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STATISTICAL TESTINGS FOR DETERMINING SIGNIFICANT SAR-IMAGE 
ORIENTATION PARAMETERS 
Joz WU, Chia-Jun LIU, De-Chen LIN 
National Central University Chungli 320, Taiwan, ROC 
Center for Space and Remote Sensing Research 
jozwu Q csrsr.ncu.edu.tw 
(Paper number: 1400) 
KEY WORDS: Airborne SAR-Image, Time Polynomials, Significance/Optimization. 
ABSTRACT 
For geometric analysis of a side-looking SAR image, it is frequently of interest to determine the time-varying 
radar antenna's position parameters along a flight path. In this paper, the time polynomials are employed to 
model the position (orientation) parameters, in association with the basic ranging/Doppler (radargrammetric) 
conditions. As usual, a least-squares adjustment yields both parameter corrections and measurement residuals. 
The estimated corrections and their variances can be used to statistically investigate their respective parameter 
significance. Equally essential are the estimated measurement residuals because the corresponding residual 
quadratic-form should theoretically reflect a minimum value. Based on the explicit expressions cited for both 
the parameter significance and the model optimization, the results of an experimental airborne SAR slant- 
range image indicate that the proposed methodology satisfactorily works. 
1. INTRODUCTION 
Side-looking synthetic aperture radar (SAR) (Moore et al., 1983) represents an active remote sensing 
technology. For a variety of technical issues, the current paper is concerned with the space resection of 
imagery resulting from the SAR sensing/data-processing. Geometrically, an SAR image is in (slant) range 
projection. Radargrammetric equations express both the radar cross-track range measurement and the along- 
track Doppler image-forming requirement. The equations are well suited for an SAR-image resection topic 
(Leberl, 1979). Based on some control points, the radargrammetric conditions serve to describe a functional 
relationship between the two-dimensional image point coordinate measurements and the three-dimensional 
ground point measurements. 
The unknown parameters in the functional relationship are, among others, the radar antenna’s time-varying 
positions. By employing a least-squares method, the SAR antenna’s orientation parameters can be estimated 
(Koch, 1999). When using a quadratic form of the estimated measurement residuals, one can further perform 
parameter significance tests (Zhong, 1997). In this manner, the SAR-image orientation parameters may be 
considered statistically optimal. 
2. SIDE-LOOKING SAR GEOMETRY 
Unlike passive optical imagery resulting from a (central) perspective projection, SAR imaging geometry is 
related to a slant-range projection, leading to such an image displacement as foreshortening. Depending on 
an off-nadir illuminating beam at an elevated target and its terrain slope (aspect angle), layover and shadowing 
phenomena can also occur. Active side-looking SAR imagery has its own radiometric and geometric 
characteristics (Fullerton et al., 1986; Gelautz et al., 1998; Toutin, 1997). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part BI. Amsterdam 2000. 347