A method for constructing a SAR satellite RD model based on an RPC model

Abstract

The application discloses a SAR satellite RD model analytic construction method based on an RPC model, and is characterized in that subjective understanding error influence in the RD model construction process is solved, and related parameters of the RD model are solved by using a step-by-step solving step, so that the rigorous physical meaning of the RD model is reserved. The method uses the universality advantage of the RPC model, combines position solving, orbit fitting, slant range and Doppler solving and other step-by-step parameter solving steps, avoids initial value dependence and instability in a nonlinear solving process, and realizes high-precision solving of RD model parameters. The application takes into account physical rigor and model universality, provides an efficient and feasible technical path for SAR image geometric modeling, and has important theoretical and engineering significance for improving SAR stereoscopic positioning precision.

Description

Technical Field

[0001] This invention belongs to the field of synthetic aperture radar geometric model construction, and particularly relates to an analytical construction method for SAR satellite RD model based on RPC model. Background Technology

[0002] The range-Doppler (RD) model of spaceborne Synthetic Aperture Radar (SAR) remote sensing imagery is not only the theoretical foundation of SAR data processing but also a key prerequisite for geometric calibration and high-precision positioning. Using SAR satellites for stereo positioning offers significant advantages such as all-weather, all-day operation and high precision, and is widely used in fields such as crop growth monitoring, forest surveys, livestock detection in pastures, deformation detection, target detection, automatic target extraction, and disaster prevention, mitigation, and emergency response. Due to its rigorous physical meaning, the RD model has long been used as the geometric positioning model for spaceborne SAR imagery in geometric calibration work. However, the limitations of RD model construction have become an uncertainty factor affecting the high-precision and high-quality development of spaceborne SAR. Although the Rational Polynomial Coefficients (RPC) model can achieve a high-precision fit to the RD model and has the advantage of cross-satellite platform versatility, the parameters of its rational polynomials do not possess rigorous physical meaning, making it unsuitable for geometric calibration.

[0003] Traditionally, RD model construction relies on manual analysis of SAR auxiliary file parameters. However, due to the complexity of the parameter system and differences in definitions between satellites, this approach suffers from subjective bias and low efficiency. In contrast, rational function models achieve parameterization using independent polynomial coefficients, offering the advantage of cross-satellite platform versatility. Therefore, this method utilizes constraints and forward intersection to transform the nonlinear problem into a system of linear equations for solution. This avoids initial value calculations while simultaneously analyzing the relevant parameters of the RD model step-by-step through position and orbit calculations. This not only preserves the rigorous physical meaning and versatility of the RD model but also reduces the subjective errors of manual parameter analysis. This innovative RPC-based analytical construction method for RD models is of great significance for improving the stereo positioning accuracy of SAR satellites.

[0004] Given the importance of RD models in spaceborne SAR-related work, this invention proposes an analytical construction method for SAR satellite RD models based on RPC models. This method can provide a theoretical basis for the development of geometric positioning models for spaceborne SAR images and is also a novel exploration of geometric calibration of RPC models. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention aims to resolve the impact of subjective perception errors during RD model construction. It proposes an analytical construction method for SAR satellite RD models based on the RPC model. First, it analyzes the parameters required for both the RPC and RD models from the perspective of the imaging geometry of spaceborne SAR images. Second, it transforms the parameter solving process into a linear solution process using forward convergence. Finally, it solves the parameters step-by-step using position calculation, orbit calculation, slant range calculation, and Doppler calculation. To achieve the above functions, this invention provides an analytical construction method for SAR satellite RD models based on the RPC model, comprising the following steps:

[0006] S1: Determine the known parameters for constructing the distance-Doppler model; unknown parameters:

[0007] (1) Determine the known parameters for constructing the range Doppler model, which mainly include the azimuth row number, range column number, range pixel interval, radar wavelength, ground point position vector, ground point velocity vector, equatorial radius of the Earth ellipsoid, flattening, and polar radius of the Earth ellipsoid in the image data.

[0008] (2) Determine the unknown parameters for constructing the range-Doppler model, mainly including satellite orbit parameters, slant range parameters, and Doppler parameters;

[0009] S2: Range-Doppler Model Analysis: Based on the DEM, two elevation planes are determined, typically the average elevation plane within the imaging range and a custom elevation difference plane. According to the principle of perspective contraction, the slant distances between ground points and the satellite at the same image point on both elevation planes are approximately equal, and the Doppler center frequencies in strip mode are also approximately equal. By selecting image points uniformly distributed along a single range scan line, the satellite's position and velocity vectors can be derived based on the approximately equal slant distances and Doppler center frequencies.

