SAR stereo and interferometric area network joint adjustment method and device based on RPC model

Abstract

This application discloses a joint adjustment method and apparatus for SAR stereo and interferometric regional networks based on an RPC model, belonging to the field of synthetic aperture radar remote sensing and photogrammetry technology. The method includes: constructing a rigorous positioning model based on range-Doppler and interferometric phase equations; fitting the rational polynomial model RPC parameters of the SAR master image and InSAR phase using virtual grid control points with the assistance of an external DEM; obtaining the unwrapped absolute phase; constructing a joint adjustment model of image coordinates and interferometric phase based on the image-side affine transformation of the master image and its error equations; constructing error equations using affine transformation parameters as virtual observations; introducing external DEM elevation as a weak constraint equation for observations when control points are scarce; solving for the affine transformation parameters by eliminating variables in all error equations; and iteratively calculating the three-dimensional coordinates of the densified points. This invention, combining SAR stereo and InSAR interferometric observations, significantly improves the three-dimensional positioning accuracy under conditions of scarce control points.

Description

Technical Field

[0001] This application belongs to the field of synthetic aperture radar remote sensing measurement and photogrammetry technology, specifically involving a joint adjustment method and system for SAR stereo measurement and InSAR interferometric regional network based on the rational polynomial coefficient (RPC) model. Background Technology

[0002] Synthetic Aperture Radar (SAR) is an active microwave remote sensing sensor with all-weather, day-and-night imaging capabilities. It can penetrate clouds and haze to acquire surface information, making it a crucial tool for Earth observation. SAR stereo mapping and Interferometric Synthetic Aperture Radar (InSAR) are two main techniques for obtaining three-dimensional information about the Earth's surface using SAR data. SAR stereo mapping determines the three-dimensional coordinates of ground points by performing stereo intersection on multiple SAR images acquired from different angles; InSAR technology uses the phase difference information between two or more SAR images to invert the surface elevation. With the continuous development of high-resolution SAR satellites (such as TerraSAR-X, COSMO-SkyMed, and Gaofen-3), SAR / InSAR technology is playing an increasingly important role in topographic mapping, deformation monitoring, and disaster assessment.

[0003] In SAR / InSAR 3D localization processing, traditional methods mainly rely on rigorous physical imaging models based on the Range-Doppler (RD) equation and the interferometric phase equation. These rigorous models directly describe the geometric relationships between the sensor's spatial position, the ground target's position, and SAR imaging parameters (slant range, Doppler frequency, and interferometric phase), exhibiting high theoretical accuracy. However, these rigorous models have the following main limitations in practical applications: First, the establishment and solution of a rigorous model require accurate auxiliary data such as satellite orbital parameters, sensor attitude parameters, and imaging time parameters. The acquisition of these parameters depends on the metadata files provided by satellite data providers. There are significant differences between different sensors and different data formats, and there is a lack of a unified processing framework.

[0004] Second, although the basic principles of the rigorous imaging models of different SAR sensors are the same, there are differences in specific parameter definitions, coordinate system selection, and time references. This leads to the need to develop different processing modules for different sensors, resulting in poor versatility and hindering the joint processing of multi-source SAR data.

[0005] Third, most existing regional network adjustment methods are designed and implemented separately for SAR stereo measurements or InSAR interferometry, meaning that regional network adjustment of SAR stereo imagery and processing of InSAR interferometric data are performed independently. This separate processing approach fails to fully utilize the complementary information between SAR stereo observations and InSAR interferometric observations, limiting the redundancy of the adjustment and the improvement of the final positioning accuracy.

[0006] Fourth, in difficult areas where there are few or no control points in the field (such as deserts, mountains, polar regions, etc.), relying solely on the autonomous positioning accuracy of a rigorous model is often insufficient to meet the requirements of high-precision surveying. Traditional methods lack effective constraints to compensate for the accuracy loss caused by insufficient control points and fail to make full use of the prior elevation information provided by external DEM data.

[0007] The Rational Function Model (RFM) is a widely used general-purpose sensor model in optical satellite remote sensing. It describes the mapping relationship between ground point coordinates and image coordinates using Rational Polynomial Coefficients (RPCs), offering advantages such as unified form, sensor independence, and ease of distribution and use. Currently, there is no systematic solution to extend the RFM to InSAR processing that incorporates interferometric phase information and to establish a unified framework for joint adjustment of SAR stereo and InSAR interferometrics.

[0008] In the process of realizing this invention, the inventors discovered that the prior art has at least the following problems: the lack of a joint adjustment framework that unifies SAR stereo observation and InSAR interferometric phase observation into a general sensor model makes it difficult to fuse multi-source data and makes it difficult to guarantee the accuracy of elevation positioning under the condition of no control points. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method and apparatus for joint adjustment of SAR stereo and interferometric regional networks based on the RPC model. By constructing a unified RFM model for SAR and InSAR, and combining image-side affine transformation refinement with virtual observation constraints, high-precision positioning can be achieved under conditions of few or no control points.

