Received 9 August 2022, accepted 21 August 2022, date of publication 25 August 2022, date of current version 1 September 2022.
Digital Object Identifier 10.1109/ACCESS.2022.3201563

Detection Error Contaminated by Outliers toClassify Density Profiles Dependent on the
Relative Speed Between a MIMO Sensor and a
Human Hand
EUGENE KIM1 , YOJI YAMADA1 , (Member, IEEE), AND SHOGO OKAMOTO2 , (Member, IEEE)
1 Department of Mechanical Systems Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan

2 Department of Computer Science, Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo 192-0397, Japan

Corresponding author: Eugene Kim (b34b349@naver.com)
This work was supported in part by FUJI Corporation (with their support and technical assistance).
This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was
granted by the Institutional Review Board of the Department of Engineering of Nagoya University under Approval No. 20-21.

ABSTRACT The detection of human hand intrusion is crucial for improving the productivity of human–robot
collaboration. Recent trends to safety-related sensors have adopted the concept of radar-based humanpresence detection. Some of them have already been commercialized. However, it has not yet been elucidated
whether radars can sufficiently detect human hand intrusion and satisfy the required safety integrity level.
In this study, we present outlier and error profiles obtained by detecting human hand intrusion based on the
motion and speeds of the human hand and radar sensor. Our experiments indicate that slow hand movements
require further studies from the viewpoint of safety. In addition, we suggest a new noise model demonstrating
random noise and temporary outliers based on the recorded noise profiles of actual human participants. The
obtained outlier and error profiles can be utilized as an outlier judgement criterion of the sensing in thespecific case of the radar.
INDEX TERMS Human hand intrusion, human–robot collaboration, noise and outliers, safety-related
sensor.

I. INTRODUCTION

Over the past few decades, significant progress has been
made in the fields of robot automation and human–robot
collaboration (HRC) [1]. This can be attributed to the recent
trends of modern manufacturing that require agility and flexibility. Moreover, the development of human presence detection technologies allows the sharing of human and robot
workspaces. Several studies have demonstrated that HRC
can potentially help in maximizing the productivity of the
manufacturing process in terms of floor space and time
costs [2], [3], [4]. Safety is the main concern when adopting
The associate editor coordinating the review of this manuscript andapproving it for publication was Wen-Sheng Zhao
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.

HRC in manufacturing sites and robots can only be controlled via proper risk assessment [5], [6], [7]. Therefore, risk
reduction (to an acceptable level) is required for satisfying
the requirements of collaborative-operation modes based onsafety standards.
The field of HRC includes many situations in which a
non-contact safety approach is required. Speed and separation monitoring (SSM) can be used as a safety method toensure operator safety during HRC tasks [8], [9]. In SSM,
human body parts must be detected using a suitablesafety-related sensor to estimate the protective separation distance (PSD) [10]. In the framework of the IEC 61496 series,
several types of electro-sensitive protective devices (EPSE),
such as light curtains, laser scanners, and vision sensors,

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed

have been discussed [11], [12], [13], [14]. In addition to theconventional safety-related sensors, radar sensors are currently being discussed by the technical committee of TC44
in addition to the IEC 61496-5. In this study, we focus onradars used as safety-related sensors considering safety issues
during human detection that must be urgently addressed.
A. CONTRIBUTIONSThis study aims to specify and suggest a new noise model
which can completely demonstrate the noise profiles when
detecting a human hand using a radar sensor. This study
focused on the potential factors that can reduce the performance of radars while detecting human hand intrusion.
The results indicate that the type and proportion of theobtained outliers are different with respect to the relative
speed and motion of the human hand. The obtained outlier
and error profiles are modelized and can be used as an outlier
assessment criterion for human intrusion sensing using radar.
Finally, based on a hand intrusion experiment involving ten
participants, we suggest a new noise model that demonstrates
random noise and characteristic outliers generated by misdetection.

that can complement misdetections, which lead to dangerous
side failure [30], [31].
Notably, the specific properties of outlier/error profiles
generated by the misdetection of human hands using radars
have not yet been reported from the viewpoint of safety.
Furthermore, the error/outlier profiles of radars may be different from those of commercially available safety-related
sensors. Therefore, in this study, the performance and error
profiles of a radar sensor were analyzed during the detectionof human hand intrusion. In particular, the potential factorsthat influence radar performance, such as the relative speed
and motion of the human hand, and radar placement, werediscussed.
III. POINT CLOUD PROCESSING ALGORITHM

