2.2 Observations 
Observations are information that we can obtain from various 
sensors. In human tracking under complex situations, people 
may be occluded by others or close to each other even if there 
are no occlusions. We may be able to identify and track multiple 
people that are close to each other by color information, using 
color difference of clothes, for example. However, color 
information is not suitable for identification of people under 
occlusions. On the other hand, range information is robust to 
occlusion thanks to difference of distance to some people closer 
and farther. Nevertheless, range information cannot distinguish 
two people in proximity because the difference in distance is 
slight. In addition, it does not bring information about 
identification of each person because the observed shape is not 
so different from person to person. In consideration of such 
conditions, we use both color and range information, which can 
redeem their demerit each other. We use stereo video camera to 
acquire them simultaneously. 
2.3 Forecasting 
Forecasting step is a step to predict a current state of a system 
from the last state by numerical model. In human tracking, it is 
corresponding to the pedestrian behavior model. It predicts 
pedestrian's current position based on the last position and 
conditions around them. Among many models such as social 
force model and cellular automaton, we use discrete choice 
model in this paper. This is because discrete choice model 
decides the next step of each pedestrian stochastically and can 
deal with interactions between pedestrians. Besides, the 
alternatives of next step are individual for each pedestrian for 
each time. Thus, we consider this forecasting process as non- 
linear process, contrary to many literatures on human tracking, 
simply assuming random walk or linear process (e.g. Ali and 
Dailey (2009)). 
24 Filtering 
Filtering step is a step to balance the predicted current state by 
forecasting step and current observations. In human tracking, it 
is corresponding to the problem to evaluate the likelihood of the 
predicted state as person. Because background is not stable in 
complex situations, we evaluate the similarity of foreground 
area, the position and shape of human. Both color and range 
information is used for this filtering. 
3. GENERAL STATE SPACE MODEL 
3.1 General State Space Model 
This data assimilation system can be described in a form of 
general state space model (Higuchi, 2003). General state space 
model is widely used in many fields recently, for it can deal 
with non-linear time-series model. As shown in figure 1, 
general state space model is composed of state vector x, and 
Observation vector z, State vector is a vector of variables of 
human position and shape, which cannot be observed directly. 
Observation vector is a vector of variables of color and range, 
which we can observe directly from sensors. Then we define 
observation model p(z/x,), a probability distribution of Z, on the 
condition of x, and system model p(xjx,;), a probability 
distribution of x, on the condition of x,,. After we obtain zy, = 
Ui 7,,..., z,}, series of observations from time 1 to f, X, is 
obtained by maximum a posteriori probability (MAP) estimate. 
   
According to Bayes' theorem, the posterior distribution of X, is 
as follows: 
p(x, | z,) oc plz, | X,)p(x, | Zi) 
(D 
= p, | X, j| p(x, | X,, )p(x, , | Zp, Yd, , 
In this equation, p(z/x,) is observation model, P(XiX,.1) is system 
model and p(x, ;[z;.,.;) is the estimation result at time #-1. 
According to the general state space model, human tracking is 
processed like this: First, prior probability of. X, is calculated by 
applying system model to the probability distribution of Mel: 
Then obtained prior probability of x, is combined with 
observation z,, and posteriori probability of x, is calculated. In 
this framework, we need to define state vector X, and 
observation vector z, and model system model P(Xix.1) and 
observation model p(z/x;)). We explain about their definition in 
section 4. 
  
State Vector x 
- cannot be observed directly 
(Human position and shape) System Model 
p(x, |x.) 
  
  
  
  
  
Observation Model 
rz |x) 
Observation Vector z 
- can be observed directly 
(Color/range information) 
  
  
  
Figure 1. General state space model 
3.2 Particle Filter 
To estimate a state vector, we need to calculate probability 
distributions in the equation (1) successively. We use particle 
filter for this calculation. Particle filter is a method to 
approximate the conditional distribution discretely by number 
of particles sampled from that distribution (Gordon et al., 1993). 
Calculation of the particle filter is processing as follows and in 
figure 2: 
I. Approximating the conditional distribution p(X,.i|z;..;) by 
number of particles independently sampled with weight 
(observation model). 
2. Resampling particles with equal weight according to the 
weight of each particle sampled at step 1. 
3. Moving each particle obtained at step 2 according to the 
system model p(x,|x,.,). 
4. Weighting particles according to the observation model 
(zx). j 
5. Estimating x, as the expected value of weighted particles 
obtained at step 4. 
  
    
   
  
   
   
   
   
   
    
    
    
   
  
  
  
  
  
  
  
   
    
   
  
  
  
  
   
   
    
    
  
     
   
  
  
   
   
  
     
   
  
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