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Nowadays Internet-of-Things and Industry 4.0 devices are often connected wirelessly. Current wireless sensor network (WSN) deployments are relying in most cases on the industrial, scientific and medical (ISM) bands without centralized resource scheduling. Thus, each device is a potential source of interference to other devices, both within its own WSN but also to devices in other collocated WSNs. If the transmission behaviour of devices from other WSNs is not random, we are able to find patterns in the time domain in their channel access. This is for example possible for periodic channel access, which is quite common for WSNs with demanding low-power and reliability requirements. The main goal of this work is to detect multiple sources of periodic interference in time slotted signal level measurements and estimate the time windows of future transmissions. This gives a WSN a certain understanding of the radio surrounding and can be used to adapt the transmission behaviour to thus avoid collisions. For this, the Multi Hypothesis Tracking algorithm is adapted and used together with timeslot-based interference measurements on low-cost sensor nodes. The applicability of the algorithm is shown with extensive simulations and the performance is demonstrated with measurements on a time division multiple access based WSN built upon the Bluetooth Low Energy physical layer.
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1
Time Slotted Multi Hypothesis Interference
Tracking in Wireless Networks
Julian Karoliny, Graduate Student Member, IEEE, Thomas Blazek, Member, IEEE, Fjolla Ademaj, Member, IEEE,
Andreas Springer, Member, IEEE, Hans-Peter Bernhard, Senior Member, IEEE
Abstract—Nowadays Internet-of-Things and Industry 4.0 de-
vices are often connected wirelessly. Current wireless sensor
network (WSN) deployments are relying in most cases on the
industrial, scientific and medical (ISM) bands without centralized
resource scheduling. Thus, each device is a potential source of
interference to other devices, both within its own WSN but
also to devices in other collocated WSNs. If the transmission
behaviour of devices from other WSNs is not random, we are
able to find patterns in the time domain in their channel access.
This is for example possible for periodic channel access, which
is quite common for WSNs with demanding low-power and
reliability requirements. The main goal of this work is to detect
multiple sources of periodic interference in time slotted signal
level measurements and estimate the time windows of future
transmissions. This gives a WSN a certain understanding of the
radio surrounding and can be used to adapt the transmission
behaviour to thus avoid collisions. For this, the Multi Hypothesis
Tracking algorithm is adapted and used together with timeslot-
based interference measurements on low-cost sensor nodes. The
applicability of the algorithm is shown with extensive simulations
and the performance is demonstrated with measurements on a
time division multiple access based WSN built upon the Bluetooth
Low Energy physical layer.
Index Terms—Bluetooth low energy (BLE), channel coexis-
tence, interference, multi hypothesis tracking (MHT), wireless
sensor network (WSN).
I. INTRODUCTION
With the rise of Internet of Things (IoT) and Industry
4.0, the number of wireless sensor networks (WSNs) and
devices with wireless transceivers is steadily increasing. Most
of these devices rely on the use of the unlicensed industrial,
scientific and medical (ISM) band. This is however limited in
capacity and each additional device is a potential source of
This work is funded by the InSecTT project (https://www.insectt.eu/).
InSecTT has received funding from the ECSEL Joint Undertaking (JU) under
grant agreement No 876038. The JU receives support from the European
Union’s Horizon 2020 research and innovation programme and Austria,
Sweden, Spain, Italy, France, Portugal, Ireland, Finland, Slovenia, Poland,
Netherlands, Turkey. (Corresponding author: Julian Karoliny.)
Julian Karoliny and Hans-Peter Bernhard are with Silicon Austria Labs
GmbH, 4040 Linz, Austria, and also with the Institute for Communications
Engineering and RF-Systems, Johannes Kepler University Linz, 4040 Linz,
Austria (e-mail: julian.karoliny@silicon-austria.com; h.p.bernhard@ieee.org).
Thomas Blazek, and Fjolla Ademaj are with the Research Unit Wireless
Communications, Silicon Austria Labs GmbH, 4040 Linz, Austria (e-mail:
thomas.blazek@silicon-austria.com; fjolla.ademaj@silicon-austria.com).
Andreas Springer is with the Institute for Communications Engineering and
RF-Systems, Johannes Kepler University Linz, 4040 Linz, Austria (e-mail:
andreas.springer@jku.at).
Copyright © 2022 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org.
interference to other devices, both within its own WSN but
also to devices in other collocated WSNs. In this context,
we consider interference as access to the channel by an
device external to our WSN, may it be cross-technology or
intertechnology interference. Especially in the 2.4 GHz ISM
band, many technologies like Bluetooth®Low Energy (BLE),
Wireless Local Area Network (WLAN), and ZigBee share the
same channels, and thus collisions are unavoidable.
Collisions with other devices can cause packet loss in a
WSN and thus result in an increasing number of retransmis-
sions. The collisions can also affect the interfering devices and
if they also rely on retransmissions, this again increases the
probability of collisions. Due to the increasing number of lost
packets and retransmissions, the energy consumption of the
devices will increase, which is especially problematic for low-
power IoT devices. Collisions can also cause the violation of
real-time constraints since the data might not reach the target
in time due to a backoff time before resending again. This is
a severe problem in safety-critical applications and industrial
control systems.
To minimize the number of collisions, it is important that
a WSN evaluates the interference behaviour of other devices
in close proximity and gains a certain awareness of the radio
frequency surrounding. A typical approach is to measure the
traffic or error rates and avoid highly occupied channels or
exclude these channels from hop lists [1]. This only considers
current or past interference events but cannot actively prevent
future collisions. However, if the interfering device shows a
certain pattern, we are able to use this information and predict
future collisions. A WSN with the possibility to reschedule
the own communication, e.g. certain time division multiple
access (TDMA)-based wireless protocols, can incorporate the
future channel access and choose different transmission times
to thus avoid collisions. For this, however, the interference has
to show a systematic pattern and cannot be purely random.
Although random access to the channel is a usual approach
for the media access control (MAC) protocol in many WSNs,
some MAC protocols show a deterministic, periodic access to
the channel, which is often the case for low-power devices
and sensor networks.
In this work, we present an approach that allows us to track
periodic multi-source interference at TDMA timeslot level
and predict future channel access of devices outside the own
WSN. We continuously measure the average signal level in the
channel of our WSN for all TDMA timeslots, which allows
us to evaluate the signal interference from external devices.
The main challenge here is to assign different measured inter-
This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
2
ference signals to different interferer sources and track them
over time. For this, we adapted the Multi Hypothesis Tracking
(MHT) algorithm, originally proposed in 1979 by Reid [2],
which is typically used for radar target or visual tracking. It
allows a systematic solution to the data association problem,
i.e. associating uncertain measurements to known tracks, by
considering all combinations of interference observations.
The contributions of this work are as follows:
We present a timeslot-based interference measurement
solution with low-cost hardware that can be used for
channel surveillance in WSNs. Based on these mea-
surements, we build the interference tracking on real
hardware.
For one example use-case, a TDMA-based wireless net-
work protocol, we include the measurement procedure
and show the periodic interference prediction for future
timeslots.
We implement and adapt the well-known MHT algorithm
to track periodic multi-source interference based on the
presented TDMA network.
With extensive simulation, we show the limitations of the
MHT for interference tracking and verify the performance
of the algorithm in the multi-source interference case.
Finally, we demonstrate the interference tracking capa-
bility of our algorithm with an example measurement.
The rest of the work is organized as follows. In Section II
we discuss and present related work in the field of WSN
interference, interference estimation, and the MHT algorithm.
The system model and our example use-case are presented
in Section III including the measurement procedure and used
protocol. Additionally, an example measurement is given.
Section IV introduces the basic idea of the MHT including
the adaptations to interference tracking. The performance of
the MHT and its applicability are evaluated in Section V by
measurements and simulations. Finally, conclusions are drawn
in Section VI.
