Bias-corrected rational polynomial coefficients for high accuracy geo-positioning of QuickBird stereo imagery

The rational function model (RFM) is widely used as an alternative to physical sensor models for 3D ground point determination with high-resolution satellite imagery (HRSI). However, owing to the sensor orientation bias inherent in the vendor-provided rational polynomial coefficients (RPCs), the geo-positioning accuracy obtained from these RPCs is limited. In this paper, the performances of two schemes for orientation bias correction (i.e., RPCs modification and RPCs regeneration) is presented based on one separate-orbit QuickBird stereo image pair in Shanghai, and four cases for bias correction, including shift bias correction, shift and drift bias correction, affine model bias correction and second-order polynomial bias correction, are examined. A 2-step least squares adjustment method is adopted for correction parameter estimation with a comparison with the RPC bundle adjustment method. The experiment results demonstrate that in general the accuracy of the 2-step least squares adjustment method is almost identical to that of the RPC bundle adjustment method. With the shift bias correction method and minimal 1 ground control point (GCP), the modified RPCs improve the accuracy from the original 23 m to 3 m in planimetry and 17 m to 4 m in height. With the shift and drift bias correction method, the regenerated RPCs achieve a further improved positioning accuracy of 0.6 m in planimetry and 1 m in height with minimal 2 well-distributed GCPs. The affine model bias correction yields a geo-positioning accuracy of better than 0.5 m in planimetry and 1 m in height with 3 well-positioned GCPs. Further tests with the second-order polynomial bias correction model indicate the existence of potential high-order error signals in the vendor-provided RPCs, and on condition that an adequate redundancy in GCP number is available, an accuracy of 0.4 m in planimetry and 0.8 m in height is attainable.     

Evaluation of the RPC Model for Ziyuan-3 Three-line Array Imagery

Ziyuan-3 (ZY-3) satellite is the first civilian stereo mapping satellite in China and was designed to achieve the 1: 50,000 scale mapping for land and ocean. Rigorous sensor model (RSM) is required to build the relationship between the three-dimensional (3D) object space and two-dimensional (2D) image space of ZY-3 satellite imagery. However, each satellite sensor has its own imaging system with different physical sensor models, which increase the difficulty of geometric integration of multi-source images with different sensor models. Therefore, it is critical to generate generic model, especially rational polynomial coefficients (RPCs) of optical imagery. Recently, relatively a few researches have been conducted on RPCs generation to ZY-3 satellite. This paper proposes an approach to evaluate the performance of RPCs generation from RSM of ZY-3 imagery. Three scenario experiments with different terrain features (such as ocean, hill, city and grassland) are designed and conducted to comprehensively evaluate the replacement accuracies of this approach and analyze the RPCs fitting error. All the experimental results demonstrate that the proposed method achieved the encouraging accuracy of better than 1.946E?04 pixel in both x-axis direction and y-axis direction, and it indicates that the RPCs are suitable for ZY-3 imagery and can be used as a replacement for the RSM of ZY-3 imagery.     

利用虚拟格网系统误差补偿进行RPC参数精化

提出了一种RPC参数精化方法,即通过消除虚拟控制格网点上的系统误差来实现RPC参数的精化。试验结果表明,对于QuickBird影像,使用本文提出的方法精化RPC参数以后,其像点的平面精度达到了±2.4 pixels;对于SPOT-5立体像对而言,基于精化RPC参数的影像目标立体定位的平面精度和高程精度分别为±5.892 m和±4.020 m。     

一种基于复共线性分析的RPC参数优选法

推导了求解有理多项式系数(RPC)的严密误差方程,从分析误差方程设计矩阵列向量间的复共线性着手,提出了一种去相关的RPC参数优选方法。对一景SPOT-5 HRG 1A级影像进行实验,结果表明,当地面控制点稀疏时,通过优选20~30个RPC参数,可以很好地消除参数间的相关性,有效消除有理函数模型(RFM)在地形拟合中出现的振荡现象,可明显提高RPC参数求解和RFM的影像几何处理精度。当地面控制点足够多时,利用此方法优选的RPC参数进行地形拟合的结果与用常规最小二乘法求解的78个RPC参数实施地形拟合的结果完全一致。     