[0010] S3: Position Calculation: Construct constraint equations based on the constraints, and solve for the satellite position vector and velocity vector corresponding to a single range scan line;

[0011] S4: Orbit Calculation: Based on S3, a fitting operation is performed. The satellite position and velocity vectors corresponding to multiple range scan lines along the azimuth direction are calculated separately and then substituted into the orbit fitting model to solve for the orbit parameters.

[0012] S5: Slant range calculation: Based on the orbital parameters of S4, the satellite position corresponding to any image coordinate is calculated. Image points that are evenly distributed in the image are selected, and the slant range at the near end and the distance pixel interval are calculated according to the distance equation of the RD model.

[0013] S6: Doppler calculation: according to the orbit fitting parameters, the satellite position vector and velocity vector corresponding to any pixel can be obtained, uniformly distributed image points in the image are selected, and the Doppler linear coefficients are solved according to the Doppler equation of the RD model;

[0014] S7: Accuracy evaluation: performing fitting accuracy analysis and positioning accuracy comparison analysis on the constructed RD model.

[0015] Further, determining the known parameters and unknown parameters for constructing the range-Doppler model in step S1 mainly includes the following steps:

[0016] (1) Determining the known parameters required by the Doppler model: mainly including the azimuth line number i and range column number j manually selected from remote sensing image data; the range pixel interval m determined according to the image resolution r , radar wavelength λ; ground position vector [X t Y t Z t and velocity vector [V xt V yt V zt are obtained by forward calculation of the RPC model, and the velocity is usually assumed to be zero in the WGS-84 coordinate system; the Earth ellipsoid parameters include the equatorial radius R e ; the flattening f, and the polar radius R calculated therefrom p ;

[0017] (2) Determining the unknown parameters to be solved for the Doppler model: mainly including satellite orbit parameters a0, a1, a2, b0, b1, b2, c0, c1, c2, which are respectively used to represent the change of the satellite's orbit position in three directions with time t, and the expression is X S =a0+a1·t+a2·t 2 , Y S =b0+b1·t+b2·t 2 and Z S =c0+c1·t+c2·t 2 ; the slant range parameter R0 is used in the slant range expression R=R0+m r ·j, which is calculated by combining the range pixel interval m r and the column number j; the Doppler parameters d0 and d1 are used in the Doppler frequency shift model f dc =d0+d1·j.

[0018] Further, the range-Doppler model analysis in step S2 mainly includes the following steps:

[0019] (1) Determine two elevation planes based on the DEM, typically the average elevation plane within the imaging range and a custom elevation difference plane. Then, based on the perspective shrinkage principle, set the image coordinates and two elevation values, use the RPC model to calculate the geodetic coordinates of the corresponding ground points, and convert them to geocentric coordinates. Finally, combine this with the slant distance equation in the RD model to construct constraint equations;

[0020]

[0021] In the formula, (X S ,Y S Z S ) T The position of the satellite is represented by an unknown parameter. The constraint in equation (1) is that the slant range difference ΔR is sufficiently small.

[0022] (2) Equal Doppler Constraints: In strip SAR imagery, the Doppler center frequency is a linear function of the slant range, and its variation along the azimuth is negligible. Based on the principle of perspective shrinkage, ground points with equal slant ranges can be found; therefore, the Doppler center frequencies of these ground points are also equal. Once the coordinates of the ground points are determined, constraint equations are constructed based on the Doppler equations of the RD model.

[0023]

[0024] In the formula, R S =(X S ,Y S Z S ) T V indicates the position of the satellite. S =(V x V y V z ) T The velocity of the satellite is represented by unknown parameters. The constraint condition of equation (2) is the Doppler center frequency difference Δf. dc Small enough;

[0025] (3) Range slant range constraint: When two points are located on the same range scan line, the two points correspond to the same satellite position, and the slant range difference between the two points is equal to the range pixel interval m. r Multiply by the pixel difference Δj between the two points. Once the ground point coordinates are determined, construct constraint equations based on the distance equation of the RD model.

[0026]

[0027] In the formula, (X S ,Y S Z S ) TThe position of the satellite is an unknown parameter. The constraint of equation (3) is that when the image coordinates between two points are different, the slant distance difference between the two points is equal to the distance pixel interval multiplied by the distance pixel difference between the two points.