A. Notation
Scalars are written as x, while vectors and matrices are
denoted as lower- and uppercase boldface respectively (xand
X). Time indices are indicated with subscript xk. Conditional
parameters are marked with |, e.g., xk|k1is the parameter x
at time kconditioned on the previous timestep k1.
II. RE LATE D WOR K
This work assumes deterministic, or more specific periodic
channel access from external devices for the interference
tracking. Therefore, we first discuss if this assumption is valid
considering the 2.4 GHz ISM band. Then we present related
work in the field of interference measurement and estimation,
followed by literature references to the used MHT algorithm.
A. Interference in Wireless Sensor Networks
We consider the access to a wireless channel in a WSN
to be either random or deterministic. If the channel access
from a device or network is purely random, no communication
pattern can be observed and used to predict future message
collisions with the own transmissions. This is the case for
random channel access within the own network and random
access of external devices. To coexist in channels with a high
percentage of random access, a common approach is the Clear
Channel Assessment (CCA) procedure [3] or simply to avoid
these highly occupied channels at all. Authors in [4], [5]
studied the type of interference and unwanted channel access
that WSNs have to face, especially in the unlicensed 2.4 GHz
ISM band.
For low-power applications, devices have to stay in energy-
saving mode as long as possible and avoid activating the radio
unit to receive packets from another device without guaranteed
transmission. A commonly used approach is to perform a part
of the communication synchronized, which results in periodic
channel access. Communication protocols like Bluetooth®
Mesh, Thread, or WLAN all include these synchronised low-
power amendments in newer releases, which shows a trend
toward a more deterministic communication. In the following,
we list the periodic behavior of some communication systems
and devices in the 2.4 GHz ISM band:
BLE connection initializer periodically polls the con-
nected devices in a TDMA fashion [6], where the connec-
tion interval (CI) defines the time interval that regularly
separates the start times of connection events. Although
frequency hopping is used in BLE, for channel selection
algorithm #1 the connection events will occur periodically
at 37 times the CI [7].
WLAN IEEE 802.11 sends beacon frames periodically
from an access point to announce its presence and provide
the SSID to the devices. They typically show a period
of 102.4 ms [8]. The Wi-Fi 6 (IEEE 802.11ax) standard
supports the Target Wake Time mechanism [9] that allows
to define a certain wake-up time for devices which will
result in a periodic channel access.
Thread is a low-power mesh network protocol for
IoT products. The Thread 1.2 specification [10] intro-
duced Synchronized Sleepy End Devices (SSEDs) for en-
hanced low-latency and low-power features. Communica-
tion with these devices happens periodically at scheduled
intervals.
ZigBee supports a beacon-enabled mode [11] for
synchronization with dedicated timeslots for devices con-
nected to the network coordinator or router.
WirelessHART is an industrial wireless communication
protocol. Due to its TDMA structure it will mostly show
periodic channel access where the period depends on the
configuration [12].
Microwave oven radiates a spectrum centered at
2.45 GHz, which can act as a severe source of interference
in the 2.4 GHz ISM band. The output cycle is tied to the
50 Hz AC input cycle [13] and therefore shows a period
of 20 ms.
Even if the majority of a communication protocol shows no
periodic behavior, the periodic parts may be enough to track
the source of interference and apply countermeasures for the
own network.
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content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
3
Our proposed method for interference tracking heavily relies
on periodic access to the channel and the algorithm fails if
the majority of the communication protocol utilizes random
channel access. One example of this would be IEEE 802.11
where the access has a strong random nature depending on
Carrier Sense Multiple Access (CSMA) and random backoff
times. However, even though the access can be considered
random, higher network layers of the communication protocol
can produce periodic access to a certain extent. Authors
in [14], [15] showed that specific applications like video
streaming on Youtube or Netflix, show a distinct pattern in
the channel access. Since the video data is mostly buffered
and transmitted with a certain rate in chunks, we can again
overall assume periodic access with a small uncertainty due
to the CSMA characteristic.
B. Interference Measurement and Estimation
While the different sources of disturbances for WSNs are
well studied, the topic of mitigating is mostly limited to
channel switching or including the risk of collisions in an
occupied channel in the requirements of the wireless link. In
recent years, there is a growing need for a better understanding
of channel usage, especially in the already very crowded
unlicenced ISM bands. Wireless networks cannot only rely
on theoretical interference, they have to observe the wireless
channel and use this information to optimally adapt to the
current circumstances. Ideally, no additional hardware like a
spectrum analyser is needed and the channel surveillance is
part of the communication system itself. Authors in [16],
[17] demonstrated methods to improve channel awareness
by evaluating the interference in different communication
channels in the 2.4 GHz ISM band. A wireless network can
use this information to select the best suitable channels for
communication while continuously evaluating the situation
and adapting to changes.
To further increase awareness, not only the link quality
of a channel is important, but also a classification of the
interference that causes link degradation is needed. Authors
in [18] demonstrated an approach to detect the presence of
interference in a channel and additionally classify it as low,
medium, or strong. Additionally, they provide estimates for
the duration of the interference. Authors in [19] evaluated
especially the interference caused by BLE and WLAN in the
2.4 GHz ISM band. They observed predictable patterns of the
interference and were able to identify and distinguish inter-
ference based on Received Signal Strength Indicator (RSSI)
measurements. Authors in [20], [21] studied the possibility
to detect and classify sources of interference in WSNs. They
proposed methods to measure interference directly on low-
cost sensor nodes by continuously measuring the RSSI of the
channel without detecting the interfering packets. Our work
uses a similar measurement approach, although we focus on
the tracking of individual sources of periodic interference
over time. This will enable the possibility to predict future
channel access. Additionally, the estimated period can provide
information about the source of interference, e.g., different
communication protocols will show different typical transmis-
sion periods.
With the knowledge of future channel access from other
devices, a wireless network can adapt its own communication
to avoid collisions. Authors in [22] showed with the example
of BLE and IEEE 802.15.4 that it is possible to minimize
the collisions and improve the performance of the network by
rescheduling the communication of one device. They assume
that the channel access of the devices is known at a central
station and can thus calculate timeframes where transmission
happens simultaneously on the same channel. With this in-
formation, the devices can react and reschedule accordingly.
However, this approach can only mitigate devices that are
known to a central coordinator and share their information.
Our work aims to passively listen to the channel and find
periodic interference which can be used similarly to this work
for rescheduling. For this we can not only analyze the current
and past interference which is typically done in the presented
literature, we have to track the current interference and need
to estimate future transmissions.
To track the source of periodic interference, one key element
is to estimate the transmission interval. Different sources will
show a distinct period or pattern in their transmit behaviour
and with an accurate period estimation future collisions with
the own communication can be predicted. Authors in [23],
[24] presented methods to estimate the period of sparse point
processes that can also be used for interference tracking.
However, without additions, the presented algorithms are not
able to track multiple sources of interference and fail in
distinguishing sources with the same interference pattern, e.g.,
multiple WLAN sources.
C. Multi Hypothesis Tracking
The main challenge in the interference tracking task is to
assign the different interference measurements to a target and
distinguish it from other sources and noise. For this, our
work uses the MHT algorithm, originally proposed in [2].
The MHT is well studied in the literature and there exist
several implementations for various applications, especially in
the field of radar and visual tracking [25]–[27].
Because of the ability to evaluate multiple possible hypothe-
ses, it provides a systematic solution to the data association
problem, which makes it perfect for periodic multi-interference
tracking. However, with an increasing number of combina-
tions, the computational complexity of the algorithm gets
challenging. Authors in [27], [28] discussed improvements
to the computational critical parts of the MHT algorithm.
