=Paper=
{{Paper
|id=Vol-3097/paper21
|storemode=property
|title=Interpersonal Proximity Detection Using RSSI–Based Techniques
|pdfUrl=https://ceur-ws.org/Vol-3097/paper21.pdf
|volume=Vol-3097
|authors=Fatemeh Mirzaei,Roberto Manduchi
|dblpUrl=https://dblp.org/rec/conf/ipin/MirzaeiM21
}}
==Interpersonal Proximity Detection Using RSSI–Based Techniques==
https://ceur-ws.org/Vol-3097/paper21.pdf
Interpersonal Proximity Detection Using RSSI–Based
Techniques
Fatemeh Mirzaei1 , Roberto Manduchi1
1
University of California, Santa Cruz, 1156 High St, Santa Cruz, CA 95064, USA
Abstract
We present an experimental study assessing the ability of two RSSI-based methods at detecting inter-
personal distances shorter than 1 meter or 2 meters. The first method uses the power received from
the smartphone carried by another person, while the second one measures the disparity in the power
received by the two smartphones from one or more fixed BLE beacons. Our results show that use of
the RSSI disparity enables discrimination results that are as good or better than using the RSSI received
from another smartphone.
Keywords
Proximity detection, interpersonal distance detection, contact tracing
1. Introduction
Interpersonal proximity detection techniques, once confined to applications such as crowd
monitoring [1] and social interaction analysis [2], have received substantial recent attention
due to their potential for COVID-19 contagion tracing. Contact tracing may help understand
the genesis of a local outbreak of the disease, and could be used to warn subscribers about a
potential contagion event due to proximity with an infected person [3].
The most common approach for interpersonal proximity detection relies on measurement of
the received signal (RSSI) from a radio source, such as a Wi-Fi transmitter [2] or a Bluetooth
Low Energy (BLE) beacon [4, 5, 6, 7, 8]. Since all modern smartphones contain a BLE transceiver,
this approach has enabled widespread adoption without the need for expensive external in-
frastructure (e.g. cameras equipped with embedded computers for visual people tracking.) The
power of the received signal decreases quadratically with the distance 𝐷 to the source, and thus
the received strength could, in principle, be used to estimate 𝐷 when the emission power is
known. For example, the Exposure Notification (EN) API produced by Google and Apple [9]
uses this mechanism to support contact tracing.
A different approach to proximity detection is based on the disparity of a measured signal,
typically an electromagnetic field generated by a transmitted (e.g., a Wi-Fi [10, 11, 12] or BLE
[13, 14]), although magnetic field measurements have also been considered [15, 16]. When two
identical receivers are placed in the same or similar location, measurements are expected to
IPIN 2021 WiP Proceedings, November 29 – December 2, 2021, Lloret de Mar, Spain
" fmirzaei@ucsc.edu (F. Mirzaei); manduchi@soe.ucsc.edu (R. Manduchi)
~ https://vision.soe.ucsc.edu/people (F. Mirzaei); https:https://vision.soe.ucsc.edu/people (R. Manduchi)
0000-0003-2479-5648 (F. Mirzaei); 0000-0003-2640-302X (R. Manduchi)
© 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
be similar (i.e., their disparity, as defined, for example, by the magnitude of their difference, is
expected to be small).
In this article, we present an experimental comparative analysis of mechanisms that use
measurement disparity (of the RSSI from fixed BLE beacons) for proximity detection, viz-a-viz
the direct measurement of RSSI from another nearby smartphone. In particular, we address the
specific problem of detecting the presence of another individual within distance thresholds of
1 meter and of 2 meters, since these are the interpersonal distances usually considered when
establishing the risk of contagion [17, 18]. Unlike other work on proximity detection, where
traces of moving individuals are analyzed to identify possible overlaps, we consider the case in
which two individuals are standing or sitting at certain distance from each other for a period of
time. This is representative of typical contagion scenarios, such as sitting at nearby tables at a
restaurant, or in nearby seats in a bus vehicle. We focus solely on RSSI data here. Although data
from other sensors (e.g. inertial [13, 14]) can be leveraged to reduce false positives, we believe
that it is important to precisely assess the contribution of each modality.
