{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T21:04:04Z","timestamp":1768511044305,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,17]],"date-time":"2017-07-17T00:00:00Z","timestamp":1500249600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Educational Commission of the Sichuan Province of China","award":["17ZA0031"],"award-info":[{"award-number":["17ZA0031"]}]},{"name":"the Educational Commission of the Sichuan Province of China","award":["16ZA0091"],"award-info":[{"award-number":["16ZA0091"]}]},{"name":"the Sichuan Excellent Engineer Education Program","award":["13Z00208"],"award-info":[{"award-number":["13Z00208"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>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\u2019 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.<\/jats:p>","DOI":"10.3390\/rs9070737","type":"journal-article","created":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T03:45:16Z","timestamp":1500349516000},"page":"737","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Mathematical Modeling and Accuracy Testing of WorldView-2 Level-1B Stereo Pairs without Ground Control Points"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1289-4027","authenticated-orcid":false,"given":"Jiang","family":"Ye","sequence":"first","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Earth Sciences, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,17]]},"reference":[{"key":"ref_1","first-page":"609","article-title":"Orientation theory of ccd line-scanner images","volume":"27","author":"Okamoto","year":"1988","journal-title":"Int. Arch. Photogramm. Remote Sens."},{"key":"ref_2","first-page":"883","article-title":"Satellite photogrammetry","volume":"4","author":"Light","year":"1980","journal-title":"Man. Photogramm."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1080\/0143116031000101611","article-title":"Review article: Geometric processing of remote sensing images: Models, algorithms and methods","volume":"25","author":"Toutin","year":"2004","journal-title":"Int. J. Remote Sens."},{"key":"ref_4","unstructured":"Giannone, F. (2017, June 23). A Rigorous Model for High Resolution Satellite Imagery Orientation. Available online: http:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.529.4356&rep=rep1&type=pdf."},{"key":"ref_5","unstructured":"Crespi, M., Giannone, F., and Poli, D. (2017, June 23). Analysis of Rigorous Orientation Models for Pushbroom Sensors. Applications with Quickbird. Available online: http:\/\/www.isprs.org\/proceedings\/xxxvi\/part1\/papers\/T02-07.pdf."},{"key":"ref_6","unstructured":"Crespi, M., Fratarcangeli, F., Giannone, F., and Pieralice, F. (2017, June 23). Sisar: A Rigorous Orientation Model for Synchronous and Asynchronous Pushbroom Sensors Imagery. Available online: http:\/\/www.isprs.org\/proceedings\/XXXVI\/1-W51\/paper\/crespi_etal.pdf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1080\/01431161.2011.608737","article-title":"A new rigorous model for high-resolution satellite imagery orientation: Application to eros a and quickbird","volume":"33","author":"Crespi","year":"2012","journal-title":"Int. J. Remote Sens."},{"key":"ref_8","unstructured":"De Venecia, K.J., Paderes, F., and Walker, A.S. (2006, January 1\u20135). Rigorous sensor modeling and triangulation for orbview-3. Proceedings of the ASPRS Annual Conference, Reno, NV, USA."},{"key":"ref_9","first-page":"705","article-title":"3d reconstruction methods based on the rational function model","volume":"68","author":"Tao","year":"2002","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_10","first-page":"1347","article-title":"A comprehensive study of the rational function model for photogrammetric processing","volume":"67","author":"Tao","year":"2001","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1080\/07038992.2001.10854900","article-title":"Use of the rational function model for image rectification","volume":"27","author":"Tao","year":"2001","journal-title":"Can. J. Remote Sens."},{"key":"ref_12","unstructured":"Cheng, P., and Toutin, T. (2001, January 5\u20139). Ortho rectification and dem generation from high resolution satellite data. Proceedings of the 22nd Asian Conference on Remote Sensing, Singapore."},{"key":"ref_13","unstructured":"Yang, X. (2000, January 4\u20138). Accuracy of rational function approximation in photogrammetry. Proceedings of the ASPRS Annual Conference, Taipei, Taiwan."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.14358\/PERS.69.1.59","article-title":"Block adjustment of high-resolution satellite images described by rational polynomials","volume":"69","author":"Grodecki","year":"2003","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_15","unstructured":"Dial, G., and Grodecki, J. (2002, January 19\u201326). Block adjustment with rational polynomial camera models. Proceedings of the ASPRS 2002 Conference, Washington, DC, USA."