In this section, human hand detection techniques are
introduced based on point cloud sample processing. For
human hand detection, the Euclidean clustering approachis presented for effectively extracting human hand intrusion
samples. In addition, a multiple input–output frequency modulated continuous wave (MIMO-FMCW) radar principle isintroduced.
A. RANGE FOURIER TRANSFORM

II. LITERATURE REVIEW

Although radars are robust to environmental conditions
such as moisture, dust, and vibration, compared with laser
scanners, typical radars have relatively low resolutions andmeasurement reliabilities [15]. In addition, currently commercialized safety-related radar sensors are limited to thedetection of human presence using a single output single
input antenna [16]. In contrast, advanced forms of radar
applications, such as target classification using thresholding
methods, artificial intelligence, or multiple input and output antenna systems, are continuously being reported at a
research level [17], [18], [19], [20], [21]. Especially, various
efforts have been reported for human presence sensing to
replace the conventional laser scanning approach by introducing the radar as an extrinsic sensor system [22], [23]. Moreover, radar applications such as sensor fusion, which includes
radar and laser scanners, or simulation approaches for layout
optimization have been proposed [24], [25]. Therefore, theproductivity of HRC using radars can be improved if highly
accurate human body detection (for example, the detection ofhuman hand) is performed.
However, it has not yet been elucidated whether the performance of radars is reliable enough to achieve the required
safety integrity level or whether they can be applied for
detecting human hand intrusion [2], [15], [26]. From theperspective of human detection and tracking, undesired background noise, known as ‘‘clutter,’’ is uniformly distributedand can be sufficiently reduced using a constant false alarm
rate method [27], [28]. However, in dynamic conditions,a constant false alarm rate method leads to incorrect detection, which must be alleviated to ensure safety [29]. Therefore, some studies have focused on pre-processing techniques
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The distance and velocity between the radar and the object
can be computed using linear chirp frequency transmission.
Each transmitted chirp can be explained with a carrier frequency (fc ), sweep sample time (tw ), or sweep frequency(fw (= 1/tw )). After a reflected chirp signal is received, theobject range can be calculated by comparing it with thetransmitted chirp profile.
r(t) =

ctw fb+ (t)
,
2fw

(1)

where r denotes the range obtained using each chirp signal,and c is the speed of light. Note that fb+ is the average beatfrequency of increment and decrement chirps, compensatinga Doppler effect.
Similarly, the velocity can be obtained using the differencein the beat frequency.
f − (t)λcv(t) = b,(2)4where v denotes the velocity, and λc is the wavelength ofa chirp. Notably, fb− denotes the difference in the beat frequency during the frequency modulation representing the
Doppler frequency.
Finally, angular estimation can be performed using multiple receiver antennas via a simultaneous sampling approach.
In other words, the estimated angle of arrival (AoA) can begiven by:λc ω(t)),(3)2πdwhere θ(t) denotes the angular estimation, ω(t) is the phasedifference between two neighboring patch antennas, and d isθ(t) = sin−1 (90577

E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speedcluster containing nonoverlapping points with all the otherclusters. Based on the Euclidean distance threshold criterion,d ∗ , every cluster should satisfy the following conditions to
avoid overlap:
Cj ∩ Ck = ∅,for j 6= k, if min||pj − pk || ≥ d ∗ ,(7)where the sets of points pj , pk ⊂ P belong to the point clusters
Cj and Ck , respectively. Finally, the cluster of interest, C ∗ ,that might be a potential human cluster can be defined withthe cluster size.
C ∗ = {Cj |Ncmin ≤ n(Cj ) ≤ Ncmax },FIGURE 1. Preliminary point cloud processing for human body-partextraction against clutter points. The closest cluster point (red) is
extracted by the pass-through filter, Euclidean clustering method, and therelationship between hazard points.

