In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
500 
_ 1 
Y —max — 
'*y N 
v H 
V XY I 11 XV 
N I J‘ 
2> 
i=1 
An Bj~ An 
(3) 
where 
• Bj is the spatial baseline, 
• Tj is the temporal baseline, 
• X is the wavelength of the sensor, 
• R is the distance from sensor to target, 
• 0 is the off nadir angle of the radar. 
The term y xy denotes the so called temporal coherence factor and 
serves as quality measure to evaluate how good the observations 
fit the assumed model. Results having a value below 0.7 are 
removed before the next step. 
In order to calculate the PS height from the height increment a 
overdetermined system of linear equation has to be solved, 
which is done by means of an iteratively reweighted least 
squares approach. Within the inversion of this system remaining 
gross errors are removed from the data (see Liu et al. (2009) for 
reference). 
The result is a height and a velocity estimate for every PS 
relative to a reference PS in the scene. While the height can be 
estimated with submeter accuracy, accuracies of the subsidence 
rate are in the order of few millimetres per year. The geocoded 
PS overlaid to the 3D model used for simulation are shown in 
Figure 2. 3 
Figure 2. 3D model of the Sony-Center overlaid with PS 
3. SAR SIMULATION 
3.1 3D city model 
The 3D city model, which was is the basis for simulation was 
derived from airborne laser scanning data. We used the free 
software tool sketchup to reconstruct surfaces from the point 
cloud. The whole procedure was conducted manually, i.e., no 
meshing algorithms were used. The result is displayed in 
Figure 2 together with the geocoded PS. 
3.2 Fast ray-tracing SAR simulation approach 
SAR simulations aiming at precise prediction of PS positions 
require high geometrical correctness, whilst radiometric features 
are less important. According to the classification of 
Franceschetti et al. (1995) SAR simulation systems can be 
differentiated into raw data and image simulation systems. For 
our application SAR image simulation systems are feasible, 
because the focus is on the geometry. To ensure geometrical 
correctness together with computational efficiency, we use ray 
tracing for our SAR simulation. Ray-tracing based SAR 
simulations can simulate the SAR geometry precisely, while 
keeping the amount of new software to be coded small by 
reusing and editing ray tracing tools developed for computer 
graphics applications (see e.g. Auer et al. 2010). 
In our experiments we use a SAR simulator prototype based on 
the GPU ray-tracing library Optix™ from NVIDIA (2009). 
Optix™ traces the rays by using the tremendous calculation 
speed of modem graphics processing units (GPU), allowing for 
real-time or near real-time ray tracing. By adjusting the library, 
a real-time SAR simulator can be developed. 
In this way, a fast, widely used, and extensively tested ray 
tracing library can be applied, which speeds up the developing 
process. 
The simulation system we used was tailored for airborne SAR 
systems. Simulating TerraS AR-X data required some 
adjustments. The distance between the sensor and the objects on 
the ground are much larger in the spacebome case, which 
caused troubles due to the limits of the 32-bit floating point 
values used in data processing. The real distances were just too 
large to be simulated. By setting the simulated sensor distance 
to around 200 km, we believe we found an acceptable 
compromise. The differences in the simulated geometry due are 
rather small, especially compared to the errors in the simulated 
building models. 
The radiometric simulation is based on the model of Zribi et al. 
(2006) model, which does not exactly fit for urban 
environments. Because for our application the simulated 
radiometry does not need to be very accurate, we believe this is 
an acceptable simplification. 
Figure 3. Mean amplitude image of the data stack