Estimating the Number of Pedestrians by Doppler Radar
Sho Komatsubara∗, Kohei Yamamoto†, Motoko Tachibana†,
Kurato Maeno† and Toshinari Kamakura‡
Abstract — In the literature, many researchers study human walking inside the room known as gait analysis by video
cameras[1, 2, 3]. We are concerned with behaviors of pedestrians outdoor, especially on the public sidewalk. However, wecannot conduct experiments using video cameras from the view point of privacy. In this article, we study the behavior ofa group of pedestrians outside with Doppler radar and propose the method of estimating the number of pedestrians in agroup. The size of the group is important to investigate the group property in the first place.

Keyword: Fourier transform; Kalman filter; Doppler radar
1Introduction

We often see a group of people walking side by side on the street. It is dangerous that so big cluster
pedestrians are walking in the narrow sidewalk and it may be prohibited in law when the behavior
is too dangerous. When these in no independent sidewalk, it will happen to get serious accidents byautomobiles and bikes. Therefore, we would like to investigate the property of groups of pedestrians.
One of the important knowledges is the size of the group. In this article, we propose a statistical methodof estimating the group size.
Doppler radar is useful for the detection of pedestrians[4]. Doppler radar responds to only moving
object. In addition, it is able to measure its speed approximately. We use multiple-frequency continuous
wave (CW) Doppler radar. The radar can measure not only speed of moving objects but also its distanceand direction. In our experiences of analysis of walking, low pass filter (cutting oﬀ high frequency ofsignals) should be useful (described the suitable in the later section). As amplitude of the response ofpedestrians is the stronger the response to the Doppler sensor, we arrange the data into thirty divided
data set in the descending order. Then, we can construct the new algorithm based on these dataassuming the multivariate normal distribution.
2Experiments

Our experiment conditions are as follows:• The subjects approach from 40 meters front of the radar and walks to 5 meters to the radar.
• On the way to walk, there are makers to make subjects walk on the straight line.
• When more than two subjects are walking, they walk in a row.
• The subjects walk as usual way.
We use multiple-frequency continuous wave Doppler radar. Specifications of the radar are as follows.
• Frequencies of transmission wave are 24.1950 [GHz], 24.1952 [GHz] and 24.1958 [GHz].
• The number of patches is 3, and its intervals are 1.4 [cm].
• Sampling rates are 50,000 [Hz] for each frequencies.
∗ Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan, E-mail:a12.x3hd@g.chuo-u.ac.jp, Tel: +81-3-3817-1740† Corporate R&D Center, Information & Technologies Planning Group, Oki Electric Industry Co., Ltd. 1-16-8 Chuo, Warabi-shi,Saitama, 335-8510 Japan‡ Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

2

Amplitude(dB)

0

Frequency (kHz)

1.5

−5−10

1−15−200.5−250−300246Time (s)Figure 1: Spectrogram of a single runner

Figure 2: Locations and intensities after removing noises
33.1Our method
Remove the noise

For our analysis, we need to remove the noise from the raw signal of the pedestrian obtained by
the experiment, checking the frequency band of the pedestrian by Fourier transform. As a result ofchecking, we regard that the suitable low pass filter can be set to less than 1,200 [Hz]. Figure 1 is thespectrogram of a single runner for Fourier transform. We can see that the signal over 1,200 [Hz] isvery few. Responses appear above this threshold if the walking speed becomes faster than this runner.
Then, we set this threshold as the low pass filter upper bound.
Figure 2 is the plot of locations and their intensities of amplitude from the signal. Here we note thatnoises are removed after applying our low pass filter.
3.2

Estimation of group size

In the following, we briefly explain our detection method. Firstly, we divide signals into the sub data
set of every thirty coordinates in descending order of amplitude. For each data set ( xi (i = 1, · · · , N) ),we assume that xi has two-dimensional normal distribution N(µi , Σi ). Ellipses in Figure 3 and Figure
4 show confidence regions of the estimated distribution for a single pedestrian and five pedestrians,5 10y−15−5 0−5 0−15y

5 10respectively. The location of pedestrian group is predicted by estimated parameter µ̂i .
(i)
For estimating the number of pedestrians, we use the eigenvalue λ2 which is smaller one in Σ̂i .
(i)Figure 5 shows the relation of λ2 and the Euclidean distance Ri from the pedestrian to the radar foreach number of pedestrians. We assume that these parameters follow a state model and Kalman filter(i)for estimating their state with their observed values. The estimated λ2 ’s and Ri ’s are shown in Figure
6.

010203040

50

010x

1.04050

Figure 4: Confidence region of fivepedestrians

The number of pedestrians
123
4
5

0.0

0.2

0.4

0.6

0.8

30x

Figure 3: Confidence region of a single pedestrianlambda22005

1015202530

R[m]Figure 5: Relation of R and λ2

4Results

In this paper, we discussed the problem of the estimation of the pedestrians’ group size. Figure 6(i)shows the relation of λ2 and Ri that smoother series of Figure 5 by Kalman filter. We see that series
are distinguished for each number of pedestrians when the value of R is small. Therefore, we candistinguish the size of the pedestrian group.

1.0
0.8
0.6
0.4
0.0

0.2

lambda2

The number of pedestrians
123
4
50

5

10

15

20

2530

R[m]Figure 6: Relation of R and λ2 by Kalman filter
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