To keep the computational manageable the MHT relies on
efficient pruning, i.e., delete unlikely combinations and only
keep promising tracks alive. Another approach is to group
the different tracks to keep the computational complexity
manageable [29]. This is, for example, needed if we can group
interference events which then show a periodic behaviour in
a larger scale. Authors in [30] surveyed various deep learning
approaches in video multi-object tracking, including the MHT
tracking. In these approaches, parts of the MHT are improved
using deep learning.
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content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
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4
III. SYS TE M MOD EL A ND IMPLEMENTATION
The idea of this work is to track periodic multi-source
interference in WSNs. The additional information about the
radio frequency surrounding can be used to identify other
devices, detect intrusion of the network, or for synchronizing
to specific interference to monitor the behaviour. The example
use-case on which we focus in this work is the prediction of
future interference events in a TDMA-based wireless network
protocol. Instead of dealing with current or past interference
like CSMA, we are able to predict future transmissions of
other devices. This enables the possibility to reschedule the
own transmission to actively avoid collisions. The interference
tracking and prediction can be performed by a central station
without power constraints, however, CSMA has to be per-
formed by each node individually, which might be infeasible
for low-power nodes. CSMA proved to be a good mechanism
to avoid collisions, however, in highly synchronized applica-
tions it cannot be applied since devices wait for packets at
specific times that cannot be delayed by CSMA.
We chose a TDMA network with high reliability and low-
power requirements, where we explain how the interference
measurement works and how we are able to track periodic
interference. The TDMA-based protocol is managed by a
central network coordinator, where each node in the network
has its own communication timeslot. We show how the needed
measurements can be performed directly within the TDMA
framework and use the MHT algorithm to perform predictions
of future interference. However, neither the following measure-
ment procedure nor the proposed algorithm for interference
tracking is limited to the presented communication protocol
or use-case.
The interference tracking itself consists of two parts: the
interference pattern measurement and the tracking with the
MHT. In the first phase, the signal level of the channel is
measured and the data is collected at a central unit. In the
second phase, the measured interference is evaluated to track
and distinguish the different sources. Important to mention is
that the interference measurement should not be performed
by energy constraint low-power sensor nodes in the network,
since this would dramatically increase the needed energy for
these devices. The interference measurement is performed
by separate nodes without energy limitations or the network
coordinator. The calculation is done at the network coordinator
side where the information can be distributed to the low-power
nodes during the regular communication with these devices.
For the tracking, the MHT algorithm described in [27] was
implemented. Since the original use-case of the MHT is object
tracking in visual or radar data, adaptations are made to tackle
the special cases that occur in the timeslot-based interference
tracking task. New measurements can be evaluated in an online
fashion and predictions for future collisions within the own
network can be made.
A. Hardware and Protocol
The TDMA protocol we use in this work is the Energy
and Power Efficient Synchronous Sensor Network (EPhESOS)
protocol [31]. In an EPhESOS network, each node gets a
specific timeslot for the communication assigned by the net-
work coordinator. All possible timeslots are collected in a so-
called superframe, which repeats periodically with a defined
superframe period. This assures a controlled and deterministic
access to the channel. It also avoids collisions within the
network since nodes are only allowed to communicate during
their assigned timeslot. Due to the fixed beacon interval and
the timeslots, the communication can be performed highly
synchronized, which allows the nodes to stay in energy-saving
mode most of the time and the time with an active radio
unit is minimized. With the periodic beacons, the interference
information can be easily distributed to the nodes and they
can react accordingly. Another advantage is the availability of
the EPhESOS source-code, which allowed us to implement the
interference measurement directly within the network protocol.
This gives us the possibility to show the interference tracking
performance of our algorithm with real measurements. Fig-
ure 1 depicts the frame format of the EPhESOS protocol,
including the beacon for synchronization followed by the
timeslots for the different nodes.
Beacon Beacon
superframe
timeslots
Fig. 1. Format of the EPhESOS superframe including the beacon for
synchronization and the timeslots of the individual nodes.
For the measurements and practical implementations in
this work, we consider the EPhESOS protocol on top of
the BLE physical (PHY) layer. As a hardware platform,
the Nordic™NRF52840 [32] controller with an integrated
transceiver unit is used.
B. Timeslot-based Interference Measurement
To perform the required measurements, we introduce sniffer
nodes, which are special sensor nodes that measure the signal
level of the channel continuously and transmit the data to the
network coordinator. Instead of direct message reception, only
the signal strength is considered, which allows observing the
interference from any communication standard. The channel
access in the EPhESOS network is only controlled within the
network, the interference of an external device can appear at
any timeslot. However, for devices interfering with the target
WSN with a periodic transmit behaviour, specific patterns can
be detected if the interference is observed across multiple
superframes. For example, if we assume a superframe period
of 100 ms, the interference of an IEEE 802.11 WLAN beacon
with a period of 102.4 ms will appear in each subsequent
superframe a certain number of timeslots later. If now mul-
tiple subsequent superframes are considered, we are able to
distinguish periodic interference from random interference. In
addition, we can distinguish multiple periodic interferences
from each other. We restrict the measurement resolution to the
timeslot duration and measure the average signal levels of the
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content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
5
timeslots using energy detection, a feature in IEEE 802.15.4
[33] and available in many commercial transceivers. It allows
an automatic averaging of the signal level of the current
channel for a duration of 128 µs, which is used to measure
the signal level within all timeslots of the superframes.
C. Example Measurement
To demonstrate the interference measurement and visualize
the patterns of periodic interference, experiments with the
following setup are conducted. A TDMA network with one
network coordinator and one sniffer node is placed in an office
environment and the interference is measured. To show the
different patterns, two interferers are placed nearby which
transmit at a period of 102.4 ms and 92.4 ms, respectively.
Both the measurement system and the interferer, use the
BLE 2M PHY layer with a 2 MHz bandwidth and Gaussian
Frequency Shift Keying as modulation scheme. This example
measurement was performed on BLE channel 22 with a center
frequency of 2.45 GHz and a transmit power of +4 dBm.
Figure 2 depicts the result of one such measurement, show-
ing the interference of the timeslots over the measured subse-
quent superframes. If in a timeslot the measured signal level
is above a 90 dBm threshold, it is marked black, otherwise
it is left empty. The first interferer transmits with a 102.4ms
period, which is larger compared to the superframe duration
tSF = 100 ms. Therefore the observation of the interference
shifts to a later timeslot (i.e. higher timeslot number) with
every new superframe. This results in the two lines with a
positive slope one can recognize among the random pattern of
interference which is shown in black rectangles in Fig. 2. The
second interferer, which transmits with a period of 92.4 ms
has a lower period as compared to the target WSN. Thus,
the resulting interference appears several timeslots earlier in
every new superframe. This pattern is difficult to detect in the
measured pattern from Fig. 2. In Section V we will see how
the MHT is able to find and track also this pattern. This and
other measurements conducted during the work are published
as an open-source dataset and can be found on GitHub and
Zenodo under InSecTT TDMA Interference Dataset [34].
The challenge now is to find the periodic interference pat-
tern in the measurements and distinguish them from each other
and from the random interference. Additionally, we want to be
able to track the interference over time and make predictions
for the appearance of interference in future superframes. This
task is solved with an adaptation to the MHT algorithm.
IV. MULT I HYP OTH ES IS INTERFERENCE TRACKING
The general idea of the MHT is to delay the data association
decision by keeping multiple hypotheses active until ambigu-
ities are solved. In each superframe, there will be multiple
interference observations, which were already shown in Fig. 2.
The goal is to find the interference observations from the
same periodic source and connect them from one superframe
to the other. These connected sequences of observations are
referred to as track hypotheses which are managed in a tree-
like structure, the so-called track trees. In each superframe, the
existing track hypotheses are updated with new measurements.