These are the principal contributions of our work:
1. We collected representative data sets from two different environments: a living room,
instrumented with three BLE beacons, and a campus shuttle bus with four BLE beacons. Within
each environment, multiple data collection sessions separated by long periods of time were
conducted in order to assess repeatability.
2. We present an in-depth statistical analysis of the data collected, and of its ability to discriminate
interpersonal distance using a threshold of 1 meter and of 2 meters.
3. We compare the system performance using different features (including RSSI from another
phone, individual and average RSSI disparities from multiple BLE beacons), as well as of a
simple additive combination of RSSI received from another phone and of mean RSSI disparity.
2. Related Work
Two approaches for contact tracing systems have been proposed in literature. 1) Network-based
sensing approach that requires no client-side involvement and uses WiFi infrastructure to
passively monitor the flow and mobility of people in a region equipped with WiFi Access Points
(AP). WiFi networks log the connections of mobile devices to APs and infers crowd movement
patterns across a region along with occupancy levels in different buildings by analyzing the
number of smartphones connecting to each AP [19, 1, 20, 10]. However, there are some issues
associated with network-based systems. First, one generally has no control on the actual
density of AP placements that results in lack of coverage for some areas of interest. Second,
the long range coverage of WiFi APs are not helpful for contact tracing purposes when higher
positional resolution is required [11]. Lohan et al.[21] reported that the short operating range
technologies such as BLE typically provides better performance than WiFi positioning in terms of
the estimated distance/ranging error. 2) Client-based sensing that requires users to install an app
and uses smartphone sensors and BLE data to perform sensing measurements. BLE technology
is well justified to be used in contact tracing systems due to its availability on most smartphones,
low cost, and energy efficient [22]. In the context of social interaction measurement previous
studies [13, 23, 6, 4] used Bluetooth RSSI either from smartphones or wearable sensors (such as
smartwatches or coin beacons) by mapping RSSI to distance via propagation model. [5] and [22]
employed wearable devices to simulate smartphone BLE measurements in order to circumvent
the iOS limitations in BLE scanning when the app is in background mode.
In principle, it could be possible to use power decay models (a.k.a. propagation models)
[24, 25] to estimate the interpersonal distance from the measured RSSI received from the other
device. However, in practice, this is extremely challenging [26] due to issues such as multipath
fading – an effect of signal reflection from nearby surfaces, time dependent signal power
variations, and diversity of smartphones/environment in the contact tracing context. Power
decay models require calibration for each environment to identify a path loss coefficient for
each device. This is not practical in contact tracing systems. [4] studied face-to-face proximity
estimation using power decay models based on Bluetooth in smartphones. They showed that
even in ideal situations (indoors, same antenna orientation), the RSSI signals measured within
1.5 meters to 3.5 meters are practically indistinguishable.
Some studies proposed learning the power decay model parameters using deep learning
models to improve the interpersonal distance estimation. Shankar et al.[14] used BLE RSSI,
IMU data, magnetic field intensity measurements and compared multiple deep learning models
such as Conv 1d , support vector machines, and decision tree-based algorithms. They observed
lack of generalization of the models trained on the MITRE dataset [27] when tested against the
National Institute of Standards and Technology (NIST) dataset [28]. The disadvantage of these
models are data inefficiency, high computational costs, and hence higher power consumption.
[29, 30, 11, 13] combined different modalities such as Ultrasound, Radio-frequency identifica-
tion (RFID), Quick Response (QR) codes, short range Wifi APs, and external BLE beacons to
improve the accuracy of the inter-personal distance detection. Along the same lines, Shankar et
al. and Trivedi et al.[14, 19] leveraged BLE beacons, WiFi, and Ultrasound co-location technolo-
gies, but in the context of social interaction detection.
