# Downing a Rogue Drone with a Team of Aerial Radio Signal Jammers

Savvas Papaioannou, Panayiotis Kolios and Georgios Ellinas The authors are
with the KIOS Research and Innovation Centre of Excellence (KIOS CoE) and the
Department of Electrical and Computer Engineering, University of Cyprus,
Nicosia, 1678, Cyprus. E-mail:{papaioannou.savvas, pkolios,
<EMAIL_ADDRESS>
This work is supported by the European Union’s Horizon 2020 research and
innovation programme under grant agreement No 739551 (KIOS CoE) and from the
Republic of Cyprus through the Directorate General for European Programmes,
Coordination and Development.

###### Abstract

This work proposes a novel distributed control framework in which a team of
pursuer agents equipped with a radio jamming device cooperate in order to
track and radio-jam a rogue target in 3D space, with the ultimate purpose of
disrupting its communication and navigation circuitry. The target evolves in
3D space according to a stochastic dynamical model and it can appear and
disappear from the surveillance area at random times. The pursuer agents
cooperate in order to estimate the probability of target existence and its
spatial density from a set of noisy measurements in the presence of clutter.
Additionally, the proposed control framework allows a team of pursuer agents
to optimally choose their radio transmission levels and their mobility control
actions in order to ensure uninterrupted radio jamming to the target, as well
as to avoid the jamming interference among the team of pursuer agents.
Extensive simulation analysis of the system’s performance validates the
applicability of the proposed approach.

##  I Introduction

Drones which have nowadays become the new emerging trend, are currently being
utilized in many applications ranging from aerial photography and critical
infrastructure inspection to emergency-response missions and aerial monitoring
tasks. Unfortunately, drones have also become a threat and a risk to public
safety. In particular, numerous times drones have threatened public safety by
targeting airports and restricted airspaces [1], attacking critical
infrastructures [2] and endangering people’s lives [3]. For this reason there
is a necessity for counter-drone systems that can detect, track, and interdict
rogue or malicious drones [4]. Although, counter-drone approaches and systems
have already been proposed in the literature [5, 6, 7], these are still in
their infancy and considerably more work is needed in order for this
technology to reach the required level of maturity.

In this work, a distributed multi-agent control framework is proposed, in
which a team of pursuer agents (i.e., pursuer drones) cooperate in order to
continuously track and radio-jam a target (i.e., rogue drone) in 3D space (as
depicted in Fig. 1), disrupting its communication and sensing circuitry and
thus ultimately forcing it to execute its fail-safe protocols [8] i.e., auto-
landing. The assumption is that the pursuer agents are equipped with a 3D
range-finding active sensor [9] with limited sensing range, which they use to
obtain noisy target measurements (i.e., radial distance, azimuth angle, and
inclination angle) in the presence of false-alarm measurements (or clutter).
In this work it is assumed that the target detection process is uncertain and
that the target can appear and disappear within the surveillance area at
random times (i.e., the target can spawn from anywhere inside the surveillance
area and additionally during tracking it can move behind obstacles or other
occlusions which results in its disappearance from the field of view of the
pursuer agents). Finally, it is assumed that the pursuer agents have the
ability to transmit power to the target via their on-board active sensor, at
discrete power-levels, with the ultimate purpose of radio-jamming its
circuitry. The main contributions of this work are two-fold:

Figure 1: A team of pursuer agents choose their mobility controls and radio
transmission levels which result in accurate tracking and uninterrupted radio
jamming of the roque target.

  * •

A novel distributed control framework is proposed for the problem of target
tracking and target radio-jamming in 3D by a team of cooperative mobile
agents. The proposed approach allows the team of pursuer agents to optimally
(a) choose their mobility control actions that result in accurate target
tracking and (b) choose their transmit power levels to cause uninterrupted
target radio jamming. The agents cooperate for improving the target tracking-
and-jamming performance of the team while minimizing the jamming interference
amongst them.

  * •

In the scenario considered, the target can exist in one of two states i.e.,
present or absent. Thus in order to be jammed, its existence probability along
with its spatial density must be estimated from a sequence of noisy
measurements in the presence of clutter, by a team of mobile agents equipped
with conic directional antennas with limited sensing range.

The rest of the paper is organized as follows. Section II discusses the
related work. Section III formulates the problem and illustrates the proposed
system architecture. Section IV develops the system model and Section V
discuses the details of the proposed approach. Finally, Section VI conducts an
extensive performance evaluation and Section VII concludes the paper and
discusses future directions.

##  II Related Work

A recent survey on detection, tracking, and interdiction techniques for
malicious drones or unmanned aerial vehicles (UAVs) can be found in [5], where
the authors discuss various drone threats and review several counter-measures
that have been investigated in the literature. In [7] the authors present a
detailed survey on the state-of-the-art anti-drone systems and discuss
techniques and technologies used for drone surveillance. The work in [10]
discusses the advantages and disadvantages of various drone detection methods
including audio-visual, thermal, and RF and proposes a low-cost stationary
system for drone detection and tracking which can be easily incorporated into
third-party anti-drone platforms. The authors in [11] focus on the problem of
detection and tracking of small and fast moving drones with the ultimate goal
of developing a system that can be used to prevent such small drones from
accessing restricted areas and facilities.

Moreover, in [12, 13, 14, 15, 16], the problems of formation control, target
tracking, and target interception with multiple agents are investigated but
without considering jamming capabilities for the pursuers. The work in [17]
develops a UAV based solution for localizing a GPS jammer and the work in [18]
proposes a low-cost ground jamming system to counteract the operation of small
drones. In [19] a team of defense agents forms a cluster around a malicious
target in order to prevent it from entering restricted airspaces. The authors
assume however the availability of a tracking system for detecting and
tracking the target. Finally, in [20, 21] the problem of jamming a rogue drone
with a team of mobile agents is investigated, however without considering
target appearance/disappearance events.

Compared to the existing techniques, the proposed framework develops a novel
cooperative technique for the problem of target tracking and target radio-
jamming in 3D by a team of mobile agents, while considering the induced
jamming interference amongst the team. The problem is investigated in the
presence of target detection uncertainty, clutter, and target
appearance/disappearance events which to the best of our knowledge has not
been investigated before.

Figure 2: Proposed system architecture. The symbols denote $\epsilon_{t}:$
target existence, $x_{t}:$ target state, $z_{t}:$ target measurement and
$u_{t}:$ agent controls.

##  III System Overview

The problem tackled in this work can be stated as follows: At each time-step
$t$ each agent $j\in[1,..,N]$ must decide its mobility control action
$u_{t}^{j}\in\mathbb{U}_{t}^{j}$ and transmit power-level
$\ell^{j}_{t}\in\mathbb{L}_{t}^{j}$ that results in accurate target tracking
and uninterrupted target radio-jamming. At each time-step the agents cooperate
to maximize the joint tracking and radio-jamming performance of the system,
while avoiding the induced radio-jamming interference amongst them.

Figure 2 illustrates the proposed system architecture. Each agent
$j\in[1,..,N]$ uses stochastic filtering in order to estimate at each time-
step $t$: (a) the probability mass function of the target existence
$p^{j}_{t}(\epsilon^{j}_{t}|Z_{1:t})$ given target measurements up to time
$t$, $Z^{j}_{1:t}$ and (b) the filtering distribution
$f_{t}^{j}(x_{t}|Z_{1:t})$ of the target state $x^{j}_{t}$. This is
illustrated by the probabilistic graphical model in Fig. 2, where the target
state $x^{j}_{t}$ and the target existence $\epsilon^{j}_{t}$ are the random
variables of an unobserved Markov process with observations $z^{j}_{t}$ (i.e.,
target measurement). In the problem considered, the target measurement
$z^{j}_{t}$ received by agent $j$ depends on the agent’s applied mobility
control action $u^{j}_{t}$ as shown in the figure. As a result, to optimally
estimate the state of the target, the agent must make optimized mobility
control decisions which is achieved by the proposed controller. The objective
of the tracking-and-jamming controller is not only to find the optimal
mobility control actions $u^{j}_{t}$ but also the optimal transmit power-level
$\ell^{j}_{t}$ for agent $j$ such that the received power at the rogue drone
is maximized in order to achieve uninterrupted radio jamming. The agents
cooperate by exchanging information (i.e., their current state and target
estimated state) in order to optimize the target radio-jamming and avoid the
jamming interference amongst them. This work does not consider a target that
has the potential to jam the pursuer agents. Moreover, it is assumed that each
agent is able to identify with absolute certainty if another entity is a
pursuer agent, i.e., an agent cannot be mistaken for a target by another
pursuer agent.

