Journal of the Indian Society of Remote Sensing

, Volume 47, Issue 1, pp 165–175 | Cite as

Rational Polynomial Coefficients Modeling and Bias Correction by Using Iterative Polynomial Augmentation

  • Bhaskar DubeyEmail author
  • B. Kartikeyan
  • Manthira Moorthi Subbiah
Research Article


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.


Rational 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.


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Copyright information

© Indian Society of Remote Sensing 2018

Authors and Affiliations

  • Bhaskar Dubey
    • 1
    Email author
  • B. Kartikeyan
    • 1
  • Manthira Moorthi Subbiah
    • 2
  1. 1.Image Analysis and Quality Evaluation Division, Space Applications CentreIndian Space Research OrganizationAhmedabadIndia
  2. 2.Optical Data Processing Division, Space Applications CentreIndian Space Research OrganizationAhmedabadIndia

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