Calibrating Depth Sensors for Pedestrian Tracking
Using a Robot as a Movable and Localized Landmark
Mitsuhiko Kimoto
IRC and Graduate School of Science andEngineering.
ATR and Doshisha Univ.
Kyoto, Japankimoto2013@sil.doshisha.ac.jp

Masahiro Shiomi
IRC.
ATR.
Kyoto, Japanm-shiomi@atr.jp

Katsunori Shimohara
Graduate School of Science and Engineering.
Doshisha Univ.
Kyoto, Japankshimoha@mail.doshisha.ac.jp

Norihiro Hagita
IRC
ATR
Kyoto, Japan
hagita@atr.jp

Abstract—Using multiple depth sensors enables us toaccurately track pedestrians in real environments. Accuratepedestrian positions are essential for building an effective
human-centered cyber world provided by location-based services.
In particular, ceiling-mounted depth sensors can robustly trackpeople in such environments. However, one important problem
for this approach is the accurate calibration of the absolutesensor positions. This problem remains unsolved due to limited
range and sensor distortions from a distance. Manual calibrationis complicated and time-consuming, and the existing calibration
method still has several limitations since it used a pedestrian as a
movable landmark. Instead of a human landmark, we propose amethod that uses a mobile robot as a movable and localized
landmark to calibrate each sensor. We compared the calibration
performance of the proposed and existing methods and showedthat the former achieved more accurate calibration for both theabsolute sensor and tracked pedestrian positions. Our proposed
method with a mobile robot not only increased the accuracy ofthe calibration processes but also decreased human efforts.
Keywords—person tracking, sensor calibration, mobile robot

I. INTRODUCTION
Wide-area pedestrian tracking in real environments is
critical for understanding human activities that provide
essential knowledge to build an effective human-centeredcyber world. Various techniques have been proposed, including
sensor networks with multiple RGB cameras, such laser range
finders (LRFs) as the Hokuyo UTM series and the Velodyne
LiDAR series, and such depth sensors as Microsoft Kinect andthe ASUS Xtion series. One promising approach for wide-areapedestrian tracking with a multiple sensor network is using
depth-based sensors on the ceiling, because this approach isrobust to occlusions from the bodies of pedestrians. Moreover,due to using only distance-based information, privacy issues
This research work was supported by JSPS KAKENHI Grant Numbers
JP16K12505, 18H04121, 18H03311, and JP18J12552.
XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Takamasa Iio
Faculty of Engineering, Information and
Systems, and IRC
Tsukuba Univ and ATR.
Tsukuba and Kyoto, Japaniio@iit.tsukuba.ac.jp

are reduced compared to using RGB cameras [1]. In fact, thisapproach is broadly used to track pedestrians in the following
real environments: for understanding the use of space by widearea pedestrian tracking to analyze and anticipate their
behaviors [2], planning approaches for pedestrian [3],providing such location-based services as distributing flyers [4],identifying a specific person using acceleration sensors [5] [6],and avoiding crowded situations due to a robot's existence [7].
One essential problem for such a ceiling-mounted depth
sensor network system is its calibration, i.e., adjusting 6 DOFs
(pan, tilt, role, x, y and z) of each sensor to keep consistentobservations between other sensors. However, common
calibration methods that use shared observations between
sensors are difficult to apply in ceiling-mounted depth sensors.
To the best of our knowledge, only one method has been
proposed that calibrates ceiling-mounted depth sensors forpedestrian tracking [8]. This study used a pedestrian as a
movable landmark to acquire shared observations between
sensors to calibrate relative/absolute sensor position
relationships. But this decision, unfortunately, created several
limitations even though it achieved good calibration accuracy;
its limitations are scrutinized in the next section. Instead of
employing a human landmark, we propose a method that uses amobile robot as both a movable and a localized landmark forcalibrating a sensor network (Fig. 1).
The remainder of this paper is organized as follows.
Section II describes why the common calibration method
cannot be applied to a ceiling-mounted depth sensor network
system for pedestrian tracking and the strengths of ourcalibration method. Section III and IV describe our systemsettings for calibration and its mechanism. Section V describes
the evaluations of our calibration method, and Sections VI andVII respectively describe our discussion and conclusion.