##  IV System Model

###  IV-A Target Dynamics

This work considers one target (e.g., a rogue drone) which can
appear/disappear at random times anywhere inside the surveillance area and
thus at any time-step the target can exist in one of two states i.e., present
or absent. When the target is present, it moves in 3D space according to a
stochastic dynamical model. More specifically, the state of the target at time
$t$ is modeled as a Bernoulli random finite set (RFS) [22, 23]
$X_{t}\in\\{\emptyset,\\{x_{t}\\}\\}$, with Bernoulli RFS [24] density
$F_{t}(X_{t})$ with parameters
$(p_{t}(\epsilon_{t}|Z_{1:t}),f_{t}(x_{t}|Z_{1:t}))$, where
$e_{t}=p_{t}(\epsilon_{t}=1|Z_{1:t})$ is the probability of target existence
given measurements $Z_{1:t}$ up to time $t$ and $s_{t}=f_{t}(x_{t}|Z_{1:t})$
is the spatial density of the target with state $x_{t}$. The dynamics of the
target are modeled as a Bernoulli Markov Process [25] with transitional RFS
density $\psi_{t|t-1}(X_{t}|X_{t-1})$ given by:

| $X_{t}=\emptyset$ | $X_{t}=\\{x_{t}\\}$
---|---|---
$X_{t-1}=\emptyset$ | $1-p_{b}$ | $p_{b}b_{t}(x_{t})$
$X_{t-1}=\\{x_{t-1}\\}$ | $1-p_{s}$ | $p_{s}\pi_{t|t-1}(x_{t}|x_{t-1})$

where $p_{b}$ denotes the probability of target birth, $b_{t}(x)$ is the birth
density (uniform inside the surveillance area), $p_{s}$ is the probability
that the target survives to the next time-step, and
$\pi_{t|t-1}(x_{t}|x_{t-1})$ is the target transitional density which in this
work it is assumed to be governed by the following discrete-time dynamical
model:

$x_{t}=\Phi x_{t-1}+\Gamma\nu_{t}$ (1)

where
$x_{t}=[\text{x},\text{y},\text{z},\dot{\text{x}},\dot{\text{y}},\dot{\text{z}}]_{t}^{\top}\in\mathcal{X}$
denotes the target state at time $t$ which consists of the position and
velocity components in 3D Cartesian coordinates and
$\nu_{t}\sim\mathcal{N}(0,\Sigma_{\text{v}})$ denotes the perturbing
acceleration noise which is drawn from a zero mean multivariate normal
distribution with covariance matrix $\Sigma_{\text{v}}$. The matrices $\Phi$
and $\Gamma$ are defined as:

$\Phi=\begin{bmatrix}\text{I}_{3}&\Delta T\cdot\text{I}_{3}\\\
\text{0}_{3}&\text{I}_{3}\end{bmatrix},\Gamma=\begin{bmatrix}0.5\Delta
T^{2}\cdot\text{I}_{3}\\\ \Delta T\cdot\text{I}_{3}\end{bmatrix}$ (2)

where $\Delta T$ is the sampling period and $\text{I}_{3}$, $\text{0}_{3}$ are
the $3\times 3$ identity and zero matrix, respectively.

###  IV-B Pursuer Agent Kinematics

A team of $N$ autonomous pursuer agents (e.g., UAV agents) operate inside the
surveillance area, each of which is subject to the following kinematic model:

$u^{j}_{t}\\!\\!=\\!u^{j}_{t-1}+\begin{bmatrix}\Delta_{R}(l_{1})\sin(l_{2}\Delta_{\phi})\cos(l_{3}\Delta_{\theta})\\\
\Delta_{R}(l_{1})\sin(l_{2}\Delta_{\phi})\sin(l_{3}\Delta_{\theta})\\\
\Delta_{R}(l_{1})\cos(l_{2}\Delta_{\phi})\end{bmatrix}\\!\\!\\!,\\!\\!\begin{array}[]{l}l_{1}=1,...,|\Delta_{R}|\\\
l_{2}=0,...,N_{\phi}\\\ l_{3}=1,...,N_{\theta}\end{array}$ (3)

where $j\in[1,..,N]$,
$u^{j}_{t}=[u^{j}_{x},u^{j}_{y},u^{j}_{z}]^{\top}_{t}\in\mathbb{R}^{3}$
denotes the state (i.e., position) of pursuer agent $j$ at time $t$,
$\Delta_{R}$ is a vector of possible radial step sizes,
$\Delta_{\phi}=\pi/N_{\phi}$, $\Delta_{\theta}=2\pi/N_{\theta}$, and the
parameters $(|\Delta_{R}|,N_{\phi},N_{\theta})$ determine the number of
possible mobility control actions. The set of all admissible control actions
of agent $j$ at time $t$ is denoted as
$\mathbb{U}^{j}_{t}=\\{u^{j,1}_{t},u^{j,2}_{t},...,u^{j,|\mathbb{U}^{j}_{t}|}_{t}\\}$
according to Eq. (3). Although in this work a simplified kinematic model for
the agents is utilized in order to demonstrate the proposed approach,
depending on the application scenario more realistic kinematic/dynamic models
can also be incorporated.

###  IV-C Agent Sensing and Jamming Model

The pursuer agents are equipped with an onboard directional active 3D range-
finding radio which they use in order to detect the target, acquire target
measurements, and transmit power to the target in order to radio-jam its
communications circuitry. The range-finding characteristics are as follows:

####  IV-C1 Sensing Profile

The radio’s sensing profile $S$ in 3D is modeled as a circular right angle
cone with Cartesian coordinates $(x,y,z)$ given by:
$[x=u\cos(v),y=u\sin(v),z=\frac{h_{a}}{r}u]$ where
$u\in[0,r],~{}v\in[0,2\pi]$, $h_{a}$ characterizes the effective sensing
range, $r=\tan(\frac{\theta_{a}}{2})h_{a}$ is the base radius of the cone, and
$\theta_{a}$ is the opening angle of the cone. Thus, a target with position
coordinates $Hx_{t}=[\text{x},\text{y},\text{z}]_{t}^{\top}$ (where $H$ is a
matrix which extracts the position coordinates from state $x_{t}$) resides
inside agent’s $j$ sensing range when $Hx_{t}\in S^{j}$. It should be
mentioned that the direction of the agent’s sensor is given at each time-step
by the direction of the vector $\vec{d}_{t}=x_{t}-u^{j}_{t}$, where $x_{t}$
and $u^{j}_{t}$ are the positions of the target and agent $j$, respectively.

####  IV-C2 Measurement Model

Each agent $j$ uses its radio received signal to acquire 3D target
measurements $z^{j}_{t}=[\rho,\theta,\phi]^{\top}_{t}\in\mathcal{Z}$ (i.e.,
radial distance $\rho$, azimuth angle $\theta$, and inclination angle $\phi$)
according to the following measurement model:

$z^{j}_{t}=h(x_{t},u^{j}_{t})+w^{j}_{t}$ (4)

The function $h(x_{t},u^{j}_{t})$ is given by:

$\left[\eta_{t},~{}\tan^{-1}\left(\frac{\Delta_{t,y}}{\Delta_{t,x}}\right),~{}\tan^{-1}\left(\frac{\sqrt{\Delta_{t,x}^{2}+\Delta_{t,y}^{2}}}{\Delta_{t,z}}\right)\right]^{\top}$
(5)

where $\eta^{j}_{t}=\left\lVert Hx_{t}-u^{j}_{t}\right\rVert_{2}$,
$\Delta_{t,y}=[\text{y}-u^{j}_{y}]_{t}$,
$\Delta_{t,x}=[\text{x}-u^{j}_{x}]_{t}$,
$\Delta_{t,z}=[\text{z}-u^{j}_{z}]_{t}$, and
$w^{j}_{t}\sim\mathcal{N}(0,\Sigma_{w})$ is zero mean Gaussian measurement
noise with covariance matrix $\Sigma_{w}$. Due to sensing imperfections, at
time $t$, agent $j$ also receives false-alarm measurements or clutter
$\\{c^{j1}_{t},\ldots,c^{jn}_{t}\\}$ (in addition to the target measurement)
with a Poisson rate of $\lambda_{c}$ (i.e., $\mathbb{E}(n)=\lambda_{c}$),
which are uniformly distributed (i.e., with clutter density denoted as
$p_{c}(c_{t})$) inside the measurement space. To summarize, at each time-step,
agent $j$ receives a set $Y^{j}_{t}$ of measurements which is given by:

$Y^{j}_{t}=\bigcup\Big{\\{}y_{1}\subset\\{\emptyset,z^{j}_{t}\\},y_{2}\subseteq\\{c^{j1}_{t},\ldots,c^{jn}_{t}\\}\Big{\\}}$
(6)

Thus, agent $j$ can receive at time-step $t$, zero or one target measurements
$z^{j}_{t}$ and a set of false-alarms measurements.