[0010] The technical solution adopted by this application to solve its technical problem is: On the one hand, a joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model is provided, including the following steps: Step S1, based on the range-Doppler equation and the interferometric phase equation, construct SAR and InSAR rigorous positioning models for single-transmit single-receive and single-transmit dual-receive modes; Step S2, based on the rigorous positioning model, with the assistance of an external DEM, construct virtual grid control points and fit the RPC parameters of the rational polynomial model of SAR master image coordinates and InSAR phase values; Step S3, obtain the unwrapped absolute phase through InSAR interferometric processing; Step S4, based on the RPC model of InSAR image coordinates and interferometric phase, construct a joint adjustment model and its error equation of SAR image coordinates and InSAR phase based on the master image image-side affine transformation refinement model; Step S5, construct the error equation of the affine transformation refinement model parameters as virtual observation values; Step S6, combine all the error equations established in Steps S4 and S5 to construct the normal equation, perform ground point coordinate elimination, solve the affine transformation parameters, iterate until convergence, and obtain the three-dimensional coordinates of the densified points.

[0011] As a preferred method, step S2 uses external DEM data to generate dense virtual grid control points, calculates the ground coordinates and phase values ​​corresponding to each grid point based on a rigorous model, and uses the least squares method to fit 12 normalized coefficients, 80 row and column coordinate RPC coefficients (40 for each row and column) and 40 phase RPC coefficients to realize a sensor-independent general imaging model.

[0012] Preferably, the image-side refinement model uses a first-order affine transformation to compensate for RPC system errors, and the joint adjustment model simultaneously considers the virtual observation constraints of SAR image coordinate observations, InSAR phase observations, and affine parameters, which significantly improves the geometric consistency of multi-source observations.

[0013] As a preferred option, when control points are extremely scarce (less than 3), the external DEM elevation is used as a weak constraint equation for the observations. The weak constraint of the DEM elevation is weighted according to the nominal accuracy of the external DEM, which neither damages the observation geometry nor prevents elevation parameter drift, thus ensuring the stability of the adjustment solution.

[0014] On the other hand, a joint adjustment device for SAR stereo and interferometric regional networks based on the RPC model is provided, including a rigorous positioning and modeling module, an RPC fitting module, an interferometric processing module, an image and phase error equation module, a virtual observation error equation module, and an adjustment solution module. Optionally, an external DEM measurement error equation module can be included, which is activated when the number of control points is insufficient, to implement the steps of the above-mentioned joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model.

[0015] One of the above technical solutions has the following advantages or beneficial effects: (1) High versatility: The rational polynomial coefficient (RPC) model is used to replace the rigorous physical model related to the sensor. The RPC model has a unified form and is independent of the sensor type. It can be applied to data acquired by different SAR sensors, realize the unified processing of multi-source SAR data, and eliminate the need to develop separate processing modules for each sensor.

[0016] (2) High accuracy of joint adjustment: For the first time, a joint adjustment framework of RPC model regional network of SAR stereo measurement and InSAR interferometry was established, which fully integrates the geometric intersection information of SAR stereo observation and the phase information of InSAR interferometry observation, increases the observation redundancy, and improves the reliability of adjustment and the accuracy of three-dimensional positioning.

[0017] (3) Good adaptability to sparse control points: By introducing the DEM elevation weak constraint error equation, when there are few or no control points in the field, the external DEM provides weak constraint information in the elevation direction, which effectively prevents elevation parameter drift and ensures positioning accuracy under difficult conditions.

[0018] (4) Good adjustment stability: By constructing virtual observation constraint equations for affine transformation parameters and reasonably setting the prior weights of each parameter, the rank deficiency and ill-conditioned problems of the adjustment model are effectively prevented, and the numerical stability of parameter solution is enhanced.

[0019] (5) High density of results: The densified points not only include the same-name connection points between multiple images, but also the three-dimensional coordinates of single InSAR high coherence coefficient feature points calculated using refined orientation parameters, which significantly improves the point density of the final three-dimensional positioning results.

[0020] (6) Model-based innovation: This invention extends the RFM model to InSAR processing that includes interferometric phase information, and proposes an extended RPC parameter fitting method with 132 coefficients (12 normalized coefficients, 80 row and column image coordinate equation coefficients (40 for each row and column), and 40 phase value equation coefficients), which lays the model foundation for the generalized processing of InSAR data.

[0021] The above-mentioned technical features of this application are combined with each other: the unified RPC model provides a general data foundation for joint adjustment, the joint adjustment framework and virtual observation constraints work together to enhance the stability of the solution, and the introduction of weak DEM constraints further complements the aforementioned features when control points are scarce, forming a complete technical closed loop from model construction, stable solution to difficult condition constraints, which together achieves a significant improvement in 3D positioning accuracy under scarce or no control conditions. Attached Figure Description

[0022] Figure 1This is a flowchart illustrating a joint adjustment method for SAR stereo and interferometric regional networks based on an RPC model, according to an exemplary embodiment. Figure 2 This is a schematic diagram of a joint adjustment device for SAR stereo and interferometric regional networks based on an exemplary embodiment. Detailed Implementation

[0023] To more clearly illustrate the technical features of this application, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0024] Example 1 like Figure 1 As shown in this embodiment, a joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model includes the following steps: Step S1: Based on the range-Doppler equation and the interferometric phase equation, construct SAR and InSAR rigorous positioning models for single-transmit single-receive and single-transmit dual-receive modes.