},{"key":"ref_16","unstructured":"Dial, G., and Grodecki, J. (2017, June 23). RPC Replacement Camera Models. Available online: http:\/\/128.46.154.21\/jshan\/proceedings\/asprs2005\/Files\/0031.pdf."},{"key":"ref_17","unstructured":"Hu, Y., Tao, V., and Croitoru, A. (2017, June 23). Understanding the Rational Function Model: Methods and Applications. Available online: http:\/\/www.isprs.org\/proceedings\/XXXV\/congress\/comm4\/papers\/423.pdf."},{"key":"ref_18","first-page":"715","article-title":"Updating solutions of the rational function model using additional control information","volume":"68","author":"Hu","year":"2002","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_19","first-page":"7","article-title":"The algorithm for parameters of rpc model without initial value","volume":"4","author":"Xuwen","year":"2005","journal-title":"Remote Sens. Land Resour."},{"key":"ref_20","unstructured":"DigitalGlobe (2017, March 09). Worldview-2 Spacecraft Information and Specifications. Available online: https:\/\/www.digitalglobe.com\/resources\/satellite-information."},{"key":"ref_21","unstructured":"DigitalGlobe (2017, March 09). Accuracy of Worldview Products. Available online: https:\/\/dg-cms-uploads-production.s3.amazonaws.com."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1109\/TGRS.2013.2249521","article-title":"Generation and quality assessment of stereo-extracted dsm from geoeye-1 and worldview-2 imagery","volume":"52","author":"Aguilar","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","first-page":"427","article-title":"Assessing geometric accuracy of the orthorectification process from geoeye-1 and worldview-2 panchromatic images","volume":"21","author":"Aguilar","year":"2013","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.isprsjprs.2016.03.012","article-title":"An automated, open-source pipeline for mass production of digital elevation models (dems) from very-high-resolution commercial stereo satellite imagery","volume":"116","author":"Shean","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_25","unstructured":"Updike, T., and Comp, C. (2017, March 09). Radiometric Use of Worldview-2 Imagery. Available online: https:\/\/dg-cms-uploads-production.s3.amazonaws.com\/uploads\/document\/file\/104\/Radiometric_Use_of_WorldView-2_Imagery.pdf."},{"key":"ref_26","unstructured":"Riazanoff, S. (2004). Spot 123-4-5 Geometry Handbook, GAEL Consultant. Tech Rep. GAEL-P135-DOC-001."},{"key":"ref_27","unstructured":"Boyd, J.P. (2001). Chebyshev and Fourier Spectral Methods, Courier Corporation. [2nd ed.]."},{"key":"ref_28","unstructured":"Barrera, T., Hast, A., and Bengtsson, E. (2004, January 17\u201322). Incremental spherical linear interpolation. Proceedings of the Annual Special Theme-Environmental Visualization Conference (SIGRAD), Gold Coast, Australia."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/S0924-2716(99)00030-1","article-title":"Atmospheric refraction effects in earth remote sensing","volume":"54","author":"Noerdlinger","year":"1999","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02522083","article-title":"Contributions to the theory of atmospheric refraction","volume":"107","author":"Saastamoinen","year":"1973","journal-title":"Bull. G\u00e9od. (1946\u20131975)"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/BF02522047","article-title":"Introduction to practical computation of astronomical refraction","volume":"106","author":"Saastamoinen","year":"1972","journal-title":"Bull. G\u00e9od. (1946\u20131975)"},{"key":"ref_32","first-page":"995","article-title":"Atmosphere refraction effectsin object locating for optical satellite remote sensing images","volume":"44","author":"Ming","year":"2015","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge regression: Biased estimation for nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/00401706.1970.10488635","article-title":"Ridge regression: Applications to nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"ref_35","first-page":"3","article-title":"The iterration by correcting characteristic value and its application in surveying data processing","volume":"15","author":"Xinzhou","year":"2001","journal-title":"J. Heilongjiang Inst. Technol."},{"key":"ref_36","unstructured":"Greenwalt, C.R., and Shultz, M.E. (1962). Principles of Error Theory and Cartographic Applications."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/7\/737\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:00Z","timestamp":1760208180000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/7\/737"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,17]]},"references-count":36,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["rs9070737"],"URL":"https:\/\/doi.org\/10.3390\/rs9070737","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,17]]}}}