Rational Polynomial Coefficients Model Research Articles

Improvement and Assessment of Gaofen-3 Spotlight Mode 3-D Localization Accuracy

The spotlight image acquired by the Gaofen-3 satellite has a resolution of 1 m, which has great potential for 3-D localization. However, there have been no public reports on the 3-D localization accuracy evaluation of Gaofen-3 spotlight synthetic aperture radar (SAR) images. Here, three study areas were selected from this perspective, and the SAR spotlight stereo images of the study area were acquired using Gaofen-3. In the case of no ground control points (GCPs), based on the Rational Polynomial Coefficient (RPC) model, these images were used for initial 3-D localization; the plane accuracy was better than 10 m in general, and the elevation accuracy was worse than 37 m in general. Subsequently, the RPC model was optimized using geometric calibration technology, and the 3-D localization accuracy was assessed again. The elevation accuracy was significantly improved, which was generally better than 5 m. The plan accuracy was also improved, and it was generally better than 6 m. It can be seen that Gaofen-3 spotlight stereo images are of good quality, and high plane accuracy can be obtained even without GCPs. Geometric calibration technology improves the 3-D localization accuracy, and the elevation accuracy optimization effect is remarkable. Moreover, the optimization effect of plane accuracy is affected by the properties of stereo-image pairs. The optimization effect of plane accuracy is obvious for asymmetric stereo-image pairs, and the optimization effect of plane accuracy is general for symmetric stereo-image pairs.

Radiometric Terrain Correction Method Based on RPC Model for Polarimetric SAR Data

Radiometric terrain correction (RTC) is an important preprocessing step for synthetic aperture radar (SAR) data application in mountainous areas. At present, the RTC processing of SAR depends on the Range Doppler (RD) positioning model. However, the solution of this model has a high threshold for ordinary remote sensing technicians. To solve this problem, we propose an RTC method based on the rational polynomial coefficient (RPC) model, which is widely used in optical remote sensing and is simpler and more practical than the RD model. China’s GF-3 polarimetric SAR data were used to verify the proposed method. The experimental results showed that the RTC method based on RPC is effective and can achieve better correction effects on the premise of reducing the complexity of the algorithm. The correction effect based on the RPC model can be similar to that based on the RD model. The proposed approach can realize the correction of 4~5 dB terrain radiation distortion to a 0.5 dB level.

Pursuing 3-D Scene Structures With Optical Satellite Images From Affine Reconstruction to Euclidean Reconstruction

How to use multiple optical satellite images to recover the 3D scene structure is a challenging and important problem in the remote sensing field. Most existing methods in literature have been explored based on the classical RPC (Rational Polynomial Coefficients) camera model which requires at least 39 GCPs (ground control points), however, it is non-trivial to obtain such a large number of GCPs in many real scenes. Addressing this problem, we propose a hierarchical reconstruction framework based on multiple optical satellite images, which needs only 4 GCPs to fully-automated reconstruct the 3D scene structure. The proposed framework is independent from the RPC model and composed of a dense affine reconstruction stage and a followed affine-to-Euclidean upgrading stage: At the dense affine reconstruction stage, a dense affine reconstruction approach is explored for pursuing the 3D affine scene structure without any GCP from input satellite images. Then at the affine-to-Euclidean upgrading stage, the obtained 3D affine structure is upgraded to a Euclidean one with 4 GCPs. Experimental results on two public datasets demonstrate that the proposed method significantly outperforms several state-of-the-art methods in most cases.

Research on Making Orthophotos of Mountainous Areas Based on WorldView-2 Images

Combining the RPC rational polynomial coefficient model, using WorldView-2 remote sensing images, combined with field surveyed control points, survey area digital elevation model DEM and other data to produce the mountain orthophoto map, combined with the detection points to analyze the accuracy of the results, solve the problem Topographic maps are difficult to measure and are subject to flight restrictions.

Feasibility of Replacing the Range Doppler Equation of Spaceborne Synthetic Aperture Radar Considering Atmospheric Propagation Delay with a Rational Polynomial Coefficient Model.

