# Doors in the Sky: Detection, Localization and Classification of Aerial
Vehicles using Laser Mesh

Wahab Khawaja, Ender Ozturk, and Ismail Guvenc
This work was supported by NASA under the award NNX17AJ94A. W. Khawaja is with
the Mirpur University of Science & Technology, Pakistan. The co-authors are
with NC State University, Raleigh, NC 27606 USA (e-mails:
<EMAIL_ADDRESS>{wkhawaj, eozturk2, iguvenc}@ncsu.edu).

###### Abstract

The stealth technology and unmanned aerial vehicles (UAVs) are expected to
dominate current and future aerial warfare. The radar systems at their maximum
operating ranges, however, are not always able to detect stealth and small
UAVs mainly due to their small radar cross-sections and/or low altitudes. In
this paper, a novel technique as an alternative to radar technology is
proposed. The proposed approach is based on creating a mesh structure of laser
beams initiated from aerial platforms towards the ground. The laser mesh acts
as a virtual net in the sky. Any aerial vehicle disrupting the path of the
laser beams are detected and subsequently localized and tracked. As an
additional feature, steering of the beams can be used for increased coverage
and improved localization and classification performance. A database of
different types of aerial vehicles is created artificially based on Gaussian
distributions. The database is used to develop several machine learning (ML)
models using different algorithms to classify a target. Overall, we
demonstrated through simulations that our proposed model achieves simultaneous
detection, classification, localization, and tracking of a target.

###### Index Terms:

Blockage, channel prediction, mmWave, UAV.

##  I Introduction

Unmanned aerial vehicles (UAVs) have applications in several areas nowadays
[1], one of which is the defense industry. The small size and ability to fly
at low altitudes make the UAVs practically invisible to conventional radar
systems [2] at long ranges. Moreover, stealth technology is the most essential
part of the current and future combat aerial vehicles. The stealth aerial
vehicles (SAVs) can avoid being detected by radars due to their small radar
cross-sections (RCS) that is achieved by using a mix of techniques to absorb
and scatter the incoming radar energy [3].

Radar technology has evolved significantly over the decades. However, there
are still known limitations of the radar systems [4]. The basic radar
principle still relies on back-scattered reflections from a potential target
[5]. For SAVs and UAVs, the back-scattered reflections are weak and the
strength of the received signal is generally below the noise floor. Therefore,
the target remains undetected by conventional radar systems over a significant
distance, i.e., insufficient slant range. In the literature, there are some
radar systems proposed for detecting targets with small RCS [6, 7, 8].
However, these radar systems are too complex, expensive, and they are designed
to use only specific wavelengths that further contributes to complexity and
high cost.

Different types of early warning radar systems can provide specific detection
capabilities against the SAVs and UAVs [9, 10]. However, the detection
capabilities (i.e, RCS as a function of detection range) vary with the
operating frequency of the radar system and the type of the aerial vehicle.
There are also laser scanning techniques available in the literature for the
detection and tracking of terrestrial moving objects [11, 12, 13]. The laser
scanning works on a similar principle to radars, i.e., relies on back-
scattered signal, and classifies a moving target based on individual laser
scans at different instances of the time obtained from different parts of a
target. Implementation of this technique is quite challenging, and there is
limited amount of work available in the literature for the detection of aerial
targets using this technique. In [14], laser-based radar is used for the
detection of UAVs. As the approach in [14] follows the basic radar principle,
it also shares the disadvantages of the radar systems.

Similar to radar systems, electro-optical/Infra-red (EO/IR) imaging is used
for detection, tracking, and classification of aerial targets [15]. The
operation of the EO/IR sensors are different from the radar systems. The EO/IR
imaging uses ultraviolet, visible and infrared spectral bands for different
types of targets. The advantage of EO/IR technique compared to radars is that
it can operate in the passive mode and the illumination is either provided by
natural sources or by the target itself. The fine details of the target
filtered from the background environment using EO/IR image processing can help
in the tracking, and classification of small and stealthy targets. However,
the selection of the spectral band for EO/IR imaging is dependent on the type
of the target. The EO/IR imaging is also affected by environmental and
atmospheric conditions, e.g. haze, fog, and clouds. The EO/IR imaging has
limited range compared to radars. The high resolution and sensitivity EO/IR
imaging is complex and expensive.

