SAR satellite RD model numerical value construction method based on RPC model

Abstract

The invention discloses an SAR satellite RD model numerical value construction method based on an RPC model. According to the method, efficient inversion of RD model parameters is realized by utilizing the high-precision geometric positioning capability of the RPC model. According to the method, firstly, parameter analysis is carried out on an RD model, a resolving model is constructed based on an RPC model and original image data, image points evenly distributed in an image range are selected, a space grid is formed in combination with RPC inversion, and the stability of a solving equation is enhanced. When a nonlinear equation set is constructed, unknown parameters are solved by adopting a least square iterative adjustment method on the basis of a distance equation and a Doppler equation in combination with an orbit fitting model. And finally, verifying the precision and stability of the established RD model through error analysis. According to the method, the complexity and subjectivity of a traditional analysis modeling process are avoided, and the geometric positioning precision of the SAR image is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of SAR remote sensing satellite data processing, and in particular relates to a numerical construction method of a SAR satellite RD model based on an RPC model. Background Art

[0002] The geometric positioning accuracy of spaceborne Synthetic Aperture Radar (SAR) imagery is crucial to realizing its application value, and this directly relies on an accurate geometric positioning model. The Range-Doppler (RD) model, with its fundamental physical significance, is crucial for achieving high-precision geometric processing. Traditional RD model construction relies heavily on manual analysis of complex parameter systems within SAR auxiliary files. This process is not only inefficient, but also prone to subjective cognitive biases due to differences in parameter definitions across different satellite platforms, which in turn affects the model's versatility and accuracy. Furthermore, traditional construction methods are no longer sufficient for large-scale, efficient processing of SAR imagery.

[0003] The Rational Polynomial Coefficients (RPC) model, a universal model independent of satellite platforms, uses polynomial coefficients to achieve parameterized expression and can accurately fit RD models. However, the rational polynomial parameters of the RPC model lack physical meaning, which limits its application in high-precision geometric processing tasks such as geometric calibration. Therefore, how to construct a physically rigorous RD model while maintaining the universality of the RPC model has become a pressing technical challenge.

[0004] In view of the above background, the present invention proposes a numerical construction method of RD model based on RPC model. This method makes full use of the high-precision fitting characteristics of RPC model and converts the solution of RD model parameters into the least squares solution problem of nonlinear equations. By systematically summarizing the RD model parameter system and constructing the numerical relationship, high-precision inversion from RPC model to RD model is achieved. This method not only breaks through the dependence of traditional RD model construction on sensor parameters in auxiliary files, but also provides a new idea with both versatility and rigor for the geometric positioning model of spaceborne SAR images. Compared with traditional methods, numerical methods can solve the unknown parameters of all RD models at the same time, improve the solution efficiency, and through the overall solution of nonlinear equations, reduce the error transmission between parameters and improve the overall accuracy of the model. Summary of the Invention

[0005] Aiming at the problem that the construction of RD model of spaceborne SAR remote sensing images in the prior art relies on manual analysis and has subjective cognitive bias, this paper proposes a numerical construction method of RD model based on RPC model. Figure 1 As shown. This method aims to construct RD models in a standardized, automated and high-precision manner, reduce manual intervention, and improve the efficiency and versatility of model construction. The technical solution of the present invention mainly includes the following steps:

[0006] Step 1: Using the known RPC model parameters, which can express the relationship between the image coordinates and the geocentric rectangular coordinates of the ground points, as the basis for constructing the RD model;

[0007] Step 2: Systematically summarize the RD model parameter system and clearly define the parameters required to construct the RD model, including orbit parameters, slant range parameters, and Doppler parameters. These parameters together constitute the rigorous physical meaning of the RD model. Then, determine the parameters required to construct the RD model, namely orbit fitting parameters, slant range parameters, Doppler parameters, etc.

[0008] Step 3: Construct a nonlinear system of equations using the range and Doppler equations of the RD model. Determine the required solution parameters of the nonlinear system by deconstructing the RD model parameters and expressing them in terms of orbit fitting parameters, slant range parameters, and Doppler parameters.

[0009] Step 4: Select evenly distributed ground points within the image range, calculate the ground point data using the RPC model, and then construct a system of equations based on this data. Use initial value iteration to solve the problem, and through continuous iteration, obtain a set of parameter values ​​that best fit the system of equations, ensuring that the residual error of the system of equations is minimized.