####  IV-C3 Target Detection and Jamming

The agents use their onboard radio to detect and jam the target. A target
detection occurs, with certain probability, when the target is illuminated
(i.e., when the agent transmits power). Hence, it is important to note here
that the same transmit signals are used to detect the target and at the same
time jam it. The detection probability i.e.,
$p^{j}_{D}=p^{j}_{D}(x_{t},u^{j}_{t},l^{j}_{t})$, that agent $j$ with state
$u^{j}_{t}$ and transmit power-level $l^{j}_{t}$ detects a target with state
$x_{t}$ is given by:

$p^{j}_{D}(x_{t},u^{j}_{t},l^{j}_{t})=\begin{cases}\frac{l^{j}_{t}}{l^{j}_{\max}}p^{\max}_{D}&\\!\\!\\!\\!\\!\\!\text{if
}\eta^{j}_{t}<R_{0}\wedge x_{t}\in S^{j}\\\
\frac{l^{j}_{t}}{l^{j}_{\max}}p^{\max}_{D}\left(\frac{R_{0}}{\eta_{t}}\right)^{n_{e}}&\\!\\!\\!\\!\\!\\!\text{if
}\eta_{t}>R_{0}\wedge x_{t}\in S^{j}\end{cases}$

where $l^{j}_{\max}$ is the maximum transmit power-level,
$\eta^{j}_{t}=\left\lVert Hx_{t}-u^{j}_{t}\right\rVert_{2}$ denotes the
Euclidean distance between the agent and the target in 3D space,
$p^{\max}_{D}$ denotes the maximum attainable detection probability of the
sensor which can be obtained when a target resides within $R_{0}$ distance
from the agent’s position and the target also resides inside the agent’s
sensing profile $S^{j}$, and $n_{e}$ is the path-loss exponent. Note that,
$p^{j}_{D}=0$, when $x_{t}\notin S^{j}$. Finally, the transmit power-level
$l^{j}_{t}$ takes its values from the discrete set of admissible transmit
power-levels $\mathbb{L}^{j}$, i.e.,
$l^{j}_{t}\in\mathbb{L}^{j}=\\{l^{j1}_{t},...,l^{jn}_{t}\\}$ with
$l^{j}_{\max}=\max~{}\mathbb{L}^{j}$. Additionally, the received power at the
target with location $Hx_{t}$ from an agent with state $u^{j}_{t}$ which
transmits at power-level $l^{j}_{t}$ is given by the following path-loss
model:

$R^{j}_{t}(Hx_{t},u^{j}_{t},l^{j}_{t})=\begin{cases}l^{j}_{t}&\text{if
}\eta^{j}_{t}<R_{0}\wedge x_{t}\in S^{j}\\\
l^{j}_{t}\left(\frac{R_{0}}{\eta_{t}}\right)^{n_{e}}&\text{if
}\eta_{t}>R_{0}\wedge x_{t}\in S^{j}\\\ \end{cases}$

Note that, $R^{j}_{t}(Hx_{t},u^{j}_{t},l^{j}_{t})=0$, when $x_{t}\notin
S^{j}$.

##  V Cooperative Tracking and Jamming

The tracking-and-jamming control module depicted in Fig. 2 seeks to find the
joint mobility and power-level control actions that result in uninterrupted
target tracking and target radio-jamming. This section discusses the details
of the proposed control approach.

###  V-A Target State Estimation

Each agent $j$ estimates the probability of target existence $e^{j}_{t}$ and
the target spatial density $s^{j}_{t}$ by maintaining and propagating in time
the multi-object probability distribution $F^{j}_{t}(X^{j}_{t}|Y^{j}_{1:t})$
of the RFS target state $X^{j}_{t}$ given measurements
$Y^{j}_{1:t}=\\{Y^{j}_{1},..,Y^{j}_{t}\\}$, using multi-object stochastic
filtering [23] as shown below (as a note, the index on the agent is dropped
for notational clarity):

$\displaystyle\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!F_{t|t-1}(X_{t}|Y_{1:t-1})=$
(7)
$\displaystyle\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!\int\psi_{t|t-1}(X_{t}|X_{t-1})F_{t-1}(X_{t-1}|Y_{1:t-1})dX_{t-1}$
$\displaystyle\\!\\!\\!\\!\\!\\!\\!\\!\\!\\!F_{t}(X_{t}|Y_{1:t})$
$\displaystyle=\frac{\phi_{t}(Y_{t}|X_{t})F_{t|t-1}(X_{t}|Y_{1:t-1})}{\int\phi_{t}(Y_{t}|X_{t})F_{t|t-1}(X_{t}|Y_{1:t-1})dX_{t}}$
(8)

where $\psi_{t|t-1}(X_{t}|X_{t-1})$ is the target RFS transitional density as
discussed in Section IV-A, $\phi_{t}(Y_{t}|X_{t})$ is the RFS measurement
likelihood function according to the measurement model discussed in Section
IV-C, $F_{t|t-1}(X_{t}|Y_{1:t-1})$ is the multi-object predictive density, and
finally $F_{t}(X_{t}|Y_{1:t})$ is the multi-object posterior filtering
density. The recursion shown here is a generalization of the Bayes filter [26]
on random finite sets [25]. The solution of the above recursion (i.e., see
[24]) for the modeling assumptions discussed in Section IV allows each agent
to compute recursively (over time) $e_{t}$ and $s_{t}$ via the Bernoulli
filter recursion [24] as:

$\displaystyle e_{t|t-1}$ $\displaystyle=p_{b}(1-e_{t-1})+p_{s}e_{t-1}$
$\displaystyle s_{t|t-1}\\!(x_{t})\\!$
$\displaystyle=\\!q_{t|t-1}\\!\\!+\\!\frac{p_{s}e_{t-1}\\!\int\\!\\!\pi_{t|t-1}\\!(x_{t}|x_{t-1})s_{t-1}\\!(x_{t-1})dx_{t-1}}{e_{t|t-1}}$

for the prediction step and

$\displaystyle e_{t}$
$\displaystyle=\frac{1-q_{t}}{1-e_{t|t-1}q_{t}}e_{t|t-1}$ $\displaystyle
s_{t}(x_{t})$ $\displaystyle=\frac{(1-p_{D})+p_{D}\sum_{y\in
Y_{t}}\frac{g_{t}(y|x_{t},u_{t})}{\lambda_{c}p_{c}(y)}}{1-q_{t}}s_{t|t-1}(x_{t})$

for the update step, where $p_{D}(x_{t},u_{t},l_{t})$ is abbreviated as
$p_{D}$, $q_{t|t-1}$ and $q_{t}$ are defined as
$q_{t|t-1}=p_{b}(1-e_{t-1})b_{t}(x_{t})e_{t|t-1}^{-1}$, $q_{t}=\int
p_{D}s_{t|t-1}(x)dx-\sum_{y\in Y_{t}}\int
p_{D}g_{t}(y|x,u_{t})s_{t|t-1}(x)dx\left(\lambda_{c}p_{c}(y)\right)^{-1}$, and
finally $g_{t}(y|x_{t},u_{t})=\mathcal{N}(y;h(x_{t},u_{t}),\Sigma_{w})$ is the
measurement likelihood function for the target generated measurement.

That said, each agent $j$ computes at each time-step $e^{j}_{t}$ and
$s^{j}_{t}$ using the recursion shown above. The final target state is then
fused as follows: The target existence probability is first exchanged among
all agents and the fused estimate is computed as
$\hat{e}_{t}=\text{mean}~{}\\{e^{j}_{t}~{}|~{}j=1,..,N\\}$. Then, the set of
agents that sense the presence of the target i.e.,
$\tilde{N}=\\{j~{}|~{}e^{j}_{t}>0.5\\}$ first extract the estimated target
state $\hat{x}^{j}_{t}$ from $s^{j}_{t}$ and its covariance matrix $C^{j}$.
Then $[\hat{x}^{j}_{t},C^{j}],~{}\forall j\in\tilde{N}$ is exchanged among all
$\tilde{N}$ agents and combined using covariance intersection [27, 28].
Finally, the fused results are communicated to all $N$ agents which they use
to sample from and update their filtering densities.

###  V-B Single Agent Tracking-and-Jamming Control

To achieve tracking-and-jamming control first observe that the posterior
target existence probability $e_{t}$, the posterior filtering density $s_{t}$,
and the target received power $R_{t}$ are all influenced by the target
detection events. Thus, optimizing $u_{t}$ and $l_{t}$ for maximum target
detection performance, results in optimized tracking-and-jamming performance.
Optimizing the target detection, results in more accurate estimation of
$e_{t}$ and $s_{t}$, from which the target state can be extracted and thus
target radio jamming can be maximized. Hence, the optimal control actions
$(\hat{u}^{j}_{t},\hat{l}^{j}_{t})$ for agent $j$ can be computed as:

$\hat{u}_{t}^{j},\hat{l}^{j}_{t}=\underset{u^{j}_{t}\in\mathbb{U}^{j}_{t},l^{j}_{t}\in\mathbb{L}^{j}_{t}}{\arg\max}~{}p^{j}_{D}(\hat{x}_{t},u^{j}_{t},l^{j}_{t})$
(9)

where $\hat{x}_{t}$ is the estimated state of the target. It should be noted,
however, that $\hat{x}_{t}$ is not available until the control actions
$\hat{u}^{j}_{t}$ and $\hat{l}^{j}_{t}$ have already been chosen and applied.
In order to bypass this problem, each agent $j$ approximates
$\hat{x}^{j}_{t}\sim\tilde{x}^{j}_{t}$ as:

$\tilde{x}^{j}_{t}=\int
x_{t}s^{j}_{t|t-1}(x_{t})dx_{t},~{}\text{iff}~{}e^{j}_{t|t-1}>0.5$ (10)

where $s^{j}_{t|t-1}(x_{t})$ is the predictive spatial density of the target
and $e^{j}_{t|t-1}$ is the predicted probability of target existence.