the preliminarily determined distance between each receiverantenna. Based on the obtained frequency samples, a rangedoppler map can be created, which can be converted into a
point cloud format to recognize specific objects.
B. POINT CLOUD AND CLUSTER PROCESSING

The raw measured point cloud obtained by the radar is usually discretely distributed [17]. In other words, it generally
does not include sufficient information for human tracking
or detection. Therefore, a process to associate the point cloud
samples using the initial observation points is essential for thetarget estimation.
Fig. 1 illustrates the preliminary point cloud and cluster processing for the detection of human hand intrusion.
Notably, an input point cloud P is defined as a set of I points
measured by the radar and is expressed as follows:
P = {pi |pi = (xi , yi , zi ) ∈ R3 , i = 1, 2, . . . , I }.

(5)

Notably, passthrough filtering is essential only for considering the object cluster points that belong to the space ofinterest.
Next, point clusters are extracted using the hierarchical
Euclidean clustering method [32].
Cj ⊂ P∗ ,j = 1, 2, . . . , J(6)where J denotes the total number of clusters generated
by hierarchical Euclidean clustering, and Cj represents the90578

where Ncmin and Ncmax represent the number of minimum andmaximum points associated with the corresponding cluster,
respectively.
IV. EXPERIMENTAL DESIGN

The detection of a quasi-stationary object is assumed to be
more challenging than that of a fast-moving object owing
to the characteristics of the radar specialized for detecting moving objects. Therefore, we experimentally compared the detection error and outlier profiles based on the
speed of the human hand. For the comparison, fast andslow movements were performed during the human hand
intrusion task by the participants. Subsequently, detection
error and outlier profiles were investigated for different
human intrusion motions. For the comparison, the participants reproduced three typical movements (back and forth,lateral swing, and vertical swing). From the viewpoint ofdetection, the back and forth movement was expected to be
the most challenging owing to its relatively small reflection area. Next, the detection error and outlier profiles
were investigated when the radar detected the dynamic
movements of human hand intrusion. Furthermore, the sensor mount was moved at three speed levels, i.e., 0, 100,
and 400 mm/s.

(4)

The first step for cluster detection involves the application ofa passthrough filter to consider only the points included in thespace of interest, pi , such as xmin < xi < xmax , ymin < yi <ymax , and zmin < zi < zmax . In particular, the point cloud P∗
belonging to the space of interest can be expressed as a subsetof the input point cloud P as follows:P∗ ⊂ P.

(8)

A. GENERAL SETUP

Fig. 2 presents the overall experimental layout of the measurement condition. A linear actuator (LEFB25S2S-1000S2A1, SMC, Japan) was used to repeatably move the radar
sensor back and forth (10 cm) [33]. The duration of theexperiment was 15 min, which is the demand rate suggested
in IEC/TS 62998 [34]. For the comparison, a motion capturesystem (Motion Analysis Co., Santa Rosa, CA, America)
with 12 cameras was used to measure the relative distanceand velocity between the sensor antenna and the hand of theparticipants. Importantly, the values measured by the motion
capture system were considered to be the true values in thisexperiment.
B. RADAR SETUP

To measure human hand intrusion, a MIMO radar(IWR6843ISK, Texas instruments, America) with a 60 GHz
standard antenna was used (The azimuth and elevation field
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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed

FIGURE 2. Hand intrusion experiment: Radar-detected human hand
intrusion for different types of intrusion scenarios. In addition, a linear
actuator was used to move the radar back and forth to demonstrate
dynamic measurement conditions. During the experiment, theparticipants were asked to reproduce the motion of a hand approaching
the target. For the comparison, motion capture cameras were used toaccurately track the human hand motion.

FIGURE 4. Example of the closest human body point perceived by radar.
The possible ground and ceiling points were removed using a
passthrough filter (green box). Each point represents the measured point
clouds and the red arrow points to the closest point involved in theclosest cluster. The visualized samples present a typical challenge fordetecting human hand intrusion: human hand samples consist of two or
three points only when the velocity of the human hand is low, ∼ 0.1 m/s.

