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In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
Figure 1. Phase of one interferogram of the stack overlaid on the mean amplitude image. 
compared to PS densities found by Barnier et al. (2009), which angle; 
can be explained by the quite strict selection criteria. It can be 
seen, that many PS reside at building façades. We expect those i n this paper we are just interested in estimating the residual 
to be generated by structures such as windows or balconies. For topography to get information about a scatterers 3D position, 
some PS it is not clear if they are caused by scattering at the We use a standard PS approach following the ideas of Ferretti et 
façade or the roof of a building since both target areas may be a /. (2000) and Liu et al. (2009) here. The phase due to 
mapped to the same image position. deformation is modelled as a linear function of time. 
After the initial selection signal processing is carried out for the Atmosphere and effects related to orbit errors are assumed to be 
candidate set, in order to discriminate between the respective low p ass components in space. Finally residual topographic 
contributions forming the interferometric phase, which can be phase is a linear function of the effective spatial baseline 
modelled according to Hooper et al. (2007) as separating every interferometric image pair. 
dispersion is a good estimate of a scatterer’s phase stability if 
the scatterer's signal exhibits a high signal to noise ratio. 
However, the quality of resolution cells with low signal to noise 
ratio is overestimated, leading to the necessity to set a quite 
strict threshold in the beginning to avoid false positives. We 
choose the amplitude dispersion threshold to be 0.2, to have a 
negligible number of those. Additionally, groups of adjacent PS 
are thinned out by just considering the best PS in a 4 
connectivity neighbourhood. The distribution of the PS is 
illustrated in Figure 1 overlaid on the mean amplitude image of 
the TSX data stack. The colours represent phase values of one 
interferogram. 
• Acp orb x i denotes the phase emerging from errors in the 
satellites orbit determination; 
• Acpe X;i is called look angle error and is caused by two 
effects. These are contributions due to residual 
topographic phase components and deviation of the 
pixels phase centre from its geometric centre in range 
direction. The latter effect is considered to be negligible 
because of the high resolution of the data. The residual 
topography terms the vertical distance between the 
reference surface and the PS. In this case the WGS 84 
ellipsoid is used as a reference surface. 
• tPn,x,i is the phase noise which is largely caused by 
changes of the pixels reflectivity with time and look 
The PS density is about 20 000 PS per km 2 , which is quite low 
where 
• tpcj e f >x> i contains the phase due to the surface movement 
projected to the sensors line of sight; 
In a first step phase differences between neighbouring PS are 
calculated, which mainly cancels out the phase caused by 
atmosphere and orbit errors. Thereby the neighbourhood is 
given by a Delaunay triangulation. For every phase difference 
between two PS at positions x and y velocity and height 
increments denoted by v xy and H xy respectively are calculated 
using a coherence maximisation approach (see for instance Liu 
et al. (2009)), which can be stated as 
• 9atm,x,i is the phase due to different atmospheric states 
during master and slave acquisitions;