[0028] (4) Range-direction Doppler constraint: When two points are located on the same range-direction scan line, they correspond to the same satellite position and velocity, and the Doppler center frequency difference between the two points is equal to the Doppler linear coefficient multiplied by the range-direction pixel difference between the two points. After the ground point coordinates are determined, constraint equations are constructed based on the range equation of the RD model.

[0029]

[0030] In the formula, R S =(X S ,Y S Z S ) T V represents the satellite's position vector. S =(V x V y V z ) T The velocity vector of the satellite is represented by position parameters. The constraint of equation (4) is that when the image coordinates between two points are different, the slant distance difference between the two points is equal to the Doppler linear coefficient d1 multiplied by the distance pixel difference between the two points.

[0031] Furthermore, the position calculation in step S3 mainly includes the following steps:

[0032] Based on equations (1), (2), (3), and (4), a system of equations can be constructed to obtain equation (5):

[0033]

[0034] Image points are selected at equal intervals along a single distance scan line, and two elevation planes H1 and H2 are set. A series of ground point coordinates can be calculated by forward transformation using the RPC model. Any two ground points can be substituted into equation (5).

[0035] 1) When the image coordinates of the two points are the same, substitute them into equation (1). The constraint condition of this equation is that the slant distance difference ΔR is small enough.

[0036] 2) When the image coordinates of two points are different, substitute them into equation (2). The constraint of this equation is that the slant distance difference is equal to the distance pixel interval m. r Multiply by the distance between the two points to the pixel difference Δj.

[0037] 3) When the image coordinates of the two points are the same, substitute them into equation (3). The constraint of this equation is the Doppler center frequency difference Δf. dc Small enough.

[0038] 4) When the image coordinates of the two points are different, substitute them into equation (4). The constraint of this equation is that the difference in Doppler center frequency is equal to the linear coefficient d1 multiplied by the distance pixel difference Δj between the two points.

[0039] Position calculation as follows Figure 2 As shown, there are three sets of ground points with equal slant distances (RT1, RT2, RT3) along the same distance-direction scan line. These points can be used to converge [X]. S Y S Z S V Sx V Sy V Sz ] T Solve it.

[0040] Furthermore, the orbital solution in step S4 mainly includes the following steps:

[0041] Based on S3, orbit fitting calculations are performed using an orbit fitting model.

[0042]

[0043] like Figure 2 As shown, by solving the satellite position vector and velocity vector corresponding to multiple range scan lines along the azimuth direction according to equation (5), multiple sets of azimuth row numbers i and corresponding satellite position vectors [X] can be obtained. S ,Y S Z S ] and the satellite's velocity vector [V Sx V Sy V Sz Substitute these values ​​into the orbital fitting model shown in equation (6) to solve for the orbital parameters a0, a1, a2, b0, b1, b2, c0, c1, c2.

[0044] Furthermore, step S5, the slope distance calculation, mainly includes the following steps:

[0045] Based on orbit calculation, slant range calculation can be performed. The essence of slant range calculation is to solve for the nearest-end slant range R0. Typically, the nearest-end slant range is the slant range corresponding to the point on the starting column of the image. Once the orbit parameters are obtained, the position of the satellite corresponding to any image coordinate can be calculated based on the orbit parameters, and then the slant range corresponding to any image coordinate can be calculated using the distance equation. The relationship between the slant range of any point and the nearest-end slant range R0 can be expressed as:

[0046] R = R0 + m r ·j (7)

[0047] In the formula, m ris the distance-oriented pixel interval, which corresponds to different fixed values ​​for remote sensing images of different resolutions and is a known constant; j is the distance-oriented column number corresponding to any point.

[0048] Control points can be selected in the imagery, and their corresponding image coordinates can be calculated using the RPC model. The satellite position vector corresponding to the image coordinates can be calculated based on orbital parameters. The slant range corresponding to that point can be calculated using the distance equation. The slant range R and the range vector pixel interval m are then calculated. r Substitute the distance nexus number j corresponding to the control point into equation (7) to solve for the near-end slope distance R0. To ensure that the solved near-end slope distance meets the accuracy requirements, points that are evenly distributed in the image can be selected as control points for solving.

[0049] Furthermore, step S6, the Doppler solution, mainly includes the following steps:

[0050] Based on the orbital and slant range calculations, a new formula is constructed to calculate the Doppler parameters.