To the best of our knowledge no one has studied the use of external beacons along with
smartphone BLE RSSI data in the context of interpersonal distance estimation for contact tracing
purposes in a bus. Leith et al.[31] ran experiments on a commuter bus and analysed the phone
BLE signals provide by EN API. They observed that increasing the exposure duration improves
the accuracy of their model at the cost of reducing the time resolution of the distance detection
system. They hypothesised that the sample rate provided by EN API is not sufficient for a
practical interpersonal distance detection in the bus where the signal propagation is under the
influence of disturbances that arise from metal-rich environments. Hence, further studying the
problem in this challenging environment by considering higher phone BLE sample rates as well
as combining that with other modalities such as external BLE beacons will get us closer to a
practical solution.
3. Interpersonal Proximity Detection Techniques
In our experiment, we considered two approaches to interpersonal proximity detection. Phone
RSSI uses the strength of the BLE signal received from another persons’ smartphone. RSSI
disparity compares the signal strength received at the same time and from the same BLE beacon
by the smartphone carried by two individuals.
3.1. Phone RSSI
In principle, one could use power decay models to measure the distance to a transmitter from
the measured RSSI [24, 25]. For example, a distance–dependent threshold could be devised as
a function of the transmitter’s characteristics. In practice multiple factors (including signal
absorption from human bodies, reflection from walls and other obstacles and the orientation of
the receiving antenna) cause substantial deviations from the model. This especially the case for
indoor environments [7].
3.2. RSSI Disparity
BLE beacons are often installed in public spaces such as airports and shopping malls, for
applications such as mobile advertising or to enable self-localization [32, 33, 34]. This existing
infrastructure can be leveraged for proximity detection. One approach could be to use the RSSI
from multiple beacons to localize the user via fingerprinting techniques [35, 36, 37, 38, 39], then
using this data to verify whether two users where in nearby locations at the same time. However,
fingerprinting information is not normally available, and accuracy of localization may be poor.
A simpler approach can be used based on the notion that if two persons are co-located, the
power received from a beacon should be similar for both users [10, 11, 12]. Thus, by comparing
the RSSI from multiple beacons for two (or more) users, one could devise a disparity index that
measures the pairwise difference in received RSSI. This disparity index could be associated with
the likelihood of these individuals being within a certain distance to each other.
It is important to note, though, that a small value of disparity does not necessarily mean that
the individuals are co-located. Ambiguity may arise when the same signal power is measured
in different locations. In order to illustrate how this can happen, consider the ideal case of
isotropic signal loss, whereby the measured signal power is only a function of the distance to
the beacon. Two different locations may result in the same measured power from a beacon
when they are at the same distance to the beacon. In the case of a single beacon, all locations
within the same circle around the beacon are ambiguous (Fig.1 (a)). Ambiguity can be reduced
or eliminated by using more beacons. In the case of two beacons, for a given the location of
one person, there is exactly one other location from which the same signal strength is received
(i.e., that is whose distance to each beacon is the same as for the first person; Fig.1 (b)). Using
more beacons, the ambiguity is resolved (i.e., two persons in different locations will receive a
different signal strength from at least one beacon; Fig.1 (c)), unless the beacons’ locations are
collinear (Fig.1 (d)). In practice, the relationship between distance to a beacon and received
signal strength is affected by the same factors mentioned in Sec. 3.1, which may contributes to
the inherent ambiguity of this method for proximity detection.
In our experiments, we use as disparity index the absolute value of the difference 𝑑𝑗 =
|𝑅𝑆𝑆𝐼𝑗 (1)−𝑅𝑆𝑆𝐼𝑗 (2)| of the received strength from the 𝑗-the beacon by the two smartphones.