FIGURE 3. During the experiment, a local coordinate of the radar
antenna, Or , was transformed into a global coordinate of O0 . The heightof the sensor mount, L, was 37 mm with a tilted angle of 45◦ around thez-axis. Finally, 1ρ changed dynamically according to the motion of linear
actuator.

of view were ±60◦ and ±20◦ , respectively). The transmit
power was set to 12 dBm with a maximum bandwidthof 4 GHz (60–64 GHz). Accordingly, the gain of the transmitting or receiving antenna was set to 12 dB. The chirpfrequency slope was set to 71.26 MHz/µs with a sampling
rate of 5279 kbps, which resulted in 222 samples for eachchirp. Therefore, the range resolution using a fast Fouriertransform with a size of 256 was 4.34 cm with a measurement
rate of 30 Hz.
After measuring the surroundings, the obtained point cloud
samples were transformed to a global coordinate following
the coordinate frame presented in Fig. 3. The aforementioned
radar was implemented using Robot Operating System (ROS)
Melodic running on Linux Ubuntu 18.04 LTS (64-bit) [35].
The three-dimensional point clouds were measured using
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FIGURE 5. Example of a clustering process extracting point clouds
belonging to human body points using radar. Each cluster color
represents linked point clouds based on the Euclidean distance threshold.
The visualized scene only shows points after the association process.

the TI mmWave ROS package1 officially provided by the
manufacturer with calibration files and serial drivers requiredfor communication between personal computers.2 The TI
mmWave ROS package was modified from the originalIndustrial Toolbox (2.3.0). All the point clouds and closest
distance points extracted by the Euclidean clustering method3
1 https://github.com/radar-lab/ti_mmwave_rospkg
2 https://github.com/wjwwood/serial.git
3 https://github.com/PointCloudLibrary/pcl

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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speedlinear actuator moved back and forth at three different speeds(vm = 0, 100, and 400 mm/s) along the rails.
D. EVALUATION METRIC
1) MEASUREMENT ERROR

To compare the measurement errors, the root mean squareerror (RMSE), , was used
=

N q
1 X
(xk − x̂k )2 + (yk − ŷk )2 + (zk − ẑk )2 ,
N

(9)

k=1

FIGURE 6. Participants demonstrated three typical intrusion patterns for
15 min: (a) Back & forth, (b) vertical swing, and (c) lateral swing. The
intrusion patterns were demonstrated for each measurement condition.

were recorded using the rosbag package with time-stamped
samples.4
Figs. 4 and 5 show the visualized point cloud samples
and possible human body part points using the ROS rviz
package. Fig. 4 reveals that distinguishing human body partsis challenging, especially the human hand, owing to their low
reflectivity and occlusion due to the complexity of humanmotions. First, to filter useful information from the measured
samples, passthrough and Voxel filters with the same lattice
length of 5 cm, which is the theoretical resolution of radars,
were used. The distance threshold, d ∗ , that is used to cluster
potential human body parts using the Euclidean clustering
method was found to be insensitive to the parameters untild ∗ was increased to 20 cm, considering a maximum human
hand length of approximately 85 cm [33]. Finally, the number of minimum (Ncmin ) and maximum (Ncmax ) points were
empirically set to be 2 and 50, respectively.
C. HAND INTRUSION

Ten healthy participants comprising five males and fivefemales were enrolled in this experiment with the permissionof the Institutional Review Board of the Department of Engineering of Nagoya University (approval no. 20–21).
1) HAND SPEED

The participants moved their hands while exhibiting two
types of speeds: fast (2 m/s)5 and slow (0.1 m/s).6 They were
instructed to reach for the target, and a metronome was used
to maintain each suggested speed (100, 20 bpm).
2) HAND MOTION

During the experiment, the participants demonstrated three
typical patterns of intrusions, as shown in Fig. 6.
3) SPEED OF SENSOR MOUNT

While the participants reproduced the intrusion motion basedon their respective speeds and motions, the radar-mounted
4 https://github.com/ros/ros_comm
5 Maximum speed of the human hand suggested in ISO 13855.
6 Slow speed is being discussed by TC/44/PT IEC 61496-5.