[0010] Step 5: Using SAR images of various resolutions as experimental data, and using evenly distributed image points as checkpoints, we compare the image coordinates before and after the forward transformation of the RPC model and the indirect operation of the RD model to verify the effectiveness of the numerical method for constructing the RD model.

[0011] Step 6: Verify the positioning accuracy based on the image of the corner reflector with the calibration field, extract the image coordinates of the corner reflector point, and compare the ground coordinates of the corner reflector directly calculated by the RD model constructed by the numerical method with the known data to further verify the positioning accuracy of the model.

[0012] Furthermore, in step 1, the back calculation is performed using the known RPC model, which is implemented as follows:

[0013] The RPC model is a known condition of the present invention, and the ground coordinates can be solved by the inverse calculation form of the RPC model, as shown in formula (1):

[0014]

[0015] Where, P i (X, Y, H) is the relevant polynomial of the RPC model. (X, Y) is the image coordinate of the ground point, and H is the elevation of the elevation plane. The geodetic coordinates of the ground point (latitude, longitude, height) can be converted into the coordinates of the Earth's geocentric space rectangular coordinate system through formula (2).

[0016] [X t Y t Z t ]=G(P,L,H) (2)

[0017] The specific conversion method of the ground point geodetic coordinates into geocentric space rectangular coordinates is as follows:

[0018]

[0019] Where a is the semimajor axis of the Earth's ellipsoid; f is the flattening of the ellipsoid; b is the semiminor axis of the Earth's ellipsoid; e is the first eccentricity of the Earth's ellipsoid; and n is the radius of curvature of the angular circle. The values ​​corresponding to the above parameters are all in the WGS-84 coordinate system.

[0020] The present invention is based on the construction of the RPC model experiment RD model. The RPC model provides the present invention with the relationship between the image coordinates (line, sample) of any pixel and the geocentric spatial rectangular coordinates (X, Y, Z) of its corresponding ground point as the main known conditions.

[0021] Furthermore, in step 2, the RD model parameter system is systematically summarized, and the summary results are as follows:

[0022] The present invention aims to construct an RD model without relying on manual analysis of satellite auxiliary files. Therefore, the parameters required for constructing the RD model include: orbital parameters (a0, a1, a2, b0, b1, b2, c0, c1, c2, prf); slant range parameter R0; and Doppler parameters d0 and d1. The orbital parameters represent the relationship between the satellite position vector and velocity vector along the azimuth direction at different times. The slant range and Doppler parameters represent the relative relationship between the satellite and the ground at any time, together forming a rigorous physical definition along the azimuth and range directions.

[0023] Furthermore, in step 3, a nonlinear equation system is constructed, and its main construction process is as follows:

[0024] The numerical method is to solve the unknowns in the RD model by constructing a set of nonlinear equations. The main requirements are orbit fitting parameters a0, a1, a2, b0, b1, b2, c0, c1, c2, close-range end slant range R0, pulse repetition frequency prf, and Doppler linear equation coefficients d0 and d1. The detailed solution process is as follows. Figure 2 As shown in Figure 1, the numerical solution of range-Doppler model parameters is mainly divided into three stages: integration of known parameters, model construction and solution, and parameter output.

[0025] The classic RD model consists of the distance equation, the Doppler equation, and the earth ellipsoid equation.

[0026]

[0027] In the formula, [X s ,Y s ,Z s ] represents the position of the satellite, [X t ,Y t ,Z t ] represents the ground point coordinates, R represents the slant distance; f d represents the Doppler center frequency, λ represents the wavelength, and R t and R s Represent the distance vector of the ground target and the satellite distance vector respectively; V t and V s Represent the ground target velocity vector and satellite velocity vector respectively; R e is the average equatorial radius of the Earth, R p is the polar radius of the Earth's ellipsoid.

[0028] Since the velocity vector of a ground point is usually zero in the WGS-84 coordinate system, the distance equation and Doppler equation in the classic RD model shown in equation (4) can be rewritten as equation (5):

[0029]

[0030] Where, contains the close-range end slant range R0 to be solved. dc It is expressed as the coefficients d0 and d1 of the Doppler linear equation. Substituting the fitting parameters a0, a1, a2; b0, b1, b2; c0, c1, c2 and the pulse repetition frequency prf in the orbit fitting model into the orbit model, the specific expression is shown in Equation (6).