Fig. 1. Ceiling-mounted depth sensors for pedestrian tracking and a mobile
robot as a movable and localized landmark for calibrating sensors

II. PROBLEM DEFINITION
A. Why Can’t the Common Calibration Method be Applied
for Ceiling-Mounted Depth Sensors?
A past study [8] thoroughly summarized the reasons for thedifficulties of applying such common calibration methods asmultiple video camera calibrations [9-11] in ceiling-mounted
depth sensors. We briefly explain them in this section byfollowing [8].
One basic approach for calibrating depth sensors is point
cloud matching, which uses static objects in the backgroundbetween sensors and resembles approaches like SLAM [12, 13].
There are two main reasons why this approach cannot be usedin ceiling-mounted depth sensors: distorted point cloud
information and the difficulties of identifying the sharedfeatures among the sensors. The former reason indicates thatsince ceiling-mounted sensors observe static objects beyond
their nominal range, many measurements are missing, andrange distortion occurs [14]. This phenomenon also
complicates extracting a floor plane, which calibrates the pitch,
the roll, and the height of the sensors. The latter reason
indicates that due to a narrow field of view from ceilingmounted sensors, identifying the features shared among them isoften difficult. This problem also complicates marker-based
calibration, which is another common approach to this problem[15], because many markers are necessary to achieve goodcalibration for ceiling-mounted sensors with narrow sensing
areas.
Based on these reasons, Glas et al. proposed a calibration
method that used the observations of a human landmark for
sensor calibration by integrating LRF and depth sensors [8],because the observations of a human head are typically within
the nominal range of ceiling-mounted depth sensors and thus
do not suffer from distortion. Furthermore, using LRF sensors
for calibration enables systems to easily find sharedobservations among sensors. Even though their study
accurately calibrates ceiling-mounted depth sensors, some
limitations exist. In the next subsection we describe these
problems and describe our approach for solving them.
B. Limitations of Existing Method for Calibrating CeilingMounted Depth Sensor and Our Approach
As described above, the past study proposed a method forcalibrating ceiling-mounted depth sensors by integrating LRF
and depth sensors. However, its method has several limitations.
In this section we describe the problems caused by them.
1) A person needs to walk around to be a movablelandmark: The past study employed a person as a movablelandmark to create shared observations among sensors.

However, it needs additional human resources for calibration,
especially in wide sensing environments. For example, a past
study covered about 900 m2 using more than 50 depth sensors,
but walking this entire environment would be quite strenuous[1].
2) Unstable height due to walking: This problem is related
to using a human landmark. The past study used fixed height
information to calibrate the sensor’s pitch, roll, and height byassuming a person’s height does not change during calibration.
But when a person is walking, her height actually does change.
Of course, since it is difficult for people to maintain the sameheight while walking, this problem is unavoidable with ahuman landmark.
3) Must overlap observation areas of the sensors: The
past study assumed that the coverage area of at least two
sensors will overlap due to shared observations. In otherwords, its approach failed to calibrate a sensor that does notoverlap its sensing area with other sensors. To cover thisproblem, it proposed using an LRF to make an overlapped
sensing area, but this step also increases the total burden to
prepare a calibration system.
4) Absolute sensor position calibration: The past study
used the shared observations among sensors to calibrate theirpositions, but the accuracy of their absolute position
calibration was strongly influenced by their initial settings.
Because the shared observations from the human landmark are
the relative position information based on the initial sensor
positions, if the initial positions are shifted, the calibration
results for the absolute sensor position also shifted.
5) Our approach: As described above, the past study’s
limitations are based on its use of a human landmark. In thisstudy, we solved these limitations with a mobile robot as a
movable and localized landmark. This approach decreasehuman’s efforts to walk around a sensing area as a humanlandmark for a calibration procedure and provides to thecalibration system accurate localized position with stableheight information while moving. Moreover, using a movableand localized landmark enables the system to calibrate asensor that does not overlap its sensing area with others,
because the robot provides global reference points for eachsensor by moving around. The next section describes thedetails of our calibration system design.
III. SYSTEM DESIGN
Figure 2 shows an overview of our entire system, which
consists of depth sensors, a mobile robot, a human-tracking
system, and a calibration system.
A. Depth Sensors
We installed 10 ASUS Xtion Pro Live 3D range sensors as
depth sensors for pedestrian tracking in our experimentenvironment (Fig. 3). The sensors were mounted in rows on theceiling at an average height of 2.6 m, covering a 8.2 m long by
4.5 m wide tracking area. They were attached to the ceilingupside-down in rows in alternate directions to minimize
interference and maximize coverage.

