ACCURACY EVALUATION OF RATIONAL POLYNOMIAL COEFFICIENTS
SOLUTION FOR QUICKBIRD IMAGERY BASED ON AUXILIARY GROUND
CONTROL POINTS
Yun Zhan a Chun Liu a,b Gang Qiao 3
a Department of Surveying and Geo-Informatics, Tongji University, Shanghai, China
b Key Laboratory of Advanced Engineering Surveying of State Bureau of Surveying and Mapping, China
Commission VI, WG VII/6
KEYWORDS: Rational polynomial coefficients, Batch iterative least-squares solution with regularization,
Incremental discrete Kalman filtering, Geo-positioning accuracy
ABSTRACT:
Relative to the rigorous physical model, rational polynomial coefficient (RPC) has been adopted as an alternative common sensor
model data for image Geometric correction exploitation. In this paper, based on collected QuickBird imagery in Shanghai region, the
iterative least-squares solution with regularization(ILSR) is derived to determine the RPCs by using 50 fair distributed ground
control points (GCPs) firstly. Two methods are then used to refine determined RPCs under different circumstance as: 1) when both
the original and the additional GCPs are available, the RPCs will be recomputed using the batch iterative least-squares solution with
regularization (BILSR) method; and 2) when only the new GCPs are available, incremental discrete Kalman filtering (IDKF) method
has been described. Meanwhile, check points are used to evaluate their geo-positioning accuracy, and their comparison is conducted.
Finally, some conclusion is then achieved when handing the high resolution imagery in metropolitan area.
1. INTRODUCTION
Satellite Imagery such as QuickBird, IKONOS has been widely
used with the development of high resolution satellite
technology. Collinearity based rigorous sensor model is the
basis of geometric positioning for high resolution satellite
imagery (HRSI). Dependence on physical parameters and
satellite orbit parameters makes the rigorous sensor model much
more complicated, thus hard to be applied with. The RPC, a
mathematical model which is sensor independent and not
rigorous, has been used widely by satellite companies for the
survey process of HRSI and as the alternative of the rigorous
sensor model. The image coordinates are denoted as the third
polynomial expression in RPC. RPC, by providing a simple and
exact relation for vendors and customers to describe the
relationship of object and image, has been successfully
employed in the terrain modeling, orthographic projection and
feature extraction. A lot of research work has been done about
the geometric correction and 3D reconstruction of IKONOS
imagery using RPC (Tao and Hu, 2001,
2002(1), 2002(2);
Dowman, 2000; Fraser, 2002; Clive, 2002).
Two methods are used for the calculation of RPC, terrain
dependant approach and terrain independent approach (Yong
Hu et al., 2004). The terrain dependent approach, without
setting up grids, is to obtain GCP through topographical
measurement or field survey to fit the imagery geometry using
sufficient parameters. Its accuracy is determined by
hypsography and the GCP number and distribution (Fraser,2006;
Liu,2006). The relativity between the RPC parameters may
result in the singularity of design matrix for normal equation.
The regularization method can improve the condition number of
the design matrix, thus avoiding the numerical instability of
least square solution (Tao and Hu,2001).
The RPC direct correction method was put forward to improve
the positioning accuracy and meet the demand of high accuracy
users. Different mathematical methods were applied for the
RPC accuracy improvement when the physical sensor model
was unknown. When the original and auxiliary GCP were both
available, BILSR was used to recalculate the RPC (Hu and
Tao,2002; Di et al.,2003). Here the original GCP denotes the
GCP used for calculating the original RPC, while the auxiliary
GCP means the auxiliary collected GCP that never used for
RPC calculation. The correction process is to include all the
GCP into the RPC solution with different power to the new and
original GCP. When there are only auxiliary GCP, the IDKF
can be employed to improve the RPC accuracy (Hu and
Tao,2002; Bang et al.,2003), which means the accuracy of RPC
is improved through the inclusion of new GCP with proper
power.
Based on the QuickBird imagery in Shanghai, China, this paper
mainly discusses the solution of RPC and accuracy after
correction applied in metropolitan area without obvious
hypsography. Experiences of application for similar data could
be learned from the models and data this paper employed.
2. RPC MATHEMATICAL MODEL
The RPC of QuickBird imagery denotes the image coordinates
as the ratio of polynomials based on the variable of longitude,
latitude and height, which is as equation (1):
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