###  V-C Centralized Tracking-and-Jamming Control

To tackle the cooperative tracking-and-jamming control problem, the induced
jamming interference among the agents must be kept below the critical value so
that the agents can remain operational at all times. The joint target
detection probability for which exactly $m$ out of $N$ agents jointly track-
and-jam the target is given by:

$\xi^{N}_{m}=\underset{1\leq i_{1}<i_{2}<,...,<i_{m}\leq
N}{\sum}~{}\prod_{j=1}^{N}~{}\frac{(1-p^{j}_{D})~{}p^{i_{j}}_{D}}{1-p^{i_{j}}_{D}}$
(11)

where $p^{j}_{D}(\bar{x}_{t},u^{j}_{t},l^{j}_{t})$ is abbreviated as
$p^{j}_{D}$ for notational clarity, and
$\bar{x}_{t}=\text{mean}\\{\tilde{x}^{j}_{t}:\forall j\\}$ denotes the mean
predicted target state from all agents $j$ with $e^{j}_{t|t-1}>0.5$. The
operator $\sum_{1\leq i_{1}<i_{2}<,...,<i_{m}\leq N}(.)$ computes the
combinations ${N\choose m}$ among the agents. To ensure that at least $n$ out
of $N$ agents effectively track-and-jam the target, while at the same time
respect the interference constraints amongst them, the cooperative tracking-
and-jamming control objective is defined as
$\Xi^{N}_{n}=\sum_{m=n}^{N}\xi^{N}_{m}$ and the problem becomes:

$\displaystyle(\hat{u}^{j}_{t},\hat{l}^{j}_{t})$
$\displaystyle=\underset{u^{j}_{t}\in\mathbb{U}^{j}_{t},l^{j}_{t}\in\mathbb{L}^{j}_{t}}{\arg\max}~{}\Xi^{N}_{n},~{}\forall
j\in[1,..,N]$ (12a) s.t. $\displaystyle~{}\sum_{j=1}^{N}R^{j}_{t}(u^{i\neq
j}_{t},u^{j}_{t},l^{j}_{t})<\delta^{i},~{}\forall~{}i\in[1,..,N]$ (12b)

where $\delta^{i}$ denotes the interference tolerance of agent $i$, i.e., the
radio-jamming interference received by agent $i$ from all other agents $j$
should be less than $\delta^{i}$ in order for agent $i$ to remain operational.

###  V-D Distributed Tracking-and-Jamming Control

The joint optimization problem of Eqs. (12a)-(12b) is a hard combinatorial
problem which quickly becomes computationally intractable as the number of
agents and the number of control actions increases.

For this reason, in order to tackle this problem and achieve the desired
system behavior in real-time, a distributed sub-optimal approach is proposed
based on the greedy randomized adaptive search procedure or GRASP [29, 30]. In
essence, GRASP is an iterative randomized sampling technique which operates in
two steps. In the first step the algorithm constructs an initial greedy
randomized solution which is further refined through local search in the
second step. The algorithm alternates between these two steps, while keeping
track of the best solution, until the stopping criteria are met (e.g., usually
the number of iterations). The two steps of GRASP are implemented as follows:

####  V-D1 Greedy Randomized Solution

An initial randomized solution is achieved via random sampling to find the
joint control actions $(\hat{u}^{j}_{t},\hat{l}^{j}_{t}),\forall j$ with the
following steps:

  * •

(a) agent $j,~{}\forall j\in[1,..,N]$ receives $u^{i\neq
j}_{t-1},\tilde{x}^{i\neq j}_{t}~{}\forall i\in[1,..,N]$ at time $t$ and using
Eq. (3) computes the set of admissible mobility control actions for all agents
$i\neq j\in[1,..,N]$ to create $N$ sets
$\mathbb{U}^{1}_{t},...,\mathbb{U}^{N}_{t}$, including its own
$\mathbb{U}^{j}_{t}$.

  * •

(b) agent $j,~{}\forall j\in[1,..,N]$ then locally computes $N$ sets of
hypothesized joint mobility and transmit power-level control actions one for
each agent $i\neq j\in[1,..,N]$ plus its own i.e.,
$\left[\\{\mathbb{U}^{1}_{t}\times\mathbb{L}^{1}_{t}\\}^{1},...,\\{\mathbb{U}^{N}_{t}\times\mathbb{L}^{N}_{t}\\}^{N}\right]^{j}$
denoted as $\left[\mathbb{Q}^{1}_{t},...,\mathbb{Q}^{N}_{t}\right]^{j}$
hereafter. The assumption here is that the agents have the same capabilities,
i.e., the agents exhibit the same number of mobility control actions and
transmit power-levels. This assumption however, is not strict and can be
relaxed depending on the application scenario.

  * •

(c) agent $j,~{}\forall j\in[1,..,N]$ samples uniformly at random with
replacement $n_{s}$ samples from their local set
$\left[\mathbb{Q}^{1}_{t},...,\mathbb{Q}^{N}_{t}\right]^{j}$ which are used to
create $n_{s}$ joint control vectors
$\omega^{j}_{i}=\left[(u^{1}_{t},l^{1}_{t})^{i},...(u^{j}_{t},l^{j}_{t})^{i},...,(u^{N}_{t},l^{N}_{t})^{i}\right]^{j},i\in[1,..n_{s}]$.

  * •

(d) Finally, each agent $j$ then solves the optimization problem in Eqs.
(12a)-(12b) by searching through $\omega^{j}_{i}$ to find an initial global
solution to the problem denoted as
$\left[(\tilde{u}^{1}_{t},\tilde{l}^{1}_{t}),...,(\tilde{u}^{j}_{t},\tilde{l}^{j}_{t})...,(\tilde{u}^{N}_{t},\tilde{l}^{N}_{t})\right]^{j}$.

####  V-D2 Local Search

Once an initial global solution is found, a local search is performed trying
to find an improvement. To do so, each agent $j,~{}\forall j\in[1,..,N]$
performs locally an exhaustive search around the neighborhood of
$\left[(\tilde{u}^{1}_{t},\tilde{l}^{1}_{t}),...,(\tilde{u}^{j}_{t},\tilde{l}^{j}_{t})...,(\tilde{u}^{N}_{t},\tilde{l}^{N}_{t})\right]^{j}$
which is defined as follows: Let $\kappa^{j}$ =
$\left[(\tilde{u}^{j-}_{t},\tilde{u}^{j}_{t},\tilde{u}^{j+}_{t})\times(\tilde{l}^{j-}_{t},\tilde{l}^{j}_{t},\tilde{l}^{j+}_{t})\right]$
be the joint combinations of mobility and power-level controls of agent $j$,
where notation $x^{+},x^{-}$ denotes two different control actions which are
close to $x$, and which are chosen at random from a list of close proximity
control actions.

The neighborhood of
$\left[(\tilde{u}^{1}_{t},\tilde{l}^{1}_{t}),...,(\tilde{u}^{j}_{t},\tilde{l}^{j}_{t})...,(\tilde{u}^{N}_{t},\tilde{l}^{N}_{t})\right]^{j}$
is then defined as the joint combinations of the control vector
$[(\tilde{u}^{i}_{t},\tilde{l}^{i}_{t}),\forall i\neq j]$ with $\kappa^{j}$.
In essence, agent $j$ performs a local search by changing only its own
controls and keeping constant the controls assigned to the other agents. Thus,
agent $j$ searches the joint control combinations given by
$\left[(\tilde{u}^{1}_{t},\tilde{l}^{1}_{t})\times....\times\kappa^{j}\times...\times(\tilde{u}^{N}_{t},\tilde{l}^{N}_{t})\right]^{j}$
(where the single pair $(\tilde{u}^{j}_{t},\tilde{l}^{j}_{t})$ is replaced
with the vector of pairs $\kappa^{j}$). Each agent $j$ exhaustively searches
the joint combinations in its neighborhood to find the best solution by
solving the problem in Eqs. (12a)-(12b).

Figure 3: A simulated tracking-and-jamming scenario, where a team of 3 pursuer
agents track-and-jam a target.

####  V-D3 Fusion

Each agent alternates between steps 1) and 2) and the best known feasible
solution over all $n_{I}$ iterations is kept as the final solution. The agents
then exchange their local best solutions to converge to the best global
solution $(\hat{u}^{j}_{t},\hat{l}^{j}_{t}),\forall j$. The best global
mobility and transmit power-level control actions are then applied to the
agents, which move to their new states, receive target measurements, and apply
the update step of the filtering algorithm discussed in Section V-A to compute
the posterior existence probability $\epsilon_{t}$ and spatial density $s_{t}$
of the target.

In this work, a distributed optimization approach based on GRASP is proposed,
for finding the joint control actions for the team of agents. Nevertheless,
the reader should note that a solution to this problem can also be obtained
with other distributed combinatorial optimization techniques including methods
based on swarm particle optimization, genetic algorithms, and others. A
comparison between different optimization techniques for this problem is left
as future work.