Depth data

Depth
sensorHuman-tracking
systemPosition data

Calibration
systemObserve

Robot

Localized
position data

Fig. 2. Overview of our calibration system
4.5 m

PC

8.2 m

Fig. 3. Sensor arrangement and environment in our study

mobile base, which is controlled using a Robot Operation
System (ROS) framework. For its localization, we used the
Adaptive Monte Carlo Localization (AMCL) method [16],which is a common probabilistic localization algorithm for
ROS-based mobile robots. In our experimental environment,
we made a map for localization beforehand, and the measured
average localization accuracy was in the order of 5 cm.
IV. CALIBRATION MECHANISM
A. Overview
Since we used the robot’s localized position, we cancalibrate each degree of each sensor one by one, unlike the past
study. In other words, using a mobile robot as a movable andlocalized landmark, we can directly calibrate the absolute
positions and the degrees for each sensor. First, the systemcalibrates the pitch, the roll, and z so all the sensors are
coplanar and then calibrates the yaw, x, and y for all sensors toadjust their absolute positions.
B. Pitch-Roll-Z Calibration
For calibrating each sensor, the system first processes pitch(𝜃) and roll (𝜓) to fit between the planes of the head part
observed from the sensors and localized from the robot. For the
pitch and roll calibration, the system conducts a grid search tofind better values that minimize the standard deviations
between the observed z positions from the sensors and therobot’s z positions through all the data sets. By this process, thehead plane coincides with the height level of the robot’s
position (ground-truth) plane. Then the system shifts the z
positions to match the observed heights with the robot’s height.
We defined the set positions of sensor i as
𝑃𝑜𝑠(𝑖) = {𝑃𝑖,0 … 𝑃𝑖,𝑡 } ,Fig. 4. Estimated positions Pi,t from the sensor i and the robot’s positions Pr,t.

B. Human-tracking and calibration systems
We captured the data from depth sensors by five desktop
PC’s with up to four sensors connected to each PC. Thesesensor data were streamed over a wired network to a Core i5
PC running tracking software written in Java [1]. In this study,
these sensors were used to detect the tops of people’s heads,
not for full-body skeleton tracking (see a previous work fordetails of the tracking algorithm [1]). For this purpose, thesensor angles were approximately 30-60 degrees from ahorizontal degree. The initial sensor positions were calibrated
by a human.
The calibration system was also written in Java andoperated on the same PC. The tracked position data and the
localized robot’s position data were sent to the software forcalibration through a wired/wireless network. For
documentation and repeatability of the results, we conductedoffline processing, but the software can be used online withlive data.
C. Mobile Robot as a Movable and Localized Landmark
Figure 1 shows our mobile robot, which has a human-sizedhead (at 135 cm height) and its shoulders are tracked as anentity by the tracking system. We used an iCart-mini robot as a(1)

where 𝑃𝑖,𝑡 is the tracked position from sensor i at time t (Fig. 4).
For a grid search of the pitch and the roll, the system calculates
the standard deviation of the Euclidean distance of the z axis
between the translated tracked positions and robot position
𝑃𝑜𝑠(𝑟). We used a rigid transformation matrix, 𝑻𝜃,𝜓 , whichrotates the observed position from the sensors with specified
pitch and roll values to calculate the following standard
deviations:
𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑒(𝜃𝑖 , 𝜓𝑖 ) =argmin𝑍𝐷𝑒𝑣(𝑃𝑜𝑠(𝑖), 𝜃, 𝜓)) (2)𝜃∈{𝜃𝑖,𝑚𝑖𝑛… 𝜃𝑖,𝑚𝑎𝑥},𝜓∈{𝜓𝑖,𝑚𝑖𝑛… 𝜓𝑖,𝑚𝑎𝑥 }𝑍𝐷𝑒𝑣(𝑃𝑜𝑠(𝑖), 𝜃, 𝜓) = 𝑆𝑇𝐷𝐸𝑉𝑧 (𝑻𝜃,𝜓 ∙ 𝑃𝑜𝑠(𝑖), 𝑃𝑜𝑠(𝑟)) ,(3)

where 𝜃𝑚𝑖𝑛 and 𝜃𝑚𝑎𝑥 , which indicate the searching range forsensor i, are between ± 60 degrees from the initial 𝜃 of sensor iwith 0.01 intervals, 𝜓𝑚𝑖𝑛 and 𝜓𝑚𝑎𝑥 , which indicate a searchingrange for sensor i, are between ± 60 degrees from the initial 𝜓of sensor i with 0.01 intervals, and 𝑆𝑇𝐷𝐸𝑉𝑧 calculates thestandard deviation of the Euclidean distance of the z axis
between two position data sets.
After calibrating the pitch and the role of each sensor, we
conducted a grid search for the z positions of each sensor thatminimized the Euclidean distance of the z axis using rigid
translation matrix 𝑻𝑧 , which translates the observed position
from the sensors in the z axis by considering of 𝑻𝜃,𝜓 , androbot’s position 𝑃𝑜𝑠(𝑟) as follows:𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑒(𝑧𝑖 ) =argmin(4)