附加视线向量修正的卫星影像区域网平差

针对传统有理函数模型(RFM)区域网平差方法局限于姿态和轨道测量误差小、相机视场角小及影像交会角良好的情况,提出了附加视线向量修正的卫星影像区域网平差方法。首先利用影像附带的有理多项式系数(RPC)计算出像元视线向量,其次根据该视线向量恢复成像时刻虚拟位置和姿态信息,然后对恢复的虚拟位置和姿态构建误差补偿模型,最后通过最小二乘方法整体解算模型参数和连接点物方坐标。该方法从系统误差产生的原因构建补偿模型,可以规避传统区域网平差方法的近似假设和条件限制。通过对模拟数据以及多套测绘卫星和非测绘卫星数据进行试验的结果表明,该方法处理大姿态角误差、大视场角以及弱交会角等各种严苛条件下的卫星影像能达到比传统方法更好的效果。     

轨道约束的资源三号标准景影像区域网平差

考虑到同轨道拍摄的长条带卫星影像具有相同的误差分布特性,针对资源三号的标准景影像产品,提出了基于轨道约束的卫星影像区域网平差方法。首先,根据同轨相邻影像的偏移量计算轨道影像坐标系下的像点坐标;其次,通过同轨每景影像的RFM重新生成轨道影像的RFM,同时生成补偿格网;然后,根据基于像方仿射变换的RFM对轨道影像进行区域网平差;最后,利用求得的轨道影像的仿射变换参数重新计算原始单景影像的仿射变换参数。利用不同地区资源三号测绘卫星影像数据的试验表明,基于轨道约束的卫星影像区域网平差（以下简称轨道平差）在稀疏控制条件下,其精度明显好于单景影像平差的精度。在6控情况下,太行山试验区达到平面2.504m高程3.117m,在渭南试验区达到了平面4.061m高程2.895m。试验结果证明了轨道平差的有效性和可行性。     

CBERS-02B卫星遥感影像的区域网平差

针对中巴资源一号卫星(CBERS-02B)卫星遥感影像姿态角误差较大的特点,提出了利用区域网平差方法提高其对地目标定位精度的策略和具体计算过程。首先对参与平差的每景影像选取4个地面控制点进行影像姿态角常差检校,然后采用与地形无关方案解求各自的RPC参数,最后选取带仿射变换项的有理函数模型(RFM)进行多重覆盖影像的区域网平差。对两个地区的0级CBERS-02B单条CCD立体影像对的区域网平差试验表明,对地目标定位的平面和高程精度均达到了±3个像元的水平,且高程精度明显优于平面精度。相对于常规的卫星遥感影像区域网平差方法,平面和高程精度均有明显提升,几乎达到国外同等高分辨率卫星遥感影像的几何定位精度。这说明中国卫星遥感影像亦具有较好的几何定位潜力,在区域网平差之前进行系统误差预改正是必要和可行的。     

Estimating regional forest cover in East Texas using Advanced Very High Resolution Radiometer (AVHRR) data

This study tested the degree to which single date, near-nadir AVHRR image could provide forest cover estimates comparable to the phase I estimates obtained from the traditional photo-based techniques of the Forest Inventory and Analysis (FIA) program. FIA program is part of the United States Department of Agriculture-Forest Service (USFS). A six-county region in east Texas was selected for this study. Manual identification of ground control points (GCPs) was necessary for geo-referencing this image with higher precision. Through digital image classification techniques forest classes were separated from other non-forest classes in the study area. Classified AVHRR imagery was compared to two verification datasets: photo-center points and the USFS FIA plots. The overall accuracy values obtained were 67 and 71%, respectively. Analyses of the error matrices indicated that the AVHRR image correctly classified more forested areas than non-forested areas; however, most of the errors could be attributed to certain land cover and land use classes. Several pastures with tree cover, which were field-identified as non-forest, were misclassified as forest in the AVHRR image using the image classification system developed in this study. Recently harvested and young pine forests were misclassified as non-forest in the imagery. County-level forest cover estimates obtained from the AVHRR imagery were within the 95% confidence interval of the corresponding estimates from traditional photo-based methods. These results indicate that AVHRR imagery could be used to estimate county-level forest cover; however, the precision associated with these estimates was lower than that obtained through traditional photo-based techniques.     