0 10 20 30 40 50 60 70 80 90 100
timeslot number
0
20
40
60
80
100
superframe number
measured interference
Fig. 2. Example measurement with the NRF52840 nodes in the presence
of two periodic interferers. Timeslots with a higher average signal level than
-90 dBm are marked black, otherwise they are left empty.
However, if for a track hypothesis in a track tree multiple ob-
servations would fit, the track hypothesis is updated with those
multiple measurements in separate branches. This of course
leads to ambiguities since now multiple track hypotheses (in
one track tree) share the same observations and all but one
of these tracks have to be eliminated, which is referred to
as pruning. For making a pruning decision we will define a
scoring to favour the track hypotheses connecting observations
from periodic interferers over random interferers. The global
hypothesis is the best set of track hypotheses (based on the
score) that are not in conflict, i.e., that do not share any
interference observation at any superframe.
To demonstrate how the MHT algorithm works for interfer-
ence tracking, Fig. 3 depicts the schematic for a simplified case
with one periodic interferer (×) and one random interferer
(). In this example the periodic interferer has a slightly
larger period compared to the superframe duration of the
TDMA protocol, hence in each subsequent superframe, the
interference occurs one timeslot later.
In the initial superframe SF1, no track hypotheses are
available for an update, hence a new track hypothesis is
started for the interference detected in TS2. In the following
superframe SF2, two interference observations are available for
this track hypothesis, so it is updated with both forming a track
tree with two separate branches. The subsequent superframes
SF3and SF4contain only one observation each and both track
hypotheses are updated accordingly. The two track hypotheses
in the track tree share now the same observations in SF1and
SF3. As mentioned before, this results in a conflict that has
to be solved in the following superframes and based on the
individual track scores, only one of these track hypotheses will
This article has been accepted for publication in IEEE Internet of Things Journal. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
6
Fig. 3. Schematic of the MHT algorithm for a simplified example with one
periodic interferer (×) and one random interferer (). The two lines mark the
track hypotheses that the MHT will consider.
survive. This procedure continues for all superframes.
Track hypotheses do not have to start at the first superframe
and therefore the MHT algorithm uses all new detections
also as the starting point of new track hypotheses. On the
one hand, this ensures that every possible track is considered,
but on the other hand, this dramatically increases the number
of track hypotheses with every superframe. This is another
reason why pruning is essential for the successful application
of MHT. Problems with updates occur if there is no suitable
detection for a track hypothesis available. This happens for
example at crossing points, i.e. the observations of multiple
interferers overlap in time and are not distinguishable, or if an
interference detection is missing due to measurement errors.
To mitigate this problem, the track hypotheses are not only
updated with detections but also with predictions.
To handle the update and prediction steps of the MHT
algorithm, a separate estimator for each track hypothesis is
used. For this, we introduce the vector xkdescribing the state
of a track hypothesis at time k
xk=sk
˙sk,(1)
where skis the timeslot number occupied at time kand ˙skis
the corresponding velocity. In the context of interferer timeslot
estimation, the velocity corresponds to the timeslot shift from
one superframe to the next. I.e., for a periodic interferer that
transmits with the same period as our network, the velocity is
zero. For the chosen state vector, the velocity is proportional
to the period of the interferer and can be used to estimate the
period and the timeslot position in the next superframe.
To provide a better overview of the individual steps, Fig. 4
depicts the flow diagram of the MHT algorithm including the
corresponding subsections where the individual blocks will
be discussed. The changes of the original MHT algorithm
for interference tracking are mainly within these blocks. One
additional block for interference tracking is overflow|underflow
marked in blue, which will be discussed in Section IV-B
and Section IV-E. Here all the special exceptions are handled
which will occur in the interference tracking case.
Track Prediction
Section IV-A
overflow|underflow
Section IV-B
Section IV-E
Gating
Section IV-C
Track Scoring
Global Hypothesis
Tree Pruning
new
measurement
start new
track trees updated tracks
remaining
track
new tracks
Section IV-D
Fig. 4. Flow diagram of the Multi Hypothesis Interference Tracking Algo-
rithm.
A. Kalman Filter and Model
The state estimates xkof the individual track hypotheses
are calculated by using a Kalman filter [35]. To represent the
behavior of the periodic interference, we propose the following
state transition model
xk=1 1
0 1
| {z }
F
xk1+w,(2)
where a constant velocity, i.e., a constant period of the
interferer, is assumed. The state noise process w N (0,Q)is
modeled as a multivariate normal distribution with zero mean
and covariance Q. For the tracking, only the timeslot number
skis accessible for measurement, therefore the observation
matrix His introduced to map xto an observation state
zk=1 0
| {z }
H
xk+v,(3)
with the measurement noise v N (0,R). The noise covari-
ance matrices Qand Rcan be used to tune the characteristics
of the Kalman filter, e.g., favor measurements over prediction.
The tracking with the Kalman filter for every new super-
frame can be divided into two steps, prediction and update. In
the prediction step, the model proposed in Eq. (2) is used to
perform a prediction for the state ˆ
xk|k1and the covariance
matrix ˆ
Pk|k1of the current timestep kusing
ˆ
xk|k1=Fˆ
xk−|1k1,(4)
ˆ
Pk|k1=Fˆ
Pk1|k1F>+Q.(5)
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In the update step, the measurement residual ykand residual
covariance matrix Skare calculated with
yk=zkHˆ
xk|k1,(6)
Sk=Hˆ
Pk|k1H>+R,(7)
where zkis the current detection. With this, the optimal
Kalman gain Kkis calculated.
Kk=ˆ
Pk|k1H>S1
k(8)
If in the current superframe a valid interference observation
exists for an update, the new state and covariance can be
calculated using
ˆ
xk|k=ˆ
xk|k1+Kkyk,(9)
ˆ
Pk|k= (IKkH)ˆ
Pk|k1.(10)
If no valid observation is available, the current state and
covariance are directly computed by the prediction steps
Eqs. (4) and (5).
B. Accounting for the Limited Number of Timeslots
A TDMA superframe consists of nTS timeslots and therefore
the proposed linear Kalman model in Eq. (1) is only valid for
{sR: 0 snTS}. For a periodic interferer with ˙s6= 0,
the estimation of the Kalman filter will always exceed nTS (or
fall short of 0) at some point in time. Due to its periodicity,
interference with ˙s > 0will simply “wrap around” and appear
in a timeslot at the beginning of the superframe. The same
happens for ˙s < 0in the other direction.
In the following, we define a falling short of the lower
bound of safter an update (s < 0) as underflow and exceeding
the upper bound of safter an update (s>nTS) as overflow,
respectively. To model this behaviour, the timeslot number s
in Eq. (1) is corrected after the prediction step according to
scor =
s, for 0snTS
mods, nTS,for s < 0(underflow)
mods, nTS,for s>nTS (overflow)
,(11)
where mod(·,·)is the modulo operation. This assures that
every Kalman prediction results in a timeslot number within
the superframe structure, i.e. 0snTS.
C. Gating
Updating every track hypothesis with every new interference
observation leads to a high number of track hypotheses and
eventually to problems in finding the global hypothesis. In
fact, most interference observations will not fit the existing
track hypotheses because it is either random interference or
interference from another source. To keep the number of track
hypotheses manageable, a simple gating mechanism is applied
to decide whether a track hypothesis is updated or not. For this
decision, we calculate the Mahalanobis distance dk[36] of a
track hypothesis for new interference observations by
d2
k=y>
kS1
kyk,(12)
where ykis the measurement residual calculated by Eq. (6)
and Skis the residual covariance matrix calculated by Eq. (7).