In the case of signal received from multiple beacons, we simply consider a one-dimensional
feature formed by the average value the individual disparity (akin to the Manhattan distance
considered in [10]). This is a reasonable choice, considering that all individual disparity values
(and thus their mean) are expected to be small at small interpersonal distances. Other choices
(e.g., taking the max value of the disparities) did not give good results in our preliminary tests.
(a) (b)
(c) (d)
Figure 1: Examples of ambiguous zero RSSI disparity situations using one beacon (a), two beacons (b),
and three or more collinear beacons (d). Ambiguity can be avoided by using three or more non-collinear
beacons (c). These examples assume isotropic signal loss and uniform emission power.
4. Experiments
4.1. A Toy Case: Instrumented Living Room
In order to evaluate the considered proximity detection techniques in a simple, controlled
scenario, we instrumented a living room with three BLE beacons (Kontakt Tough Beacon
TB15-1) configured as iBeacons and set to the power level 2 (RSSI of -81 dBm at 1 meter) and
advertisement interval of 350 ms. The beacons were placed at a height of 2.5 meters, at the
locations shown in Fig. 2. One iPhone 7 and one iPhone 8 were used in the study. An app was
installed in each phone, designed to record time stamped RSSI data from the other phone’s
BLE beacons, as well as from the external BLE beacons. Phone RSSI and BLE beacons reading
rate were 40 and 3 samples per second respectively. We scanned Phone RSSI and BLE beacons
measurements using Core Bluetooth and Core Location frameworks respectively. Data was
collected while two experimenters, carrying one iPhone each, stood at different locations as
shown in Fig.2, with interpersonal distance of 1, 2, 3, and 4 meters. For each location pair, the
experimenters first collected data for two minutes while holding the smartphones in their hand;
then they placed their iPhones in their front pants pocket and collected data for two more
minutes. The experimenters faced each other at all times. This data collection was repeated
three times: in May of 2020 (Set 1), in December of 2020 (Set 2), and in April of 2021 (Set 3). Data
sets from each location pair and each phone placement were compiled together into a single
sequence (Combined set).
The data collected at each location pair and for each phone placement was pre-processed
as following. Missing RSSI measurements were replaced with a small value (-100 dBm). The
resulting sequence was run through median filter of length 15, in order to reduce the variance
of noise.
In order to analyze the statistical characteristics of the various indicators considered, we
plotted the probability density function (pdf) of the associated measurements conditioned on
Figure 2: Home data collection layout: Set 1 data collection at (A1, F1), (A2, F2), (A3, F3), (A, F) location
pairs at 1, 2, 3, and 4 meters interpersonal distance respectively. Set 2 and Set 3 data collection at (A,
B), (A, C), (A, D), (A, E) location pairs at 1, 2, 3, and 4 meters interpersonal distance respectively. For
Set 2 and 3, one experimenter stood still in position A, while the second experimenter moved in turn
on the other locations.
Phone RSSI
0.1 1m
2m
3m
0.08
Conditional pdf
4m
0.06
0.04
0.02
0
-85 -80 -75 -70 -65 -60 -55 -50 -45 -40
dBm
Figure 3: The pdf of the Phone RSSI, conditioned on the four different interpersonal distances consid-
ered (Home data collection).
the interpersonal distance in Figs. 3–4 (Combined set). We used Matlab’s ksdensity function
to generate these plots. In the case of the Phone RSSI indicator, one would expect the mode
of the conditional pdf to move leftwards (smaller RSSI values) for larger distances. From the
plots in Fig. 3, it can be seen that the distributions of the Phone RSSI indicator at each distance
are actually multimodal. As expected, the distributions allocate more mass towards lower RSSI
values as the interpersonal distance increases, although a large overlap can be noticed for the
pdf conditioned on distances of 2 and 3 meters.