[0025] The rigorous positioning model uses a geocentric rectangular coordinate system as a reference to establish a functional relationship between ground point coordinates and slant range, Doppler frequency, and interferometric phase parameters, expressed as follows: , In this context, subscript 1 represents the relevant parameters of the main image. R 1. f d1 and f R represents the slant distance, Doppler frequency, and interference phase value at the column and row coordinates (c, r) of the main image point, respectively. 10 and G 1c These represent the initial slant range and slant range resolution of the main image, respectively; λ is the radar wavelength; and Q is the transmit / receive mode coefficient, taking values ​​of 2 and 1 for single-transmit / single-receive and single-transmit / dual-receive respectively. , , )and( , , (X,Y,Z) represent the spatial locations of the interference points when the primary and secondary image sensors acquire data, respectively, and (X,Y,Z) represent the primary image points. c , r The corresponding ground point coordinates, , and The velocity component is the primary image sensor.

[0026] The rigorous positioning model uses a geocentric rectangular coordinate system as a spatial reference to establish functional relationships between ground point coordinates and slant range, Doppler frequency, and interferometric phase parameters. For the single-transmitter / single-receiver mode, both transmission and reception are handled by the same antenna, and Q=2 is used in the interferometric phase calculation. For the single-transmitter / dual-receiver mode, one antenna transmits the signal, and two antennas receive it separately, and Q=1 is used in the interferometric phase calculation. The establishment of this rigorous model provides a theoretical basis for subsequent RPC parameter fitting.

[0027] Step S2: Based on the rigorous positioning model, virtual grid control points are constructed with the assistance of an external DEM to fit the RPC parameters of the rational polynomial model (RFM) of the SAR master image coordinates and InSAR phase values.

[0028] The RPC parameters of the rational polynomial model for fitting the SAR main image coordinates and InSAR phase values ​​include the following steps: Step S21: Obtain basic data, including the InSAR rigorous positioning model constructed in step S1, external DEM data, SAR master image and InSAR interferometric phase data, and complete coordinate system unification and format preprocessing of all data. Step S22: Based on the InSAR rigorous positioning model and combined with the elevation information provided by the external DEM, a virtual grid is uniformly divided in the image space of the SAR main image and the elevation space of the image coverage area. Step S23: Based on the divided virtual grid, a rigorous positioning model is used to generate virtual control points at each grid point. A sufficient number of virtual control points are generated in the whole scene image. Each virtual control point contains unique image coordinates, elevation value, and ground point coordinates and phase value calculated by the rigorous model. That is, each control point is composed of image coordinates, phase value and ground point coordinates. Step S24: Determine the target model for RPC parameter fitting and solve for a total of 132 RPC coefficients, including: 12 normalized coefficients (offsets and scaling factors for image row, column, phase, and ground coordinates), 80 image coordinate equation coefficients (40 row coordinate equations and 40 column coordinate equations), and 40 phase value equation coefficients; wherein, the denominator constant term of each rational polynomial is normalized to 1, the 12 normalized coefficients are obtained by statistical calculation of virtual control points, and the remaining parameters are obtained by solving the error equation constructed by virtual control points; Step S25: Substitute the ground point coordinates of all virtual control points and their corresponding image point coordinates and phase values ​​into the rational polynomial model to construct a set of fitting equations and solve for all coefficients in a unified manner. Step S26: Solve the fitted equation system to obtain 12 normalized coefficients, 40 row image coordinate equation coefficients, 40 column image coordinate equation coefficients and 40 phase value equation coefficients, for a total of 132 RPC parameters, where the denominator constant term of each rational polynomial is normalized to 1; Step S27: Using virtual control points and checkpoints, the accuracy of the 132 extracted InSAR RPC parameters is verified, and abnormal fitting results are removed to ensure that the parameters meet the requirements of the RFM model.

[0029] The rational polynomial model RFM normalizes geodetic coordinates ( B n , L n , H n ) and normalized image point coordinates ( r n , c n ) and normalized phase value ( f n The relationship is expressed in the form of a ratio polynomial, and the model form is as follows: , in, P 1. P 2. P 3. P 4. P 5. P 6 is the normalized latitude B n ,longitude L n and elevation H n The ternary cubic polynomials, each containing 20 coefficients, and the constant term of the denominator polynomial normalized to 1, together constitute 132 RPC parameters to be determined.

[0030] Step S3: Obtain the unwrapped absolute phase through InSAR interferometry.

[0031] Interferometric processing is performed on InSAR image pairs, including registration, interferogram generation, filtering, and phase unwrapping, to obtain unwrapped absolute interferometric phase data, which is used as one of the observations for subsequent joint adjustment.

[0032] Step S4: Based on the RPC model of InSAR image coordinates and interferometric phase, construct a joint adjustment model and its error equation for SAR image coordinates and InSAR phase based on the master image image-side affine transformation refinement model.

