SENSOR ORIENTATION FOR HIGH-RESOLUTION SATELLITE IMAGERY: 
FURTHER INSIGHTS INTO BIAS-COMPENSATED RPCs 
H.B. Hanley, C.S. Fraser 
Department of Geomatics, University of Melbourne, Vic 3010, Australia 
hanley@sunrise.sli.unimelb.edu.au, c.fraser@unimelb.edu.au 
Commission I, WG 1/2 
KEY WORDS: High-resolution satellites, sensor orientation, RPC bundle adjustment, IKONOS, QuickBird 
ABSTRACT: 
As high-resolution satellite imagery (HRSI) attracts usage in a broader range of mapping and GIS applications, so the demand for 
higher 3D accuracy increases. One of the notable recent innovations in sensor orientation modelling for HRSI has been bias 
compensated RPC bundle adjustment, which has shown that geopositioning to high accuracy can be achieved with minimal ground 
control; indeed, only one control point may be required. Bias-compensated RPCs and related issues are further examined in this 
paper, with attention being paid to the impact of terrain height variation and the issue of scanning mode. Image scanning 
characteristics can significantly influence metric performance, with the effect being more pronounced for HRSI sensors that 
dynamically vary their orientation during scene capture. Through experimental testing with IKONOS and QuickBird stereo imagery, 
the authors demonstrate that bias-corrected RPCs are capable of yielding sub-pixel geopositioning from base-level imagery products. 
Thus, bias-compensated RPCs are not only favourable in regard to optimising accuracy capability; they also offer cost advantages. 
1. INTRODUCTION 
One of the recent innovations in alternative sensor orientation 
modelling for high-resolution satellite imagery (HRSI) has been 
bias-compensated RPC bundle adjustment, where the ‘RPC’ in 
the name stands for Rational Polynomial Coefficients. It has 
been shown in a number of practical applications that this 
rational functions-based approach can yield sub-pixel 
geopositioning with only a single ground control point (GCP). 
The reader is referred, for example, to Hanley et al. (2002), 
Grodecki & Dial (2003) and Fraser & Hanley (2003). 
As a sensor orientation model for stereo satellite image 
configurations, rational functions have a history of application 
spanning nearly two decades (Dowman & Doloff, 2000). 
However, it was not until the deployment of the IKONOS high- 
resolution imaging satellite in September, 1999 that widespread 
industry attention was paid to this ‘replacement’ model for 
sensor orientation and ground point determination. Indeed, the 
commercial photogrammetric industry had little option but to 
embrace RPC-based restitution, since this was the only means 
provided by Space Imaging for customers to extract accurate 
object space information from IKONOS imagery. 
There was some early unease associated with the employment 
of rational functions, but it was soon apparent that the metric 
accuracy potential of IKONOS would not necessarily be 
compromised through use of Space Imaging produced RPCs. 
Indeed, Grodecki (2001) reported that the integrity of modelling 
the rigorous sensor orientation by RPCs was better than 0.05 
pixels. Notwithstanding the very impressive results obtained 
with IKONOS image restitution via the bias-compensated RPC 
bundle adjustment approach, some uncertainties have persisted 
regarding the universal applicability of this sensor orientation 
approach. Some of this uncertainty can be attributed to the 
false association of vendor produced RPCs with those 
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empirically determined by users through the use of dense arrays 
of GCPs. More curious, however, have been suggestions that 
RPCs supplied with HRSI would somehow be influenced by 
variations in the terrain within the scene (eg Cheng et al., 2003). 
One area of justifiable concern relates to the impact of sensor 
scanning mode upon the metric performance of RPCs. This 
effect is anticipated to be more pronounced with HRSI sensors 
in imaging modes where the look-orientation is varying 
significantly during scene capture. For example, in the ‘normal’ 
Reverse scanning mode of IKONOS, the elevation angle of the 
sensor is near constant, yet in Forward scanning mode it is 
changing at close to l'/sec. For Quickbird, the sensor 
orientation is always varying, in either Forward or Reverse 
scanning mode. 
There is a higher likelihood of small residual components of 
systematic scan velocity errors in platforms that are 
dynamically re-orienting during image recording. This may 
well be a factor in the reported 0.1 to 0.3 pixel level of 
agreement between the rational function model and the rigorous 
sensor model for Quickbird imagery (Robertson, 2003). 
Robertson (ibid.) has also observed that such levels of 
discrepancy would typically be dwarfed by other errors in any 
orthorectification process. From a practical standpoint, 
however, the distinction between agreement levels of 0.05 
pixels and, say 0.2 pixels, seems rather academic, since 
theoretical expectations for maximum achievable 
geopositioning accuracy in practise are around 0.3-0.4 pixels in 
planimetry and 0.5-0.6 pixels in height. 
This paper, which is a condensed version of Fraser & Hanley 
(2004), describes the bias-compensated RPC model in the form 
that accommodates first-order ‘drift’ effects as well as image 
space shifts induced by small biases in sensor exterior 
orientation. It also illustrates, by way of a practical example, 
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