In the case of individual RSSI disparity indices (Fig. 4), one can notice that the conditional pdf
are relatively narrow and centered around small values for distances of 1 and 2 meters, while
RSSI disp. B1 RSSI disp. B2
0.4 1m 0.4 1m
2m 2m
Conditional pdf 0.35 3m 0.35 3m
Conditional pdf
0.3 4m 0.3 4m
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 5 10 15 20 25 0 5 10 15 20 25
dBm dBm
(a) Beacon 1 (b) Beacon 2
RSSI disp. B3 Mean RSSI disp.
0.4 1m 0.4 1m
2m 2m
0.35 3m 0.35 3m
Conditional pdf
Conditional pdf
0.3 4m 0.3 4m
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 5 10 15 20 25 0 5 10 15 20 25
dBm dBm
(c) Beacon 3 (d) Mean RSSI
Figure 4: The pdf of the measured RSSI disparity, conditioned on the four different interpersonal
distances considered (Home data collection). The last plot refers to the mean of the RSSI disparity over
the three beacons.
they become broader (larger variance) for distances of 3 and 4 meters. Indeed, only the disparity
from Beacon 2 appears to be useful for discrimination between distances of 1 and 2 meters. The
mean RSSI disparity index reflects this overall behavior, with the pdf conditioned on distances
at 1 and 2 meters fairly well separated from those at 3 and 4 meters.
Given that both the phone RSSI index and the RSSI disparity index have distributions that
correlate, to some extent, with interpersonal distances, it can be of interest to analyze the joint
statistics of these two features. Specifically, we consider the vector formed by phone RSSI and
mean RSSI disparity, and study how the distribution of this vector conditioned on distances
larger or smaller than a given threshold 𝐷0 . Fig. 5 displays the logarithm of the ratio of the
joint pdf of this vector, conditioned on 𝐷 ≤ 𝐷0 and on 𝐷 > 𝐷0 , respectively with 𝐷0 equal
to 1 or 2 meters. Region with large positive or negative values of this quantity indicate good
discriminability. These figures suggest that discrimination using individual indicators may
be challenging, and that a 2-D classifier with non-separable boundaries may be called for. In
this study, we considered a very simple linear classifier that assigns equal weights to the two
features. In other words, this classifier applies a threshold to an index equal to the mean RSSI
disparity minus the phone RSSI index (indicated as Phone + RSSI disp. in the figures). Large
values of this index are likely to indicate large interpersonal distance.
ROC curves (plotting true positive rate, TPR, against false positive rate, FPR) are shown in
Log likelihood ratio - Distance threshold = 1 m
Mean RSSI disp. (dBm)
2
15
1.5
1
10 0.5
0
-0.5
5 -1
-1.5
-2
0
-80 -75 -70 -65 -60 -55 -50 -45
Phone RSSI (dBm)
Log likelihood ratio - Distance threshold = 2 m
16 2.5
Mean RSSI disp. (dBm)
2
14
1.5
12
1
10 0.5
8 0
-0.5
6
-1
4
-1.5
2 -2
0 -2.5
-80 -75 -70 -65 -60 -55 -50 -45
Phone RSSI (dBm)
Figure 5: The log likelihood ratio of the vector formed by phone RSSI and mean RSSI disparity, condi-
tioned on the interpersonal distances being smaller (null hypothesis) or larger (alternative hypothesis)
than the considered threshold of 1 m or 2 m (Home data collection).
Fig. 6. Each curve is obtained by varying a threshold on the considered measurements, where
a value larger than the thresholds (or smaller, in the case of phone RSSI) indicates a distance
𝐷 > 𝐷0 , for 𝐷0 equal to 1 or 2 meters. The values of the area under the curve (AUC) for the
relevant features are shown in Tab. 3, 4.