[0031]

[0032] Substituting the parameters in equation (6) into equation (5) together forms a nonlinear equation group as shown in equation (7).

[0033]

[0034] Where, f n is the distance equation, f m is the Doppler equation.

[0035] According to formula (7), the nonlinear equations shown in formula (8) are constructed by combining the parameters to be solved and the known parameters. A total of 2n equations (n ​​is the number of control points) are used to solve 13 unknowns.

[0036]

[0037] Where n represents the distance equation and m represents the Doppler equation.

[0038] According to the ground control points obtained by RPC, i is equal to 1~n, representing the control points solved in the image. Δj represents the column number of the ground point image coordinate distance. Linearize equation (8) to construct the error equation group:

[0039]

[0040] The error equation of formula (9) can be expressed as,

[0041] V=Bx-l (10)

[0042] Where,

[0043]

[0044] Furthermore, in step 4, the nonlinear equations of the numerical method are solved, the known parameters are substituted into the error equations, and the correction numbers of the equations are solved according to the initial value iteration method. The specific implementation algorithm of this process is as follows:

[0045] (1) According to the RPC model, the start time, end time and middle time of the image formation moment are selected in the azimuth direction, and the image coordinates of the start column number, end column number and middle column number are selected in the distance direction, and the corresponding geodetic coordinates are solved according to the average elevation surface.

[0046] (2) According to formula (2), calculate the corresponding terrain spatial rectangular coordinates and compare them with the distance pixel interval m r and radar wavelength λ are substituted into formula (8).

[0047] (3) Substitute all unknown parameters that need to be solved into formula (10) with (a0, a1, a2, b0, b1, b2, c0, c1, c2, R0, prf, d0, d1) = (0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0) as the initial values.

[0048] (4) According to equations (8), (9), and (10), calculate the correction value of all unknown parameters x = [Δa0 Δa1 Δa2 Δb0 Δb1 Δb2 Δc0 Δc1 Δc2 ΔR0 Δprf Δd0 Δd1] T .

[0049] (5) Update the parameters, i.e., (a0+Δa0, a1+Δa1, a2+Δa2; b0+Δb0, b1+b1, b2+Δb2; c0+Δc0, c1+Δc1, c2+Δc2, R0+ΔR0, prf+Δprf, d0+Δd0, d1+Δd1).

[0050] (6) Continuing to recalculate the correction value x according to equations (8), (9) and (10): [Δa0 Δa1 Δa2 Δb0 Δb1 Δb2 Δc0 Δc1 Δc2 ΔR0 Δprf Δd0 Δd1] T , determine whether the unknown parameter corrections Δa0 Δa1 Δa2 Δb0 Δb1 Δb2 Δc0 Δc1 Δc2 ΔR0 Δpref Δd0 Δd1 are all less than 10 -3 If it is less than , the iteration is terminated, otherwise continue to execute 4) for iterative operation.

[0051] (7) After the iteration is terminated, the output parameters are a0, a1, a2, b0, b1, b2, c0, c1, c2, R0, prf, d0, d1.

[0052] (8) Based on the output orbit fitting parameters a0, a1, a2, b0, b1, b2, c0, c1, c2 and prf, the orbit fitting equation (6) is used to solve the satellite position vector and velocity vector corresponding to the image point at any time.

[0053] (9) According to the output of the near-end slant distance R0, the slant distance R corresponding to the coordinates of any image point can be solved according to the RD model.

[0054] (10) According to the output Doppler linear equation coefficients d0, d1, the Doppler center frequency f corresponding to any image point coordinate can be solved according to the RD model. dc .

[0055] (11) The image coordinates of the ground control points are calculated based on the constructed RD model and compared with the image coordinates calculated by the original RPC model.

[0056] Furthermore, in step 5, the effectiveness of the numerical method to construct the RD model is verified. The detailed process is as follows:

[0057] (1) SAR images of various resolutions are used as experimental data, and evenly distributed image points are used as checkpoints.

[0058] (2) Compare the image coordinates before and after the forward transformation of the RPC model and the indirect operation of the RD model to verify the effectiveness of the numerical method to construct the RD model.

[0059] (3) Through this step, the accuracy of the RD model constructed by the numerical method in image coordinate transformation can be ensured.

[0060] Furthermore, in step 6, the positioning accuracy of the RD model generated by the parameters is verified. The detailed process is as follows:

[0061] (1) Verify positioning accuracy based on images with calibration field angle reflectors.

