The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
Normally pairs of nearby PSs are chosen to form a number of 
arcs, the phase differences of these arcs are thought to be 
atmospheric delay free, i.e. 
(2) 
variances for topographic errors and deformation rates are 
added, however the spatial correlations of deformation rates are 
considered and relevant variance and covariances for 
deformation rate differences are formulated under assumption 
of constant strain rate tensor. The equation (5) can be written in 
a matrix form as: 
where x,y are nearby points. According to Kampes (2006), ^ A x a + Bf + e 
the phase differences of arcs caused by topographic error and 
deformation can be written as the following: 
where, 
(6) 
4 n 
/1 
T K Av 
(3) 
(4) 
where &h x y is the topographic error difference between 
x and y and Av v is the SOL(Sight of Looking) rate 
difference between x and y , and a linear SOL rate is assumed 
for the deformation; T k is the time baseline, and equals 
acquisition time difference between slave image k and the 
master image; Jf k is an attitude to phase changing factor which 
is a function of interferometric baseline and radar wave length. 
So the observation equation of the wrapped double phase 
difference for the arc time series is 
Ti = 
7^ 
2b 
iN 
■■■ r 0,1 ’ 
...^0,4 5^0,4 5 
AN -\T 
*** r0,4 J 
a = 
[a 0 1 ,<2 0 ,i v 
V 
•• a 0,l’- 
1 2 
..a 04 ,a 04 , 
_N -,T 
...<3 0 4 J 4AM 
b = 
[ A/Zq i , A/?q 2, Ah t 
0,3 > ^^0,4 ’ ^ V 0,l ’ ^ V 0,2 ’ L 
e - 
\e l e 2 
L e o,i’ e o,i’" 
e N 
• c o,i 
e 1 e 2 
• e 0,4> c 0,4 v 
e 0 4 \ 4 AM 9 
they are wrapped phase difference vector, unknown ambiguity 
vector, unknown topographic error and deformation rate vector, 
and white noise error vector respectively; A ] , 5, are 
respectively 4N x 47V and 4N x 8 coefficient matrix. 
The pseudo observation equations are added as: 
y 2 - A 2 a + B 2 b + e 2 
(7) 
= —2na k + J3 X ■ Ah x 
— r* Av„+ e ' 
(5) 
where A 2 is an 8x4N matrix with all elements zero, B 2 is 
an 8 x 8 identity matrix, and y 2 - 0 • The covariance matrix of 
y and y 2 are assumed as following: 
where a* is the integer ambiguity and e k is white noise. This is 
an underdetermined problem with N equations for N+2 
unknown parameters. Pseudo observations which composed of 
assumed, or statistical variances of topographic errors and 
deformation rates have been added for solving this problem in 
Kampes (2006) with a LAMDA method. There is no spatial 
information has been applied in these pseudo observations. In 
this paper we expanded the equation (5) to a set of quaternary 
arc series as in Fig.l. Then we have 4N equations for 4N+8 
unknown parameters. 
Figured Quaternary arcs by PSs 
For solving this quaternary arc underdetermined equations, 
similar pseudo observations with value of zeros and a priori 
Q» 
q;; c1 o o o 
0 Q£ 2 0 0 
o 0 Q£ 3 0 
0 0 0 Q£* 
(8) 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
0 
fj, 2 
*13 
0-14 
0 
0 
0 
0 
C7 2 i 
d 
cr 23 
a 24 
0 
0 
0 
0 
CJ31 
^32 
0-34 
0 
0 
0 
0 
CT 41 
^42 
cr 43 
crj 
where Q™’ is variance matrix of the i‘ h arc phase difference 
observations which can be estimated from error propagation 
law (Kampes, 2006); & is the standard deviation of 
topographic error differences, a 2 d is the variance of deformation 
rate difference and <j is the covariance of deformation rate 
v 
difference between the I th and the j th arc. The SOL deformation