[0051]

[0052] In the formula, λ is the radar wavelength, which is a known constant. The parameters on the left side of the equation can all be obtained from the orbit calculation and range calculation. At least two control points are selected in the image, and their corresponding image coordinates are calculated through the RPC model. The satellite position vector and velocity vector corresponding to the image coordinates are calculated according to the orbit parameters. The slant range corresponding to the point is calculated according to the range equation. The slant range, position vector, velocity vector, range nexus number of the two control points, and the position vector and velocity vector of the satellite are substituted into equation (8) to solve for the Doppler linear equation coefficients d0 and d1. In order to ensure that the solved Doppler linear coefficients meet the accuracy requirements, points that are uniformly distributed in the image can be selected as control points for solving.

[0053] Furthermore, the accuracy verification in step S7 mainly includes the following steps:

[0054] (1) Fitting Accuracy Verification: Based on the RPC model, the fitting accuracy of the constructed RD model is verified. Image points that are uniformly distributed and cover the entire image area are selected. The ground point coordinates corresponding to the image points are calculated according to the RPC model, and the constructed RD model is used for indirect calculation. The image coordinates before and after are compared, and the fitting accuracy of the constructed RD model is evaluated by the mean square error. The formula for calculating the mean square error is as follows:

[0055]

[0056] Where: σ is the mean square error of the image, X is the coordinates of the corresponding points obtained from the stereo positioning calculation of the RD model, and M is the coordinates of the undetermined point measured by RTK technology. This is the summation symbol for numbers from 1 to n.

[0057] (2) Positioning accuracy verification: Based on the analytical construction method of the RPC model, the positioning accuracy of the constructed RD model is verified. Corner reflector points within the image range are selected as control points, and the coordinates are calculated using the constructed RD model and compared with the known ground coordinates of the corner reflector points. The positioning accuracy of the RD model is evaluated by calculating the mean square error.

[0058] Beneficial effects: Compared with existing technologies, the analytical construction method of SAR satellite RD model based on RPC model has the following advantages:

[0059] (1) By leveraging the high-precision fitting characteristics of the RPC model, the parameters of the RD model can be directly inverted using its polynomial coefficients, avoiding the manual analysis process, reducing subjective errors, and significantly improving the efficiency of model construction.

[0060] (2) The RD model is inverted through the RPC model, which retains the rigorous physical meaning of the RD model (such as the distance equation and Doppler equation), making it applicable to tasks such as geometric calibration and high-precision positioning.

[0061] (3) By performing step-by-step analysis (position calculation, orbit calculation, slant range calculation, Doppler calculation), the nonlinear problem is transformed into a linear problem, which requires no initial value and has higher stability. Attached Figure Description

[0062] The description of the invention will become apparent and readily understood in conjunction with the following drawings, wherein:

[0063] Figure 1 This is a range-oriented imaging geometry diagram illustrating the analytical construction method of a SAR satellite RD model based on the RPC model according to the present invention.

[0064] Figure 2 This is a schematic diagram illustrating the model principle of the SAR satellite RD model analytical construction method based on the RPC model of the present invention.

[0065] Figure 3 This is a flowchart of a method for constructing a SAR satellite RD model based on an RPC model, according to the present invention. Detailed Implementation

[0066] according to Figure 3 The steps shown below provide a detailed explanation of the analytical construction method for SAR satellite RD model based on RPC model according to the present invention.

[0067] Step 1: Determine the known and unknown parameters for constructing the distance-Doppler model. This includes the following specific steps:

[0068] (1) Determining known parameters required for the Doppler model: mainly including the manually selected azimuth line number i and range column j from remote sensing image data; the range pixel interval m determined according to the image resolution r , radar wavelength λ; ground position vector [X t Y t Z t and velocity vector [V xy V yt V zt are obtained by forward operation of the RPC model, and the velocity is generally assumed to be zero in the WGS-84 coordinate system; Earth ellipsoid parameters include equatorial radius R e ; flattening f, and polar radius R p ;

[0069] (2) Determining unknown parameters to be solved for the Doppler model: mainly including satellite orbit parameters a0, a1, a2, b0, b1, b2, c0, c1, c2, which are respectively used to represent the variation of satellite orbit position in three directions with time t, and the expression is X S =a0+a1·t+a2·t 2 , Y S =b0+b1·t+b2·t 2 and Z S =c0+c1·t+c2·t 2 ; the slant range parameter R0 is used in the slant range expression R=R0+m r ·j, and is calculated by combining the range pixel interval m r and column number j; Doppler parameters d0 and d1 are used in the Doppler frequency shift model f dc =d0+d1·j.