##  VI Evaluation

###  VI-A Simulation Setup

The simulation setup used to evaluate the performance of the proposed approach
is as follows: The agents and the target maneuver inside a bounded 3D
surveillance area of size $100\text{m}\times 100\text{m}\times 100\text{m}$.
The dynamics of the target are according to Eq. (1) with
$\Sigma_{\text{v}}=0.5\text{I}_{3}~{}\text{m}/\text{s}^{2}$ and $\Delta T=1$s.
The dynamics of the pursuer agent are according to Eq. (3) with
$\Delta_{R}=[1,3,5]$m, $N_{\phi}=8$, and $N_{\theta}=8$, unless otherwise
specified. The pursuer agent detection and jamming model is according to Eq.
(IV-C3) with $p_{D}^{\text{max}}=0.95$, and transmit power levels
$\mathbb{L}=[\text{off},-50,-7,0.5]$dB, i.e., $l^{j}_{\text{max}}=0.5$dB
$~{}\forall j$. The path-loss exponent $n_{e}=2$ and $R_{0}=6$m. The agent
measurement model has
$\Sigma_{\text{w}}=\text{diag}([0.8\text{m},\pi/50\text{rad},\pi/50\text{rad}])$
and clutter rate $\lambda_{c}=3$. The conic sensing profile $S$ of each agent
has $h_{a}=40$m and $\theta_{a}=80$deg and the interference value for each
agent $\delta^{j}$ is set at $-40$dB. The Bernoulli filter parameters are
$p_{b}=0.02$, $p_{s}=0.98$ and the birth density $b_{t}(x)$ is uniform inside
the surveillance space. Finally, the tracking-and-jamming objective function
used in the experiments is given by Eq. (12a) as $\Xi_{2}^{N}$ with $N=3$ and
the jamming constraints are given by Eq. (12b). To handle the non-linear
measurement model, the Bernoulli filter was implemented as a particle filter
[24]. Finally, in the implementation of the GRASP-based optimization
$n_{s}=10^{4}$ samples and $n_{I}=100$ iterations were used.

###  VI-B Results

The first experiment, shown in Fig. 3, aims to demonstrate the overall
behavior of the proposed approach. More specifically, in this simulated
scenario which takes place over 30 time-steps, a team of $N=3$ pursuer agents
cooperate in order to track-and-jam the target. In particular, Fig. 3(a) shows
the trajectories of the agents (i.e., blue, purple and orange) while tracking
and jamming the target (i.e., ground truth is shown with black line, estimated
is shown with cyan line). The agents are initially located at the $(x,y,z)$
coordinates $[30,30,30]^{\top},[20,10,10]^{\top},[10,15,15]^{\top}$ and the
target is spawned inside their sensing range with initial state
$[20,20,20,1.5,2,1.7]^{\top}$. As shown in the figure, the agents maneuver
around the target in such a way so that (a) the tracking-and-jamming
performance is maximized while (b) the jamming interference amongst the team
is kept below the critical value of -40dB. More specifically, Fig. 3(b) shows
the transmit power level of each agent during this experiment and Fig. 3(c)
shows the jamming agents (i.e., due to jamming interference). For instance,
agent 1 is being jammed by agent 3 during time-steps 1 to 3 and then again
during time-steps 16 and 17. Additionally, during time-steps 16 to 18 agent 1
is also being jammed by agent 2 as shown in the first row of Fig. 3(c). Then,
Fig. 3(d) shows the target received power (i.e., red line) and the agent
jamming interference in dB indicated by the colored circles. Figure 3(e) shows
the estimated target existence probability and Fig. 3(f) shows the tracking
error i.e., the optimal sub-pattern assignment (OSPA) metric [31] of order 2
with cut-off value of 10m i.e., OSPA(p=2,c=10). In this experiment the target
is occluded between time-steps 14 to 17 and thus from the agents’ perspective
the target seems to disappear at time-step 14 and then to re-appear at time-
step 18 as shown in Fig. 3(e). The agents try to estimate the target’s
appearance and disappearance events captured by the existence probability
(i.e., red line) in Fig. 3(e).

From the results it is also observed that during the first few time-steps the
agents cause interference to each other. For this reason, the agents transmit
at lower power levels to accommodate this interference as shown in Figs.
3(b)-(c). Moreover, at time-step 16, agent 1 is being jammed by agent 2 and
agent 3 as shown in Fig. 3(c). Subsequently, agents 2 and 3 switch off their
antennas as shown in Fig. 3(b) in order to respect the interference limit of
agent 1. Figure 3(d) verifies that at time-step 16 agent 1 does not receive
any power from agents 2 and 3. Figure 3(g) shows the configuration of the
agents’ sensing profile at this particular time step and as it can be seen,
agent 1 resides inside the jamming range of agents 2 and 3. Then, the spike in
the tracking error at time-step 15 is due to a cardinality estimation error,
i.e., the agents believe that the target is present at time-step 15, however
in reality the target at time-step 15 is absent. This error, however, is
corrected in the next time-step. Finally, Fig. 3(h) shows the configuration of
the agents at time-step 30 along with their antenna orientations. As
illustrated, the agents take positions which avoid interferences with each
other, while at the same time the positions taken by the agents maximize the
target received power.

Figure 4: Impact of the number of mobility controls and the size of the
opening angle $\theta_{a}$ of sensing profile $\mathcal{S}$ on the performance
of the proposed approach.

The second experiment aims to investigate in more detail the impact of the
various parameters on the behavior of the proposed approach. In particular, it
investigates the impact of the opening angle $\theta_{a}$ of the sensing
profile $S$ and the number of total mobility control actions on the
performance of the system. Intuitively, it is expected that as $\theta_{a}$
increases, the sensing range increases, and thus the number of times the
agents interfere with each other increases as well. However, as the system’s
degrees of freedom, i.e., the number of admissible mobility control actions,
increase, additional options are provided for the agents to try to avoid the
interference.

TABLE I: Parameter Configurations Config. # | # Mob. Controls |  $\theta_{a}$ (deg)
---|---|---
1 | 11 | 60
2 | 11 | 80
3 | 11 | 100
4 | 11 | 120
5 | 79 | 60
6 | 79 | 80
7 | 79 | 100
8 | 79 | 120

To verify this assumption the parameter configurations shown in Table I were
used. This table shows that for configurations 1-4 each agent has a total of
11 mobility control actions, whereas configurations 5-8 allow for a total of
79 mobility actions per agent. Moreover, the opening angle $\theta_{a}$ takes
increasing values from 60deg to 120deg. The experimental setup is as follows
(with all the other parameters taking values according to Section VI-A): First
the target is randomly spawned within the surveillance area. Then, the initial
locations of 3 purser agents are randomly sampled, from within a sphere with
radius 20m centered at the target location. The antennas of the agents point
to the center of the sphere. For each configuration shown in Table I the
system runs for 30 time-steps (i.e., one trial). This process is performed for
each configuration 20 times and the results are averaged and shown in Fig. 4.
More specifically, Fig. 4(a) shows the average jamming incidents per trial per
agent for each configuration, Fig. 4(b) shows the average received power for
the target and agents, Fig. 4(c) shows the average transmit power-level in
Watts at each time-step for the 8 configurations, and finally Fig. 4(d) shows
the average tracking error. It can be observed from these results that with 11
mobility control actions as the opening angle $\theta_{a}$ becomes larger the
number of times that the agents are jamming each other increases and so does
the agent received power due to interference as shown in Figs. 4(a)-(b). This
is due to the limited number of admissible control actions which prohibit the
agents to acquire positions which are interference free. In addition, since
the target detection is linked to the transmit power-level (as shown in Eq.
(IV-C3)), the agents by turning off their antennas put themselves in a
disadvantage regarding their tracking performance which can result in complete
tracking failure. To overcome this issue, the agents try to transmit at low
power-levels (i.e., Fig. 4(c)). This however, not only causes reduced tracking
performance (i.e., Fig. 4(d)) but also reduced target jamming performance
(i.e., Fig. 4(b)). On the other hand, once the system’s degrees of freedom are
increased, large opening angles can be handled more efficiently with improved
jamming and tracking performance and reduced interference as illustrated in
Fig. 4 for configurations 5-8.

Figure 5: Impact of the interference constraints i.e., Eq. (12b), on the
tracking and jamming performance.

The last experiment aims to investigate how the interference constraints in
Eq. (12b) affect the tracking and jamming performance of the system. Again,
the same simulation setup discussed in the previous paragraph is followed,
where a target is randomly spawned inside the surveillance area and then
within a sphere around the target location 3 agents are spawned. The system
runs for trials with duration 30 time-steps and evaluated with the
interference constraints enabled and disabled. Twenty (20) trials are
conducted for each case with the simulation parameters and values set
according to Section VI-A. The average results are shown in Fig. 5. As
expected, by disabling the interference constraints the number of jamming
incidents per agent increases as shown in Fig. 5(a). As a result, the average
received power per agent also increases as shown by Fig. 5(b) significantly
above the critical value, and thus the system is driven into failure. On the
other hand, it is shown in Fig. 5(c) that the target received power is higher
with the interference constraints turned off. The results show that when the
interference constraints are disabled the agents can get much closer to the
target and to each other. As a result, the target receives much higher power
compared to the power received with the interference constraints enabled.
Similarly, with the interference constraints turned off, the agents optimize
the joint target detection probability of Eq. (12a) without any constraints
and this results in better tracking performance as shown in Fig. 5(d).
However, from the aforementioned results it is clear that the interference
constraints are vital for keeping the system operational at all times while
achieving a satisfactory tracking and jamming performance as shown in Fig. 5.