[0062] (2) The image coordinates of the corner reflector point are extracted and the ground coordinates of the corner reflector directly calculated by the RD model constructed by the numerical method are compared with the known data.

[0063] (3) The positioning accuracy of the model is verified by comparison to ensure that the RD model constructed by the numerical method can achieve high-precision positioning in practical applications.

[0064] Compared with the prior art, the beneficial effects of the present invention are mainly reflected in the following aspects:

[0065] (1) The automated construction of the RD model is achieved through numerical methods, which reduces the manual analysis process and improves the efficiency, accuracy and versatility of model construction.

[0066] (2) It avoids the subjective cognitive bias caused by manual analysis of SAR auxiliary file parameters and improves the objectivity of model construction.

[0067] (3) It provides a reliable RD model for high-precision geometric processing such as geometric calibration, which helps to improve the geometric positioning accuracy of spaceborne SAR images and promote the development of remote sensing image processing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] The description of the contents of the present invention will become more apparent and easier to understand when taken in conjunction with the following drawings, in which:

[0069] Figure 1 Schematic diagram of the solution idea of ​​a numerical construction method of a spaceborne SAR range Doppler model based on the RPC model of the present invention;

[0070] Figure 2 The present invention provides a flow chart of the parameter solving process of a method for numerically constructing a spaceborne SAR range Doppler model based on an RPC model. DETAILED DESCRIPTION

[0071] To further illustrate the numerical method for constructing an RD model based on the RPC model proposed in the present invention, the implementation process of this technology is described below in combination with implementation details:

[0072] Step 1: Use the known RPC model to select and generate control point parameters. The specific implementation is as follows:

[0073] In the range of SAR image, nine evenly distributed pixel points are selected using the nine-square grid layout strategy, and the image coordinates [i, j] of each image point are recorded. The RPC model corresponding to the image is used to back-project each image point and solve its corresponding geodetic coordinates [L, B, H]. The WGS84 spatial rectangular coordinates [X t ,Y t ,Z t The calculated ground points can be regarded as "virtual control points" with geometric constraints. The formula for converting geodetic coordinates to spatial rectangular coordinates is:

[0074]

[0075] Where N is the radius of the circle, a is the semi-major axis of the Earth's ellipsoid, and b is the semi-minor axis of the Earth's ellipsoid.

[0076] Step 2: Statistical analysis of known and unknown parameters of the RD model. The specific analysis is as follows:

[0077] The classic RD model consists of the distance equation, the Doppler equation, and the earth ellipsoid equation.

[0078]

[0079] In the formula, [X s ,Y s ,Z s ] represents the position of the satellite, [X t ,Y t ,Z t ] represents the ground point coordinates, R represents the slant distance; f d represents the Doppler center frequency, λ represents the wavelength, and R t and R s Represent the distance vector of the ground target and the satellite distance vector respectively; V t and V s Represent the ground target velocity vector and satellite velocity vector respectively; R e is the average equatorial radius of the Earth, R p is the polar radius of the Earth's ellipsoid.

[0080] When constructing the RD model, all parameters of the Earth ellipsoid equation are known. Therefore, the main focus is on analyzing the parameter distribution of the distance equation and the Doppler equation. The slant range R from the satellite to the ground point can be expressed as the distance sampling interval m. r , image point column number j and initial slant range R0; the Doppler center frequency can be expressed as a first-order polynomial about column number j; and the ground point velocity vector, with the WGS-84 coordinate system as the reference system, is zero. Therefore, the distance equation and Doppler equation can be expressed as,

[0081]

[0082] In the formula, [V sx ,V sy ,V sz ] represents the velocity component of the satellite in each direction in the WGS84 coordinate system. The satellite orbit can be approximately regarded as a parabola, so the satellite position in each direction can be expressed as a quadratic polynomial with time as the variable. Time t is the ratio of the image point row number to the pulse repetition frequency, so we have,

[0083]

[0084] According to formula (16) and formula (17), the known parameters of the RD model include the image point coordinates [i, j], the ground space rectangular coordinates [X t ,Y t ,Z t ] and the range sampling interval; the unknown parameters include: orbit parameters (a0, a1, a2, b0, b1, b2, c0, c1, c2, prf), initial slant range R0, Doppler parameters d0 and d1, a total of 13.

