Rational Polynomial Coefficients Modeling and Bias Correction by Using Iterative Polynomial Augmentation
- 32 Downloads
In this article, we establish an update procedure for rapid positioning coefficients or rational polynomial coefficients (RPCs) via iterative refinements using polynomial augmentation and reference images. RPCs are widely popular in establishing a ground-to-image relationship without using physical sensor model. However, the accuracies of RPCs are degraded due to unavoidable errors in physical sensor model based on colinearity conditions. These inaccuracies essentially arise due to undulating terrain, residual errors in attitude parameters, viz. roll, pitch and yaw, inexact modeling of drift and micro-vibration, orbit error, etc. In the paper, first an initial estimate of RPCs is obtained by using \(L^2\)-regularized least square estimation. Subsequently, the RPCs are refined by using iterative affine augmentation. The RPC accuracy is further improved by a second-order polynomial augmentation. The results show that with the improved RPCs the average scan and pixel errors are within 0.5 pixel. The results of the paper are employed and validated on Resourcesat-2 imagery.
KeywordsRational function model Bias compensation RPC refinement Ground control points (GCPs)
The authors would like to thank Director Space Applications Centre, Ahmedabad, for his support and encouragement toward this work. Authors further thank Group Director, Signal and Image Processing Group, Space Applications Centre, Ahmedabad, for unabated support and keen interest in the study. Support from IAQD and ODPD team members is thankfully acknowledged. We sincerely express our gratitude to anonymous reviewers for their valuable comments that resulted in the current form of the paper.
- Diala, G., & Grodecki, J. (2005). RPC replacement camera models. The International Archives of Photogrammetry, Remote Sensing, and Spacial Information Science, 34, 1–9.Google Scholar
- Dowman, I., & Dolloff, J. (2000). An evaluation of rational functions for photogrammetric restitution. International Archives of Photogrammetric Engineering and Remote Sensing, 33(B3), 254–266.Google Scholar
- Dowman, I., & Tao, V. (2002). An update on the use of rational functions for photogrammetric restitution. ISPRS Highlights, 7(3), 22–29.Google Scholar
- Dubey, B., & Kartikeyan, B., (2018). A novel approach for estimation of residual attitude of a remote-sensing satellite. International Journal of Remote Sensing. https://doi.org/10.1080/01431161.2018.1483086.
- Hoffman, K., & Kunze, R. (1961). Linear algebra. Upper Saddle River: Prentice-Hall.Google Scholar
- Koh, K., Kim, S., & Boyd, S. (2007). An interior-point method for large scale regularized logistic regression. Journal of Machine Learning Research, 8, 1519–1555.Google Scholar
- Shen, X., Li, Q., Wu, G., & Zhu, J. (2017a). Bias compensation for rational polynomial coefficients of high resolution satellite imagery by local polynomial modeling. Remote Sensing. https://doi.org/10.3390/rs9030200.
- Singh, S., Naidu, S., Srinivasan, T., Krishna, B., & Srivastava, P., (2008). Rational polynomial modelling for cartosat-1 data. In International archives of the photogram. Remote sensing and spacial information science. ISPRS, Beiging, part B1.Google Scholar
- Tao, C. (2001). A comprehensive study of the rational function model for photogrammetric processing. Photogrammetric Engineering and Remote Sensing, 67(12), 1347–1357.Google Scholar