[0033] The constructed joint adjustment model uses the RPC model of the main image as a benchmark, and introduces image-side affine transformation refinement models for other SAR images and InSAR phase data involved in the adjustment. The refinement models for image coordinates and phase values ​​are both based on the image-side coordinates of the main image. r 0, c 0) Related affine transformation forms: , In the formula, r 0、 c 0、 f 0 represents the original values ​​of the image's row and column coordinates and phase. r , c , f Let be the image-side affine transformation refinement values. a 0、 a 1. a 2 represents the affine transformation parameters for row coordinates. b 0、 b 1. b 2 represents the affine transformation parameters for column coordinates. n 0、 n 1. n 2 represents the phase affine transformation refinement parameter.

[0034] The joint adjustment model uses the RPC model parameters of the main image as a benchmark, and introduces image-side affine transformation refinement models for the image point coordinates and InSAR interferometric phase values ​​of other SAR images. The image coordinate refinement model adopts an affine transformation model related to the image-side coordinates of the main image, where the image point coordinates involved in the InSAR phase refinement model are reduced to the image point coordinate positions of the main image. Based on the refined RPC model, observation equations for image coordinates and phase values ​​are established for the tie points, and after linearization, error equations are obtained with affine transformation parameters and ground point coordinate corrections as unknowns.

[0035] Step S5: Construct the error equation for the affine transformation refined model parameters as virtual observations.

[0036] The affine transformation parameters introduced in step S4 (including the affine transformation parameters for image point coordinates) a 0、 a 1. a 2 and b 0、 b 1. b 2, and the affine transformation parameters of the phase refinement model. n 0、 n 1. n 2) Constraint equations are established using the prior values ​​as virtual observations. Virtual observation constraints effectively prevent the rank deficiency problem in the adjustment model and enhance the stability of parameter solutions.

[0037] When there are few or no ground control points, and the number of control points is less than 3, the external DEM elevation is introduced as a weak constraint equation for the observation value after step S5 and before step S6. That is, the plane coordinates obtained by the image grid points through the initial positioning of InSAR are used to extract the elevation value of the corresponding position from the external DEM as a low-precision observation value. Weights are assigned according to the DEM elevation accuracy to establish an elevation constraint equation, and this constraint equation is added to the normal equation in step S6 to participate in the overall solution.

[0038] Step S6: Combine all the error equations established in steps S4 and S5 to construct the normal equations, perform ground point coordinate elimination, solve for the affine transformation parameters, iterate until convergence, and obtain the three-dimensional coordinates of the densified points.

[0039] The specific steps of step S6 are as follows: Step S61: Combine the image coordinate and phase observation error equations established in step S4 and the virtual observation constraint equations established in step S5 into a set of overall error equations to form the normal equations. Step S62: Taking advantage of the independence between the unknown ground point coordinates, the unknown ground point coordinates are eliminated by elimination method to obtain the reduced equation containing only affine transformation parameters. Step S63: Solve the reduction equation to obtain the affine transformation parameter corrections, and then solve for the corrections of the coordinates of each ground point. Step S64: Iterate the calculation until the parameter correction is less than the preset threshold to obtain the final affine transformation refinement parameters and the three-dimensional coordinates of all encrypted points.

[0040] Preferably, the encrypted points include two types: corresponding connection points extracted between multiple InSAR images through a matching algorithm, and feature points selected within the range of a single InSAR image whose interferometric coherence coefficient is higher than a preset coherence coefficient threshold (e.g., 0.6-0.8); the latter uses refined orientation parameters to calculate its three-dimensional coordinates through single-image InSAR three-dimensional positioning.

[0041] All error equations established in steps S4 and S5 are combined to construct a unified set of normal equations. An elimination method is used to first eliminate a large number of unknown ground point coordinates, resulting in a reduced set of normal equations with affine transformation parameters as unknowns. These equations are then solved to obtain the affine transformation refinement parameters for each image. The solutions to the affine transformation parameters are then substituted back into the equations to calculate the 3D coordinates of each densified point. These densified points include not only the corresponding tie points between multiple InSAR images and their 3D coordinates, but also the 3D coordinates of the refined orientation parameters and selected single InSAR high coherence coefficient feature points, thus obtaining dense 3D positioning results.

[0042] This constraint equation does not require high accuracy of the DEM elevation. It is introduced into the normal equation as a weak constraint to provide necessary external constraint information for the elevation direction under the condition of no control points, so as to avoid the drift of the elevation parameters.

[0043] Example 2 like Figure 2 As shown in this embodiment, a joint adjustment device for SAR stereo and interferometric regional networks based on an RPC model includes: The rigorous positioning modeling module is used to construct rigorous SAR and InSAR positioning models for single-transmit single-receive and single-transmit dual-receive modes based on the range-Doppler equation and the interferometric phase equation. The RPC fitting module is used to fit the RPC parameters of the rational polynomial model RFM of SAR main image coordinates and InSAR phase values ​​based on the rigorous positioning model and with the assistance of an external DEM by constructing virtual grid control points. The interferometry module is used to obtain the unwrapped absolute phase through InSAR interferometry. The image and phase error equation module is used to construct a joint adjustment model and its error equations for SAR image coordinates and InSAR phase based on the RPC model of InSAR image coordinates and interferometric phase, which is based on the master image image-side affine transformation refinement model. The Virtual Observation Error Equation module is used to construct the error equations for virtual observations by refining the affine transformation model parameters. The adjustment and solution module is used to construct normal equations from all jointly established error equations, perform ground point coordinate elimination, solve for affine transformation parameters, iterate until convergence, and obtain the three-dimensional coordinates of the densified points.