[0085] Step 3: Construct the nonlinear equations to be solved by the RD model. The specific steps are as follows:

[0086] According to formula (16), combined with the row and column coordinates of the image point and the corresponding geodetic coordinates, the slant range residual equation f1 and the Doppler residual equation f2 can be constructed.

[0087]

[0088] This system of equations clearly establishes error functions for range and azimuth, forming the basis for subsequent optimization. Furthermore, each parameter in this system of equations can be represented by 13 unknowns and the known coordinates of control points. However, experimentally, when iterating all 13 parameters simultaneously, the resulting iterative results are significantly inconsistent with the actual parameters of the RD model due to the significant numerical differences between the parameters and the resulting parameter-to-parameter shadowing. Therefore, the present invention employs a step-by-step iterative method to perform least-squares fitting of the parameters.

[0089] Step 4: Iterate the correction values ​​of the nine orbital parameters (except prf). The specific steps are as follows:

[0090] Temporarily take the pulse repetition frequency (prf), initial slant range, two Doppler parameters, and range interval as known parameters, assign them prior values ​​and bring them into the equation group, and first perform fitting correction on the nine orbital parameters.

[0091] After these five parameters are brought into the range residual function and the Doppler residual function, the known control point coordinate information, including the image point coordinates and the spatial rectangular coordinates, are brought into these two residual equations to obtain the residual vector.

[0092]

[0093] According to formula (5), the first-order partial derivatives of the slant range residual and Doppler residual functions of each control point are calculated for the nine orbital parameters to form a Jacobian matrix J1 with 2n rows and 9 columns (n ​​is the number of virtual control points, and the experiment uses 9 control points). The constructed Jacobian matrix is ​​roughly in the form of:

[0094]

[0095] Step 5: Least squares solution of orbital parameters. The specific steps are as follows:

[0096] The Gauss-Newton method is used for nonlinear least squares optimization. The specific iterative process is as follows:

[0097] (1) Initialize the parameter vector x = [a0, a1, a2, b0, b1, b2, c0, c1, c2] T , set the maximum number of iterations M1 and the convergence threshold ε1;

[0098] (2) Calculate the residual vector l1 and Jacobian matrix J1 based on the current parameter estimates;

[0099] (3) Construct the normal equation, J1 T J1△x=J1 T l1, solve for the correction vector △x;

[0100] (4) Update parameter: x k+1 =x k +△x;

[0101] (5) If ||△x||<ε1 or k>M1, stop the iteration and output the fitting orbital parameter results; otherwise, let k=k+1 and return to step (2) to continue the iteration.

[0102] Step 6: Iterate the correction values ​​of the other four parameters. The specific steps are as follows:

[0103] Substitute the obtained orbital parameter corrections into the range residual equation and the Doppler residual equation to iteratively correct the five imaging parameters: pulse repetition frequency, initial slant range, range sampling interval, and Doppler parameter. As in step 4, substitute the control point information into the two residual equations to obtain the residual vector.

[0104] According to formula (18), the first-order partial derivatives of the slant range residual and Doppler residual functions of each control point are calculated for the four imaging parameters to form a Jacobian matrix J2 with 2n rows and 4 columns.

[0105]

[0106] Step 7: Least squares estimation of imaging parameters

[0107] The Gauss-Newton method is also used for nonlinear least squares optimization. The specific iterative process is as follows:

[0108] (1) Using the prior values ​​used above, initialize the parameter vector y = [PRF, R0, m r ,d0,d1] T , set the maximum number of iterations M2 and the convergence threshold ε2;

[0109] (2) Calculate the residual vector l2 and Jacobian matrix J2 based on the current parameter estimates;

[0110] (3) Construct the normal equation, J2 T J2△y=J2 T l2, solve for the correction vector △y;

[0111] (4) Update parameter: y k+1 =y k +△y;

[0112] (5) If ||△y||<ε2 or k>M2, stop the iteration and output the fitting imaging parameter results; otherwise, set k=k+1 and return to step (2) to continue the iteration.

[0113] Step 8: Verify the results of the numerical method and the positioning accuracy of the RD model generated by 13 parameters. The specific steps are as follows:

[0114] Fitting accuracy analysis: Forward project the geodetic coordinates of the virtual control points onto the image plane to obtain the predicted image point coordinates, compare them with the original image point coordinates, calculate the plane distance error of all points, and calculate the error σ r ;

[0115] Positioning accuracy analysis: The image point coordinates of the corner reflector are converted to ground coordinates, compared with the ground coordinates of the original corner reflector, and the spatial distance error of all points is calculated, and the error σ is obtained. g .