From Fig. 6, it is seen that the mean RSSI disparity performs better than individual RSSI
disparities, at least for small values of FPR. The mean RSSI disparity index proved largely
superior to the phone RSSI index in terms of distance discrimination for this data set. Depending
on the distance threshold, the best results (in terms of AUC) are obtained by either by the mean
RSSI disparity or by the phone+RSSI disparity feature. The effect of the distance threshold
𝐷0 was relatively minor, with the best value at 𝐷0 = 1 meter obtained with the phone + RSSI
disparity feature (AUC=0.86), and the best value at 𝐷0 = 2 meter obtained with the mean RSSI
disparity feature (AUC=0.886).
It is important to note that we observed a large variance across data sets, even though all
three data sets were acquired using similar modalities. For example, as shown in Tab. 4, data
from Set 1 gave substantially worse discrimination results than for the other sets, especially
when the distance threshold was set to 𝐷0 = 2 meters.
Distance threshold = 1 m Distance threshold = 2 m
1 1
0.9 0.9
0.8 0.8
0.7 0.7
0.6 0.6
TPR
TPR
0.5 0.5
0.4 0.4
0.3 0.3
Phone RSSI Phone RSSI
0.2 0.2
RSSI disp. B1 RSSI disp. B1
RSSI disp. B2 RSSI disp. B2
0.1 RSSI disp. B3 0.1 RSSI disp. B3
Mean RSSI disp. Mean RSSI disp.
Phone + RSSI disp. Phone + RSSI disp.
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FPR FPR
Figure 6: ROC curves using the considered measurements for proximity detection at distance thresh-
olds of 1 m and 2 m (Home data collection).
4.2. A Realistic Case: Campus Shuttle Bus
Public transit is arguably one of the most appealing application scenarios for proximity detection.
Social distancing may be difficult to observe inside a bus vehicle or a train car, which calls
for mitigation measures based, among other things, on contact tracing. In addition, proximity
measurements may be used to generate a crowdedness index, which could be broadcast to
passengers waiting at bus stops or train stations. Passengers can then decide whether to board
that bus vehicle or wait for the next one, or board a less crowded train car.
In order to evaluate the different considered features for proximity detection, we instrumented
a bus shuttle vehicle in our campus with four BLE beacons, of the same type and with the
same advertisement rate as in the previous case (see Fig. 7). Signal propagation is known to
be complex in buses due to the existence of a strong radio signal reflector such as metal [31].
We conducted two data collection exercises, the first with the Power level of the beacons set
to 1 (October 2020), the second, with power level set to 2 (February 2020). Power level is the
strength of the signal that a beacon broadcasts. Signal strength (RSSI) is in decibels relative to
a milliwatt (dBm). The maximum power that is available in iBeacons is 7 (4 dBm) that can be
ranged up to 70 m. We set the power level to 1 (-20 dBm) and 2 (-16 dBm) that can be ranged
approximately up to 4 m and 10 m. Note that while a higher emission power enables longer
transmission distances, it also reduces the life time of a battery-operated beacon. With default
power settings (power level equal to 3 or -20 dBM and advertisement interval set to 350𝑚𝑠 )
the battery can last up to 2 years. Two experimenters used an iPhone 7 and an iPhone 8 for
data collection from the sequence of seat pairs described in Tab. 1 and 2. Note that these sets
contain a larger variety of interpersonal distances than for the Home data set, and that data for
the same distance could come from multiple location pairs.
For each seat pair, both experimenters first collected data for two minutes while holding their
phone in their hand, then for two minutes while keeping their phone in their front pants pocket.
Data was collected while the vehicle was driven along its route, with passengers occasionally
boarding and leaving the bus. At most three passengers were in the bus at the same time during
data collection (note that, due to social distancing restrictions, at most six passengers were
allowed in the vehicle at the same time.)
Figure 7: Shuttle data collection layout representing the location of the beacons deployed on the
shuttle ceiling and seat numbers. Right of the figure is the front of the shuttle. Crossed red circle seats
are blocked seats for COVID-19 distancing.