Figure 1: Laser mesh created by two airborne UAVs that are quasi-static. A
uniformly spaced laser array is considered on each airborne UAV. The laser
array platform is tilted at each airborne UAV. The coverage area and shape of
the elements of the mesh can be changed by changing the spacing between the
individual laser beams and changing the position of airborne UAVs or changing
the tilt of the array platform.

In this paper, a new alternative to radar systems for the detection,
classification, localization, and tracking of aerial objects is provided. In
our work, a novel concept of the mesh of laser beams in the sky is proposed. A
simple illustration of the concept using two UAVs is shown in Fig. 1. The
laser mesh forms a web-like structure in the sky. Laser beams in the mesh can
be transmitted either from a satellite or a high altitude platform (HAP) such
as hot air balloons, medium altitude rotary-wing UAVs, or both. The
transmitted laser beams can be received either directly on the ground or
rotary-wing UAVs near the ground. Any flying object that crosses the laser
mesh will block the path of the laser beams and will be detected and
subsequently localized. Laser mesh steering is introduced to steer virtual
gates at different azimuth positions. The laser steering in the azimuth plane
helps in localization, classification, and tracking of moving aerial objects,
and increases the coverage area. A mathematical model of the blockage of the
laser beam of the Gaussian profile is provided. Moreover, Gaussian training
data that has the features of 3D shape, maximum velocity, pitch and drift
angles, and a maximum altitude is used for model development. Dataset is
created for eleven different type of flying objects grouped in four
categories. The results obtained from simulations proves the viability of our
proposed approach.

The main advantages of our proposed approach compared to radar systems are
summarized as follows:

  * •

Our proposed approach is energy efficient compared to the radar systems. The
radar systems broadcast the radio signals in the free space and the
transmitted energy spreads in different directions. A small fraction of the
transmitted energy from the radar is received back. On the other hand, in our
approach, a point-to-point connection is established without significant
spreading of the transmitted energy towards the receiver (RX). Moreover, the
received laser energy can be recycled into other forms.

  * •

The energy emissions from the radar can be detected from a long distance,
hence, exposes them to the risk of detection. However, in the proposed
approach, there are no long-range emissions sourced from the transmitter (TX)
or the RX.

  * •

Radar systems use complex algorithms for clutter rejection. These algorithms
have limitations dependent on the size and height of the flying target, the
motion of the objects in the surrounding, and the terrain type. In the
proposed approach, no clutter rejection is required.

  * •

The radar systems depend on the delay of the received pulses to range a target
and pulse repetition frequency needs to be correctly selected to avoid range
ambiguity. In our approach, a target is detected instantaneously without delay
and range ambiguity issue.

  * •

Large and bulky antennas are required for long-range transmission and
reception of radar signals. There are additional maintenance overheads for
rotating radars. On the other hand, laser beam generation, and reception are
performed using electronic and optical equipment that are concise and more
efficient compared to mechanically controlled radar systems.

  * •

Complex sounding signals and processing techniques are used for the detection,
localization, and classification of sophisticated targets e.g., terrain
hugging drones and missiles. Our proposed approach does not require complex
sounding signals and associated processing techniques.

  * •

The probability of detection of different types of aerial targets with the
proposed approach is significantly higher compared to the conventional radar
systems. The probability of false alarms using our approach is also small
compared to radar systems as the detection is solely dependent on the
interruption of the laser link.

  * •

We can achieve simultaneous detection, classification, localization, and
tracking (SDCLT) using our approach with high accuracy and without any
significant complexity. For radar systems, SDCLT requires complex operations
and accuracy depends on the reflected energy that can be manipulated by the
target.

  * •

The common countermeasure for engaging incoming aerial targets mainly consists
of firing projectiles towards the incoming aerial object. The interception
procedure is highly complicated and requires constant tracking of the aerial
object from multiple sources. However, using the proposed setup, the
interception procedure can be significantly simplified.

  * •

The range resolution of traditional radar systems has a trade-off with the
detection range [16]. Similarly, the angular resolution has a trade-off with
the instantaneous field of view of the radar system. On the other hand, for
our proposed approach, the resolution of the target depends only on the
density of the laser beams.

  * •

The main information of a target obtained by a radar system is its RCS. The
accurate determination of the RCS of a target is important for the
classification of modern aerial threats. The RCS of a target depends on many
factors e.g., frequency of the radar system, angle of illumination, and
physical properties of the target. Therefore, the RCS of a target varies
during measurements. No RCS variations are present using our approach.