𝑍𝐷𝑖𝑠𝑡(𝑃𝑜𝑠(𝑖), 𝑧))𝑧∈{𝑧𝑖,𝑚𝑖𝑛… 𝑧𝑖,𝑚𝑎𝑥 }𝑍𝐷𝑖𝑠𝑡(𝑃𝑜𝑠(𝑖), 𝑧) = 𝐷𝑖𝑠𝑡𝑧 (𝑻𝒛 ∙ 𝑃𝑜𝑠(𝑖), 𝑃𝑜𝑠(𝑟)) ,(5)

where 𝑧𝑚𝑖𝑛 and 𝑧𝑚𝑎𝑥 indicate a searching range for sensor i
between ± 1000 mm from the initial z position of sensor i at 5mm intervals and 𝐷𝑖𝑠𝑡𝑧 calculates the Euclidean distance ofthe z axis between the position data sets.
C. Yaw-X-Y Calibration
After calibrating the pitch, the roll, and z for each sensor,
the system processes the yaw (𝜙) and then again calibrates thex and y positions by a grid search. For a grid search of the yaw,
similar to the pitch and roll calibration, the system calculates
the standard deviation of the Euclidean distance of the x and yaxes between the translated tracked positions with rigid
transformation matrix 𝑻𝜙 , which rotates the observed position
from the sensors with specified yaw values, and the robot’s
position 𝑃𝑜𝑠(𝑟) as follows:
𝑋𝑌𝐷𝑒𝑣(𝑃𝑜𝑠(𝑖), 𝜙))(6)

𝑋𝑌𝐷𝑒𝑣(𝑃𝑜𝑠(𝑖), 𝜙) = 𝑆𝑇𝐷𝐸𝑉𝑥,𝑦 (𝑻𝜙 ∙ 𝑃𝑜𝑠(𝑖), 𝑃𝑜𝑠(𝑟)),(7)

𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑒(𝜙𝑖 ) =argmin𝜙∈{𝜙𝑖,𝑚𝑖𝑛… 𝜙𝑖,𝑚𝑎𝑥 }where 𝜙𝑚𝑖𝑛 and 𝜙𝑚𝑎𝑥 indicate a searching range for sensor i
between ± 60 degrees from the initial 𝜙 of sensor i with 0.01
intervals and 𝑆𝑇𝐷𝐸𝑉𝑥,𝑦 calculates the standard deviation of the
Euclidean distance of the x and y axes between the two
position data sets.
After calibrating the yaw of each sensor, we conducted agrid search for the x and y positions of each sensor thatminimized the Euclidean distances of the x and y axes using
rigid translation matrix 𝑻𝑥,𝑦 , which translates the observed
position from the sensors in the x and y axes and robot’s
position 𝑃𝑜𝑠(𝑟) as follows:
𝐶𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑒(𝑥𝑖 , 𝑦𝑖 ) =argmin𝑋𝑌𝐷𝑖𝑠𝑡(𝑃𝑜𝑠(𝑖), 𝑥, 𝑦)) (8)𝑥∈{𝑥𝑖,𝑚𝑖𝑛… 𝑥𝑖,𝑚𝑎𝑥 },𝑦∈{𝑦𝑖,𝑚𝑖𝑛… 𝑦𝑖,𝑚𝑎𝑥}