The log ratio of the joint pdf of the vector formed by phone RSSI and mean RSSI disparity,
conditioned on distances larger and smaller, respectively, of a threshold 𝐷0 , are shown shown
in Fig. 8 for 𝐷0 =1 meter and 2 meters. As in the Home data collection case, we compiled data at
identical interpersonal distance into the same set (Combined). We should note that, unlike the
House data collection, various occluding surfaces (such as the backs of the vehicle seats) affected
signal transmission even for small interpersonal distances (except when the participants were
sitting next to each other.) This may be one of the reasons for the broad distribution of the
phone RSSI values when 𝐷 ≤ 𝐷0 (ranging from -80 dBm to -35 dBm).
ROC curves for the considered features are shown in Fig. 9 for the Combined set and 𝐷0 =1
meter and 2 meters. AUC values for the individuals sets (at different BLE power level) as well for
the combined case are shown in Tab. 5 and 6. Performances were substantially inferior to the
those obtained with the Home data set, especially for 𝐷0 = 1 meter. In all cases, the best results
were seen using either mean RSSI disparity, or the phone + RSSI disparity feature. However, the
improvement with respect to the phone RSSI was relatively marginal.
As in the case of the Home data collection, we observed a large variation of performance
using phone RSSI for the two individual sets at different BLE power levels. This is somewhat
baffling, considering that the BLE power from the beacons level should not affect the received
RSSI from another phone. It may be that other uncontrolled factors (e.g., the presence of other
passengers) may have contributed to this discrepancy. Interestingly, better results were obtained
for the mean RSSI disparity feature using power level 1 than for power level 2 (see also the
ROCs shown in Fig. 10.)
5. Discussion and Conclusions
We have presented a comparative analysis of RSSI–based techniques for proximity detection
in different environments. Our goal was to assess how well different types of measurements
Distance (m) Seat pairs
0.5 (4, 3), (7a, 8), (19b, 19a), (18, 19a)
1.0 (4, 2)
1.8 (7a, 19a), (4, 21)
2.5 (4, 20a), (4, 25), (5a, 19a)
3.28 (7a, 15)
4.0 (4, 19a)
Table 1
Power level 1 data collection seat pairs
Distance (m) Seat pairs
(4,3), (7a, 7b), (20b, 20a), (18, 19a),
0.5
(5a, 6a)
1.0 (4, 2)
1.5 (7a, 19b), (11, 9)
(7a, 19a), (11, 15), (4, 21), (4, 5a),
1.8
(21, 25), (5a, 7a), (5a, 20a)
2.5 (4, 20a), (4, 25), (7a, 20a), (7a, 11)
3.28 (7a, 15)
4.0 (4, 19a)
4.88 (11, 20a)
6.0 (4, 11)
Table 2
Power level 2 data collection seat pairs
AUC (D=1m) Set 1 Set 2 Set 3 Combined
Phone RSSI 0.680 0.793 0.783 0.770
Mean RSSI Disp. 0.605 0.883 0.733 0.805
Phone + RSSI Disp. 0.708 0.915 0.876 0.860
Table 3
AUC results for Home data sets when the distance threshold was set to 𝐷0 = 1 meter. Best results for
each column are shown in boldface.
AUC (D=2m) Set 1 Set 2 Set 3 Combined
Phone RSSI 0.588 0.72 0.834 0.735
Mean RSSI Disp. 0.689 0.987 0.755 0.886
Phone + RSSI Disp. 0.648 0.909 0.923 0.872
Table 4
AUC results for Home data sets when the distance threshold was set to 𝐷0 = 2 meters.