  * •

The RXs of modern radar systems are complex and expensive. The complexity is
mainly due to processing of the 1) weak received echoes, 2) range and Doppler
ambiguities, 3) clutter rejection, and 4) finding the precise position of the
target in the azimuth and elevation planes. In comparison, no complex
processing is required at the RXs of our approach. The RX components of our
proposed approach are also simple and inexpensive.

  * •

Generally, a single radar cannot perform all the tasks related to an aerial
target. For example, there are separate search, tracking, and fire-control
radar systems. These radar systems require networking for a combined response.
The networking is vulnerable to failures, jamming, and delays. Our proposed
laser mesh setup provides a single front-end for detection, tracking,
classification, and fire-control guidance.

  * •

Radar Systems are more vulnerable to mechanical and electronic jamming
compared to our proposed approach.

  * •

The performance of a particular radar system depends on the terrain. For
example, the performance of a particular radar system is different in a hilly
area compared to an urban area. In comparison, our proposed approach is
independent of the terrain.

Figure 2: A mesh element is created by laser beams from two sources. The
divergence of the laser beams along the direction of propagation is also
shown. The divergence of the laser beams is considered small resulting in
approximately the same beam radius along the direction of propagation.

The rest of the paper is organized as follows: The proposed laser mesh setup
is provided in Section II, Section III discusses the detection of a target,
the classification features of a target are provided in Section IV, Section V
provides classification, localization, and tracking of a target, the
limitations of the proposed approach are discussed in Section VI, the
simulation results are provided in Section VII, and Section VIII concludes the
paper.

##  II Proposed Laser Mesh Setup

In this section, the details of the laser mesh setup and laser mesh steering
are provided.

###  II-A Mesh of Laser Beams

Laser is a concentrated beam of light obtained through stimulated emission of
electromagnetic radiation [17]. The main advantage of a laser is spatial
coherence resulting in higher directivity compared to radio waves. A single
laser beam has a small coverage area due to high directivity. Therefore, to
cover a large area, multiple laser beams are required. The coverage area of a
single laser beam at a given distance from the TX depends on the divergence of
the beam. The divergence of the laser beam with distance results in the
broadening of the beam, as shown in Fig. 2. We consider that the divergence of
the laser beams is small (e.g. collimated laser beams). The small divergence
of laser beam results in approximately constant radius of the beam with
distance. In Fig. 2, $\Omega$ and $\Omega^{\prime}$, are the solid angles of
the beams, and $w_{0}$ and $w_{0}^{\prime}$ are the beam waists of the two
sources. Given $r$ as the radius of the beam, and $\Delta x$ as the separation
between the two beams such that $\Delta x\gg r$, the area of a mesh element in
Fig. 2 is approximated as $A_{\rm e}=(\Delta x)^{2}$ [18]. The area of the
laser mesh element, $A_{\rm e}$, is selected depending on the type of the
aerial threat.

In our proposed approach, the TXs (and RXs) of the laser beams can be either
on a satellite, a HAP, or on a medium altitude hovering UAV. The RXs (or TXs)
can be on the ground or over a hovering UAV. Multiple laser beams can be
transmitted from a single TX. A blockage to the path of a laser beam by any
aerial object (taken as target) is readily identified. Localizing a target in
both azimuth and elevation planes based on the blockage to the path of the
laser beams by the target will require at least two sources of laser beams as
shown in Fig. 1. The laser beams from two different sources in a laser mesh
can be overlapping or non-overlapping. Different wavelength lasers will be
needed to avoid co-channel interference in case of overlapping beams.

###  II-B Laser Mesh Steering

The coverage area of the laser mesh, i.e., the size of the net, in the azimuth
plane depends on the number and separation distances of the laser RXs. We will
assume that the laser RXs are placed on the ground. The top view of the
steered laser positions (RXs) in the $(x,y)$ plane is given in Fig. 3. In this
figure, a single two dimensional (2D) laser mesh from an airborne UAV (e.g.
UAV1 in Fig. 1) is composed of $L\times M$ laser RXs at $i^{\rm th}$ steering
position. The 2D mesh contains $j=1,2,3,\ldots,L$, one dimensional (1D) array
of laser RXs, and $M$ is the number of RX elements at each array, shown in
Fig. 3.