##  VII Conclusion

This work investigated the problem of cooperative target tracking and target
radio-jamming with a team of pursuer agents. A novel distributed control
framework is presented, in which a team of pursuer agents select their
mobility and transmit power-level control actions that result in accurate
target tracking and uninterrupted target radio-jamming, while avoiding the
jamming interference amongst them. Future directions include a real-world
implementation of the proposed system and its extension to multiple targets.

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# Performance of OpenBCI EEG Binary Intent Classification with Laryngeal
Imagery

Samuel Kuhn
Department of Psychology and Neuroscience
Regis University
Denver, CO 80221
<EMAIL_ADDRESS>
Nathan George
Data Sciences Department
Regis University
Denver, CO 80221
<EMAIL_ADDRESS>

###### Abstract

One of the greatest goals of neuroscience in recent decades has been to
rehabilitate individuals who no longer have a functional relationship between
their mind and their body. Although neuroscience has produced technologies
which allow the brains of paralyzed patients to accomplish tasks such as spell
words or control a motorized wheelchair, these technologies utilize parts of
the brain which may not be optimal for simultaneous use. For example, if you
needed to look at flashing lights to spell words for communication, it would
be difficult to simultaneously look at where you are moving. To improve upon
this issue, this study developed and tested the foundation for a speech
prosthesis paradigm which would utilize the innate neurophysiology of the
human brain’s speech system. In this experiment, two participants were asked
to respond to a yes or no question via an EEG-based BCI of three different
types; SSVEP-based, motor imagery-based, and laryngeal-imagery-based. By
comparing the accuracy of the two established BCI paradigms to the novel
laryngeal-imagery paradigm, we can establish the relative effectiveness of the
novel paradigm. Machine learning algorithms were used to classify the EEG
signals which had been transformed into frequency space (spectrograms) and
common spatial pattern (CSP) dimensions. The SSVEP control task was able to be
classified with better accuracy (62.5%) than the no information rate of 50% on
the test set, but motor activity/imagery and laryngeal activity/imagery
control tasks were not. Although the laryngeal methods did not produce
accuracies above the no information rate, it is possible that with a larger
amount of higher-quality data, this could prove otherwise. In the future,
similar research should focus on reproducing the methods used here with better
quality and more data.

_Keywords_ BCI $\cdot$ brain-computer interface $\cdot$ EEG $\cdot$
electroencephalography $\cdot$ OpenBCI $\cdot$ Laryngeal Imagery $\cdot$ SSVEP
$\cdot$ motor imagery $\cdot$ machine learning

##  1 Introduction

A brain-computer interface (BCI) is a computing system which is responsible
for interpreting and extracting electrical signals from the brain to send to a
functional output device (Sur and Sinha, 2009). A BCI can also be a system
which is used for sending information into the brain via electrical
stimulation of some kind. BCIs currently offer practical benefits to
individuals with severe epilepsy, ALS, stroke, locked-in syndrome, and
paralysis (Morrell, 2011; Yuan and He, 2014). In one of its most common forms,
BCI spellers, BCIs use actions such as looking at flashing lights or imagining
arm movement to control letter selection systems (Guy et al., 2018; Sellers et
al., 2014). This letter selection system is controlled by measurements of
electrical activity of the individual’s brain, often using implants or
electroencephalography (EEG) sensors (Yuan and He, 2014; Rezeika et al.,
2018). The non-intuitive ways of making selections with these systems can be
slow and confusing to control. However, BCI are capable of recognizing
different kinds of subtle artifacts in the electrical activity of the brain
which might be used to create more effective BCI spellers and systems. The
reason BCI are capable of assisting individuals who lack motor control is that
BCIs recognize activity in the brain as opposed to motor movements (e.g.
pressing keys on a keyboard) in order to transfer information. If our goal is
to increase the quality of life of motor-deficient individuals, then we should
provide them with BCIs which are intuitive to use, such as a communication
system based on activity in the speech centers of the brain as opposed to the
motor or visual centers. BCI paradigms may be more easily integrated when the
innate functionality of the neural source of control matches the functionality
of the output device. Ideally, motor centers of the brain would drive motor
BCI, and communication centers of the brain (e.g. the speech centers) would
drive communication BCI.

BCI spellers are the most common BCI application at the time of this writing,
and there are three main types of electrical artifacts which BCI spellers look
for: a P300 event-related potential (ERP), steady-state visual evoked
potentials (SSVEP), and motor imagery (MI) (Rezeika et al., 2018). A P300 is
an electrical artifact in response to a stimulus which increases in amplitude
when greater attention is paid to the stimulus (Sur and Sinha, 2009). A SSVEP
is another kind of event-related potential which occurs in response to a
consistent flashing visual stimulus (İşcan and Nikulin, 2018). It can be
difficult to compare different BCI systems, because of the large numbers of
differences between different BCIs. For this reason, it is best to compare
BCIs on the basis of their accuracy at completing a task with discrete
outcomes (Mowla et al., 2018). The maximum accuracies of P300, a SSVEP, and a
MI BCI spellers as reported by Rezeika et al. (2018) were 99.7%, 98.78%, and
85%, respectively. BCIs for motor imagery tasks, such as imagining using one’s
left or right hand, have yielded accuracies in the range of roughly 65% to 95%
in the literature, but these systems often require long training periods for
reliable use (Quiles et al., 2020; Irimia et al., 2018). The P300 and SSVEP
control paradigms are also beneficial, because the P300 and SSVEP artifacts in
EEG signals occur naturally and therefore these BCI do not require much
training (McFarland and Wolpaw, 2017; Rezeika et al., 2018). Although MI-based
BCI tend to be less accurate and require more training, they are better for
controlling more complex multidimensional output such as moving a cursor on a
screen or a robotic arm (McFarland and Wolpaw, 2017).

In order to improve the effectiveness of communication in BCIs this study
proposes a new way of controlling BCI by using imagined humming (laryngeal
motor imagination). The larynx is a muscular structure located in the throat
which moves the vocal folds in the throat to form different vocal pitches
(Zarate, 2013). Using laryngeal motor imagination may improve BCI in the long-
term by allowing individuals to utilize part of their brain already involved
in voluntary speech: the laryngeal motor cortex (LMC) (Simonyan, 2014). This
study aims to demonstrate comparable classification accuracy of this novel
laryngeal MI paradigm in relation to the established classification methods:
SSVEP and traditional MI. If the laryngeal MI-BCI performs significantly worse
in terms of classification accuracy than the other methods in this study, then
clearly laryngeal MI-BCI will have been shown to be less effective than
established methods. If this laryngeal MI-BCI is comparably effective at
providing a non-motor control mechanism, then this system could serve as a
foundation for a more sophisticated speech prosthesis which would convert
imagined speech into sound or text generated by electronics. This may be more
intuitive for use than using other cognitive artifacts like converting
imagined arm movement into speech, and could increase the quality of life for
the individuals in need of speech prostheses as well as lead to the
development of other related technologies.

##  2 Methodology

###  2.1 Materials and Tools

This study used an OpenBCI EEG Mark IV headset with the Cyton, Daisy, and WiFi
boards, which collects data from 16 EEG channels. Dry comb EEG electrodes with
an Ag-AgCl coating were used with two ear clips as reference electrodes. An
elastic strap that connects to the sides of the OpenBCI headset and sits under
the participant’s chin was used to ensure good sensor contact. Without this
strap, good sensor contact could not be achieved. Data collection and
processing was done with the OpenBCI GUI and Python with packages including
brainflow, MNE, and pycaret. Data was collected using the brainflow Python
package over a direct WiFi connection to a computer.

The EEG sensor locations used the 10-20 system, with locations Fp1, Fp2, CP1,
CP2, FC1, FC2, O1, O2, F7, F8, Fz, Cz, T3, T4, P3, P4 as shown in Figure 1.
These were chosen to spread out the sensors while having sufficient sensors
near the visual cortex for SSVEP/alpha wave detection and sensors near the
motor cortex to detect motor activity and motor movement. Data was collected
at a frequency of 1000Hz.

Figure 1: The 16 sensor locations that were used are shown as thick red
circles. This is a top-down view where the anterior part of the brain faces
the top of the page. The original image used as a template was from OpenBCI’s
website (noa, ).

###  2.2 Experiment Procedure

Participants were asked to read and sign an informed consent form approved by
the Regis University IRB. The participant was instructed to wear an OpenBCI
headset for recording EEG data and to face a computer screen where the
experimental protocol was presented. The OpenBCI GUI was then used to ensure
that sensors made sufficient contact with the scalp. This was done by
examining the impedance of the EEG sensors, which should be at most 50 kOhm.
While the participant closed their eyes for a few seconds, a live spectrogram
using the OpenBCI GUI with the O1 and O2 EEG sensor channels was used to
confirm that alpha waves (a peak around 10Hz; see Figure 2) appeared when the
participant closed their eyes. Once the headset had been adjusted so that the
sensor contact was sufficient, the experiment was initiated.