Only if dkis below a defined gating threshold dth, the track
hypothesis will be updated with the new interference obser-
vation. The Mahalanobis distance is originally used to whiten
different measurements. However, one additional advantage is
that the residual covariance matrix Skwill naturally adapt the
gating. At initialization of the Kalman filter, Skwill be large,
allowing a higher residual. With increasing Kalman updates,
Skwill decrease, resulting in a tighter bound and fewer
false track updates. If RSSI values of the measurements are
available, an additional gating with these values can be applied
to improve the distinction of the individual track hypotheses.
At no other point of the MHT algorithm, the RSSI values are
directly needed for tracking.
D. Managing the Individual Track Hypotheses
Since the MHT algorithm allows to update every track
hypothesis with every observation in a superframe, ambigu-
ities are unavoidable. With no countermeasure, the number
of track hypotheses in the individual track trees will grow
exponentially, since in every new superframe new branches
are generated. Therefore, a good scoring of the individual
track hypotheses and the pruning of unlikely paths as soon as
possible is crucial for the feasibility of the algorithm. To keep
the number of track hypotheses at a manageable level, after an
update the steps track scoring, finding the global hypothesis,
and tree pruning are applied:
1) Track Scoring: The individual track hypotheses are
scored using the log likelihood ratio (LLR) between the
target hypothesis and the false alarm hypothesis with the
corresponding probabilities PT,K and PF ,K at timestep K.
The target hypothesis is defined as the marginal likelihood of
the observation distribution of the Kalman filter. It is defined as
Gaussian distribution with Nzk;Hˆ
xk|k1,Sk. As we have
no information about the false hypothesis, i.e. an uninformative
prior, the likelihood is chosen uniformly distributed across the
nTS possible timeslots with PF,k =n1
TS . This results in the
LLR as
LLRK= log PT ,K
PF,K
= log
K
Y
k=0
1
2πdetSkexp(1
2y>
kS1
kyk)
n1
TS
.
(13)
To score the track hypotheses in an online fashion the LLR
can be calculated recursively with
LLRk=LLRk1+ LLRk,(14)
LLRk=(log (1 PD)no track update
log nTS 1
2log |2πSk| 1
2d2
ktrack update ,
(15)
where PDis the expected probability of detection, Skthe
residual covariance from Eq. (7), and dkthe Mahalanobis
distance from Eq. (12) for timestep k.
2) Global Hypothesis: After the update step and scoring,
we now have to find the most likely combination of all track
hypotheses given the set of track trees, the global hypothesis.
This multidimensional assignment problem can be formulated
as a Maximum Weighted Independent Set (MWIS) problem
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as stated in [27] and can be solved exactly with a standard
Integer Linear Programming (ILP) solver. This part is the most
computational intense and one reason to keep the number of
possible track hypotheses low.
3) Tree Pruning: The global hypothesis provides the set
of track hypotheses with the highest scores which are not in
conflict with each other. Track hypotheses or whole track trees
that show a conflict with this solution have to be pruned to
solve ambiguities. This ensures that the track trees will not
grow uncontrolled and only the most likely track hypotheses
survive. For this, the N-scan pruning approach described in
[27] is used, which can be summarized in two steps: first, the
result of the global hypothesis is used and the corresponding
track trees are identified. Second, for all track hypotheses
(the branches in the track trees), we go back Nsteps in
the corresponding track trees and delete all tree branches
that diverge from the optimal track hypothesis, i.e., the one
with the highest score. These steps are repeated for each new
superframe.
E. Adaptations to the Original MHT Algorithm
The standard MHT algorithm assumes that in each frame
the objects to be tracked are only at exactly one position (one
observation per superframe per interferer), though sometimes
the corresponding observation is missing due to measurement
errors. For the original use case—the tracking of physical
objects—this assumption is valid since a real object can
neither be in two different positions at the same time nor
suddenly disappear. However, this assumption does not hold
for the TDMA interference tracking and the two special cases,
overflow and underflow, have to be considered separately.
Figure 5 depicts the differences to the initial assumption for an
overflow and underflow for a simplified example with nTS = 4.
Overflows occur for periodic interferers with a higher period
compared to the superframe duration. Due to this longer
period, at some point, the whole superframe will be skipped as
depicted for SF5in Fig. 5a. This happens when the interference
observation is near the right border (here TS4in SF4) and the
next corresponding observation has a difference larger than
the superframe duration. As a result, the observation is at the
beginning of SF6in this example. In this case, no observation
of the corresponding interferer will occur in the superframe in-
between and the MHT algorithm has to be adapted to skip all
updates for the corresponding track hypothesis. Underflows,
on the other hand, occur if an interferer has a lower period
compared to the superframe duration. As depicted in Fig. 5b,
it is inevitable that at a certain point, two observations of the
same periodic interference source occur in one superframe.
Here the MHT algorithm has to accept two updates and
consider the possibility that the corresponding observations for
one or both of these updates are missing due to measurement
errors.
In addition to the updating, these special cases need also
to be considered in the global hypothesis and pruning of the
track trees.
(a)
(b)
Fig. 5. Simplified example with only four timeslots to demonstrate the two
special cases, overflow and underflow, that can occur in the interference
tracking. (a) Overflow. (b) Underflow.
F. Limitations of the MHT Algorithm
The MHT algorithm was originally proposed for multi-
object tracking in video data, therefore it processes the mea-
surements frame by frame. Additionally, it is assumed that
objects will not change the position between the frames much,
therefore, the best performance for our use-case is for an
interferer period close to the superframe period. The frame-
by-frame approach of the algorithm brings also a limitation to
the trackable interference. The upper bound for the interferer
period which can be tracked by our algorithm is two times
the superframe period. In the case of a larger period, the
interference is only observable in every second superframe
and since the algorithm assumes that each measurable object
is present in every frame, the MHT fails at this point. One way
to overcome this is to run an additional MHT algorithm that
considers only every second superframe. Here, the algorithm
would simply estimate half the period which can be corrected
easily afterward.
The lower bound for the interferer period which can be
tracked by our algorithm is not as strictly defined as the upper
bound. Below half the superframe period, interference obser-
vations will start to occur two times in the same superframe
for the same periodic interferer. The frame-to-frame approach
will not allow detecting interrelated interference, hence the
algorithm will simply use two separate track hypotheses for the
same interference. For predicting future interference events,
this brings no disadvantage and the separate tracks can be
merged by postprocessing, e.g., by combining suitable track
hypotheses with nearly the same RSSI level.
Another limitation is the amount of interference that can
be processed with the MHT algorithm. If there is too much
periodic or random interference per considered superframe,
the number of track hypotheses will dramatically increase
and hence also the computational complexity of the MWIS
problem. At this point the MHT may still be able to predict
future unoccupied timeslots, however, there might not be
enough free timeslots left for the nodes to react to blocked
timeslots. In this case, it may be beneficial to follow the
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9
classical approach of switching to a less occupied channel.
Additionally, the time resolution of the measurements has
to be considered. Since the measurements are timeslot based,
the duration of one slot will define our measurement res-
olution. We will not be able to detect interference with a
much smaller transmission duration compared to the timeslot
duration. However, this will not affect our use-case, since these
very short interferences may not disturb the functionality of
our network. If a higher time resolution is needed, the signal
level of fractions of a timeslot can be measured and used for
tracking.
V. EVAL UATIO N OF T HE INTERFERENCE TRACKING
PERFORMANCE
In this section, the interference detection capability of the
MHT algorithm is verified with simulations and real-world
measurements. For this, the proposed TDMA frame structure
for the EPhESOS network with the configuration from Table I
is used, where tSF is the superframe duration and tTS the
timeslot length. As depicted in Fig. 1, this will leave a window
of 10 ms reserved for the beacon and the additional guard
times which is also the duration in each superframe where
no measurements are available. These parameters are used for
both, the simulations and the real-world measurements with
the EPhESOS network.