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where N denotes the number of observed vector samples
included in each trial; xk , yk , and zk denote the measured
position obtained from the radar for each axis; x̂k , ŷk , andẑk represent the measured position obtained from the motion
capture system for each axis.
Further, a Gaussian mixture model was used to distinguishbetween the group of errors derived from the outliers [36].
The misdetection of a human hand is classified into twocases. In one case, the human hand is lost or misdetected
and, instead, the human arm is detected. In the other case,instead of the human hand, the human body trunk is detected.
We call these phenomena as ‘‘target shifting’’. Therefore,
three Gaussian distributions were fitted to each experimental
case. Then, the mean () and deviation values were compared.
2) OUTLIER JUDGEMENT

HRC systems, especially the safety-related parts should satisfy the required performance level, PLr = d [37]. In thelatest IEC/TS 62998 standard issued in 2018, a coverageinterval concept was introduced, which enables the quantitative evaluation of measurement uncertainty assuming thatthe measurement error follows a Gaussian distribution [34].
Assuming that the upper limit of the required probability of
failure per hour is PFHu , the coverage probability (Cp ) canbe expressed as
Cp ≤ 1 −

PFHu
,
rd

(10)

where r d represents the demand rate of the collaborative
system. According to the IEC/TS 62998, if the required safety
integrity level is PLr = d, the upper limit of PFH is 10−6 , andthe suggested demand rate (r d ) is approximately 4h−1 . Notethat the unit of demand rate is the average number of times
per hour the safety-related device is demanded. Therefore,
Cp , which satisfies the corresponding safety integrity level isobtained as 1 − 2.5 × 10−7 . Finally, the coverage interval that
includes such a probability is ±5.16 σ , which can be derived
using the statistical measurement error of the sensor system.
In this study, assuming that the standard deviation of the error(σ ) is 4 cm,7 the calculated range of ± 20.64 cm corresponds
to the acceptable error. Moreover, the measurement samples
7 The error profile of the radar was obtained in advance using a test piecemodeled after a human hand based on the IEC 61496 series after conducting
measurements for 15 min, which is a demand rate satisfying PLr = daccording to IEC/TS 62998.
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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed

FIGURE 7. Outliers are classified into three types based on the risks theypose: innovative outlier (IO), additive outlier (AO), and temporary outlier(TO). The dotted and normal lines represent the true values and observed
measurements, respectively.

FIGURE 8. Example of typical error profile for the case of fast verticalswing motion of the human hand when the speed of the sensor mount is
0 mm/s. The Gaussian mixture model is used to distinguish between thegroup of errors.

that belong outside the scope of the border are treated as
outliers.
As shown in Fig. 7, the outliers are classified into three
types based on the observations [38]: first, the innovative
outlier (IO), which generates irreversible trends after observations; second, the additive outlier (AO), which affects asingle observation; and third, the temporary outlier (TO),
which generates transitory trends during certain time intervals. In particular, the outliers can further be classified basedon their expected risks into a negative outlier (safety side) anda positive outlier (hazardous side).
V. RESULTS

In this section, the analysis of detection error contaminatedby outliers is presented based on the evaluation metric statedin IV-D.
A. ERROR PROFILES

Table 1 summarizes the error profiles against each relative
speed between the radar and human hand. The Gaussiancomponent whose mean RMSE is the smallest is the firstcomponent. Similarly, the second and third components were
determined on the basis of their mean RMSEs.
B. OUTLIER PROPORTION

Fig. 9 summarizes the results of the outlier proportion basedon the hand speed of the participants. The results reveal that,compared to when the participant’s hand speed was fast, when
it was slow, the inlier decreased by 6% from 92% to 86% In
particular, TO-pos increased from 2.7% to 12%, whereas the
TO-neg decreased from 3.6% to 1.6%.
Fig. 10 summarizes the results of the outlier proportion
based on the hand motion of the participants. The results
reveal that LS had the highest inlier proportion among thehand motions (Back and forth: 87%, Lateral swing: 94%,
Vertical swing: 87%). Further, LS had the lowest proportion
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FIGURE 9. Comparison of outlier proportion between the fast and slow
hand speeds of the 10 participants. The result indicted that the outlier
increased when the hand speed was slow. In particular, the proportion of
the positive TO (TO-pos) increased when the speed of the hand was slow.

