or distribution of X; is 
(D 
Z4 Y 
lel, p(Xjx,.1) is system 
ult at time #1. 
el, human tracking is 
of x, is calculated by 
y distribution of x, 
, 18 combined with 
of x, is calculated. In 
state vector x, and 
model p(x/x.;) and 
out their definition in 
stem Model 
p(x, |x) 
servation Model 
pz |x) 
e model 
:alculate probability 
ely. We use particle 
r is a method to 
iscretely by number 
Gordon et al., 1993). 
ng as follows and in 
ition p(X,.1|Z1..1) by 
mpled with weight 
ht according to the 
2 according to the 
observation model 
' weighted particles 
  
  
1. Discrete approximation by weighted particles 
Conditional distribution 
    
2. Resamplin 
  
     
  
Conditional distribution 
p(x, | zi.) 
5. Estimating x, as expected value of this particles 
Figure 2. Calculation flow of particle filter 
4. MODELLING 
In this section, we define and model the components of general 
state space model. 
4.1 State Vector 
State vector is corresponding to the position and shape of each 
person. We define a state vector as an ellipsoid and its 
coordinates, which is human shape and position, shown in 
figure 3. State vector is described as follows: 
X 7 (x, y, z, w, h, d) Q) 
where (x, y, z) = central coordinates of ellipsoid 
(w, h, d) = length of each axis 
   
     
h: height 
x92 
central coordinate 
w: width d'depih 
Figure 3. State vector 
4.0 Observation Vector 
We also define an observation vector as observations from 
sensor. Stereo video camera is used in this work so we acquire 
both color and range information. Observation vector at pixel (i, 
J) 1s as follows: 
Z7 (Xp Yi Zi. lis £i bj) (3) 
where (X, Y, Z) — coordinates of observation point corresponds 
to pixel (i, /) 
(r, g, b) = pixel value of red, green and blue at pixel (i, j) 
     
   
  
  
   
   
   
  
  
  
  
  
   
    
    
   
  
   
    
  
4.3 System Model 
System model explains sequential change of state vector. We 
define system model using simulation model of pedestrian 
behavior. We apply the model by Robin et al. (2009) because 
the parameters are evaluated on real data. This model describes 
features of pedestrian behavior, such as keeping direction, going 
toward destination, accelerating if current velocity is slow and 
vice versa, following the person in front of them and avoiding 
collision. Choice set is fan-shaped shown in figure 4. 
Alternatives of choice set are 33 in total, three for velocity 
(acceleration, constant speed and deceleration) and 11 for angle. 
The utility function is described as follows: 
V. Frs count, wlio | @)keep direction 
tf o dir, La side 
uw num Up la somme 
+B dist, 
c (b) toward destination 
+B Adi, 
e 
x Bl, ue (v, / Vepax ) à (4) 
AncelS 
= Lia tel on (v, / Vinax LS ) i 
A, iccHS. 
HA octets! nue (v, / Vina ) € 
(c) free flow acceleration 
BD A A 
tL, cele ce Kr ac DE ; Av, A 6; 
; = , ?(d) leader - follower 
I 2 at De Ay A i 
,dec ^ v,dec 
+/ 
v,dec 
I, ace" AVE Ax } (e) collison avoidance 
where f, 4, a, p, y, À = parameters 
Vmax = Maximum speed of pedestrian (constant) 
Vmaus = if pedestrian's current speed is below vga, 
utility to accelerate increases (constant) 
I = dummy for each alternatives 
dir = angle between current direction and direction to 
alternatives 
ddir = angle between directions to destination and 
alternatives from current position 
ddist = distance from alternatives to destinations 
D, ^v, AO — distance between pedestrians, difference in 
speed of pedestrians and difference in angle between 
current direction of pedestrians, respectively 
Using this choice model, we define system model as follows: 
XX Vet We (5) 
Where v, is the vector determined according to the choice from 
discrete choice model at time /-1, that is, the alternative with 
maximum utility. w is noise term with its expected value 0 and 
variance 6”. 
       
ACC. Const. Dec. Dec. Const. Acc. 
Figure 4. Choice set from Robin et al. (2009)