Figure 2: A spectrogram showing alpha waves that appear when a subject closes
their eyes.

The experimental procedure was started by running the data collection
software. After initial parameters for data collection were set (data storage
location, EEG configuration) within the program, data collection was
initiated. Instructions were shown to the participant explaining the
procedures in the experiment. In the instructions, a warning was shown
explaining that the steady state visually evoked potentials (SSVEP) portion of
the experiment shows rapidly flashing squares on the screen and that people
with epilepsy or other conditions that may result in harmful responses to
flashing lights should end the experiment immediately by pressing the “x” key.
Six sets of tasks, with 10 trials in each task, were then presented on the
screen, in order: an eyes opened/closed task, an SSVEP task, a motor activity
task, a motor imagery task, a laryngeal activity task (humming/rest), and a
laryngeal imagery task (imagined humming/rest).

In the eyes open/closed task, instructions were shown to the participant
explaining the task. A lower-pitched sound was then played, and the
participant closed their eyes. After 5 seconds, a higher-pitched sound was
played, and the participant opened their eyes for 5 seconds. This was repeated
several times. An example of alpha waves from one of these trials is shown in
Figure 2.

In the next 5 sets of tasks, a cartoon picture of an elephant was shown to the
user, either inside or outside of a box. If the elephant was inside the box,
the participant should respond “yes” by pressing the right arrow key on the
keyboard. If the elephant was outside the box, the user should respond “no” by
pressing the left arrow key. If the participant pressed the wrong key, they
were shown a warning and then the same configuration of the elephant and box
was shown again until the participant pressed the correct key. The “yes” or
“no” response then also corresponded to an SSVEP, motor action/imagery, or
laryngeal action/imagery task. Ten trials were recorded in each of the 5
control paradigms. An example of this section of the experiment GUI is shown
in Figure 3.

Figure 3: The screen capture shown above is an example from the experimental
protocol GUI. The protocol gathers data pertaining to alpha waves, SSVEP,
motor activity of the right arm, right arm motor imagery, laryngeal activity
(humming) and laryngeal imagery (imagined humming).

The second task used SSVEP control. Box-shaped visual stimuli (video files)
were created to flash at frequencies of 10Hz and 15Hz. The SSVEP boxes were
generated using sine waves so that the box would be completely white at the
peak of the sine wave and completely black in the trough of the sine wave
(with brightness proportional to the sine wave intensity in between peak and
trough). These frequencies were chosen to have substantial separation to make
signal detection easier, as well as being slow enough that conventional
computer monitors could display them. The frequencies are also resonant with
the 60Hz refresh rate common with computer monitors which helps ensure the
correct frequencies will be shown. In the experiment, the user first pressed
the correct key to signify the elephant was in or out of the box, then the two
flashing squares were shown; one on the right of the screen (10Hz) and one on
the left (15Hz). The flashing stimuli squares were presented approximately 4
in apart in 3.5 in x 3.5 in squares. The participant should look at the square
on the right side of the screen to signify “yes” (the elephant was in the box)
or look at the square on the left of the screen to signify “no”. After looking
at the appropriate flashing square for 5 seconds, the next iteration of the
SSVEP trial began. This was repeated 10 times.

The next task was actual motor activity. After the user pressed the correct
key to signify the elephant was in or out of the box, the user was instructed
to raise their right arm for “yes” or rest for “no” for a duration of 5
seconds. This was repeated 10 times.

The next task was imagined arm movement. After the user pressed the correct
key to signify the elephant was in or out of the box, the user was instructed
to imagine raising their right arm for “yes” or rest for “no” for 5 seconds.
This was repeated 10 times.

The next task was laryngeal motor actuation. After the user pressed the
correct key to signify the elephant was in or out of the box, the user was
instructed to make a humming sound for “yes” and rest for “no” for 5 seconds.
This was repeated 10 times.

The final task was laryngeal motor imagery. After the user pressed the correct
key to signify the elephant was in or out of the box, the user was instructed
to imagine making a humming sound for “yes” or rest for “no” for 5 seconds.
This was repeated 10 times.

The data was then saved using the MNE Python package as .fif and Python pickle
files. The data is available on the project’s GitHub repository which can be
found at https://github.com/nateGeorge/openbci_laryngeal_imagery (George and
Kuhn, 2021).

###  2.3 Data preparation

Before analysis, data was cleaned to remove noise. The first few seconds of
OpenBCI data collected through brainflow and Python usually has a large spike
in the signal, so the first 2 seconds of data from each experiment was
removed. A bandpass filter from 5 to 50Hz was used, which removed signal
drift, and a 60Hz notch filter was used to remove electrical noise from the
surrounding electronics. Lastly, standardization (subtraction of the mean and
division by the standard deviation) was used separately on each channel to
minimize the contribution from noisy channels (which had larger standard
deviations). Another solution was tried where the noisy channels were
flattened to 0, but standardization seemed to reduce noise in spectrograms
more effectively. An example of the first few seconds of a few channels of the
raw EEG data is shown in Figure 4. This figure demonstrates noise from the
WiFi transceiver in this sample of data (periodic wavelets). Independent
component analysis (ICA) was attempted as a way to remove this noise, but was
unsuccessful.

Figure 4: The above figure shows a 5 second window of EEG data from 5 of the
16 available sensors. The Cz channel shows some artifacts from the WiFi board
on the OpenBCI headset that show up as periodic wavelets.

To create SSVEP and alpha wave spectrograms, the channels O1, O2, P3, and P4
were used since these sensors were closest to the visual cortex where visual
processing is most likely to be recorded (McFarland and Wolpaw, 2017). For
laryngeal activity and imagery spectrograms, all channels were used. For all
spectrograms, 2000 datapoints (2s of data) were used in the window for each
Fourier transform, and each window overlapped by 1000 datapoints (1s). A range
of 5-50Hz was used for spectrogram features in machine learning algorithms. If
the maximum frequency was not restricted to 50Hz and was instead 100Hz or
500Hz, the ML classifiers tended to use high frequencies as the most important
features (near the top of the frequency range). This was confirmed by
examining feature importances from a light gradient boosting model.

For spectrogram-based machine learning classification (on the SSVEP and
laryngeal tasks) spectrograms were created as described above. To prevent data
leakage between train and validation/test sets, each 5s epoch of data was
labeled as a group. Train and test datasets were created by taking a random
set of 80% of the data (by groups or 5 second continuous experimental
sections) as the train set, and the remainder as the test set. This ensures
the train and test sets have no overlapping data and no data possible leakage
(i.e. no training data used in the validation or test sets). This data was
then used with the pycaret auto machine learning Python package to try several
machine learning models and select the best model by accuracy. The accuracies
on the train set were calculated by 3-fold cross-validation (CV). Group labels
in the train set were then re-labeled so that three distinct subsets remained
in the training set. Accuracy of the best machine learning model was evaluated
on the train and test sets. The best machine learning models with respect to
each of the five tasks are shown in Table 1.

Task | Model |  Train set accuracy (%) |  Test set accuracy (%)
---|---|---|---
SSVEP (look at 10Hz or 15Hz square) |  Logistic regression with L2 regularization | 72.4 | 62.5
Motor activity (raise right arm or rest) | Decision tree | 81.2 | 40.0
Motor imagery (imagine raising right arm or rest) | Linear SVM | 41.2 | 60.7
Laryngeal activity (hum or rest) CSP features | Linear SVM | 65.4 | 42.2
Laryngeal imagery (imagine humming or rest) CSP features | Linear SVM | 56.0 | 47.6
Laryngeal activity (hum or rest) Spectrogram features |  Quadratic discriminant analysis | 57.3 | 48.0
Laryngeal imagery (imagine humming or rest) Spectrogram features | k-nearest neighbors | 65.4 | 50.0
Table 1: Binary tasks with the best-performing machine learning model and
accuracy scores on the train and test sets (80% of data was in the training
set).

For motor activity/imagery tasks and laryngeal activity/imagery tasks, common
spatial pattern (CSP) transforms were used. The CSP fit and transform was
performed on the train set, and the test set was transformed by the CSP
operation. Train and test sets were constructed in the same way as the SSVEP
data, using group labels for continuous 5s data chunks and using separate
groups in the train and validation/test sets. Again, pycaret was used to
select the best performing machine learning model by accuracy. Accuracy was
evaluated on the train and test sets.

###  2.4 Participants and Datasets

Two participants (the paper’s authors) were used for data collection: both
males aged 21 and 34 at the time of the experiment. Both participants had
substantial amounts of hair which made dry sensor contact more difficult.
Three datasets from each participant were collected for a total of 6
experiments. Several alpha wave epochs were collected for each experiment (at
least 5). Ten epochs for each of the five control paradigms (SSVEP, motor
activity, motor imagery, laryngeal activity, laryngeal imagery) were
collected, except for the last experiment, which had 10 of each of the control
paradigms but only 3 of the laryngeal imagery epochs due to a
misconfiguration. This means that for analysis there were 60 trials in each of
the control paradigms (with 30 of each of the "yes" and "no" sections) except
for the laryngeal imagery which had 53 trials.