稀少控制条件下的SPOT 5 HRS影像定向试验

通过生产试验,探讨了不同控制点数量及分布下的SPOT 5 HRS影像的定向精度问题,分析了稀少控制点定向后SPOT 5 HRS影像的误差分布情况,为SPOT 5 HRS影像在外业控制点获取困难地区的应用提供了可行方法。     

直线特征约束的高分辨率卫星影像区域网平差方法

以"像方观测直线与像方预测直线必须重合"作为几何约束条件,以有理函数模型(RFM)作为高分辨率卫星影像的几何处理模型,提出了一种直线特征约束的高分辨率卫星影像区域网平差方法。本文方法仅需像方直线与物方直线相对应,无须像方直线上的像点与物方直线上的地面点一一对应。通过对圣迭戈试验区的两景IKONOS影像、斯波坎试验区的两景QuickBird影像和普罗旺斯试验区的两景SPOT-5影像进行试验,结果表明:本文方法可以充分利用直线特征作为控制条件,有效补偿RPC参数中的系统误差,获得的IKONOS、QuickBird和SPOT-5影像区域网平差的平面与高程精度均优于1个像素。     

资源三号全国无控制整体区域网平差关键技术及应用

介绍了资源三号卫星三线阵立体像对全国无控制整体区域网平差的关键技术及应用,主要包括高精度稳态重成像处理技术、基于虚拟控制点的平差模型构建技术、粗差（包括几何精度异常影像、误匹配点）的探测与剔除技术以及超大规模平差方程的高效解算方法。在此基础上,对覆盖全国的8 802个资源三号三线阵立体像对（共26 406景影像）在无控制条件下整体一张网的平差结果及精度验证情况进行分析。实验结果表明,该方法不但可以保证区域网整体的绝对无偏估计,还可以有效控制区域网内部几何误差的传递与累积,从而避免网的变形,以保证网内几何精度的一致性与均匀性。此外,还列出了本技术在全球测图工程中德国试验区的示范应用情况。     

Direct georeferencing of oblique and vertical imagery in different coordinate systems

Reconstruction of 3D models through integrating vertical and oblique imagery has been studied extensively. For a 3D reconstruction, object point cloud coordinates could be calculated using direct georeferencing (DG) obtained from the direct orientation data of a GPS/INS system. This paper implemented DG approaches for vertical and oblique imagery in the earth centered earth fixed frame (e-frame), local tangent frame (l-frame), and map projection frame (p-frame), respectively. In the p-frame, the earth curvature correction formulas were derived through naturalizing oblique imagery to vertical imagery to achieve a high positioning precision. Five basic stereo-pair models for vertical and oblique imagery were simulated to verify the positioning accuracy of different frames. Simulation experiments showed that DG in the e-frame and l-frame of these five scenarios were rigorous, and no systematic errors were imported by the DG model as these frames are Cartesian. DG in the p-frame has obvious systematic errors which are aroused by the earth curvature and projection deformation unconformity in the vertical and horizontal directions. These errors, however, can be compensated effectively through correcting image coordinates of the oblique imagery by extending the standard image coordinate correction approach and the exterior orientation (EO) height term. After the correction, the absolute positioning error is lower than 1/20 GSD for simulation test-1. In the p-frame, the process is straightforward, and it is convenient for producing maps. For high accuracy DG, though, it is recommended to adopt e-frame or l-frame options.     

An improved geopositioning model of QuickBird high resolution satellite imagery by compensating spatial correlated errors

A lot of studies have been done for correcting the systematic biases of high resolution satellite images (HRSI), which is a fundamental work in the geometric orientation and the geopositioning of HRSI. All the existing bias-corrected models eliminate the biases in the images by expressing the biases as a function of some deterministic parameters (i.e. shift, drift, or affine transformation models), which is indeed effective for most of the commercial high resolution satellite imagery (i.e. IKONOS, GeoEye-1, WorldView-1/2) except for QuickBird. Studies found that QuickBird is the only one that needs more than a simple shift model to absorb the strong residual systematic errors. To further improve the image geopositioning of QuickBird image, in this paper, we introduce space correlated errors (SCEs) and model them as signals in the bias-corrected rational function model (RFM) and estimate the SCEs at the ground control points (GCPs) together with the bias-corrected parameters using least squares collocation. With these estimated SCEs at GCPs, we then predict the SCEs at the unknown points according to their stochastic correlation with SCEs at the GCPs. Finally, we carry out geopositioning for these unknown points after compensating both the biases and the SCEs. The performance of our improved geopositioning model is demonstrated with a stereo pair of QuickBird cross-track images in the Shanghai urban area. The results show that the SCEs exist in HRSI and the presented geopositioning model exhibits a significant improvement, larger than 20% in both latitude and height directions and about 2.8% in longitude direction, in geopositioning accuracy compared to the common used affine transformation model (ATM), which is not taking SCEs into account. The statistical results also show that our improved geopositioning model is superior to the ATM and the second polynomial model (SPM) in both accuracy and reliability for the geopositioning of HRSI.     