[0044] Preferably, the device further includes an external DEM measurement error equation module, used to introduce the external DEM elevation as a weak constraint equation for the observations when control points are lacking. Under conditions of few or no ground control points, when the number of control points is less than three, a weak constraint error equation for the external DEM elevation is introduced.

[0045] Example 2 is used to implement the joint adjustment method of SAR stereo and interferometric regional network based on RPC model as described in Example 1.

[0046] Example 3 The specific implementation process of the joint adjustment of SAR stereo and interferometric regional network based on RPC model in this embodiment is as follows.

[0047] Step S1: Based on RD and phase equations, construct SAR and InSAR rigorous positioning models for single-transmit single-receive and single-transmit dual-receive modes.

[0048] The fundamental geometric relationships of SAR imaging are described by the range-Doppler (RD) equation, while InSAR elevation measurements are achieved through the interferometric phase equation. This step establishes a rigorous functional relationship between the three-dimensional coordinates (X,Y,Z) of ground points and SAR imaging parameters, using the geocentric rectangular coordinate system (ECEF) as a unified spatial reference frame.

[0049] The specific form of the InSAR rigorous localization model is as follows: , Wherein, subscript 1 represents the relevant parameters of the main image; R 1. f d1 and f These are the column and row coordinates of the main image points ( c , r The slant range, Doppler frequency, and interference phase at point R; 10 and G 1c λ represents the initial slant range and slant range resolution of the main image, respectively; λ is the radar wavelength; Q is the transmit / receive mode coefficient, Q=2 in single-transmit single-receive mode and Q=1 in single-transmit dual-receive mode; (Xs1,Ys1,Zs1) and (Xs2,Ys2,Zs2) are the image points of the main image ( c , r ) Obtain the spatial coordinates of the main antenna and auxiliary antenna at the specified time; (X,Y,Z) represents the main image image point ( c , r The coordinates of the ground target point are: |S1-P| and |S2-P| represent the slant distances from the main antenna and the auxiliary antenna to the ground point P, respectively.

[0050] In single-transmit, single-receive mode, the same antenna transmits and receives radar signals at different times, forming an interference pair. Therefore, the radar wave experiences a complete path difference on both the transmission and reception paths, and the phase difference needs to be multiplied by a coefficient Q=2. In single-transmit, dual-receive mode, one antenna transmits a signal, and two antennas (the main antenna and the auxiliary antenna) simultaneously receive the echo signal. The radar wave only experiences a path difference on the reception path, so Q=1.

[0051] Step S2: Based on the rigorous model, with the assistance of an external DEM, fit the RPC parameters of the rational polynomial model RFM of the SAR master image and InSAR phase using virtual grid control points.

[0052] The purpose of this step is to convert the rigorous sensor-related model established in step S1 into a general RFM model expression. The specific process is as follows: S2.1 Data Preparation and Preprocessing: Obtain the InSAR rigorous model parameters (including satellite orbit data, imaging parameters, etc.) constructed in step S1, external DEM data (such as SRTM DEM, ASTER GDEM, etc.), SAR master image data, and InSAR phase data. Perform preprocessing on all data, including coordinate system 1 conversion, format conversion, outlier detection and removal, etc., to ensure consistency in subsequent processing.

[0053] S2.2 Virtual Grid Division: Determining the image space range of the SAR main image (row coordinate range [r]). min , r max ] and column coordinate range [c min , c max ]) and the elevation range of the external DEM within the coverage area [H min H max A three-dimensional virtual grid is formed by uniformly dividing the grid along the row, column, and elevation directions. The grid spacing needs to be selected to ensure that a sufficient number of virtual control points are generated to ensure the accuracy and stability of RPC parameter fitting. Typically, 15-30 layers are divided in each row and column direction, and no less than 5 layers are divided in the elevation direction.

[0054] S2.3 Virtual Control Point Generation: At each node location in the virtual grid, based on its image-side coordinates (c, r) and elevation H, forward calculations are performed using the InSAR rigorous model from step S1 to obtain the geodetic coordinates (B, L, H) and interferometric phase values ​​of the corresponding ground point. f Each virtual control point contains a complete mapping between image coordinates, ground coordinates, and phase values.

[0055] S2.4 RFM Model Definition and RPC Parameter Fitting: The RFM model used in this invention normalizes the geodetic coordinates of ground points ( B n , L n , H n ) and normalized image point coordinates ( r n , c n ) and normalized phase value ( f n To enhance the stability of parameter solving, the ground point coordinates, corresponding image coordinates, and phase values ​​are all normalized to the range [-1, 1].

[0056] The specific form of the RFM model is: , Where P1, P2, P3, P4, P5, and P6 are normalized latitudes.B n ,longitude L n and elevation H n The ternary cubic polynomial is of the form: , In the formula, m = 1, 2, 3, 4, 5, 6; for each m, there are 20... f mijk The coefficients are i,j,k=0,1,2,3 and satisfy the constraint 0≤i+j+k≤3.

[0057] The normalization calculation formula is: , In the formula, o r , o c , o φ They are respectively r , c , f The normalized translation parameters, s r , s c , s φ This is the normalized scaling parameter.