Usually, the rational polynomial coefficient (RPC) model of spaceborne synthetic aperture radar (SAR) is fitted by the original range Doppler (RD) model. However, the radar signal is affected by two-way atmospheric delay, which causes measurement error in the slant range term of the RD model. In this paper, two atmospheric delay correction methods are proposed for use in terrain-independent RPC fitting: single-scene SAR imaging with a unique atmospheric delay correction parameter (plan 1) and single-scene SAR imaging with spatially varying atmospheric delay correction parameters (plan 2). The feasibility of the two methods was verified by conducting fitting experiments and geometric positioning accuracy verification of the RPC model. The experiments for the GF-3 satellite were performed by using global meteorological data, a global digital elevation model, and ground control data from several regions in China. The experimental results show that it is feasible to use plan 1 or plan 2 to correct the atmospheric delay error, no matter whether in plain, mountainous, or plateau areas. Moreover, the geometric positioning accuracy of the RPC model after correcting the atmospheric delay was improved to better than 3 m. This is of great significance for the efficient and high-precision geometric processing of spaceborne SAR images.

SOLVING THE RATIONAL POLYNOMIAL COEFFICIENTS BASED ON L CURVE

Abstract. The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.

Assessment of geometric correction of remote sensing satellite images using RPC versus GCP

Geometric distortions are common problems when dealing with remote sensing satellite images. Therefore, geometric correction is a necessary process for preparing remote sensing satellite images for many applications. Physical sensor model is formed by integrating the geometry of imaging sensor and positioning sensors as GPS and star trackers with system calibration parameters. Physical sensor model is not available in common but a Rational Polynomial Coefficient (RPC) model is provided as an alternative representation of sensor model. The RPC model is used for geometric correction of satellite image to get the spatial data of image features. The accuracy of the resultant image depends on the accuracy of RPC model which is not known as common. The research objective is to assess the accuracy of geometric correction of the satellite image using RPC model versus geometric correction using Ground Control Points (GCPs), along with their effect on the final accuracy of the output spatial features. The available data is IKONOS-2 image with its RPC file and seven GCPs with high accuracy obtained from ground survey for the study area. The input image is corrected using two available data separately. First degree of polynomial is used for transformation process for the case of GCPs. Bilinear interpolation technique is used to determine the pixel value of the newly resultant corrected images for the two cases. GCPs is preferred when available because the resultant image with RPC geometric correction has 15.0 meters average linear error while 3.0 meters error in case of GCPs geometric correction.

Geometric Accuracy Analysis for GaoFen3 Stereo Pair Orientation

Due to the all-weather and all-day advantage and the high geometric accuracy, the spaceborne synthetic aperture radar (SAR) stereo pair has a wide application in digital elevation model (DEM) production and ground control points (GCPs) extraction around the world. The GaoFen3 (GF3) remote sensing satellite is the first C-band multipolarization SAR satellite with a resolution of 1 m in China and plays an important role in commercial exploitation and scientific research. This letter performs a comprehensive analysis of the geometric accuracy for GF3 stereo pair orientation. By analyzing the orientation error sources, it is proven that the affine transformation model in image space can effectively compensate the unmodeled errors in GF3 imagery. Based on the rational polynomial coefficient model, the integrated orientation model for the GF3 stereo pair is presented here. Moreover, the model parameters and weight determination are further studied to analyze the influence of weight matrixes on geometric accuracy. Experimental results demonstrate that the proposed integrated orientation model can be effectively used for the GF3 stereo pair. The GCPs, convergent angle, and weight setting are the key factors influencing the geometric accuracy.

Mathematical Modeling and Accuracy Testing of WorldView-2 Level-1B Stereo Pairs without Ground Control Points

With very high resolution satellite (VHRS) imagery of 0.5 m, WorldView-2 (WV02) satellite images have been widely used in the field of surveying and mapping. However, for the specific WV02 satellite image geometric orientation model, there is a lack of detailed research and explanation. This paper elaborates the construction process of the WV02 satellite rigorous sensor model (RSM), which considers the velocity aberration, the optical path delay and the atmospheric refraction. We create a new physical inverse model based on a double-iterative method. Through this inverse method, we establish the virtual control grid in the object space to calculate the rational function model (RFM) coefficients. In the RFM coefficient calculation process, we apply the correcting characteristic value method (CCVM) and least squares (LS) method to compare the two experiments’ accuracies. We apply two stereo pairs of WV02 Level 1B products in Qinghai, China to verify the algorithm and test image positioning accuracy. Under the no-control conditions, the monolithic horizontal mean square error (RMSE) of the rational polynomial coefficient (RPC) is 3.8 m. This result is 13.7% higher than the original RPC positioning accuracy provided by commercial vendors. The stereo pair horizontal positioning accuracy of both the physical and RPC models is 5.0 m circular error 90% (CE90). This result is in accordance with the WV02 satellite images nominal positioning accuracy. This paper provides a new method to improve the positioning accuracy of the WV02 satellite image RPC model without GCPs.