[0116] If σ is satisfied r <ε r And σ g <ε g , the model solution is considered to be converged and effective; otherwise, the threshold is lowered and iterated again until the accuracy requirement is met.

[0117] The method of the present invention integrates the universal geometric positioning capability of the RPC model and the physical description capability of the RD model, and realizes the robust parameter estimation of the RD model through an iterative optimization mechanism, providing an effective technical path with strong versatility and high degree of automation for high-precision geometric processing of SAR images. The specific embodiments described in this article are only used to illustrate the principles and technical solutions of the present invention. For ordinary technicians in the relevant technical field, various forms of modification, replacement or deformation can be made to the specific embodiments without departing from the basic concept and substantive content of the present invention, and these should all fall within the scope of protection defined by the claims of the present invention.

Claims

1. A numerical construction method of SAR satellite RD model based on RPC model, characterized by: The steps include: The first step is to select n spatially evenly distributed image points in the SAR image, calculate the corresponding geodetic coordinates through back-projection of the known RPC model, and then convert the geodetic coordinates into WGS84 spatial rectangular coordinates as known control points; The second step is to clarify the known and unknown parameters required for RD model construction. After analysis, the known parameters for solving the RD model include the image coordinates of the known control points, the rectangular coordinates of the ground space, and the distance sampling interval (m r ); unknown parameters include: 10 orbital parameters (a0, a1, a2, b0, b1, b2, c0, c1, c2, prf), initial slant range R0, Doppler parameters d0 and d1, a total of 13; The third step is to construct an equation system based on the distance equation and Doppler equation of the RD model, with the 13 unknown parameters in the RD model as variables; The fourth step is to derive the range and Doppler residual functions with respect to 13 parameters to obtain the Jacobian matrix J; The fifth step is to use the Gauss-Newton method for least squares iterative optimization. The steps include: calculating the residual vector l and the Jacobian matrix, constructing the normal equation J T J△x=J T l, and solve the correction numbers of 13 parameters; Step 6: Add the correction to the current parameter estimate; Step 7: Determine whether the correction number is less than the preset threshold. If not, continue iterating. If so, output the final correction results of the 13 parameters. In the eighth step, the mean error of the fitting accuracy is calculated using the known control points obtained through RPC, and the mean error of the positioning accuracy is calculated using the ground corner reflector control points to determine whether the estimation results are qualified. If the accuracy of all control points meets the preset tolerance standard, the model result is considered valid.

2. The method according to claim 1, characterized in that The selection of virtual control points in the first step adopts a spatially uniform distribution strategy, and preferably uses a nine-square grid pattern to distribute the control points within the SAR image range to ensure geometric coverage of the entire imaging area, thereby improving the numerical stability and solution convergence of parameter estimation.

3. The method according to claim 1, characterized in that The virtual control points are generated by back-projection of the RPC model without relying on ground measured data. The RD model parameter solution framework is constructed based on the control points, which significantly enhances the adaptability and versatility of the RD model in multi-source SAR data processing.

4. The method according to claim 1, wherein The RD model parameter construction method described in the second step is uniformly represented by thirteen variables, including 10 orbital parameters and 3 imaging parameters. The orbital parameters are the coefficients of the quadratic time function of the x, y, and z directions (a0, a1, a2, b0, b1, b2, c0, c1, c2), and the imaging parameters are the initial slant range R0 and the Doppler center frequency polynomial coefficients d0 and d1. A standardized RD model solution structure is defined to facilitate the automated analysis and engineering deployment of the model.

5. The method according to claim 1, wherein The parameter estimation in the third and fourth steps adopts a step-by-step iterative strategy, that is, first fixing the imaging parameters to solve the orbital parameters, and then fixing the orbital parameters to solve the imaging parameters, which effectively avoids the nonlinear coupling effect caused by the joint iteration of all parameters and improves the numerical stability and solution accuracy of the least squares estimation.

6. The method according to claim 1, characterized in that During the parameter estimation process, the iteration termination conditions are set, including the maximum number of iterations and the correction amount convergence threshold. When the correction amount of any iterative variable is lower than the preset threshold or the cumulative number of iterations reaches the upper limit, the iteration of this stage is terminated and the current parameter estimation result is output.

Images