TABLE I
CONFIGURATION FOR SIMULATION AND MEASUREMENTS.
BLE Channel nTS tSF tTS
22 100 100 ms 0.9 ms
To assess the performance of the MHT algorithm, we com-
pare the estimated tracks with the observations without noise
and random interference. For the simulations, the observations
of the periodic interferer are directly accessible. However, for
the real-world measurements we cannot make this separation.
Therefore, we performed reference measurements directly at
the interferer sources and measured the timing. These addi-
tional measurements are only available in our test scenario and
are not accessible for the real application since the interference
is generally assumed unknown with no possibility to measure
it individually.
To measure the performance, the problem is mapped to a
binary classification, i.e., does interference appear in a timeslot
and is it estimated correctly. As metrics the true positive
rate (TPR) and true negative rate (TNR) are used, which are
defined as
TPR =true positive
true positive + false negative ,(16)
TNR =true negative
true negative + false positive .(17)
Since we are more interested in the timeslots with detected
interference and the data is highly unbalanced, i.e. we have
much more free timeslots than timeslots with interference ob-
servations, the TPR is the better performance metric. However,
for binary classification, the TPR alone is not sufficient. If
for example the MHT algorithm always identifies interference
in all timeslots, the TPR leads to a perfect result, which is
obviously not the case. This is because the TPR does not
consider the false positives and therefore, we also included the
TNR in our evaluation. The false negative rate (FNR) and false
positive rate (FPR) are not considered, since in our mapped
binary classification they are just the “one-minus-version” of
the true rates.
The interference simulation and tracking with the MHT
algorithm are implemented in Python, which gives us the
possibility to perform the evaluations on different platforms.
Except for the computational effort, the simulation has no
limitations like simulation length or the number of simulated
interferers. A computational critical part in the MHT algorithm
is solving the MWIS problem as mentioned in Section IV-D.
To solve this, we used two different ILP solver Gurobi [37]
and CBC [38]. For the comparison of the computational effort,
the Python library CProfile is used which allows for evaluating
the code execution time of the individual blocks of the MHT
algorithm.
A. Performance for Different Interference Periods
The MHT works best for interference with a period similar
to the superframe duration. However, in this section we eval-
uate the performance for all trackable interferer periods with
simulations. For this, we test the MHT within the theoretical
limits defined in Section IV-F. The upper bound, i.e. two times
the superframe period, results for the given configuration in
200 ms. As the lower bound is not clearly defined, i.e., tracks
with a too low period can be split into multiple tracks with
a higher period, we will consider interferer periods down to
20 ms, which will result in 5 track hypotheses for such an
interferer. This is also the period with which a microwave
oven might interfere in the 2.4 GHz frequency band.
20 40 60 80 100 120 140 160 180 200
interferer period in ms
0.80
0.85
0.90
0.95
1.00
true rates
true positive rate
95% confidence interval
true negative rate
95% confidence interval
Fig. 6. True rates for all interferer periods in the defined limitations for
the algorithm including the 95% confidence interval calculated over the 1000
Monte Carlo realisations.
Figure 6 depicts the TPR and TNR for all interferer periods
in the defined range. Additionally to the periodic interference,
5% of the timeslots are occupied by random interference
from different sources. For the presented results 1000 Monte
Carlo realisations with a random starting point of the periodic
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10
interference and noise were conducted for 1000 superframes
each. The curves represent the mean true rates of all 1000
realisations including the 95% confidence interval, which fits
the mean quite well and is therefore hardly distinguishable.
Within the defined limits, the interference tracking shows good
results with an expected performance drop near the upper
bound of 200 ms. In this region, the measured distance of
interference timeslot numbers is becoming too large until,
finally, the interference starts to skip every second superframe,
thus making it unable for the MHT algorithm to track it
anymore. For lower periods a performance fluctuation can
be observed since here multiple track hypotheses for each
periodic interferer are generated, which also increases the
possible combinations among the track hypotheses and the
random noise. As a result, additional wrong track hypotheses
are generated which will lower the TPR. The simulation shows
significant performance differences for selected frequencies,
especially between 20 ms and 60 ms. Even with an increasing
number of Monte Carlo realisations, there is no averaging
effect observable. For interferer periods below half the su-
perframe duration, the MHT algorithm has to use multiple
tracks for one interferer (see Section IV-F). For certain periods,
multiple track solutions exist and some sub-optimal solutions
lead to a lower TPR. However, even for these sub-optimal
solutions, the TPR always stays above 0.9, which we consider
a good performance. Overall, the MHT was able to detect
over 95% of the timeslots with interference most of the time
and at least 90% for periods under 40 ms. The TNRs curve
shows that also the number of wrongly identified interference
observations was good for all simulations.
B. Performance for Multiple Interferer
The previous evaluation only covered the single periodic in-
terferer case. However, now we want to show the performance
and capability of the MHT for multiple sources of periodic
interference. For this, we again performed interference simu-
lations and applied the MHT algorithm. We conducted 25 000
different interference scenarios, where for each we first choose
a random number of periodic interferer nint from 1 to 5 and
then selected for each a random period from 50 ms to 150 ms.
Like before we mapped the problem to a binary classification
and calculated the TPR and TNR for the real interference
compared with the tracked one. Fig. 7 shows the empirical
Cumulative Distribution Function (eCDF) of the results where
we additionally marked the 5% and 50% probability including
the corresponding TPR and TNR. In the multi-interference
case, only 5% of the results showed a TPR below 0.9558
and a TNR below 0.9937. This shows that even with multiple
periodic interferences the MHT is capable of separating the
individual sources and performing predictions.
Fig. 7 considered the combined results for all nint, however
we additionally want to evaluate how the performance of the
MHT algorithm depends on the number of interferer. Figure 8a
shows the eCDF of the TPR for 1, 3 and 5 interferers. The
TNR does not change significantly for the different nint and
is not depicted in this figure. With increasing number of
interferer the performance of the MHT drops, however, even
0.9400
0.9777
0.9558
0.9985
0.9937
true rates
0.0
0.2
0.4
0.6
0.8
1.0
eCDF
TPR
TNR
P50
P05
Fig. 7. eCDF of the true rates for 25 000 periodic interference realisations
with a random number of interferer between 1 and 5, and random period
between 50 ms to 150 ms.
for nint = 5 the TPR is still 0.9489 for 95% of the simulations.
Additionally to the TPR we also calculate the root mean
squared error (RMSE) between the estimated track of the MHT
and the detected interference. Fig. 8b depicts the empirical
Complementary Cumulative Distribution Function (eCCDF)
for the RMSE, again for 1, 3 and 5 interferers. Here, we can
again see a performance decrease if the MHT has to estimate
multiple interferers.
Table II summarizes the main results of Fig. 8 for all
simulated nint. The results in the P05 columns depict, for
example, the performance of the MHT which can be expected
for 95% of the simulations. By increasing the number of
interferers, the TPR only changes minimal since here we
only evaluate if the interference was detected in the right
timeslot. The changes in the RMSE are higher, however, for
nint = 5 we still could achieve a RMSE of 0.6255 ms. This
can be considered a good performance since the simulated
measurement resolution is 0.9 ms, which is the duration of
one timeslot.
TABLE II
TPR AN D RMSE RES ULTS O F THE I ND IVI DUA L nint FOR T HE P50 A ND
P05 PRO BAB ILI TY M ARK .