𝑋𝑌𝐷𝑖𝑠𝑡(𝑃𝑜𝑠(𝑖), 𝑥, 𝑦) = 𝐷𝑖𝑠𝑡𝑥,𝑦 (𝑻𝒙,𝒚 ∙ 𝑃𝑜𝑠(𝑖), 𝑃𝑜𝑠(𝑟)),(9)where 𝑥𝑚𝑖𝑛 and 𝑥𝑚𝑎𝑥 , which indicate a searching range forsensor i, are between ± 1000 mm from the initial x position of
sensor i with 5 mm intervals, 𝑦𝑚𝑖𝑛 and 𝑦𝑚𝑎𝑥 indicate asearching range for sensor i between ± 1000 mm from theinitial y position of sensor i at 5 mm, and 𝐷𝑖𝑠𝑡𝑥,𝑦 calculates a
Euclidean distance of the x and y axes between the position
data sets.
V. EVALUATION
A. Procedure
Following the past study, we investigated the performanceof our proposed calibration system based on two perspectives:
the sensor’s absolute positions and the detected head positions.
For each of these evaluation measurements, we compared theperformances of our proposed method and the alternative
method that is previously proposed approach [8].
We only used depth sensors for the calibration in this study(no LRFs), and used our mobile robot to record position data
for evaluating both methods with offline processing as
described above, to clearly compare the performance of thetwo methods by using robot’s localized position as groundtruth. The robot needs six minutes to cover all sensing area.
B. Sensor Position Accuracy
We again followed the past study’s procedure [8] for sensor
position accuracy: a laser range measurement device (Leica
Geosystems, Leica DISTO X310) that measured the location ofeach sensor in an (𝑥, 𝑦, 𝑧) coordinate system relative to theroom’s walls. In this study, the initial sensor positions for the
tracking system were calibrated by a human experimenter withadequate experience with manual calibration tasks, without
knowledge about actual measurement information. The
calibrated sensor positions have 369.39 mm error in averagecompared to the measured sensor positions. The sensor
positions are well calibrated from a relative position
relationship perspective and enable a human-tracking system torobustly track people. But since these absolute positions wereslightly moved from the actual sensor positions, a certain
amount of shifted positions is directly influenced by the above
position errors. To calibrate the sensor positions, our mobile
robot moved around the environment once, and its data wasused to calibrate sensor positions with both methods.
C. Head-Tracking Accuracy
Next, we used both the calibrated sensor position data fromeach method to track the head positions. For this purpose, weagain tracked our mobile robot by our system; the robot moved
around the same route twice. We used the robot’s localized
position as the ground-truth positions for the performance
evaluations, which is another reason why we did not use ahuman landmark for the alternative method. We gathered atotal of about 4000 paired sensor data for both trials, which are
sufficient for evaluation purposes because since the past study
used 360 measurement points at specific positions only.
D. Results
Fig. 5 shows the robot’s localized positions (a), theobserved positions from the tracking system (b) and integrated
them (c), note that the sensor positions for the tracking systemwere manually calibrated by a human experimenter. Eachsensor’s observations plotted with different colors in the Fig. 5.
Fig. 6 shows the integrated trajectories with the calibrated
sensor positions by the proposed method (a) and the alternative
method (b). All of the figures showed that the shapes of theobserved trajectories from the tracking systems resembled therobot’s trajectories, but the absolute positions were shifted
more than the robot trajectories without the proposed method.
Table I shows the evaluation results of the sensor position
calibration and the head-tracking accuracies. We computed theroot-mean-squared (RMS) error in x, y, z and combined them.
The results of the sensor position showed that the proposed
method achieved 100.17 mm error, and the alternative method
achieved 346.97 mm error on average. The larger errors in thealternative method were caused by its initial sensor positions,which were calibrated by a human experimenter. The relative
position relationship between the sensors was well calibrated,but the absolute sensor positions slightly shifted compared to
the real sensor positions, as described above. Therefore its
position errors influenced the alternative method’s
performance. On the other hand, our proposed methodcalibrated the absolute sensor positions well regardless of theinitial sensor positions, because it used the localized position
from the mobile robot system. Our proposed method showed
better accuracy than the alternative method.
The results of the tracked human positions showed that the
proposed method achieved 135.29 mm error, and thealternative method achieved 694.04 mm error in average. The
larger error of the tracking positions was also caused by the
initial sensor positions. Even though the human-tracking
system tracked the people well from relative position
relationships, the absolute positions were different than theactual positions. Again, the proposed method tracked therobot’s position well regardless of the errors of the initial
positions of the sensors.
Compared to the past study’s evaluation results [8], in our
setting, the performance of the alternative method is slightly
inaccurate from the original results for reasons based on its
sensors’ initial positions and the small overlapping sensing
area among the sensors. Our proposed method achieved similar
performance with the past study’s evaluation results using both
depth and LRF sensors, and this result also indicates its
promising performance.

TABLE I.

EVALUATION RESULTS ABOUT SENSOR POSITION AND
POSITION TRACKING ACCURACIES

Sensor position accuracy(RMS, mm)
Position tracking accuracy(RMS, mm)
TABLE II.