[0070] Step 2: Range Doppler model analysis. It includes the following specific steps:

[0071] (1) Under normal circumstances, two reference elevation planes can be determined based on the Digital Elevation Model (DEM): one is the average elevation plane of the imaging area, and the other is a custom elevation difference plane set according to requirements. Based on the principle of foreshortening deformation, the RPC model is first used to convert image coordinates and two known elevation values into geodetic coordinates of corresponding ground points, and then convert them into the geocentric coordinate system. Subsequently, by combining the slant range equation in the RD model, corresponding geometric constraint conditions can be established;

[0072]

[0073] In the formula, (X S ,Y S ,Z S ) TThe position of the satellite is represented by an unknown parameter. The constraint in equation (1) is that the slant range difference ΔR is sufficiently small.

[0074] (2) Equal Doppler Constraints: In strip SAR imagery, the Doppler center frequency is a linear function of the slant range, and its variation along the azimuth is negligible. Based on the principle of perspective contraction, ground points with the same slant range have the same Doppler center frequency. Once the coordinates of the ground points are determined, the corresponding geometric constraints can be established using the Doppler equations of the RD model.

[0075]

[0076] In the formula, R S =(X S ,Y S Z S ) T V indicates the position of the satellite. S =(V x V y V z ) T The velocity of the satellite is represented by unknown parameters. The Doppler center frequency difference Δf in equation (2) is a constraint condition. dc Small enough;

[0077] (3) Range slant range constraint: When two ground points are located on the same range scan line, they correspond to the same satellite position, and the difference in their slant range can be expressed as the range pixel interval m. r The product of the pixel difference Δj between the two points. Given the coordinates of the ground points, corresponding geometric constraints can be established based on the distance equation of the RD model.

[0078]

[0079] In the formula, (X S ,Y S Z S ) T The position of the satellite is an unknown parameter. The constraint of equation (3) is that when the image coordinates between two points are different, the difference in slant distance between the two points is equal to the distance pixel interval multiplied by the distance pixel difference between the two points.

[0080] (4) Range-direction Doppler constraint: For two ground points located on the same range-direction scan line, they share the same satellite position and velocity vectors. In this case, the Doppler center frequency difference between the two points can be expressed as the product of the Doppler linear coefficient and the range-direction pixel difference. Given the ground point coordinates, the corresponding Doppler constraint conditions can be established based on the range equation of the RD model.

[0081]

[0082] In the formula, R S =(X S ,Y S Z S ) T V represents the satellite's position vector. S =(V x V y V z ) T The velocity vector of the satellite is represented by position parameters. The constraint of equation (4) is that when the image coordinates between two points are different, the slant distance difference between the two points is equal to the Doppler linear coefficient d1 multiplied by the distance pixel difference between the two points.

[0083] Step 3: Location Calculation. This includes the following specific steps:

[0084] Based on equations (1), (2), (3), and (4), a system of equations can be constructed to obtain equation (5):

[0085]

[0086] Image points are selected at equal intervals along a single distance scan line, and two elevation planes H1 and H2 are set. A series of ground point coordinates can be calculated by forward transformation using the RPC model. Any two ground points can be substituted into equation (5).

[0087] 1) When the image coordinates of the two points are the same, substitute them into equation (1). The constraint of this equation is that the slant distance difference ΔR is small enough.

[0088] 2) When the image coordinates of two points are different, substitute them into equation (2). The constraint of this equation is that the slant distance difference is equal to the distance pixel interval m. r Multiply by the distance between the two points to the pixel difference Δj.

[0089] 3) When the image coordinates of the two points are the same, substitute them into equation (3). The constraint of this equation is the Doppler center frequency difference Δf. dc Small enough.

[0090] 4) When the image coordinates of the two points are different, substitute them into equation (4). The constraint of this equation is that the difference in Doppler center frequency is equal to the linear coefficient d1 multiplied by the distance between the two points to the pixel difference Δj.

[0091] Position calculation as follows Figure 2 As shown, there are three sets of ground points with equal slant distances (RT1, RT2, RT3) along the same distance-direction scan line. These points can be used to converge [X]. S Y S Z S V Sx V Sy V Sz ]T Solve it.

[0092] Step 4: Orbit Calculation. This includes the following specific steps:

[0093] Based on step 3, orbit fitting calculations are performed using an orbit fitting model.