TPR RMSE
nint P50 P05 P50 P05
1 0.9840 0.9676 0.1620 ms 0.3595 ms
2 0.9809 0.9621 0.2368 ms 0.4368 ms
3 0.9778 0.9588 0.3060 ms 0.5020 ms
4 0.9741 0.9542 0.3634 ms 0.5680 ms
5 0.9704 0.9489 0.4144 ms 0.6255 ms
C. Computational Effort
The MHT algorithm solves the data association problem by
evaluating every existing track against every new measurement
and therefore heavily relies on the ability to keep the number
of active tracks low. The computational demanding parts of
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11
0.9400
0.9840
0.9676
0.9778
0.9588
0.9704
0.9489
1.0000
true positive rate
0.0
0.2
0.4
0.6
0.8
1.0
eCDF
nint = 1
nint = 3
nint = 5
P50
P05
(a) eCDF of the TPR for the individual number of interferer.
0.0000
0.1620
0.3595
0.3060
0.5020
0.4144
0.6255
0.7500
RMSE in ms
0.0
0.2
0.4
0.6
0.8
1.0
eCCDF
nint = 1
nint = 3
nint = 5
P50
P05
(b) eCCDF of the RMSE for the individual number of interferer.
Fig. 8. Individual simulation results for 1, 3 and 5 interferer with random
period between 50 ms and 150 ms.
the MHT algorithm are the prediction steps for all tracks with
the Kalman filter and solving the MWIS problem for finding
the best set of tracks (see Section IV-D). The other parts of
the algorithm are mostly for managing the individual tracks
in a tree structure, however, they are still not neglectable due
to the large number of tracks. Authors in [39] presented a
detailed analysis of the computational complexity of the MHT
algorithm. The computation effort depends on the number of
active tracks in the last superframe and the new interference
measurements in the current frame. They also state that finding
the best set of tracks, in our case solving the MWIS problem,
has the highest computational complexity.
We assume that the tracking will not be performed by
the wireless nodes or the network coordinator, but by an
edge computing device with more computational power. To
evaluate the feasibility of our MHT implementation we con-
ducted simulations similar to before with 1 to 10 periodic
interferers with random periods. For the evaluation, we used
the Python library cProfile, which provides the execution
time and number of executions of the individual components
in the MHT implementation. The absolute measured time
heavily relies on the hardware and timer accuracy, however, it
gives a good estimation of the computational effort, especially
regarding the increasing number of interferers. We conducted
the simulations on two hardware platforms, on a Windows
computer with an Intel(R) Core(TM) i7-8665U 1.90GHz CPU
with 16 GB RAM, and on a Raspberry Pi 4 with 4 GB
RAM. We consider the computation feasible if the tracking
can be performed faster than the superframe period, which
is 100 ms in our simulations. On the Windows platform with
the higher computational power, we could easily perform the
computations and could satisfy our real-time constraints in
most cases, including enough time to transfer the results to the
network. Only for more than 8 interferers, the computations
could not be performed in sufficient time for some cases.
We tried both presented ILP solvers for the MWIS problem
and noticed large performance differences. The commercial
solver Gurobi outperformed the open-source solver CBC. The
simulations on the Raspberry Pi 4 could for some realisations
not satisfy the real-time constraints. Especially for 5 and
more interferers, the number of realisations with too high
computational time increased. The reason for this is not only
the limited computational power of the Raspberry Pi 4 but
also because of the not optimized ILP solver CBC on ARM
controllers.
Our evaluation also confirmed that the two most computa-
tionally demanding tasks are the track prediction and finding
the best tracks. Figure 9 depicts the measured computational
time for the Kalman predictions and for solving the MWIS
problem for increasing number of interferences. Similar to
the literature, we observed that the computational time of the
prediction step increases linear with the number of interferers,
while the computational time for finding the best tracks
increases quadratically. This holds for an increasing number of
periodic interferers, but also for random interferers. We fitted
the depicted curves with the measurements as 0.556nint +0.40
for the Kalman predictions and 0.1888n2
int 0.146nint + 1.70
for the MWIS problem. The result showed that while for
our simulation the computational time was feasible in most
cases, in real applications, further optimizations of our MHT
implementation have to be considered.
D. Measurement Results
In addition to the simulations, we prove the applicability
of the MHT for interference tracking with measurements.
For this, we use the measurement setup described in Sec-
tion III-C and perform the MHT algorithm on the exam-
ple measurement from Fig. 2. This measurement is avail-
able in the InSecTT TDMA Interference Dataset [34] under
“dataset/artificial periodic interference1”
However, in a real-world scenario, the duration of the
interference, e.g. the interference duration, can be larger than
one timeslot which results in detecting the same interference
over several consecutive timeslots. Aside from that, even if
the interference duration is shorter compared to the timeslot
duration, it can be detected in two timeslots if the interference
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content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
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12
2 4 6 8 10
number of interferer
0
5
10
15
20
mean computation time in ms
MWIS
Kalman Prediction
Fig. 9. Mean computational time per superframe for different number of
interferer for the two most computational intense tasks in the MHT algorithm.
occurs at the boundary between the two. Though the MHT
can also handle this situation by constructing a separate track
hypothesis for each occupied timeslot, it may be beneficial to
only use one timeslot for each assumed source of interference.
To find the center of the interference we apply a peak detection
based on the RSSI values of the individual timeslots. A peak
is defined as any timeslot whose two direct neighbours have
a lower RSSI value after applying a threshold. If there are
multiple peaks with the same RSSI value, the mean timeslot
number is used. The number of consecutive timeslots can
be saved in addition to the center for reconstructing the
interference duration after applying the MHT algorithm.
Figure 10 depicts the results of the peak detection with the
subsequently applied MHT algorithm. The raw measurements
after the peak detection are marked with black squares and the
estimated periodic interferer positions with circles. The MHT
algorithm is clearly able to track both periodic interferers (with
periods of 102.4 ms and 92.4 ms) present. In the beginning,
the algorithm needs a few superframes to find the individual
track hypotheses, though once synchronized the MHT is able
to perfectly follow the interference, even in the overflow and
underflow cases discussed in Section IV-E. The time it takes
to find the track hypotheses strongly depends on the timeslot
position at the start of the algorithm. E.g., track hypotheses that
start too close to the superframe borders will take more time to
be recognized. This effect can also be observed in Fig. 10, as
the 102.4 ms interference appears at high timeslot numbers
in the first few superframes considered by the MHTs and
thus too close to the immeasurable area. The MHT algorithm
is also able to track the 92.4 ms interference which is quite
hard to distinguish from random noise in Fig. 2 by optical
inspection only. Also crossing points of both interferences
are no problem and the algorithm can easily separate both
tracks. It can be observed that for some estimations there is
no corresponding raw measurement. This shows that even if
the physical detection of the sniffer nodes is missing, the MHT
algorithm is able to reconstruct the tracks due to the prediction
of the Kalman filter.
Comparing the MHT estimation with the reference data
results in TPR = 0.890 and TNR = 0.998. These results show
0 10 20 30 40 50 60 70 80 90 100
timeslot number
0
20
40
60
80
100
superframe number
measured interference
MHT track (92.3975 ms)
MHT track (102.3998 ms)
Fig. 10. Example measurement with peak detection and MHT applied.
The black rectangles mark the measurements and the connected circles the
estimated tracks.
a lower TPR compared to the simulations. However, by closer
inspection we observed that most errors are due to an off-by-
one timeslot prediction. The output of the Kalman filter in the
MHT algorithm is a float number. However, after rounding
to integer numbers for the TPR calculation, the estimation
appears in some cases one timeslot before or after. By counting
off-by-one errors as correct, we scored TPR = 0.999, which
shows that the lower TPR is due to the described integer
rounding. If the MHT is used for interference avoidance, this is
only a minor problem, since here in addition to the estimated
occupied timeslot number, a guard time has to be added to
guarantee no collisions.