DEM generation based on RPC model using relative conforming estimate criterion

A critical step in the Digital Elevation Model (DEM) generation is image georeferencing establishing sensor orientation, which is performed using ground control points. Geometric sensor models are used in image processing to model the relationship between object space and image space and to transform image data to conform to a map projection. There are two popular sensor models: the rigorous model and Rational Polynomial Coefficients (RPC) model. Using the RPC model has an advantage because users are not required to know specific information on the satellite sensors. A small number of inaccurate or unreliable source values of the Ground Control Point (GCP) coordinates can cause errors in computing the RPC model by traditional methods. Georeferencing requires accurate 3D ground coordinates, and our method can satisfy this requirement. We propose a new method of computing the RPC model using relative conforming estimate criterion.

Automatic estimation of bias parameters of RPC model and ground coordinates from multi-directional satellite images

Advanced Land Observing Satellite (ALOS)/Panchromatic Remote-sensing Instrument for Stereo Mapping (PRISM) measured triplet images at forward, nadir and backward view directions, and the digital surface model (DSM) is generated from set of triplet images. Existing methods generate multiple DSMs from individual triplet images, and eliminate the effects of outliers by taking average. The proposed method in this paper solves multiple observation equations from all triplet images, and simultaneously determines bias parameters contaminated in the rational polynomial coefficient (RPC) model and ground coordinates. The experimental results showed that errors of the coordinates estimated by using multi-temporal triplet images were almost as small as those estimated with manually determined bias parameters in case of 4 or more sets of triplet images. As a result, we conclude that the proposed method is effective for stably generating accurate DSMs from multi-temporal triplet images.

Comparison and Analysis of Geometric Correction Models of Spaceborne SAR.

Following the development of synthetic aperture radar (SAR), SAR images have become increasingly common. Many researchers have conducted large studies on geolocation models, but little work has been conducted on the available models for the geometric correction of SAR images of different terrain. To address the terrain issue, four different models were compared and are described in this paper: a rigorous range-doppler (RD) model, a rational polynomial coefficients (RPC) model, a revised polynomial (PM) model and an elevation derivation (EDM) model. The results of comparisons of the geolocation capabilities of the models show that a proper model for a SAR image of a specific terrain can be determined. A solution table was obtained to recommend a suitable model for users. Three TerraSAR-X images, two ALOS-PALSAR images and one Envisat-ASAR image were used for the experiment, including flat terrain and mountain terrain SAR images as well as two large area images. Geolocation accuracies of the models for different terrain SAR images were computed and analyzed. The comparisons of the models show that the RD model was accurate but was the least efficient; therefore, it is not the ideal model for real-time implementations. The RPC model is sufficiently accurate and efficient for the geometric correction of SAR images of flat terrain, whose precision is below 0.001 pixels. The EDM model is suitable for the geolocation of SAR images of mountainous terrain, and its precision can reach 0.007 pixels. Although the PM model does not produce results as precise as the other models, its efficiency is excellent and its potential should not be underestimated. With respect to the geometric correction of SAR images over large areas, the EDM model has higher accuracy under one pixel, whereas the RPC model consumes one third of the time of the EDM model.