[0094]

[0095] like Figure 2 As shown, by solving the satellite position vector and velocity vector corresponding to multiple range scan lines along the azimuth direction according to equation (5), multiple sets of azimuth row numbers i and corresponding satellite position vectors [X] can be obtained. S ,Y S Z S ] and the satellite's velocity vector [V Sx V Sy V Sz Substitute these values ​​into the orbital fitting model shown in equation (6) to solve for the orbital parameters a0, a1, a2, b0, b1, b2, c0, c1, c2.

[0096] Step 5: Slope distance calculation. This includes the following specific steps:

[0097] Based on orbit calculation, slant range calculation can be performed. The essence of slant range calculation is to solve for the nearest-end slant range R0. Typically, the nearest-end slant range is the slant range corresponding to the point on the starting column of the image. Once the orbit parameters are obtained, the position of the satellite corresponding to any image coordinate can be calculated based on the orbit parameters, and then the slant range corresponding to any image coordinate can be calculated using the distance equation. The relationship between the slant range of any point and the nearest-end slant range R0 can be expressed as:

[0098] R = R0 + m r ·j (7)

[0099] In the formula, m r is the distance-oriented pixel interval, which corresponds to different fixed values ​​for remote sensing images of different resolutions and is a known constant; j is the distance-oriented column number corresponding to any point.

[0100] Control points can be selected in the imagery, and their corresponding image coordinates can be calculated using the RPC model. The satellite position vector corresponding to the image coordinates can be calculated based on orbital parameters. The slant range corresponding to that point can be calculated using the distance equation. The slant range R and the range vector pixel interval m are then calculated. r Substitute the distance nexus number j corresponding to the control point into equation (7) to solve for the near-end slope distance R0. To ensure that the solved near-end slope distance meets the accuracy requirements, points that are evenly distributed in the image can be selected as control points for solving.

[0101] Step 6: Doppler calculation. This includes the following specific steps:

[0102] Based on the orbital and slant range calculations, a new formula is constructed to calculate the Doppler parameters.

[0103]

[0104] In the formula, λ is the radar wavelength, which is a known constant. The parameters on the left side of the equation can all be obtained from the orbit calculation and range calculation. At least two control points are selected in the image, and their corresponding image coordinates are calculated through the RPC model. The satellite position vector and velocity vector corresponding to the image coordinates are calculated according to the orbit parameters. The slant range corresponding to the point is calculated according to the range equation. The slant range, position vector, velocity vector, range nexus number of the two control points, and the position vector and velocity vector of the satellite are substituted into equation (8) to solve for the Doppler linear equation coefficients d0 and d1. In order to ensure that the solved Doppler linear coefficients meet the accuracy requirements, points that are uniformly distributed in the image can be selected as control points for solving.

[0105] Step 7: Accuracy Verification. This includes the following specific steps:

[0106] (1) Fitting Accuracy Verification: Based on the RPC model, the fitting accuracy of the constructed RD model is verified. Image points that are uniformly distributed and cover the entire image area are selected. The ground point coordinates corresponding to the image points are calculated according to the RPC model, and the constructed RD model is used for indirect calculation. The image coordinates before and after are compared, and the fitting accuracy of the constructed RD model is evaluated by the mean square error. The formula for calculating the mean square error is as follows:

[0107]

[0108] Where: σ is the mean square error of the image, X is the coordinates of the corresponding points obtained from the stereo positioning calculation of the RD model, and M is the coordinates of the undetermined point measured by RTK technology. This is the summation symbol for numbers from 1 to n.

[0109] (2) Positioning accuracy verification: Based on the analytical construction method of the RPC model, the positioning accuracy of the constructed RD model is verified. The image coordinates of the corner reflector points within the image range are extracted as control points, and the constructed RD model is directly calculated and compared with the known ground coordinates of the corner reflector points. The positioning accuracy of the constructed RD model is evaluated by the mean square error.

[0110] This invention provides an analytical construction method for SAR satellite RD models based on RPC models. It transforms the parameter solving process into a linear solving process by using forward convergence, and solves the parameter distribution according to the steps of position calculation, orbit calculation, slant range calculation and Doppler calculation, successfully avoiding the shortcomings of traditional methods.