Sensor position accuracy(RMS, mm)

Alternative

Proposed

346.96100.17694.04135.29ADDITIONAL EVALUATION RESULTS
Alternative

Proposed

379.53115.91

E. Additional Evaluation with Non-overlapped Sensors
The proposed method showed the advantages of thecalibration performance compared to the past study. In thissubsection, we conducted an additional evaluation to calibrate
sensors whose sensing areas do not overlap with other sensors
to show different advantages of our proposed method
compared to the alternative method. With a mobile robot as alandmark, each sensor can get global reference points from therobot’s localized results, and this position information can beused for calibration without shared observations with otherdepth sensors.
In this evaluation, we only used five depth sensors in the
middle of the room to create a sparse sensing area and again
calibrated these sensor positions with the alternative andproposed methods. We again used our mobile robot to be
tracked by the system, and it moved around for six minutes
twice on the same route.

(a) Robot’s positions(b) Observed positions (c) Integrated both positions

Fig. 5. Robot’s positions and observed positions from tracking system using
human-calibrated sensor positions.

The performance of this evaluation with the sparse data set
is shown in Table II. The proposed method’s performance isslightly incorrect (about 15 mm) compared to the performancethat used all of the sensors. But the alternative approach’s
performance was twice as bad (about 30 mm). These results
indicate that using a mobile robot to provide global reference
points is more robustness for calibrating absolute sensor
positions than just using relative reference points.

VI. DISCUSSION
A. Implications
The evaluation results showed the advantages of using amobile robot as a movable and localized landmark instead of apedestrian landmark. The calibrated sensor positions andtracking results through our proposed method outperformed thealternative method’s results, and the proposed method
decreased the human efforts to gather sensor data. Theseadvantages will be effective with large sensing areas, such as asensor network system that covers an entire shopping mall.
(a) Proposed method(b) Alternative method

Fig. 6. Robot’s positions and observed positions from tracking system

One possible future work will integrate both anenvironmental human-tracking system and an onboard humantracking system of a robot. If the robot’s tracking systemestimates the people’s position during calibration, it can beused as different global reference points to increase theaccuracy of the calibration processes. From another perspective,
if the robot can change its height and send its information to
the calibration system, z-axis calibration will be more accurate.
B. Possible Applications
We used a mobile robot to provide global reference points
for calibrating a human-tracking system. We believe that sucha localized landmark can be used for calibrating different kindsof systems, such as Wi-Fi or any wireless signal-based systems.
In fact, a past study previously tried to automatically calibrate aultra-wide-band-tracking system with a mobile robot [17].
Mobile robots can be used not only as movable logger devices
but also as a tool to calibrate several kinds of sensor positions.
C. Limitations
This study has several limitations. Since its was conductedwith our sensing environment and a mobile robot, we need toinvestigate our proposed system’s performance in different
environments. In particular, in a large environment, the robot’s
localization error will increase and influence the accuracy ofthe calibration procedures. Moreover, we used a grid search
approach to calibrate each sensor due to its simplicity and to
avoid local minimum problems, but we did not test othermethods such as MCMC that may realize fast calculation. The
accuracy of the map information for localizing the robot
position also influences the accuracy of the calibration
processes. However, we believe that our setting offers essential
knowledge for researchers who are interested in autonomous
calibration by ceiling-mounted depth sensors.

VII. CONCLUSION
We proposed a method that calibrates with ceiling-mounted
depth sensors using a mobile robot as a movable and localized
landmark. This approach enables us to calibrate a humantracking system without additional human resources andincreases the accuracy of the sensor arrangement, which is
directly related to the usefulness of the system and the accuracyof the tracking positions. Our proposed method calibrates each
degree and the position of each sensor by directly comparing
the paired positions between the robot’s localized position andthe detected robot’s position by the tracking system. The
system calibrated them by minimizing the deviation of the
Euclidean distance to calibrate the pitch, the roll, and the yaw,
and minimizing the Euclidean distance of x-y-z for calibrating
the x, y, and z positions.
The proposed method achieved higher accuracy than thepast study from two viewpoints: sensor position accuracy andthe tracking performance of the head part. The evaluation
results showed that the proposed method calibrated the sensor
positions regardless of the initial sensor position errors, unlike
the past study’s method. An additional evaluation using sparse
sensor arrangements showed that the proposed systemcalibrated sensors that did not overlap with other depth sensors
with a robot’s landmark. These evaluation results showed thepotential of a calibration system that uses a mobile robot.

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