##  3 Results and Discussion

The first experiment in the series was SSVEP, where a flashing square with a
frequency of 15Hz was shown on the left (for a selection of "no") and a
flashing square with a frequency of 10Hz was shown on the right (for a
selection of "yes"). After pre-processing, spectrograms were created to
visualize quality of the data. Ideally, sharp signals at the frequency of the
flashing stimulus (and their harmonic frequencies such as 20Hz and 30Hz) would
be present, and the signal at the frequency that the participant looked at
would be strongest (Rezeika et al., 2018; Yuan and He, 2014). As can be seen
in Figure 5, some data had clear SSVEP signals present while others did not.
In fact, the majority of experimental sections did not have clear SSVEP
signals visible from spectrograms. Additionally, a few spectrograms that
should have had the 15Hz signal showed the 10Hz signal, and vice versa. It is
not clear why this happened. We can also see from Figure 5 that the second
harmonic (20Hz) signal was clearly visible where the 10Hz signal was shown,
and this second harmonic was stronger than the 10Hz signal itself. This was
true in most of the 10Hz SSVEP signals, but not the 15Hz signals.

Figure 5: The left column of spectrograms show 15 Hz SSVEP signals, while the
right column of spectrograms show 10 Hz SSVEP signals. The top row of
spectrograms shows data with SSVEP signals present, and the bottom row of
spectrograms shows examples when the SSVEP signals were not present.

After using pycaret to select the best machine learning algorithm with the
labeled spectrogram data, a logistic regression model was found to perform
best with 72.4% accuracy on the train set and 62.5% accuracy on the test set.
The accuracies beat the no information rate of 50%, but were not high enough
to provide for a reliable information output channel. This is likely due to
noisy data and the issue of 15 and 10Hz signals in the spectrogram analysis
occasionally showing up in the wrong epochs (for example, a 10Hz signal
showing up where 15Hz is expected).

The motor/laryngeal activity and imagery data was processed with CSP (common
spatial pattern) transforms and machine learning performed on these CSP
transforms. The laryngeal activity and imagery data was also processed in the
same way as the SSVEP data by creating spectrograms from all channels. The
reason for trying a spectral approach with the laryngeal but not the motor
action/imagery data was that it was not clear if the features from making and
imagining sounds would show up in the spatial or spectral domain of the EEG
data. The best model for each control paradigm was selected with pycaret
autoML, and the results of the best ML models for each scenario are shown in
Table 1.

We can see that ML categorization of these motor and laryngeal tasks had
similar accuracies on the train and test sets, with none of them beating the
no information rate of 50% except for motor imagery. This indicates EEG
signals from both the motor and laryngeal control paradigms could not be
successfully classified in this study. Although the motor imagery shows an
accuracy comparable to SSVEP and above the 50% random guessing baseline, the
accuracy on the train set was only 41.2%, decreasing confidence that the
result on the test set is meaningful. Additionally, we would expect the
accuracy for motor activity to be greater than that of motor imagery, but it
had an accuracy 20.7% less than the motor imagery paradigm. The results here
are near the lower end of the range of 65% to 95% accuracy for classification
of left versus right hand movements via dry EEG electrodes in the literature
(Quiles et al., 2020; Irimia et al., 2018).

Many of the best models for motor and laryngeal control paradigms ended up
being linear support vector machines (SVMs), although decision tree, quadratic
discriminant analysis, and k-nearest neighbors models were also found to
perform best for some of the specific control paradigms and data preparation
types (FFT spectrograms and CSP filters).

The low ML classification accuracies of motor and laryngeal control are likely
due to noisy data and using a small amount of data. Data quality may be low
due to the use of dry sensors, using the OpenBCI WiFi transmitter which seemed
to cause artifacts in the data, and electrical noise (e.g. from computers,
cell phones, and other electronics in the room at the time of data
collection). It is expected that using the Bluetooth transmitter and saving
data to an on-board SD card could improve data quality, or other electrical
modifications to the OpenBCI circuit board. More data could be collected by
repeating the experiment or using a different headset which allows for more
sensors to be used. Using wet sensors should improve data quality as well.

Since the imagery and movement tasks used CSP filters to preprocess data, we
can examine the results of the CSP transforms to look for trends in location
of motor and laryngeal activity. Although the data seemed noisy in general,
the amount of noise was not constant, even in a single experiment. This was
observed by looking at spectrograms of different sections of the experiment.
So we may still be able to glean information from the CSP-transformed data.
Figure 6 shows the filters for motor activity, motor imagery, laryngeal
activity, and laryngeal imagery. The CSP filters are ordered from left to
right by order of magnitude and importance. The first two CSP filters
demonstrate that motor activity strongly centers around the C3, CP1 and FC2
10-20 EEG sensor locations. This is in line with other findings and the
location of the motor cortex (Chen, ). We also see a strong signal around the
T6 sensor location (on the back right of the head), which is bordered by
sensors O2, P4, and T4. This may be in part due to noise on some of the
experiments in the P4 sensor.

Figure 6: This figure shows the common spatial pattern (CSP) transforms of (a)
motor activity (raising one’s right arm), (b) motor imagery (imagining raising
one’s right arm), (c) laryngeal activity (humming), and (d) laryngeal imagery
(imagining humming). This is a top-down view of the activity of the head with
the anterior of the brain facing the top of the page.

For the motor imagery, we see similar but weaker results. The same T6 spot
shows activity, but the second CSP filter has a strong signal on the left side
of the head from the C3 sensor down to the T3 sensor. The CSP highlighting the
left side of the brain make sense for our particular motor action and imagery
(imagining or actually raising the right arm), because control of lateralized
movements of the body occur in the contralateral hemisphere of the brain.
However, the CSP signal around the T6 sensor location could be due to noise in
the data or the small dataset size. The CSP results give hope that data
quality was enough to see some evidence of signal where it was expected, even
though this was not enough to accurately classify the data using ML.

For laryngeal action and imagery, very different areas were highlighted by the
CSP filters. In the case of laryngeal action, we see activity near the Cz
sensor near the motor strip as we would expect (the pre-motor areas near the
laryngeal motor cortex, or LMC). The FC2 sensor also shows a signal in the
second CSP filter. However, the CSP transforms show very little activity in
the motor and pre-motor areas in the case of laryngeal imagery. Laryngeal
imagery seemed to produce greater activity in the pre-frontal cortex near the
Fp1 and Fp2 sensors. This is consistent with the pre-frontal cortex’s role in
executive decision making and working memory, since these are often associated
with the prefrontal cortex (Koechlin et al., 2000). This may be evidence for
planning movement of the larynx, but this does not necessarily allow for
classifying laryngeal imagination as distinct from any other form of planning.

Since the performance of the ML algorithms on the motor and laryngeal data was
no better than random chance, we should not give too much weight to the
results of these CSP transforms, although they could be used as a basis for
future studies.

##  4 Conclusions

EEG data was collected to evaluate a novel BCI control paradigm, imagined
laryngeal activity. This was compared to other BCI control paradigms, and all
paradigms were used to signal a binary choice of yes or no. The performance of
one optimized machine learning classifier for each of the paradigms is
presented in Table 1. This includes paradigms used for reference such as motor
activity and laryngeal activity. Due to the unknown nature of the laryngeal
EEG signature, laryngeal activity and imagination were analyzed in the spatial
domain (CSP) and the frequency domain (FFT spectrograms). The established
paradigms, SSVEP and MI were found to have accuracies of 62.5% and 60.7% when
analyzed on the test set using a logistic regression with L2 regularization
classifier and a linear support vector machine (SVM), respectively.

Laryngeal activity and imagery classification was done on the spatial domain
(CSP), with the best models resulting in linear SVMs and on the frequency
domain using Quadratic discriminant analysis and k-nearest neighbors
classifiers. These classification methods yielded accuracies of 42.2%
(spatial-domain laryngeal activity), 47.6% (spatial-domain laryngeal imagery),
48.0% (frequency-domain laryngeal activity), and 50.0% (frequency-domain
laryngeal imagination). None of these paradigms, even the control paradigms
where laryngeal activity was present, were able to overcome the 50% no
information rate. This seems to add evidence that significant noise was
present in the data. This can be improved upon by using wet electrodes, taking
measures to remove noise from the WiFi OpenBCI circuit board, and by simply
collecting a larger data set.

CSP filters showed that motor and laryngeal activity tended to result in EEG
signals over the motor cortex consistent with functional neuroanatomy.
However, in the case of laryngeal imagery, activity seemed more intense in the
pre-frontal cortex. Due to the failure to establish high accuracies in the
established BCI paradigms, this experiment can draw no conclusion about the
efficacy of the imagined laryngeal signal for its use as a BCI control
paradigm. It is still unknown if imagined laryngeal activity can be detected
from EEG signals. Future research with more and higher quality data is needed
to answer the question of whether laryngeal imagination can be used as a
control mechanism with EEG signals.

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