[0111] The above description is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analytically constructing a SAR satellite RD model based on an RPC model, characterized in that, Includes the following steps: S1: Determine the known parameters for constructing the distance-Doppler model; unknown parameters: (1) Determine the known parameters for constructing the range Doppler model, including the azimuth row number, range column number, range pixel interval, radar wavelength, ground point position vector, ground point velocity vector, equatorial radius of the Earth ellipsoid, flattening, and polar radius of the Earth ellipsoid in the image data; (2) Determine the unknown parameters for constructing the range-Doppler model, including satellite orbital parameters; Slope range parameters and Doppler parameters; S2: Distance Doppler Model Analysis: Based on the DEM, two elevation planes are determined: the average elevation plane within the imaging range and the custom elevation difference plane. Then, based on the perspective shrinkage distortion principle, the image coordinates and two elevation values ​​are set. The geodetic coordinates of the corresponding ground points are obtained using the RPC model and converted to geocentric coordinates. Finally, the constraint equation is constructed by combining the slant distance equation in the RD model. (1) In the formula, Let the satellite's position be an unknown parameter, and the constraint condition of equation (1) be the slant range difference. Small enough; Equal Doppler Constraints: For strip-mode SAR imagery, the Doppler center frequency is a linear function of the slant range. Based on the principle of perspective contraction, ground points with equal slant ranges are identified; therefore, the Doppler center frequencies of these ground points are also equal. Once the coordinates of these ground points are determined, constraint equations are constructed based on the Doppler equations of the RD model. (2) In the formula, The wavelength is the radar wavelength, which is a known constant. Indicates the satellite's location. The velocity of the satellite is represented by unknown parameters. The constraint condition of equation (2) is the Doppler center frequency difference ∆f. dc Small enough; Range slant range constraint: When two points are located on the same range scan line, they correspond to the same satellite position, and the slant range difference between the two points is equal to the range pixel interval m. r Multiply by the difference in pixel column number between the two points Once the ground point coordinates are determined, constraint equations are constructed based on the distance equation of the RD model. (3) In the formula, The position of the satellite is an unknown parameter. The constraint of equation (3) is that when the image coordinates between two points are different, the difference in slant distance between the two points is equal to the distance pixel interval multiplied by the difference in distance pixel column number between the two points. Range-direction Doppler constraints: When two points are located on the same range-direction scan line, they correspond to the same satellite position and velocity, and the difference in Doppler center frequencies between the two points is equal to the Doppler linear coefficient multiplied by the difference in range-direction pixel column numbers between the two points; after the ground point coordinates are determined, constraint equations are constructed based on the range equation of the RD model. (4) In the formula, Indicates the satellite's location. The velocity of the satellite is an unknown parameter. The constraint of equation (4) is that when the image coordinates between two points are different, the slant distance difference between the two points is equal to the Doppler linear coefficient d1 multiplied by the distance to the pixel difference between the two points. S3: Position Calculation: Construct constraint equations based on the constraints, and solve for the satellite position vector and velocity vector corresponding to a single range scan line; S4: Orbit Calculation: Based on S3, perform fitting calculations; solve for the satellite position vector and velocity vector corresponding to multiple range scan lines along the azimuth direction, and substitute them into the orbit fitting model to solve for the orbit parameters; S5: Slant range calculation: Based on the orbital parameters of S4, the satellite position corresponding to any image coordinate is calculated. Image points that are evenly distributed in the image are selected, and the slant range at the near end and the distance pixel interval are calculated according to the distance equation of the RD model. S6: Doppler solution: Based on the orbit fitting parameters, calculate the satellite position vector and velocity vector corresponding to any pixel, select uniformly distributed image points in the image, and solve for the Doppler linear coefficients according to the Doppler equation of the RD model; S7: Accuracy Evaluation: Perform fitting accuracy analysis and positioning accuracy comparison analysis on the constructed RD model.

2. The method for analytically constructing a SAR satellite RD model based on an RPC model according to claim 1, characterized in that, Step S1 includes the following steps: (1) Known parameters required to determine the Doppler model: including the azimuth row number i and range column number j manually selected from remote sensing image data; and the range pixel interval m determined based on image resolution. r and radar wavelength λ; ground position vector [X] t ,Y t Z t ] and velocity vector [V xt V yt V zt The velocity is obtained from the forward operation of the RPC model and is zero in the WGS-84 coordinate system; the Earth ellipsoid parameters include the equatorial radius R. e Flattening f, and the polar radius R calculated from it. p ; (2) Determine the unknown parameters to be solved in the Doppler model: These include satellite orbital parameters a0, a1, a2, b0, b1, b2, c0, c1, and c2, which represent the changes in the satellite's orbital position in three directions with time t, and their expressions are as follows: , and The slope distance parameter R0 is used in the slope distance expression. In the middle, combining the distance to the pixel interval m r The values ​​are calculated from column number j; the Doppler parameters d0 and d1 are used in the Doppler frequency shift model. middle.