Log likelihood ratio - Distance threshold = 1 m
1.5
Mean RSSI disp. (dBm)
15
1
0.5
10
0
5
-0.5
-1
0
-80 -75 -70 -65 -60 -55 -50 -45 -40 -35
Phone RSSI (dBm)
Log likelihood ratio - Distance threshold = 2 m
Mean RSSI disp. (dBm)
1.5
15
1
0.5
10
0
-0.5
5
-1
0
-80 -75 -70 -65 -60 -55 -50 -45 -40 -35
Phone RSSI (dBm)
Figure 8: The log likelihood ratio of the vector formed by phone RSSI and mean RSSI disparity, condi-
tioned on the interpersonal distances being smaller (null hypothesis) or larger (alternative hypothesis)
than the considered threshold of 1 m or 2 m (Shuttle data collection at BLE power level 1 and 2).
Distance threshold = 1 m Distance threshold = 2 m
1 1
0.9 0.9
0.8 0.8
0.7 0.7
0.6 0.6
TPR
TPR
0.5 0.5
0.4 0.4
0.3 0.3
Phone RSSI Phone RSSI
RSSI disp. B1 RSSI disp. B1
0.2 0.2
RSSI disp. B2 RSSI disp. B2
RSSI disp. B3 RSSI disp. B3
0.1 RSSI disp. B4 0.1 RSSI disp. B4
Mean RSSI disp. Mean RSSI disp.
Phone + RSSI disp. Phone + RSSI disp.
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FPR FPR
Figure 9: ROC curves using the considered measurements for proximity detection at distance thresh-
olds of 1 m and 2 m (Shuttle data collection at BLE power level 1 and 2).
(namely, direct RSSI measurement from another user’s phone, and disparity of RSSI signals
received from multiple BLE beacons) can discriminate between interpersonal distances of 1
meter and 2 meters. The results show that the mean RSSI disparity index performs as well or
better than the direct phone RSSI index for these tasks, and that a simple combination of the
two indices often produces the best results.
While our experimental setups were effective for data collection (and, in the case of the
Shuttle data set, representative of real-world conditions), our study has a number of limitations.
Distance threshold = 1 m Distance threshold = 2 m
1 1
0.9 0.9
0.8 0.8
0.7 0.7
0.6 0.6
TPR
TPR
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.1 Power level 1 0.1 Power level 1
Power level 2 Power level 2
0 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FPR FPR
Figure 10: ROC curves using mean RSSI disparity for proximity detection at distance thresholds of
1 m and 2 m. Shuttle data collection at BLE power level 1 (blue curve) and at BLE power level 2 (red
curve).
AUC (D=1m) Pwr. level 1 Pwr. level 2 Combined
Phone RSSI 0.492 0.720 0.626
Mean RSSI Disp. 0.670 0.653 0.652
Phone + RSSI Disp. 0.568 0.727 0.646
Table 5
AUC results for Shuttle data sets when the distance threshold was set to 𝐷0 = 1 meter.
AUC (D=2m) Pwr. level 1 Pwr. level 2 Combined
Phone RSSI 0.595 0.772 0.720
Mean RSSI Disp. 0.831 0.760 0.783
Phone + RSSI Disp. 0.698 0.782 0.754
Table 6
AUC results for Shuttle data sets when the distance threshold was set to 𝐷0 = 2 meters.
We only used two models of one smartphone brand (iPhone). It is well known [40] that different
smartphones have different characteristics in terms of the received signals from a BLE beacon,
and a more exhaustive study with multiple smartphone brands would be necessary before
these results can be generalized. Our “toy case" of an instrumented living room may not be
representative of a more complex and crowded environment such as a shopping mall or an
office building. It is likely that different BLE beacon placements would result in widely different
performances, and we plan to experiment with different placement layouts in the future. Only
few passengers were present during the study, and we are planning for a more extensive data
gathering once social distancing rules are relaxed and more students will be using our campus
transportation system. The use of more sophisticated mechanisms than the linear classifier
used in our tests (see e.g. [20, 13]) could be considered, provided that enough data is collected
to enable good generalization.
Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant
No. NSF IIP-1632158. Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the author(s) and do not necessarily reflect the views of the National
Science Foundation.
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