Corresponding author. 
A QUATERNARY PROTOTYPE FOR SPATIOTEMPORAL ANALYSIS OF 
PERMANENT SCATTER INTERFEROMETRY 
J. Wu 2, *, J. Cai\ C. Hu a , F. Xiao 3 , C. Liu a 
aDept. of Surveying and Geo-Informatics, Tongji University, 1239 Siping Road, Shanghai, 200092, China- 
(jcwu,cwhu)@mail.tongji.edu.cn, xfxf2001 @ 163.com, 290202.student@sina.com 
blnstitute of Geodesy, Stuttgart University, Geschwister-Scholl-Str. 24D, 70174 Stuttgart, Germany - cai@gis.uni- 
stuttgart.de 
Commission VII, WG VII/2 
KEY WORDS: Satellite Remote Sensing, Modeling, interferometric SAR (InSAR), SpatioTemporal Analysis, Ground 
Deformation Hazards 
ABSTRACT: 
In this paper, a set of quaternary arc time series of the double phase differences formed by a PS (Permanent Scatter) with its 
surrounding four PSs in each quadrant are processed together, where the spatial constrains on the parameters are included directly in 
the adjustment model. Equations of this spatiotemporal analysis model are formulated. A simulation example using this new method 
is presented. It shows that a priori information of the crustal deformation can be integrated into the integer least squares adjustment 
model to improve the accuracy of parameters estimated. 
1. INTRUDUCTION 
Repeat-pass satellites SAR interferometry (InSAR) technology 
has been used for providing EDMs with meter accuracy and 
terrain deformations with millimetric accuracy (Hanssen, 2001). 
It has significant advantages over traditional geodetic methods 
for its larger spatial coverage with high spatial resolutions and 
all weather running. InSAR technology has been used for 
crustal deformation monitoring, such as ground subsidence, 
slope slides, volcanoes and so on. However, the essential 
limitations of InSAR are due to temporal and geometrical 
decorrelation and atmospheric inhomogeneities effects on 
interferometric phases. In 1999, a new interferometric method 
based on permanent scatters, named PS-InSAR is proposed 
(Ferretti, et al., 1999). This method uses the long time reliable 
coherence properties of PSs to overcome the temporal and 
geometrical decorrelation and also uses the time series of 
interferometric phase differences of adjacent PSs to eliminate 
the effects of the atmospheric inhomogeneities. Actually, in 
Permanent Scatter Interferometry (PSI), a stack of N differential 
interferograms of PSs are analyzed for phase unwrapping and 
deformation parameters estimation. The conventional method 
processes the time series of phase differences of the adjacent 
PSs (usually called as double difference of arcs) using the 
Integer Least Squares (ILS) method, such as the LAMBDA 
(Least squares AMBiguity Decorrelation Adjustment method) 
(Teunissen, 1995). Then the spatial closure conditions among 
arcs are applied for validations and corrections of phase 
ambiguities and parameters of models estimated (Kampes, 
2006). And the temporal and spatial information in the 
interferograms are used separately. This PSI method sometimes 
fails to give correct estimations, so an integrated spatiotemporal 
analysis method is expected to be able to solve this kind of 
problem more efficiently. 
Considering a set of quaternary arcs of time series radiated from 
one chosen PS bearing both spatial and temporal information of 
model parameters, we use these quaternary arcs of time series 
as an elementary adjustment cell for double difference phase 
ambiguity estimation. At first a prototype of the quaternary 
spatiotemporal adjustment model is given. Then a simulated 
example is demonstrated and the results are obtained. At last a 
conclusion of this research is given. 
2. QUATERNARY ADJUSTMENT MODEL 
Supposing we have N+l SLC SAR images, based on the 
optimal baseline (spatial and temporal) distribution (Adam, et 
al., 2004), one image is chosen as master and the others as 
slaves. Each slave image has been coregistered with the master 
and N interferograms are obtained. With methods based on 
temporal stability of amplitudes or phases of a pixel, the PS 
candidates can be obtained (Kampes, 2006; Hooper, 2006). On 
each PSs, the wrapped phase <j>* in differential interferogram k 
can be decomposed to 
=m*,+<c+<o<o <» 
where W {■} is the wrapping operator, is the phase caused 
by uncompensated topography, <fl k d is the phase caused by 
displacement of the target in the time between master and 
corresponding slave image acquisitions, a is the phase caused 
by atmospheric delays, and ^ is the additive noise term, the 
subscript x presents the position of the PS.