Quality Assessment Of Digital Surface Models Generated From IKONOS Imagery

The growing applications of digital surface models (DSMs) for object detection, segmentation and representation of terrestrial landscapes have provided impetus for further automation of 3D spatial information extraction processes. While new technologies such as lidar are available for almost instant DSM generation, the use of stereoscopic high-resolution satellite imagery (HRSI), coupled with image matching, affords cost-effective measurement of surface topography over large coverage areas. This investigation explores the potential of IKONOS Geo stereo imagery for producing DSMs using an alternative sensor orientation model, namely bias-corrected rational polynomial coefficients (RPCs), and a hybrid image-matching algorithm. To serve both as a reference surface and a basis for comparison, a lidar DSM was employed in the Hobart testfield, a region of differing terrain types and slope. In order to take topographic variation within the modelled surface into account, the lidar strip was divided into separate sub-areas representing differing land cover types. It is shown that over topographically diverse areas, heighting accuracy to better than 3 pixels can be readily achieved. Results improve markedly in feature-rich open and relatively flat terrain, with sub-pixel accuracy being achieved at check points surveyed using the global positioning system (GPS). This assessment demonstrates that the outlook for DSM generation from HRSI is very promising.     

仅用虚拟控制点的超大区域无控制区域网平差

利用光学卫星影像进行无控制测图是摄影测量追求的目标。针对超大区域无控制测图的需求,本文提出了一种以单景影像为平差单元,基于虚拟控制点的光学卫星影像超大规模无控制区域网平差方法。该方法利用待平差影像的初始RPC模型生成虚拟控制点,并将其作为带权观测值引入平差模型中以改善平差模型的状态,克服了在无控制点条件下平差精度不稳定、误差过度累积引起的网的扭曲变形等问题。为了验证本方法的有效性和精度,利用资源三号卫星获取的覆盖全国的26 406景影像进行区域网平差试验,并利用全国范围内分布的约8000个高精度控制点对平差后自动生产的DOM和DSM产品的几何精度进行验证。试验结果表明,平面和高程中误差均达到了4m以内,同时,区域网内部相邻影像之间的几何拼接精度优于1个像素,满足无缝拼接的要求。     

Orthorectification of VHR optical satellite data exploiting the geometric accuracy of TerraSAR-X data

Orthorectification of satellite data is one of the most important pre-processing steps for application oriented evaluations and for image data input into Geographic Information Systems. Although high- and very high-resolution optical data can be rectified without ground control points (GCPs) using an underlying digital elevation model (DEM) to positional root mean square errors (RMSEs) between 3 m and several hundred meters (depending on the satellite), there is still need for ground control with higher precision to reach lower RMSE values for the orthoimages. The very high geometric accuracy of geocoded data of the TerraSAR-X satellite has been shown in several investigations. This is due to the fact that the SAR antenna measures distances which are mainly dependent on the terrain height and the position of the satellite. The latter can be measured with high precision, whereas the satellite attitude need not be known exactly. If the used DEM is of high accuracy, the resulting geocoded SAR data are very precise in their geolocation. This precision can be exploited to improve the orientation knowledge and thereby the geometric accuracy of the rectified optical satellite data. The challenge is to match two kinds of image data, which exhibit very different geometric and radiometric properties. Simple correlation techniques do not work and the goal is to develop a robust method which works even for urban areas, including radar shadows, layover and foreshortening effects. First the optical data have to be rectified with the available interior and exterior orientation data or using rational polynomial coefficients (RPCs). From this approximation, the technique used is the measurement of small identical areas in the optical and radar images by automatic image matching, using a newly developed adapted mutual information procedure followed by an estimation of correction terms for the exterior orientation or the RPC coefficients. The matching areas are selected randomly from a regular grid covering the whole imagery. By adjustment calculations, parameters from falsely matched areas can be eliminated and optimal improvement parameters are found. The original optical data are orthorectified again using the delivered metadata together with these corrections and the available DEM. As proof of method the orthorectified data from IKONOS and ALOS-PRISM sensors are compared with conventional ground control information from high-precision orthoimage maps of the German Cartographic Survey. The results show that this method is robust, even for urban areas. Although the resulting RMSE values are in the order of 2-6 m, the advantage is that this result can be reached even for optical sensors which do not exhibit low RMSE values without using manual GCP measurements.     