of the TO among the hand motions (Back and forth: 9.9%,
Lateral swing: 4.7%, Vertical swing: 8.1%).
Fig. 11 summarizes the results of the outlier proportion based on the speed of the sensor mounter during
the experiment. Compared to when the speeds of thesensor mounter were 0 mm/s and 100 mm/s, when the
speed was 400 mm/s, the inlier increased (87%, 87%, and91%, respectively).
C. COMPREHENSIVE RELATIVE SPEED ANALYSIS

Fig. 12 illustrates the probability density of the obtained
positive temporary outliers according to the relative speed
between the human hand and sensor. The samples were measured based on the instant relative speed when the samples
were classified as the positive temporary outliers. Note that90581

E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed

TABLE 1. Error profiles for each case of the human hand motion against each speed of the sensor mounter vm . For the comparison, the profiles of theerror were categorized using the Gaussian mixture model, where P, , and σ represent the proportions, root mean square error, and standard deviation ofeach distribution, respectively.

FIGURE 10. Comparison of outlier proportion between each hand motionof the 10 participants. The result of the three motions reveals that thelateral swing motion (LS) had the least outliers. Remarkably, the outliers
belonging to Temp-p were greater than those belonging to Temp-n.

the instant relative speed measured by the motion capturesystem was used as the sample.
Fig. 13 displays the probability density for obtained samples to be classified as the positive temporary outlier considering the total number of obtained samples. Note that the
curve fitting was carried out by using the exponential function
with each of the histogram bins.
VI. DISCUSSIONS
A. RELATIONSHIP BETWEEN HAND SPEED AND OUTLIER

As expected, during the detection of human hand intrusion using radar, the detection of a static or quasi-static
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FIGURE 11. Comparison of outlier proportion between each speed of thesensor mounter for the hand intrusion of the 10 participants. As a result,the proportion of the Temp-p was the lowest when the speed of thesensor mounter was vm = 400 mm/s.

intrusion was more challenging than that of a dynamic
intrusion (Fig. 9). The error-profile results were categorized using the Gaussian mixture model. Specifically, thethird component was assumed to be an outlier distribution owing to its distinctive mean value and large standard
deviation of the error (Fig. 8). Notably, the outlier proportion increased when the hand speed was low for all thehand-intrusion movements.
When the speed was low, most of the outliers were identified as TOs. Moreover, the proportion of the AOs was
relatively lower than that of the TOs. Hence, misdetection ismore probable when the hand intrusion speed is low. Consequently, further iterative measurement or observations must
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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed(Fig. 10). Moreover, when comparing the mean value of thesecond component, the values of the vertical swing and backand-forth motions were found to be higher than the averagevalue of the first component (Table 1). The challenge in thegeneration of a cross-section area can be attributed to the
dynamically changing vertical plane of the radar. Therefore,
owing to the diversity of human hand intrusion, it is preferable
to evaluate the intrusion with a three-dimensional movement
such as a vertical swing.
C. RELATIONSHIP BETWEEN SENSOR MOUNT SPEEDAND OUTLIER RATIOFIGURE 12. Probability density at which obtained sample is classified as
the positive (hazardous) temporary outlier according to the relative
velocity for every human hand intrusion cases. Samples were gathered
based on the instant relative speed when the measured samples wereclassified as the positive temporary outlier.

As expected, the maximum inliers were observed at a speedof 400 mm/s. A minimal difference was observed between theinliers at the speeds of 0 and 100 mm/s (Fig. 11). In addition,
the outlier proportion decreased when the sensor mount speed
increased in the cases of the back-and-forth and vertical swing
motions (Table 1). Therefore, the relative speed due to intrusion and the position of the sensor affects the misdetectionof radars. However, the ratio of the TO-pos at 100 mm/s
increased more than those at 0 mm/s. Although these results
indicate that small differences in the relative speed do notsignificantly affect misdetection, a limitation exists where therange of the mount speed is small and must be tested undervarious patterns of operations.
D. NOISE PROFILEFIGURE 13. Proportion of positive (hazardous) temporary outliers amongobservations at each relative speed. Curve fitting was carried out
considering the total number of samples.

be performed for redetection. Therefore, we can conclude thatslow hand intrusion motions require further analyses from theviewpoint of safety.
B. RELATIONSHIP BETWEEN HAND INTRUSION MOTIONAND OUTLIERS