In Fig. 3, there are $2N+1$ azimuth positions due to beam steering. The
steering centers at the azimuth positions are
$i=-N,-N+1,\ldots,0,1,2,\ldots,N$. The distance between the consecutive RXs is
represented as $\Delta x$, the distance between two consecutive 1D arrays is
represented as $\Delta y$ and the distance between the two consecutive
steering positions is $\Delta P$. The $\Delta x$ and $\Delta y$ should be
carefully chosen to classify the aerial targets based on their dimensions.
From Fig. 3, a matrix of dimensions $L(2N+1)\times M$ is obtained over all the
steering positions.

Figure 3: Top view of the RXs on the ground for laser beams from a UAV (e.g.
UAV1 in Fig. 1). Laser mesh steering is used to steer the transmitted laser
beams to different RXs positions on the ground. There are $2N+1$ steering
positions, and each steering position has $L$ number of 1D array of laser RXs.
The number of laser beam RXs in each 1D array is $M$.

If $h$ is the height of the TX from the RXs at the central steering position,
$i=0$, $j=L/2$, the slant range, $d_{i,j}$ from the TX to $i^{\rm th}$
steering position ($i\neq~{}0$) and $j^{\rm th}$ 1D array is
$d_{i,j}=\sqrt{h^{2}+\big{(}(j-L/2)\Delta y+i\Delta P\big{)}^{2}}$. The total
azimuth distance covered during steering is $2N\Delta PL\Delta y$. In
addition, the speed of the steering between any two consecutive steering
positions is given as $v_{\rm s}=\frac{\Delta P}{\Delta t_{\rm s}}$, where
$\Delta t_{\rm s}$ is the time to steer between consecutive steering
positions. If $v$ is the maximum speed of the incoming target, then it is
required that $v_{\rm s}\gg v$ in order to accurately detect and localize the
moving object.

##  III Detection of a Target

In this section, a Gaussian laser beam is considered and the blockage to the
path of a Gaussian beam is mathematically modeled. The model is then used to
detect the presence of a target.

###  III-A Mathematical Modeling of Blockage of a Laser beam

Laser beams considered in this work are modeled as Gaussian beams [19].
Consider a single Gaussian beam illustrated in Fig. 4. The direction of the
propagation of the beam is along the $x$-direction and the beam is polarized
in the $z$-direction. The incident electric field $\textbf{E}^{\rm(inc)}(r,x)$
for the beam at a distance $x$ from the source, using paraxial approximation,
given as [20]

$\displaystyle\textbf{E}^{\rm(inc)}(r,x)=$ $\displaystyle
E_{0}\boldsymbol{\hat{\textbf{z}}}\frac{w_{0}}{w_{\rm
b}(x)}\exp\bigg{(}\frac{-r^{2}}{w_{\rm
b}^{2}(x)}\bigg{)}\exp\bigg{(}-j(kx+\frac{kr^{2}}{2R(x)}-\phi(x))\bigg{)},$
(1)

where $r$ represents the radial distance from the beam’s central axis, $E_{0}$
is the electric field amplitude at origin and at time instance $t_{0}=0$.
$w_{\rm b}(x)$ is the width of the beam along the direction of propagation,
which is given as [20]

$\displaystyle w_{\rm b}(x)=w_{0}\sqrt{1+\frac{x}{x_{R}}},$ (2)

where $x_{R}$ is the Rayleigh range given by $x_{R}=\frac{\pi
w_{0}^{2}n_{0}}{\lambda}$, $\lambda$ is the wavelength, and $n_{0}$ is the
index of refraction of the free space. In 1, $k=\frac{2\pi n_{0}}{\lambda}$ is
the wavenumber, $R(x)$ is the radius of curvature of the wavefront of the beam
at an axial distance $x$, given by
$R(x)=x\bigg{[}1+(\frac{x_{R}}{x})^{2}\bigg{]}$, and $\phi(x)$ is the Gouy
phase. The divergence of the laser beam in Fig. 4 is represented by angle
$\theta$ for $x\gg x_{R}$ as
$\displaystyle{\theta=\lim_{x\to\infty}\arctan\big{(}\frac{w_{\rm
b}(x)}{x}}\big{)}$. Similarly, the apex angle of the cone is given as
$\psi=2\theta$, and solid angle $\Omega=\pi\sin^{2}\theta$. Moreover, the
incident magnetic field $\textbf{H}^{\rm inc}(r,x)$ polarized in the
$y$-direction is given as
$\textbf{H}^{\rm(inc)}(r,x)=\frac{\boldsymbol{\hat{\textbf{y}}}}{\eta_{0}}{E}^{\rm(inc)}(r,x)$,
where $\eta_{0}$ is the impedance of the free space.