3. The method for analytically constructing a SAR satellite RD model based on an RPC model according to claim 1, characterized in that, S3 includes the following steps: Based on equations (1), (2), (3), and (4), we construct a system of equations to obtain equation (5): (5) Image points are selected at equal intervals along a single distance scan line, and two elevation planes H1 and H2 are set. A series of ground point coordinates are obtained by forward transformation of the RPC model. Two ground points are randomly selected and substituted into equation (5). 1) When the image coordinates of these two points are the same, substitute them into equation (1). The constraint of this equation is the slant distance difference. Small enough; 2) When the image coordinates of two points are different, substitute them into equation (3). The constraint of this equation is that the slant distance difference is equal to the distance pixel interval m. r Multiply by the difference in pixel column number between the two points ; 3) When the image coordinates of the two points are the same, substitute them into equation (2); the constraint of this equation is the Doppler center frequency difference. Small enough; 4) When the image coordinates of two points are different, substitute them into equation (4). The constraint of this equation is that the difference in Doppler center frequencies is equal to the linear coefficient d1 multiplied by the difference in pixel column numbers between the two points. ; In position calculation, there are a total of [number] on the same distance-direction scan line. , , Three sets of ground points with equal slope distances can be connected by this forward convergence. and Solve it.

4. The method for analytically constructing a SAR satellite RD model based on an RPC model according to claim 1, characterized in that, S4 includes the following steps: Based on S3, orbit fitting calculations are performed using an orbit fitting model. (6) Multiple range scan lines are selected along the azimuth direction, and the imaging time corresponding to each range scan line is obtained. The satellite position vectors and velocity vectors corresponding to multiple range scan lines are solved according to equation (5) to obtain multiple sets of azimuth row numbers i and their corresponding satellite position vectors. and the satellite's velocity vector Substitute each imaging time and its corresponding satellite position vector and satellite velocity vector into the orbit fitting model shown in (6) to solve for orbit parameters a0, a1, a2, b0, b1, b2, c0, c1, c2.

5. The method for analytically constructing a SAR satellite RD model based on an RPC model according to claim 1, characterized in that, S5 includes the following steps: Based on the orbital calculation, the slant range is calculated; the essence of the slant range calculation is to solve for the slant range at the nearest point. The near-end slant range is the slant range corresponding to a point on the starting column of the image. After obtaining the orbital parameters, the position of the satellite corresponding to any image coordinate is calculated based on the orbital parameters, and then the slant range corresponding to any image coordinate is calculated using the distance equation. The slant range of any point and the near-end slant range... The relationship between them is represented as follows: (7) In the formula, m r is the distance-axis pixel interval, which corresponds to different fixed values ​​for remote sensing images of different resolutions and is a known constant; j is the distance-axis column number corresponding to any point; Multiple control points are uniformly selected within the image area. Their corresponding image coordinates are calculated using the RPC model. The satellite positions corresponding to these image coordinates are calculated based on orbital parameters. The slant range for each control point is then calculated using the distance equation. Distance to pixel interval m r Substitute the distance nexus number j corresponding to the control point into (7) to solve for the near-end slope distance. .

6. The method for analytically constructing a SAR satellite RD model based on an RPC model according to claim 1, characterized in that, S7 includes the following steps: (1) Fitting accuracy verification: Based on the RPC model, the fitting accuracy of the constructed RD model is verified; image points that fill the entire image area and are evenly distributed are selected, and the ground point coordinates corresponding to the image points are calculated according to the RPC model. The constructed RD model is used for indirect calculation; the image coordinates before and after are compared, and the fitting accuracy of the constructed RD model is evaluated by the mean square error; the mean square error calculation formula is as follows: (8) in: The mean square error of the image is denoted as . To construct the RD model, the coordinates of the corresponding points obtained from the stereo positioning calculation are used. These are the coordinates of the control points measured using RTK technology. This is the summation symbol for numbers from 1 to n; (2) Positioning accuracy verification: Based on the RPC model, the RD model is constructed using analytical construction method to verify the positioning accuracy of the constructed RD model; the image coordinates of the corner reflector points within the image range are extracted as control points, and the constructed RD model is directly calculated and compared with the known ground coordinates of the corner reflector points; the positioning accuracy of the constructed RD model is evaluated by the mean error.

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