[0058] The model contains a total of 132 RPC coefficients to be determined: 12 normalized coefficients ( o r , o c , o φ , s r , s c , s φ and the corresponding ground coordinate normalization coefficients o B , o L , o H , s B , s L , s H), 80 row and column image coordinate equation coefficients (20 each for P1 and P2, with 39 actually solved after the first term coefficient of P2 is normalized to 1; P3 and P4 are similar, with 39 actually solved), and 40 phase value equation coefficients (20 each for P5 and P6, with 39 actually solved after the first term coefficient of P6 is normalized to 1).

[0059] S2.5 Solving the fitting equations: Substitute the data of all virtual control points into the error equations of the RFM model above, construct the fitting equation system using the least squares method and solve it to obtain all 132 RPC parameters.

[0060] S2.6 Accuracy Verification: A virtual checkpoint is constructed at the center of the virtual grid to verify the accuracy of the fitted RPC parameters. The fitting residuals of the image coordinates and phase values ​​are calculated to ensure that the residuals meet the accuracy requirements (typically, the image coordinate residuals are better than 0.01 pixels, and the phase residuals are better than 0.01 radians). Results that do not meet the accuracy requirements are analyzed and refitted.

[0061] Step S3: InSAR interferometry is used to obtain the unwrapped absolute phase.

[0062] This step performs standard interferometric processing on the InSAR image pairs: (1) Image registration: The auxiliary image is accurately registered to the coordinate system of the main image to ensure the accurate correspondence of pixels with the same name; (2) Interferogram generation: The registered master and slave images are multiplied by conjugate to generate an interferometric phase map; (3) Interferogram filtering: Adaptive filtering is performed on the interferogram phase diagram to reduce phase noise and improve phase quality; (4) Phase unwrapping: The wrapped interference phase is restored to a continuous absolute phase by using a phase unwrapping algorithm (such as the minimum cost flow algorithm, the branch cutting method, etc.); (5) Absolute phase determination: Combine orbital parameters and external elevation data to determine the integer ambiguity of phase unwrapping and obtain the final absolute interference phase data.

[0063] The absolute interferometric phase after unwrapping is an important observation in the subsequent joint adjustment, and its accuracy directly affects the final three-dimensional positioning result.

[0064] Step S4: Based on the RPC model of InSAR imagery and interferometric phase, construct a joint adjustment model and its error equation for SAR imagery and InSAR phase based on the master image image-side affine transformation refinement model.

[0065] This step is the core of the joint adjustment. Using the RPC model of the master image as a benchmark, image-side affine transformation refinement models are introduced into other SAR images and InSAR phase data involved in the adjustment to eliminate systematic residuals in the RPC model parameters.

[0066] The image coordinate and phase value refinement models both employ affine transformation models related to the image-side coordinates of the master image. For the k-th image, the refinement models for its row coordinates, column coordinates, and phase values ​​are as follows: , In the formula, r 0、 c 0、 f 0 represents the original values ​​of the image's row and column coordinates and phase. r , c , f Let be the image-side affine transformation refinement values. a 0、 a 1. a 2 represents the affine transformation parameters for row coordinates. b 0、 b 1. b 2 represents the affine transformation parameters for column coordinates. n 0、 n 1. n 2 represents the phase affine transformation refinement parameter.

[0067] It is worth noting that the image point coordinates involved in the InSAR phase refinement model are reduced to the image point coordinates of the main image, which ensures the consistency between the multi-view InSAR phase observations and the main image coordinate system.

[0068] For each connection point (corresponding point), an observation equation is established based on its observed coordinates and phase values ​​on each image: , In the formula, , and These are respectively derived from ground coordinates ( The theoretical row number, theoretical column number, and theoretical interference phase value obtained by inverse calculation; By linearizing the above observation equations using Taylor expansion at the approximate values, we obtain a set of error equations with the affine transformation parameter corrections and the ground point coordinate corrections as unknowns.

[0069] Step S5: Construct the error equations for the affine transformation parameters as virtual observations. To prevent rank deficiency in the adjustment model and enhance solution stability, the affine transformation parameters are introduced to establish virtual observation constraints.

[0070] Step S6: In cases with few or no control points, introduce low-precision autonomous positioning InSAR external DEM elevation as a weak constraint equation for the observations.

[0071] In situations where field control points are scarce or nonexistent, this invention introduces weak external DEM elevation constraints to prevent free drift of elevation direction parameters. The specific implementation is as follows: (1) Select grid points at certain intervals on the SAR main image; (2) Using the InSAR initial positioning parameters (RPC parameters that have not been adjusted and refined), perform three-dimensional forward intersection on each grid point to obtain its initial planar coordinates (B0, L0); (3) Extract the elevation value H at the corresponding location from the external DEM using bilinear interpolation based on the initial plane coordinates. DEM ; (4) H DEM As a low-precision observation of the elevation direction at this point, an elevation constraint equation is established: , Where H is the elevation coordinate to be determined for this grid point.

[0072] This weakly constrained elevation equation does not require the external DEM to have high accuracy (for example, the nominal accuracy of the SRTM DEM is about 10-16 meters, which is sufficient). Its function is to provide a rough constraint range for the elevation direction, prevent large drift of elevation parameters under the condition of no control points, and avoid introducing unreasonable systematic deviations due to excessive constraints.

