, and roll directions when the camera temperature is T.

3. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 2, characterized in that, The scale factor m is calculated according to the following ellipsoid equation: In the above formula, is Δy cs,T , Δp cs,T , Δr cs,T are all set to 0, A a = a e + h, B b = b e + h, a e = 6378137.0 m, b e = 6356752.3 m, where h is the ellipsoidal height.

4. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 1, characterized in that, The decomposition of the camera mounting angle error described in Step 2 into a low-frequency long-period error model and a high-frequency short-period error model is as follows: In the above formula, Δp cs1,D , Δr cs1,D , Δy cs1,D are respectively the low-frequency long-period error models of the camera mounting angles in the pitch, roll, and yaw directions with the imaging time D as the unit; Δp cs2,T , Δr cs2,T , Δy cs2,T are respectively the high-frequency short-period error models of the camera mounting angles in the pitch, roll, and yaw directions with the camera temperature T as the unit; is the temperature-related camera mounting angle error expression fitted from the low-frequency long-period error model and the high-frequency short-period error model.

5. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 4, characterized in that, The low-frequency long-period error model is a linear model with the imaging time D as the independent variable, and the form is as follows: In the above formula, a0, b0, and c0 are the constant term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively, and a1, b1, and c1 are the first-order term coefficients of the low-frequency long-period error model in the pitch, roll, and yaw directions respectively; D is the imaging time, D = 1, 2,..., N, N≥2, and the unit is days.

6. A method for modeling and compensating the positioning error of the temperature change characteristics of a geosynchronous satellite according to claim 4, characterized in that, The high-frequency short-period error model takes the camera temperature T as the independent variable, and the form is as follows: In the above formula, p A , r A , y A are the amplitudes of the harmonics in the pitch, roll, and yaw directions of the camera mounting error at temperature T, respectively; f p , f r , f y are the frequencies of the harmonics in the pitch, roll, and yaw directions of the camera mounting error at temperature T, respectively; p0, r0, and y0 are the initial phases of the harmonics in the pitch, roll, and yaw directions of the camera mounting error at temperature T, respectively.

7. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 5, characterized in that The method for solving the parameters of the low-frequency long-period error model is: T1. According to the variation of the temperature of the camera mounting base plate at different times within a day, the camera mounting angle errors at different temperatures are obtained, and the mean errors of Δp cs , Δr cs , and Δy cs are respectively statistically analyzed for each day, and the low-frequency long-period errors Δp cs1,D , Δr cs1,D , and Δy cs1,D for each day are obtained. For D = 1, 2, …, N, the low-frequency long-period error model described in claim 5 is established; T2. According to the low-frequency long-period error model, construct the residual function model F of the low-frequency long-period error in the pitch, roll, and yaw directions p,D , F r,D , F y,D : T3. For low-frequency long-period errors Δp, Δr, and Δy over N days where N ≥ 2, with D = 1, 2, …, N, construct the standard error equation: cs1,D , Δr cs1,D , Δy cs1,D , D = 1, 2, …, N, construct the standard error equation: V D = A D X D - L D In the above formula: is the residual vector of the low-frequency long-period error term; A D is a 3N×6-dimensional design matrix composed of partial derivatives of unknowns, and its representation form is as follows: X D is an unknown matrix, and iterative calculations are performed according to the least squares adjustment principle. Its expression form is: X D = [a0 a1 b0 b1 c0 c1] T ; L D is obtained by substituting the current calculated value of the unknown matrix X D into F p,D , F r,D , F y,D , and is a constant term matrix obtained from the expression of F, and is expressed as follows: L D = [F p,1 F r,1 F y,1 … F p,N F r,N F y,N T ;​ T4. According to the least squares adjustment principle, solve a0, a1, b0, b1, c0, and c1 when the iteration stops.

8. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 7, characterized in that In Step T1, when solving the camera mounting angle error at each temperature, it includes the following steps: S1: Establish a detector pointing angle residual function model according to the geometric calibration model for high-orbit satellites in orbit; Where: F x is the detector pointing angle residual function model of the satellite along the orbit direction, and F y is the detector pointing angle residual function model of the satellite across the orbit direction; define R as an orthogonal matrix; S2: Use the three-dimensional coordinates of M, M≥3 control points on the to-be-calibrated sequential images to construct a standard error equation; V i = A i X - L i In the above formula: V i = [v Fx,1 v Fy,1 … v Fx,M v Fy,M T is the residual vector of the normalized exploration element pointing angle;​ A i It is a 2M×3-dimensional design matrix composed of partial derivatives of unknowns, and its representation form is as follows; X is an unknown matrix, and iterative calculations are performed according to the least squares adjustment principle. The expression form is: X = [Δp cs,T , Δr cs,T , Δy cs,T T ;​ L i is obtained by substituting the current calculated value of the unknown matrix X into F x in the expressions g1, d1, e1, g3, d3, e3, F y in the expressions g2, d2, e2, g3, d3, e3 to obtain a constant term matrix, and the representation form is as follows: L i = [F x,1 F y,1 … F x,M F y,M T ;​ S3. Solve the camera mounting angle errors Δp cs,T , Δr cs,T , Δy cs,T when the iteration stops according to the least squares adjustment principle; the condition for judging the iteration stop is that the differences between the Δp cs,T , Δr cs,T , Δy cs,T calculated in the current and previous two times are all within the preset threshold, which is regarded as the iteration convergence and the iteration stops.

9. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 6, characterized in that, The method for solving the parameters of the high-frequency short-period error model is: Step 1. Subtract the low-frequency long-period errors Δp cs,T , Δr cs,T , Δy cs,T from the camera mounting angle errors Δp cs1,D , Δr cs1,D , Δy cs1,D obtained at different temperatures when establishing the low-frequency long-period error model, to obtain the corresponding groups of high-frequency short-period errors Δp cs2,T , Δr cs2,T , Δy cs2,T , and establish the high-frequency short-period error model described in claim 6; Step 2. According to the high-frequency short-period error model, construct the residual function models \(F_{\theta}\), \(F_{\varphi}\), \(F_{\psi}\) of the high-frequency short-period error in the pitch, roll, and yaw directions p,T where \(F_{\theta}\) r,T is y,T : Step 3: Construct a standard error equation for the high-frequency short-period errors at K, K≥3 different temperatures; V T = A T X T - L T In the above formula: is the residual vector of the low-frequency long-period error term; A T is a 3K×9-dimensional design matrix composed of partial derivatives of unknowns, and its representation form is as follows: Where: Q 11 = p0 + 2πT1f p , Q 12 = r0 + 2πT1f r , Q 13 = y0 + 2πT1f y Q K1 = p0 + 2πT K f p , Q K2 = r0 + 2πT K f r , Q K3 = y0 + 2πT K f y X T is an unknown matrix, and iterative calculations are performed according to the least squares adjustment principle. The expression form is as follows: X T = [p A f p p0 r A f r r0 y A f y y0] T ; L T is obtained by substituting the current calculated value of the unknown matrix X T into F p,T , F r,T , F y,T , and is a constant term matrix obtained from the expression of F, and its representation is as follows: Step 4. Solve for p at the iteration stop according to the least squares adjustment principle A , r A , y A , f p , f r , f y , p0, r0, y0.

10. A method for modeling and compensating the positioning error of the temperature change characteristics of a high-orbit satellite according to claim 1, characterized in that, The geometric calibration model for high-orbit satellites in orbit described in Step 3 updates the parameters of the low-frequency long-period error model and the high-frequency short-period error model in the expression for the camera mounting angle error at regular intervals of 1 to 3 months, so that the geometric calibration model for high-orbit satellites in orbit can be applied for a long time.

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