International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
deformation measurements and analysis were done (Acar et al., 
of the position with respect to time. Matrix form of the motion 
2003). 
model used for the prediction of motion parameters by Kalman 
filtering technique in 3D networks can be given as follows: 
According to the geotechnical investigations, excluding the 
artificial disturbance of natural equilibrium, the reason of soil 
  
  
  
  
    
       
  
movements depends upon the changes in conditions related to rad Te 
underground water, seismic forces arising after earthquakes and 
the decrease in sliding strength in fissured (capilar fissures) and y 
heavily consolidated clays. The area where the study was z a Z (2) 
carried out is an old landslide region where slope equilibrium P [ I(t, -1) Tu > % 
was formed gradually. As a result of movements in the form of + r 
(mz 170 Q Face wo z > Cp > a 1 Y = V = 0 I T a =) V 
small-sized flours due to surface water and the settlement in the 
area, the equilibrium was disturbed, causing mass movements V. 0 0 / V. 
(Fig.l) In order to prevent soil movements, drainage was d. jail. 
performed (Altan et al, 1994). a a 
y y 
==. Base level of rosion during pre lacal time La: Te LY: Je 
| d — Measurement area ——l He New formation 
7th an L—— Old formation ——31 
Ek Se Von 2 lun or (3) 
related 
n i I | ion » Current Sea-level h 
bained 20 — — 7? Where 
Old Sea-level 
hathad lp = Emel 2 
mostly Yeas : state vector at time bet 
of the Y : state vector at time f 
08 Figure 1 The landslide model of the Büyükçekmece region T uu : transition matrix from time Lot at 
esie Altan et al., 1994 © ; ; 
second 8l. 1994) I : unit matrix 
s of the : 
rmation Eq. 3 is the basic prediction equation of Kalman Filtering. The 
les. The 3. KINEMATIC DEFORMATION MODEL system noise is considered as the noise matrix S that consists of 
cements the terms of the last column given in Eq. (3). The noise matrix S 
Time-dependent 3D kinematic model that contains position, is given below in Eq. (6). 
velocity and acceleration can be expressed by the following 
formula: 
c points YatfTarh +81, ta, (4) 
ited. In 
relation ; ] 
pO) _ (k) _ =. nn 2 
so taken NN eA hv ) a 7n) ay 2T TT S s? (5) 
I PF, belo = SELF o Y k^ kel. Tn ui kel 
E 7(k+1 (k) 2 I 
plied so Yum (tert )vy t2 7h) ay () 
Kalman s 
ic + 3 1 9 5 
analysis gun = zn Fl = WW, +, “Ya : ].Qu7hY y 7 ; (6) 
inematic 2 Siu = do en Ga 7H) 
nique is T 
ad been 
sections, where 
analysis where 
XD) y 7) : coordinate of point j at time (t+). period a : the random noise vector between periods t,., 
i 254 n5 
: dame : and t, 
(0 y^ 70 : coordinate of point j at time (t). period e : 
X, SS Pom (6). P Q : the cofactor matrix of state vector at time L 
EA : or n i yn s 
v VI, : velocities of X, Y, Z coordinates of point j : D 
x. py ; id a. : the cofactor matrix of system noises at time t 
Gürpinar a a ai. : accelerations of X, Y, Z coordinates of point j d 
, without Te Cad ; 
uildings, k=1,2,...,1 (i: measurement period number) The random noise vector a is uncertain and as a rule it cannot 
fter the j=1,2,...,n (n: number of points) be measured. Therefore, for a, pseudo observation vector can be 
on the used as a=0. The effect of noise on positions can be determined 
order to Kalman filtering technique is employed for the prediction of from former any bs Sh Xe i motion and 
ettlement present state vector using state vector information of known acceleration, hobs can be ity plaies . The eme 
roughout motion parameters at period t, and the measurements collected of hoise ücce Py em e ene using noise matrix j 
geodetic at period tj. The state vector of motion parameters consists of às given below (Bayrak, Yalçinkaya ). l/ 
position, motion and acceleration variables. The motion and | 
acceleration parameters are the first and the second derivations 
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