Vol. XXXVIII, Part 7B 
In: Wagner W„ Székely. B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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A NEW RIGOROUS SENSOR MODEL FOR RADAR IMAGERY 
BASED ON EXTERIOR ORIENTATION ELEMENTS 
Chunquan CHENG a ’ b ’*, Jixian ZHANG a , Kazhong DENG b , Li ZHANG a 
a Chinese Academy of Surveying and Mapping,Beijing,BeiJing,China. - (cspring, Zhangjx, Zhangl)@casm.ac.cn 
b China University of Mining and Technology,Xuzhou,China - kzdeng@cumt.edu.cn 
Commission VII, WG VII/1 
KEY WORDS: Imaging Equation,SAR, Side-Looking Radar, Sensor Model, Image Positioning, Geocoding, photogrammetry. 
ABSTRACT: 
Imaging equations are always considered as the most essential and basic part in photogrammetry and image mapping with remote 
sensing images. Rigourism and conciseness should be held as their basic characteristics.In this paper,using sensor exterior 
orientation including three lines and two attitude elements as the orientation parameters, new imaging equations for side-looking 
radar or SAR image positioning were derived. The model was based on the distance condition between sensor and object point and 
the azimuth condition of sensor scanning plane including antenna and radar beam center. Three forms of range-coplanarity equation 
were derived, the first form was in the tangent plane rectangular coordinate system, the second was in the geocentric rectangular 
coordinate system, and the third was the range-coplanarity equation with coordinates of image point as explicit function. The model 
could be easily used for side-looking radar and SAR image processing in photogrammetry field. 
1. INTRODUCTION 
1.1 The existing radar imaging equations 
(1) Based on Range-Doppler condition model 
R-D model is built with distance conditions and Doppler 
conditions, It is F.Leberl model when Doppler frequency value 
is set to zero. 11,21 . 
(2) Collinearity equation model: 
The imaging equation based on collinearity equation is 
similar with that based on optical images. This equation uses 
exterior orientation elements as its orientation parameters. 
Generally, Radar images are processed as optical linear array 
sensor images. Some scholars have made a modification on the 
collonearity equation, e.g. G.Konecny et al. [3] put forward an 
improved collinearity equation in which the effect of terrain on 
image point location was taken into account. 
(3) Polynomial model: 
The application of general polynomial model in radar 
images is similar to that in optical images. The imaging 
mechanism was not considered in this model, while the 
polynomial model was used in it to convert all images by the 
same translation type. 
1.2 The deficiency of R-D and collinearity equation model 
in Image Positioning 
Doppler frequency is directly correlated with the speed of 
the sensor related to the object surveyed. Thouth it is difficult 
to provide Doppler frequency of every object point, they can 
be acquired by assuming that it is a fixed value, or acquired by 
linear or polynomial model in side-looking radar images. 
While the discrepancy of doppler frequency may rapid 
increased by polynomial model in front or squint side-looking 
radar images, it may influence the precision of image 
positioning. 
Researchers in the field of optical photogrammetry expected 
that the same orientation parameters as those in optical image 
orientation could be used in radar image positioning, thus 
collonearity equation could be introduced into radar images 
accordingly. Because of the differences in imaging mechanisms 
between optical and radar sensor, the precision of radar image 
positioning is often low with collonearity equation. Many 
scholars had made modifications on the model 131 , but the image 
equations are more complicated. By now, the major application 
of collonearity equation in radar images is geocoding, and 
complex photogrammetric processing such as in stereo 
positioning, especially in block adjustment is still uncommon. 
2. COPLANARITY EQUATION 
2.1 The principle of orientation with range-coplanarity 
equation 
The model is established with the range-coplanarity equation 
by satisfying the range condition and coplanarity condition. 
The range between the sensor and ground object point is 
equal to the calculation values by image column coordinate 
which is same as range condition in R-D model. 
* Corresponding author.