Airborne LIDAR and high resolution satellite data for rapid 3D feature extraction

Abstract. This work uses the canopy height model (CHM) based workflow for individual tree crown delineation and 3D feature extraction approach (Overwatch Geospatial's proprietary algorithm) for building feature delineation from high-density light detection and ranging (LiDAR) point cloud data in an urban environment and evaluates its accuracy by using very high-resolution panchromatic (PAN) (spatial) and 8-band (multispectral) WorldView-2 (WV-2) imagery. LiDAR point cloud data over San Francisco, California, USA, recorded in June 2010, was used to detect tree and building features by classifying point elevation values. The workflow employed includes resampling of LiDAR point cloud to generate a raster surface or digital terrain model (DTM), generation of a hill-shade image and an intensity image, extraction of digital surface model, generation of bare earth digital elevation model (DEM) and extraction of tree and building features. First, the optical WV-2 data and the LiDAR intensity image were co-registered using ground control points (GCPs). The WV-2 rational polynomial coefficients model (RPC) was executed in ERDAS Leica Photogrammetry Suite (LPS) using supplementary *.RPB file. In the second stage, ortho-rectification was carried out using ERDAS LPS by incorporating well-distributed GCPs. The root mean square error (RMSE) for the WV-2 was estimated to be 0.25 m by using more than 10 well-distributed GCPs. In the second stage, we generated the bare earth DEM from LiDAR point cloud data. In most of the cases, bare earth DEM does not represent true ground elevation. Hence, the model was edited to get the most accurate DEM/ DTM possible and normalized the LiDAR point cloud data based on DTM in order to reduce the effect of undulating terrain. We normalized the vegetation point cloud values by subtracting the ground points (DEM) from the LiDAR point cloud. A normalized digital surface model (nDSM) or CHM was calculated from the LiDAR data by subtracting the DEM from the DSM. The CHM or the normalized DSM represents the absolute height of all aboveground urban features relative to the ground. After normalization, the elevation value of a point indicates the height from the ground to the point. The above-ground points were used for tree feature and building footprint extraction. In individual tree extraction, first and last return point clouds were used along with the bare earth and building footprint models discussed above. In this study, scene dependent extraction criteria were employed to improve the 3D feature extraction process. LiDAR-based refining/ filtering techniques used for bare earth layer extraction were crucial for improving the subsequent 3D features (tree and building) feature extraction. The PAN-sharpened WV-2 image (with 0.5 m spatial resolution) was used to assess the accuracy of LiDAR-based 3D feature extraction. Our analysis provided an accuracy of 98 % for tree feature extraction and 96 % for building feature extraction from LiDAR data. This study could extract total of 15143 tree features using CHM method, out of which total of 14841 were visually interpreted on PAN-sharpened WV-2 image data. The extracted tree features included both shadowed (total 13830) and non-shadowed (total 1011). We note that CHM method could overestimate total of 302 tree features, which were not observed on the WV-2 image. One of the potential sources for tree feature overestimation was observed in case of those tree features which were adjacent to buildings. In case of building feature extraction, the algorithm could extract total of 6117 building features which were interpreted on WV-2 image, even capturing buildings under the trees (total 605) and buildings under shadow (total 112). Overestimation of tree and building features was observed to be limiting factor in 3D feature extraction process. This is due to the incorrect filtering of point cloud in these areas. One of the potential sources of overestimation was the man-made structures, including skyscrapers and bridges, which were confounded and extracted as buildings. This can be attributed to low point density at building edges and on flat roofs or occlusions due to which LiDAR cannot give as much precise planimetric accuracy as photogrammetric techniques (in segmentation) and lack of optimum use of textural information as well as contextual information (especially at walls which are away from roof) in automatic extraction algorithm. In addition, there were no separate classes for bridges or the features lying inside the water and multiple water height levels were also not considered. Based on these inferences, we conclude that the LiDAR-based 3D feature extraction supplemented by high resolution satellite data is a potential application which can be used for understanding and characterization of urban setup.

Improved Non-Parametric Geometric Corrections For Satellite Imagery Through Covariance Constraints