[0073] Step S7: Combine all error equations to construct the normal equation, perform ground point coordinate elimination, solve for the affine transformation parameters, and calculate the three-dimensional coordinates of the densification points.

[0074] The image coordinate and phase observation error equations established in step S4, the virtual observation constraint equations established in step S5, and the DEM elevation weak constraint equations established in step S6 (if any) are combined to construct the overall normal equation set.

[0075] Because the number of unknowns in the ground point coordinates is much greater than the number of unknowns in the affine transformation parameters, and the ground points are independent of each other (N in the normal equations) xx (This is a block-diagonal matrix), so the unknown coordinates of the ground points are first eliminated using the elimination method: , Solving the above reduction equations yields the corrections δt for the affine transformation parameters, which are then substituted back to obtain the corrections for the coordinates of each ground point. , The subscript i represents the i-th ground point.

[0076] The calculation is iterated until the parameter correction is less than the preset threshold, and the final affine transformation refinement parameters and the three-dimensional coordinates of all encrypted points are obtained.

[0077] The encryption points in this invention include two types: (1) Corresponding connection points among multiple InSAR images: Corresponding image points extracted by matching algorithm in the overlapping area of ​​multiple InSAR images are combined and adjusted to obtain high-precision three-dimensional coordinates. (2) High coherence coefficient feature points in single InSAR: Select feature points with high interferometric coherence coefficient within the range of a single InSAR image, and use the refined orientation parameters (RPC model + affine transformation refined parameters) to calculate their three-dimensional coordinates through InSAR three-dimensional positioning.

[0078] The introduction of the second type of densification points significantly increased the point density of the final positioning results, enabling high-density three-dimensional positioning results to be obtained throughout the entire survey area.

[0079] In Example 3, the DEM-assisted fitting in step S2 and the DEM weak constraint in step S6 (or when control points are scarce) can use the same external DEM data source, or they can use different DEM data respectively, and both should be considered to fall within the protection scope of this application.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation methods of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model, characterized in that, Includes the following steps: Step S1: Based on the range-Doppler equation and the interferometric phase equation, construct rigorous SAR and InSAR positioning models for single-transmit single-receive and single-transmit dual-receive modes. Step S2: Based on the rigorous positioning model, with the assistance of an external DEM, virtual grid control points are constructed to fit the RPC parameters of the rational polynomial model of SAR main image coordinates and InSAR phase values. Step S3: Obtain the unwrapped absolute phase through InSAR interferometry; Step S4: Based on the RPC model of InSAR image coordinates and interferometric phase, construct a joint adjustment model of SAR image coordinates and InSAR phase based on the master image image-side affine transformation refinement model and its error equation. Step S5: Construct the affine transformation to refine the model parameters as the error equation for the virtual observations; Step S6: Combine all the error equations established in steps S4 and S5 to construct the normal equations, perform ground point coordinate elimination, solve for the affine transformation parameters, iterate until convergence, and obtain the three-dimensional coordinates of the densified points.

2. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to claim 1, characterized in that, The rigorous positioning model uses a geocentric rectangular coordinate system as a reference to establish a functional relationship between ground point coordinates and slant range, Doppler frequency, and interferometric phase parameters, expressed as follows: ， In this context, subscript 1 represents the relevant parameters of the main image. R 1. f d1 and φ R represents the slant distance, Doppler frequency, and interference phase value at the column and row coordinates (c, r) of the main image point, respectively. 10 and G 1c These represent the initial slant range and slant range resolution of the main image, respectively; λ is the radar wavelength; and Q is the transmit / receive mode coefficient, taking values ​​of 2 and 1 for single-transmit / single-receive and single-transmit / dual-receive respectively. , , )and( , , (x, y, z) represent the spatial locations of the interferometric points when the primary and secondary image sensors acquire data, respectively, and (x, y, z) represent the ground coordinates corresponding to the primary image point (c, r). , and The velocity component is the primary image sensor.

3. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to claim 1, characterized in that, The RPC parameters of the rational polynomial model for fitting the SAR main image coordinates and InSAR phase values ​​include the following steps: Step S21: Obtain basic data, including the InSAR rigorous positioning model constructed in step S1, external DEM data, SAR master image and InSAR interferometric phase data, and complete coordinate system unification and format preprocessing of all data. Step S22: Based on the InSAR rigorous positioning model and combined with the elevation information provided by the external DEM, a virtual grid is uniformly divided in the image space of the SAR main image and the elevation space of the image coverage area. Step S23: Based on the divided virtual grid, a rigorous positioning model is used to generate virtual control points at each grid point. A sufficient number of virtual control points are generated in the whole scene image. Each virtual control point contains unique image coordinates, elevation value, and ground point coordinates and phase value calculated by the rigorous model. That is, each control point is composed of image coordinates, phase value and ground point coordinates. Step S24: Determine the target model for RPC parameter fitting and solve for a total of 132 RPC coefficients, including: 12 normalized coefficients, 80 image coordinate equation coefficients, and 40 phase value equation coefficients; wherein, the denominator constant term of each rational polynomial is normalized to 1, the 12 normalized coefficients are obtained by statistical calculation of virtual control points, and the remaining parameters are obtained by solving the error equation constructed by virtual control points; Step S25: Substitute the ground point coordinates of all virtual control points and their corresponding image point coordinates and phase values ​​into the rational polynomial model to construct a set of fitting equations and solve for all coefficients in a unified manner. Step S26: Solve the fitted equation system to obtain 12 normalized coefficients, 40 row image coordinate equation coefficients, 40 column image coordinate equation coefficients and 40 phase value equation coefficients, for a total of 132 RPC parameters, where the denominator constant term of each rational polynomial is normalized to 1; Step S27: Using virtual control points and checkpoints, the accuracy of the 132 extracted InSAR RPC parameters is verified, and abnormal fitting results are removed to ensure that the parameters meet the requirements of the RFM model.

4. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to claim 3, characterized in that, The rational polynomial model normalizes geodetic coordinates ( B n , L n , H n ) and normalized image point coordinates ( r n , c n ) and normalized phase value ( φ n The relationship is expressed in the form of a ratio polynomial, and the model form is as follows: ， Where P1, P2, P3, P4, P5, and P6 are normalized latitudes B. n Longitude L n and elevation H n The ternary cubic polynomials, each containing 20 coefficients, and the constant term of the denominator polynomial normalized to 1, together constitute 132 RPC parameters to be determined.

5. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to claim 1, characterized in that, The joint adjustment model constructed in step S4 uses the RPC model of the main image as a reference, and introduces image-side affine transformation refinement models for other SAR images and InSAR phase data participating in the adjustment. The refinement models for image coordinates and phase values ​​are both based on the image-side coordinates of the main image. r 0, c 0) Related affine transformation forms: ， In the formula, r 0、 c 0、 φ 0 represents the original values ​​of the image's row and column coordinates and phase. r , c , φ These are the refined values ​​of their image-side affine transformation; a 0、 a 1. a 2 represents the affine transformation parameters for row coordinates. b 0、 b 1. b 2 represents the affine transformation parameters for column coordinates. n 0、 n 1. n 2 represents the phase affine transformation refinement parameter.

6. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to claim 1, characterized in that, The specific steps of step S6 are as follows: Step S61: Combine the image coordinate and phase observation error equations established in step S4 and the virtual observation constraint equations established in step S5 into a set of overall error equations to form the normal equations. Step S62: Taking advantage of the independence between the unknown ground point coordinates, the unknown ground point coordinates are eliminated by elimination method to obtain the reduced equation containing only affine transformation parameters. Step S63: Solve the reduction equation to obtain the affine transformation parameter corrections, and then solve for the corrections of the coordinates of each ground point. Step S64: Iterate the calculation until the parameter correction is less than the preset threshold to obtain the final affine transformation refinement parameters and the three-dimensional coordinates of all encrypted points.

7. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to any one of claims 1 to 6, characterized in that, When there are few or no ground control points, and the number of control points is less than 3, an external DEM elevation weak constraint error equation is introduced after step S5 and before step S6. That is, the plane coordinates obtained by the image grid points through InSAR initial positioning are used to extract the elevation values ​​of the corresponding positions from the external DEM as low-precision observation values. Weights are assigned according to the DEM elevation accuracy to establish an elevation constraint equation, and this constraint equation is added to the normal equation in step S6 to participate in the overall solution.

8. The joint adjustment method for SAR stereo and interferometric regional networks based on the RPC model according to any one of claims 1 to 6, characterized in that, The encrypted points include two types: corresponding connection points extracted between multiple InSAR images through a matching algorithm, and feature points selected within the range of a single InSAR image whose interferometric coherence coefficient is higher than a preset coherence coefficient threshold; the latter uses refined orientation parameters to calculate its three-dimensional coordinates through single-image InSAR three-dimensional positioning.

9. A joint adjustment device for SAR stereo and interferometric regional networks based on the RPC model, characterized in that, include: The rigorous positioning modeling module is used to construct rigorous SAR and InSAR positioning models for single-transmit single-receive and single-transmit dual-receive modes based on the range-Doppler equation and the interferometric phase equation. The RPC fitting module is used to fit the RPC parameters of a rational polynomial model of SAR main image coordinates and InSAR phase values ​​based on the rigorous positioning model and with the assistance of an external DEM by constructing virtual grid control points. The interferometry module is used to obtain the unwrapped absolute phase through InSAR interferometry. The image and phase error equation module is used to construct a joint adjustment model and its error equations for SAR image coordinates and InSAR phase based on the RPC model of InSAR image coordinates and interferometric phase, which is based on the master image image-side affine transformation refinement model. The Virtual Observation Error Equation module is used to construct the error equations for virtual observations by refining the affine transformation model parameters. The adjustment and solution module is used to construct normal equations from all jointly established error equations, perform ground point coordinate elimination, solve for affine transformation parameters, iterate until convergence, and obtain the three-dimensional coordinates of the densified points.

10. The SAR stereo and interferometric regional network joint adjustment device based on the RPC model according to claim 9, characterized in that, Also includes: The External DEM Measurement Error Equation module is used to introduce external DEM elevations as weak constraint equations for observations when control points are lacking.

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