As expected, compared with those of the back and forthmotion, the results of lateral motion contained fewer outliers
owing to its relatively large cross-section area (Fig. 10).
This may be because, unlike the back and forth motion,in the Lateral swing motion, the hand cross-section is valid
continuously along the arm. In the case of a vertical swing
motion, although the cross-section of the hand is continuously
generated, similar to that in the Lateral swing motion, theresults are rather similar to those of the back and forth motion
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This study confirmed that, contrary to the noise profile suggested by IEC 61496, the noise profile of human
hand intrusion obtained from our experiment was in
the form of a nonparametric distribution [39]. In termsof the detection/removal of outliers, a criterion basedon a distribution different from the actual error profile may result in outlier overestimation/underestimation.
In contrast, despite the numerous efforts invested in
the detection and removal of outliers, the existing algorithms for outlier simulation focus on AOs. However, theactual results showed that TOs were dominant during
radar detection [40], [41], [42].
Therefore, methods that include TOs and nonparametric methods for the outlier assessment criterion andoutlier generating algorithms, respectively, can be highly
effective. Accordingly, we propose a novel noise
profile that satisfies the aforementioned criterion,
given by(∼ (1 − λ)N (µ1 , R) + λN (µ2 , αR) at 1 − ρ,z
∼ N (µ3 , βR)at ρ,  > 0,(11)where µ1−3 denotes the position vectors of the primary(hand), secondary (arm), and tertiary (trunk) targets. The
constant λ is the additive contamination ratio, and α, and β
denote the scale factor. The constant ρ represents the temporary contamination ratio that contributes to the generationof TOs. Notably, the second case that demonstrates target
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E. Kim et al.: Detection Error Contaminated by Outliers to Classify Density Profiles Dependent on the Relative Speed

shifting is initiated only when  is positive to generate dangerside outliers. Moreover, the valid range of parameters forgenerating adequate noise profiles are 1 < α, 1 < β, 0 <λ < 1, and 0 < ρ < 1. However, choosing the precise
parameter to demonstrate the realistic outlier ratio is challenging. Nevertheless, the results from the comprehensive
relative-speed analysis indicate that the proportion of TO-pos
can be accounted for by the instant relative speed between thehuman hand and sensor, indicating that ρ is the function of
vr . Therefore, to validate the robust techniques when using
radar as a human hand intrusion sensor, relative speed should
be considered as a critical index for the positive temporary
outlier.
VII. CONCLUSION

This study presented outlier profiles obtained during thedetection of human hand intrusion using MIMO-radar. Threepotential factors that degraded the radar performance, that is,hand intrusion speed, movement, and sensor mount speed,
were investigated. Ten participants were enrolled in our
experiments. The experimental results indicated that, insteadof dynamic movements, the stationary and quasi-stationary
movements between the human hand and radar needed to befurther analyzed because they frequently resulted in misdetection. Furthermore, temporary outliers were found to be
more dominant. Thus, we proposed a novel noise generation
algorithm that included a TO generating sequence.
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YOJI YAMADA (Member, IEEE) received the
Ph.D. degree from the Tokyo Institute of Technology. Since 1983, he has been with the Toyota
Technological Institute, Nagoya, Japan. In 2004,
he joined the Safety Intelligence Research Group,
National Institute of Advanced Industrial Scienceand Technology (AIST), as a Leader. In 2009,
he joined the Department of Mechanical Scienceand Engineering, Graduate School of Engineering,
Nagoya University, as a Professor.

EUGENE KIM was born in Busan, South Korea,
in 1992. He received the B.S. degree in engineering from the Nagoya Institute of College, Nagoya,Japan, in 2016, and the M.S. and Ph.D. degrees inengineering from Nagoya University, Nagoya, in2018 and 2021, respectively.

SHOGO OKAMOTO (Member, IEEE) received
the Ph.D. degree in information sciences fromTohoku University, in 2010. From 2010 to 2021,
he was with Nagoya University. He is currently
an Associate Professor with the Department ofComputer Science, Tokyo Metropolitan University. His research interests include haptics, assistive robotics, human-centered informatics, andaffective engineering.

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