Satellite imagery enables rapid data collection and assessment for several earth and environmental sciences. However, the obtained raw imagery cannot be used directly for spatial data collection and assessment and should be further processed for geometric distortions. The usefulness and reliability of the data obtained from satellite images heavily relies on the geometric correction process and it can be applied through either parametric or non-parametric methods. Parametric methods require physical sensor model parameters which are generally available only to the vendor. The Rational Polynomial Coefficients (RPCs) supplied by several vendors provide global geometric correction, however they are usually available for specific high resolution imagery systems. Other polynomials methods provide geometric corrections locally but applicable for nearly all satellite imagery systems. Depending on the degree of the employed polynomial, the topography, the distribution and the quality of the control points, local geometric corrections could provide lower misfits at GCPs (Ground Control Points) while they might produce very large misfits at ICP (Independent Check Points). In particular, when the available number of GCPs is limited and they are poorly distributed over the image area. In this study, 2D and 3D Affine functions with covariance constraints are introduced to improve the geometric correction when the available GCP are of limited accuracy and poorly distributed. The efficiency of the proposed method was numerically shown in two applications. The results show that the proposed method provides a compromise between the local and global misfits without using any ICP coordinates and enables robust and efficient geometric correction of satellite imagery which lacks a precise RPC model such as TUBITAK RASAT satellite.

Positioning Accuracy Analysis and Application for Worldview-1 Stereo Imagery

Abstract. This article introduced the progress of processing the WorldView-1 satellite image by using the air triangulation method．And different adjustment models were used to improve the vendor provided RPC (Rational Polynomial Coefficients) accuracy. WorldVfew-1 images in Beijing are used to test the correction accuracy of these adjustment models．Results show that the systematic errors of RPC model can be eliminated using a small amount of control points. The planar RMSE can reach 1.6 pixels (0.9 meter)．

Geometric model for high-resolution SAR-GEC images

SAR Geocoded Ellipsoid Corrected (GEC) imagery is often taken as a post product processed from slant or ground range radar images. However, its geometric specific, being corrected to a constant ellipsoid height, makes it a coarse geocoded reference for users who are interested in accurate absolute localisation in applications, such as ‘ortho-image’ generation and digital elevation model (DEM) production. In order to improve the usefulness of SAR GEC imagery, the specific geometric distortions induced by the terrain require corresponding geometric models to perform geometric corrections to the imagery. In this article, both the rigorous physical model and the Rational Polynomial Coefficient (RPC) model for SAR GEC imagery are studied. First, the specific geometry of GEC imagery is illustrated. Then the procedure of reconstructing the rigorous physical model of GECs, which actually is mathematically combined with the normal range–Doppler model, is described in detail. The RPC estimator for replacing this rigorous physical model is then derived. Finally, based on numerous tests with the rigorous physical model available, the modelling error of the RPC is analysed. Four different kinds of high resolution SAR GEC images, i.e. TerraSAR-X, COSMO-SkyMed, RADARSAT-2 and ALOS-PALSAR, are used as experimental data. The experimental results show that using the third-order RPC model with unequal denominators as a substitute for the GEC imaging rigorous physical model, delivers accuracies for different high-resolution SAR GEC images that are all better than 0.01 pixels. The RPC model can be a robust and efficient substitute for the GEC imaging rigorous physical model to perform geometrical processing.

RADARGRAMMETRIC DIGITAL SURFACE MODELS GENERATION FROM TERRASAR-X IMAGERY: CASE STUDIES, PROBLEMS AND POTENTIALITIES

Abstract. The interest for the radargrammetric approach to Digital Surface Models (DSMs) generation has been growing in last years thanks to the availability of very high resolution imagery acquired by new SAR (Synthetic Aperture Radar) sensors, as COSMO-SkyMed, Radarsat-2 and TerraSAR-X, which are able to supply imagery up to 1 m ground resolution. DSMs radargrammetric generation approach consists of two basic steps, as for the standard photogrammetry applied to optical imagery: the imagery (at least a stereo pair) orientation and the image matching for the generation of the points cloud. The steps of the radargrammetric DSMs generation have been implemented into SISAR (Software per Immagini Satellitari ad Alta Risoluzione), a scientific software developed at Geodesy and Geomatics Institute of the University of Rome “La Sapienza”. Moreover, starting from the radargrammetric orientation model, a tool for the Rational Polynomial Coefficients (RPCs) for SAR images have been implemented. The possibility to generate RPCs, re-parametrizing a rigorous orientation model through a standardized set of coefficients which can be managed by a Rational Polynomial Coefficients (RPFs) model (similarly to optical high resolution imagery) sounds of particular interest since, at present, the most part of SAR imagery (except from Radarsat-2) is not supplied with RPCs, although the corresponding RPFs model is available in several commercial software. In particular the RPCs model has been used in the matching process and in the stereo restitution for the DSMs generation, with the advantage of shorter computational time. This paper discusses the application and the results of the implemented algorithm for radargrammetric DSMs generation from TerraSAR-X SpotLight imagery, acquired in Spotlight mode over Trento (Northern Italy). Urban and extra-urban (forested, cultivated) areas were considered in two different tiles, and a final overall accuracy ranging from 4.5 to 6 meters was achieved as regards the point clouds, enough well distributed independently from the land cover; moreover, it was highlighted the benefit to filter the originally derived points cloud with a global DSM as SRTM DEM, what leads to an accuracy improvement of about 20% paying a loss of matched points of about 10 %.