Rational function optimization using genetic algorithms

In the absence of either satellite ephemeris information or camera model, rational functions are introduced by many investigators as mathematical model for image to ground coordinate system transformation. The dependency of this method on many ground control points (GCPs), numerical complexity, particularly terms selection, can be regarded as the most known disadvantages of rational functions. This paper presents a mathematical solution to overcome these problems. Genetic algorithms are used as an intelligent method for optimum rational function terms selection. The results from an experimental test carried out over a test field in Iran are presented as utilizing an IKONOS Geo image. Different numbers of GCPs are fed through a variety of genetic algorithms (GAs) with different control parameter settings. Some initial constraints are introduced to make the process stable and fast. The residual errors at independent check points proved that sub-pixel accuracies can be achieved even when only seven and five GCPs are used. GAs could select rational function terms in such a way that numerical problems are avoided without the need to normalize image and ground coordinates.     

An improved approach for the production of satellite-based geospatial reference imagery

Abstract

An innovative and practical satellite image product is described that is ideal for applications in Northern Canada because of its wide area coverage and mapping-quality features. This product is generated from a new procedure developed at the Canada Centre for Remote Sensing (CCRS) for processing Landsat 7 imagery, and by extension, imagery from other Earth Observation satellites. By working with multiple satellite passes, each containing the equivalent of multiple scenes, the new procedure could dramatically reduce the turn-around time for generating georeferenced image products, and also increase their geometric and radiometric accuracy compared to those produced by the current methods. The objective of the process has been to generate satellite image mosaics covering large areas (e.g. >500 000 km²) with uniformly distributed errors at sub-pixel resolution. The paper discusses the theoretical basis of a photogrammetric adjustment for satellite imagery and the results obtained from several tests. The process is generic, involving a sensor model, a satellite orbit model and ground control information; thus it may be easily adapted to any satellite that allows for repeat coverage with overlapping paths. By performing an adjustment to correct the satellite position and attitude data prior to the production of orthoimage products, it is possible to create a mosaic with a single resampling process which minimises both the radiometric and geometric resampling artifacts. The results from three separate tests are presented, along with a discussion of the procedures that were followed in each case. All three tests have successfully demonstrated that sub-pixel sample size errors may be consistently obtained over large areas. A by-product process developed to support the measurement of ground control point coordinates for the satellite adjustment was the automatic matching of geographic features such as lakes and islands in vector data format. This has been a significant development in that it has eliminated manual intervention in the measurement of these features in the imagery, allowing the ground control for entire passes containing several scenes to be obtained in minutes instead of hours.     

天绘一号03星无控定位精度改进策略

“全球连续覆盖模式”传输型摄影测量卫星系动态摄影，无控定位模式下难以达到框幅式像片定位水平。本文在天绘一号已有研究基础上，深化03星摄影测量无控定位精度改进模式的探讨研究。在相机参数在轨标定中增加对相机内方位元素的附加改正，解决相机结构宽高比（卫星条带摄影覆盖宽度与卫星轨道高度的比值）太小对主距标定结果的影响，进而削弱系统误差，提高卫星影像的平面定位精度。通过境外地区检测，无控定位精度达到高程2.4 m（RMS），平面3.7 m（RMS）。检测结果表明，只依靠星上GNSS接收机、星敏感器，利用相机参数在境内标定结果，“全球连续覆盖模式”单航线卫星影像无控定位结果达到理论设计指标。     

Improving georeferencing accuracy of Very High Resolution satellite imagery using freely available ancillary data at global coverage

ABSTRACT

While impressive direct geolocation accuracies better than 5.0?m CE90 (90% of circular error) can be achieved from the last DigitalGlobe’s Very High Resolution (VHR) satellites (i.e. GeoEye-1 and WorldView-1/2/3/4), it is insufficient for many precise geodetic applications. For these sensors, the best horizontal geopositioning accuracies (around 0.55?m CE90) can be attained by using third-order 3D rational functions with vendor’s rational polynomial coefficients data refined by a zero-order polynomial adjustment obtained from a small number of very accurate ground control points (GCPs). However, these high-quality GCPs are not always available. In this work, two different approaches for improving the initial direct geolocation accuracy of VHR satellite imagery are proposed. Both of them are based on the extraction of three-dimensional GCPs from freely available ancillary data at global coverage such as multi-temporal information of Google Earth and the Shuttle Radar Topography Mission 30?m digital elevation model. The application of these approaches on WorldView-2 and GeoEye-1 stereo pairs over two different study sites proved to improve the horizontal direct geolocation accuracy values around of 75%.