International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
m -4 
Q a a 4(t,,, -f) Qs, (7) 
where, 
Os : covariance matrix for the noise components of 
positions at period k. 
The residual vector for the observations at period k+1 is formed 
as follows: 
Lit + Visa = AeaYea (8) 
| : measurements at time t, 
Vikel : residuals 
Aya : coefficients matrix 
Y ol . State vector at time t, | 
The matrix form of functional and stochastic models of Kalman 
filtering technique can be obtained by combining Eq. 4 and Eq. 
8 as follows: 
KEK pe NOT D Or. sn ? (9) 
Ir Ata e Vr ka Ne 0 Quia 
By this model, motion parameters and cofactor matrix are 
computed. Kalman gain matrix is given as follows: 
Gi = Orr. eri Quin + AO. ala? (10) 
= Ow ea aD 
Using the equations above, innovation vector dy, State vector 
filtered at time ty; y, Hd? predicted state vector; Vy, 
residual vector of observations at time ty can be computed by 
the following equation: 
di. - Au I 
Y, I- Gyr den Gi v (1 1) 
Vr ku | Gin Ain Gin p. | 
VL Oy x Dre Qaa 
Actually, the filtering phase is based on classical least squares 
adjustment. The most important difference from the classical 
adjustment procedure is that, contrary to the classical approach, 
in the filtering the number of observations can be less than the 
number of unknowns. Through the filtering, adjusted values of 
state unknowns are computed using weighted combination of 
measurements and a priori estimations (Gülal, 1999; Bayrak 
and Yalçinkaya, 2002). 
4. NUMERICAL APPLICATION 
In order to determine the point displacements in the landslide 
area, a deformation network consisting of 13 points was set up. 
The control points were established in stable areas out of the 
landslide region. The locations of the deformation points were 
determined according to the geotechnical investigations in the 
landslide region. The geodetic measurements used in the project 
were GPS measurements that were carried out in four periods 
between July 1996 and March 1998. In this study, the 
measurements of periods March 1997, October 1997 and March 
1998 have been evaluated. The GPS data was collected in rapid 
static mode using 6 Leica SR399 and 4 Trimble SSI receivers. 
In all periods 2 sessions of GPS observations (10 minutes at 
each point) were realised. The data has been processed using 
commercial Leica SKI-Pro software. The measurements in each 
period have been adjusted through free network adjustment 
procedure and their adjusted values and variance-covariance 
matrix have been computed (Acar et al., 2003). 
As a first step, static deformation analyses were carried out 
through the evaluation of adjusted coordinates and their 
variance-covariance information. In the analysis, Codeka3D 
deformation analysis software was used. 
In the second part of the study, the kinematic deformation 
analysis procedure based on Kalman filtering technique as 
described in the previous section has been applied. By the 
application of this model, the motion parameters of network 
points have been computed. Afterwards, whether or not the 
obtained results are statistically significant have been tested. 
The maximum values of the velocities and accelerations of the 
points found after the kinematic analysis are given below in 
Table 1. 
  
  
  
  
Position Velocities Accelerations 
(cm/month) (cm/month^2) 
X 41.75 2.663 
Y -42.66 -2.787 
Z -23.32 -1.506 
  
  
  
  
  
Table 1 Maximum velocities and accelerations 
As the final step, the solutions obtained through the kinematic 
model have been compared with the static deformation analysis 
results. The comparison showed that both models give almost 
identical results. The horizontal and vertical displacements 
obtained through kinematic deformation analysis are given in 
Table 2. As seen from the table, on 4 network points, horizontal 
and vertical displacements took place. Despite having no 
vertical displacement, Point 9 has horizontal movements. This 
is the only difference from the static deformation analysis 
where this point has been found stable. 
  
  
  
  
  
  
  
  
  
Point dx (cm) 1 dz (cm) 
9 0.58 3.65 1.11 
1886 4.30 -9.39 -12.12 
1996 116.99 -110.17 -112.83 
2396 367.74 -363.98 -202.01 
2496 150.43 -147.74 -140.834 
  
  
  
Table 2 Point displacements 
684 
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