Accuracy Assessment of Digital Surface Models Based on WorldView-2 and ADS80 Stereo Remote Sensing Data

Digital surface models (DSMs) are widely used in forest science to model the forest canopy. Stereo pairs of very high resolution satellite and digital aerial images are relatively new and their absolute accuracy for DSM generation is largely unknown. For an assessment of these input data two DSMs based on a WorldView-2 stereo pair and a ADS80 DSM were generated with photogrammetric instruments. Rational polynomial coefficients (RPCs) are defining the orientation of the WorldView-2 satellite images, which can be enhanced with ground control points (GCPs). Thus two WorldView-2 DSMs were distinguished: a WorldView-2 RPCs-only DSM and a WorldView-2 GCP-enhanced RPCs DSM. The accuracy of the three DSMs was estimated with GPS measurements, manual stereo-measurements, and airborne laser scanning data (ALS). With GCP-enhanced RPCs the WorldView-2 image orientation could be optimised to a root mean square error (RMSE) of 0.56 m in planimetry and 0.32 m in height. This improvement in orientation allowed for a vertical median error of −0.24 m for the WorldView-2 GCP-enhanced RPCs DSM in flat terrain. Overall, the DSM based on ADS80 images showed the highest accuracy of the three models with a median error of 0.08 m over bare ground. As the accuracy of a DSM varies with land cover three classes were distinguished: herb and grass, forests, and artificial areas. The study suggested the ADS80 DSM to best model actual surface height in all three land cover classes, with median errors <1.1 m. The WorldView-2 GCP-enhanced RPCs model achieved good accuracy, too, with median errors of −0.43 m for the herb and grass vegetation and −0.26 m for artificial areas. Forested areas emerged as the most difficult land cover type for height modelling; still, with median errors of −1.85 m for the WorldView-2 GCP-enhanced RPCs model and −1.12 m for the ADS80 model, the input data sets evaluated here are quite promising for forest canopy modelling.

Application of the RPC model for spaceborne SAR image geometric processing

An increasing number of low, medium, and high resolution SAR satellites creates a demand for a generalized sensor model to replace the rigorous sensor model (RSM). The rational polynomial coefficient (RPC) model is a generic sensor model which accurately fits the object-image geometry for various sensor systems with different coefficient values. It has been widely used as an alternative to RSM for photogrammetric processing of optical images, but its applications to SAR images are rarely discussed in publications. In this paper, the feasibility and practicability of the RPC model for SAR images are studied. The RPC model can not only be used to replace the RSM (range–Doppler model for SAR), but also applied to the processing chain for SAR data, thus facilitating the processing of SAR and InSAR data for end users.

Application of RPC Model in Orthorectification of Spaceborne SAR Imagery

AbstractIt has been widely accepted that the rational polynomial coefficient (RPC) model can be used as an alternative to rigorous sensor models of high resolution optical satellites for photogrammetric processing. In the application of the RPC model to synthetic aperture radar (SAR) image processing, it has been confirmed that the range‐Doppler model can be replaced by the RPC model. Until now, however, orthorectification with the RPC model in SAR image processing has not been considered. This paper investigates how to perform orthorectification in SAR image processing with the RPC model. Following a brief introduction about the RPC model for spaceborne SAR imagery, an optimisation model is established and a method of conducting simulations with the RPC model is proposed. Finally, a series of experiments are performed in order to verify the correctness of the theory using TerraSAR‐X, COSMO‐SkyMed, ERS‐2 and Envisat ASAR images as test data. By comparing the actual accuracy and the theoretical accuracy of the orthorectified imagery, the theory and methodology proposed in this paper are confirmed.