To give an idea of how precisely we are able to estimate
the timing of the interference observations, we additionally
calculated the RMSE between the MHT estimation and the
corresponding measurement. This resulted in a RMSE of
0.146 ms, which shows that the MHT is able to estimate the
position of the interference with a higher resolution than the
0.9 ms timeslot duration of the measurement system.
Due to the Kalman filter and the chosen model Eqs. (1)
and (2),in addition to the timeslot number of the interference,
also an estimation of the velocity ˙sis available. With this, we
can directly calculate the corresponding interference period ti
in ms using
ti=tTS ˙s+tSF ,(18)
with the superframe period tSF = 100 ms and the timeslot
duration tTS = 0.9ms. Figure 11 shows the error of the period
estimation for both track hypotheses over the superframe
number. Here the estimations of the track hypotheses do not
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content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2022.3204820
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
13
0 10 20 30 40 50 60 70 80 90 100
superframe number
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
absolute error in ms
estimated period (92.3975 ms)
estimated period (102.3998 ms)
Fig. 11. Absolute error of the period estimation over the measured super-
frames for both tracks. The tracking of the interference starts at superframe
3 and 12, respectively.
start right at the beginning and show a large error for the
first estimations. This is due to the fact that the Kalman filter
is initialized with ˙s= 0. However, once the interference is
identified the error rapidly drops in the following superframes
and reaches a steady-state after a few superframes. In the
steady-state, this measurement shows and RMSE of 0.024 ms
which is a good result since the measurement resolution, i.e.,
the timeslot length, is 0.9 ms.
VI. CONCLUSION
In this work, we showed the applicability of the MHT al-
gorithm for interference tracking in WSNs. With the proposed
algorithm we were able to track periodic interference and
distinguish it from random interference. The estimated period
can also provide additional knowledge of the interfering device
since different communication protocols show different be-
haviour on the channel access. We demonstrated the approach
with measurements from a TDMA based WSN. However, our
approach is not limited to these kinds of networks. As long
as continuous measurements of the channel signal level are
available, the proposed algorithm can be applied. We are able
to synchronize to periodic sources and are able to provide
predictions about the time at which the interference will appear
in future times.
If the interference prediction is combined with a TDMA
based network protocol, a central coordinator is able to
reschedule the timeslots of the nodes to avoid sending at
predicted interference. This will reduce the collisions with
devices external to the WSNs and thus improve the coexistence
in the wireless channel. Moreover, it will not only reduce the
number of re-transmissions in the own WSN, but also for other
devices.
The performance of our approach is shown with extensive
simulations and real-world measurements. In both scenarios,
the MHT algorithm was able to separate the periodic interfer-
ence from the random interference and to score a TPR of over
0.9 and a RMSE of 0.146 ms for the measurement set. The
period estimation allows to distinguish the sources of interfer-
ence and the tracking allows to apply counter-measures, e.g.,
predicting future occupied timeslots and avoiding collisions.
ACK NOW LE DG EM EN T
The document reflects only the author’s view and the
Commission is not responsible for any use that may be made
of the information it contains.
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Julian Karoliny (Graduate Student Member, IEEE)
received the B.Sc. and Dipl.Ing. (M.Sc. equivalent)
degrees in mechatronic from the Johannes Kepler
University Linz, Austria, in 2018 and 2020, re-
spectively. From 2020, he is with Silicon Austria
Labs GmbH, Linz, Austria working as a Junior
Scientist. In cooperation with the Silicon Austria
Labs Doctoral College (SAL-DC) he is currently
pursuing the Dr.Tech. degree (Ph.D. equivalent) with
the Johannes Kepler University in Linz (JKU), under
supervision of Prof. Andreas Springer. His research
interests include wireless sensor networks, signal processing, and machine
learning.
Thomas Blazek (Member, IEEE) received the B.Sc.
degree in electrical engineering, the Dipl.Ing. degree
(M.Sc. equivalent) in telecommunications, and the
Dr.Tech. (Ph.D. equivalent) degree in telecommuni-
cations from the Technical University of Vienna (TU
Wien), Vienna, Austria, in 2013, 2015, and 2019,
respectively. His Dr.Tech. dissertation was on the es-
sential aspects of reliable vehicular communications.
He is employed at Silicon Austria Labs. His research
interests include vehicular network topologies and
radiofrequency machine learning solutions.
Fjolla Ademaj (Member, IEEE) received the M.Sc.
degree (Hons.) in electrical engineering from the
Faculty of Electrical and Computer Engineering,
University of Prishtina, Pristina, Kosovo, in 2014,
and the Dr.Techn. degree (Ph.D. equivalent) (Hons.)
in telecommunications engineering from Technische
Universitaet (TU) Wien, Vienna, Austria, in 2019.
From 2014 to 2019, she was a Project Assistant
with the Institute of Telecommunications, TU Wien,
where she co-developed the Vienna LTE-A and 5G
system level simulators. From 2019, she is with
Silicon Austria Labs GmbH, Linz, Austria, research center working as a
Postdoctoral Researcher. Her research interests include wireless communi-
cations, system level modeling and simulations, channel modeling, and signal
processing.
Andreas Springer (Member, IEEE) received the
Dipl.-Ing. degree in Electrical Engineering from the
Technical University of Vienna, Austria, in 1991,
the Dr. techn. (Ph.D) degree and the Univ.-Doz.
(Habilitation) degree both from the Johannes Kepler
University Linz (JKU), Austria, in 1996 and 2001,
respectively. From 1991 to 1996 he was with the
Microelectronics Institute at JKU. In 1997, he joined
the Institute for Communications and Information
Engineering at the same university, where he became
a full professor in 2005. Since July 2002 he is
also head of the Institute for Communications Engineering and RF-Systems
(formerly Institute for Communications and Information Engineering) at JKU.
In the Austrian K2 Center for Symbiotic Mechatronics he serves as a Research
Area Coordinator. Since 2017 he is co-leader of the “Christian Doppler Lab for
Digitally Assisted RF Transceivers for Future Mobile Communications”. He
was member of the editorial board of the International Journal of Electronics
and Communications from 2012 to 2019, and he serves as reviewer for
a number of international journals and conferences. His current research
interests are focused on wireless communication systems, architectures and
algorithms for multi-band/multi-mode transceivers, wireless sensor networks,
and recently molecular communications. In these fields, he has published more
than 280 papers in journals and at international conferences, one book, and
two book chapters. In 2006 he was corecipient of the science prize of the
German Aerospace Center (DLR). Dr. Springer is a member of the IEEE
Microwave Theory and Techniques, the Communications, and the Vehicular
Technology societies, OVE, and VDI. From 2002 to 2012 he served as Chair
of the IEEE Austrian Joint COM/MTT Chapter.
Hans-Peter Bernhard (Senior Member, IEEE) is
Principal Scientist, Head of Research Unit Wireless
Communications at Silicon Austria Labs and Senior
Scientist at the Institute of Communications and RF
Systems at the Johannes Kepler University Linz,
Austria. Hans-Peter Bernhard holds a Masters degree
in electrical engineering in 1991 and a PhD in
Technical Sciences from the Technical University
Vienna in 1997. He was Assistant Professor at TU-
Vienna until 1998 and joined the JKU as Lecturer
in 1999. In 2014 he started as Senior Scientist
at Johannes Kepler University and at Silicon Austria Labs in 2018. He
was Guest Researcher at Prague Academy of Science and at University of
Cambridge. He has organized/co-organized several special sessions at ETFA,
WFCS, NOMS, WF-IoT and serves as general chair of WFCS2021 and
organizing Chair of EWSN2022. He is an active member of the IEEE P1451
standard technical committee, IEEE Senior Member, Member of IEEE IES
TC Industrial Informatics, Industrial Internet-of-Things, Industrial Cloud and
Edge Computing and IEEE IES TC Factory Automation.
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