This section describes the pedestrian counting system, binary sensor models, the compound-eye sensor model used in the system, and a pedestrian mobility model.
System overview
Figure 1 shows the pedestrian counting system, which consists of a monitoring server and sensor nodes. A sensor node consists of a wireless transceiver such as MICAz, IRIS Mote (IRIS Mote 2014) and Neo Mote (Neo Mote 2014) and multiple binary sensors, i.e. compound-eye sensor. A sensor node sends a data packet to the monitoring server when the output of its binary sensor changes. A data packet contains the sensor’s output value and a timestamp. The monitoring server uses the presence or absence of information from sensors for estimating the number of pedestrians walking in opposite directions. For simplicity, we assume that the system has a single sensor node, that data packets are reliably sent to the monitoring server, and that transmission latency is negligible.
In this section, the system is used for wide streets where a large number of pedestrians walk in two directions, such as in a local shopping street and a sidewalk in a downtown area. As the compound-eye sensor, we use mat-type binary sensors, such as piezo sensors (Measurement specialties Piezo Film Sensor 2014), on grid lines.
Binary sensor model
We assume a rectangular sensing region as shown in Figure 2. We refer to the distance of one side of the sensing region as the “sensing length.” We denote the sensing length for the pedestrians’ movement direction as r
x
and the sensing length for the vertical direction of the pedestrians’ movement direction as r
y
. A binary sensor outputs a value of 1 when a foot of pedestrian steps on its sensing region and 0 when a foot of pedestrian steps away from its sensing region.
Compound-eye sensor model
The compound-eye sensor consists of multiple binary sensors bx,y (1≤x≤2,1≤y≤N) which are on grid lines by placing two binary sensors along the pedestrians’ movement direction, and N binary sensors along the vertical direction of the pedestrians’ movement direction as shown in Figure 3.
The region that is inside of sensing region of any binary sensor is denoted as the sensing region of the compound-eye sensor. The output of sensor bx,y at time t is denoted as ox,y,t∈{0,1}. Furthermore, the output of the compound-eye sensor at time t is denoted as
When all outputs of binary sensors are 0, the number of pedestrians in the sensing region of the compound-eye sensor can be estimated as zero. We refer to this as an observable state. For other outputs the number of pedestrians cannot be determined, and this is referred to as an unobservable state. The interval from the moment when the state of the compound-eye sensor undergoes transition from an observable state to an unobservable state to the moment when the state undergoes transition to an observable state again is denoted as the unobservable interval.
Mobility model of pedestrians
We need to decide location where a foot of a pedestrian steps, timing when a foot of a pedestrian steps on or steps away from ground since mat-type binary sensors are assumed. Therefore, we need a mobility model of pedestrians.
We first define the direction of moving from binary sensor b1,y toward binary sensor b2,y as right, and the opposite direction as left. We assume that pedestrians move either left (“leftward” pedestrians) or right (“rightward”) within the monitoring area, and they do not change their movement direction or velocity. The velocity distribution of pedestrians v is a normal distribution with mean v
m
and deviation v
σ
.
The step length of pedestrians s
l
follows a normal distribution with average sl,m and deviation sl,σ. The step width s
w
, the foot length f
l
, and the foot width f
w
of pedestrians are constant values since their variations are negligible compared to the variation of velocity of pedestrians v and that of step length of pedestrians s
l
. Figure 4 shows the step length, the step width, the foot length, and the foot width of pedestrians.
Next, we explain the timing of stepping on and stepping away from the ground. According to (Akutsu 1975), when we focus on one leg of pedestrian, the walking motion is classified four states as shown in Figure 5. For example, a pedestrian’s right leg steps away from the ground in the state 1, moves in the air in the state 2, steps on the ground in the state 3, and supports stepping away of a left leg in the state 4. In this paper, based on the walking motion model, the timing of stepping on and stepping away from the ground is defined as follows. The position of a pedestrian is defined as a position of groin. A back leg steps away from the ground when the position of a pedestrian reaches to the distance of the step length from the position of the back leg. An anterior leg steps on the ground when the position of the pedestrian reaches to half distance of the step length from the position of the back leg.