Figure 4: A Gaussian profile of a single laser beam propagating in the
$x$-direction.

The incident intensity distribution is given by

$\displaystyle I^{(\rm inc)}(r,x)=$ $\displaystyle\frac{{\rm
Re}\bigg{(}E^{(\rm inc)}\times H^{*(\rm inc)}\bigg{)}}{2},$ $\displaystyle=$
$\displaystyle\frac{|E_{0}|^{2}}{2\eta_{0}}\bigg{(}\frac{w_{0}}{w_{\rm
b}(x)}\bigg{)}^{2}\exp\bigg{(}\frac{-2r^{2}}{w_{\rm b}^{2}(x)}\bigg{)},$ (3)

where $\frac{|E_{0}|^{2}}{2\eta_{0}}$ is the intensity at the beam’s waist. In
the case of blockage, the incident electric field is divided into reflected
and transmitted electric fields given as $\textbf{E}^{\rm(rfl)}(r,x)$, and
$\textbf{E}^{\rm(tx)}(r,x)$, respectively. Therefore, the incident electric
field can be written as
$\textbf{E}^{\rm(inc)}(r,x)=-\textbf{E}^{\rm(rfl)}(r,x)+\textbf{E}^{\rm(tx)}(r,x)$.
The reflected component, $\textbf{E}^{\rm(rfl)}(r,x)$ is mainly specular as
the wavelength is significantly small compared to the size of the target. The
transmitted component is significantly small compared to the reflected
component for solid surface targets. The reflected and transmitted intensity
distributions represented, respectively, as $I^{(\rm rfl)}(r,x)$ and $I^{(\rm
tx)}(r,x)$ are

$\displaystyle I^{(\rm rfl)}(r,x)$ $\displaystyle=\Gamma_{1}^{2}I^{(\rm
inc)}(r,x),$ $\displaystyle I^{(\rm tx)}(r,x)$
$\displaystyle=\Gamma_{2}^{2}I^{(\rm inc)}(r,x),$ (4)

where
$\Gamma_{1}=\frac{\big{|}E^{\rm(rfl)}(r,x)\big{|}}{\big{|}E^{\rm(inc)}(r,x)\big{|}}$
is the reflection coefficient, and
$\Gamma_{2}=\frac{\big{|}\textbf{E}^{\rm(tx)}(r,x)\big{|}}{\big{|}\textbf{E}^{\rm(inc)}(r,x)\big{|}}$
is the transmission coefficient.

###  III-B Detection of the Target based on Blockage of Laser Beam

The RXs of laser beams at $i^{\rm th}$ azimuth steering position and $j^{\rm
th}$ mesh, at a distance $d_{i,j}$ from the TX, and an aperture radius of
$r^{\rm(RX)}$ expects an intensity $I^{(\rm RX)}(r^{\rm(RX)},d_{i,j})$ (See 3
) in case there is no blockage. The intensity, $I^{(\rm RX)}$, as a function
of $r^{\rm(RX)}$ and $d_{i,j})$ is given as

$\displaystyle I^{(\rm
RX)}(r^{\rm(RX)},d_{i,j})=\frac{|E_{0}|^{2}}{2\eta_{0}}\bigg{(}\frac{w_{0}}{w_{\rm
b}(d_{i,j})}\bigg{)}^{2}\exp\bigg{(}\frac{-2r{{}^{(\rm RX)}}^{2}}{w_{\rm
b}^{2}(d_{i,j})}\bigg{)}.$ (5)

The corresponding received power at the RX side is given as [21]

$\displaystyle P^{\rm(RX)}(r^{(\rm
RX)},d_{i,j})=\frac{\pi\big{|}E_{0}|^{2}w_{0}^{2}\bigg{[}1-\exp\bigg{(}\frac{-2r{{}^{(\rm
RX)}}^{2}}{w_{b}^{2}(d_{i,j})}\bigg{)}\bigg{]}}{4\eta_{0}}.$ (6)

Finally, the signal-to-noise ratio (SNR) represented as $S/n_{\rm G}$ at the
RXs of $i^{\rm th}$ steering position and $j^{\rm th}$ mesh in the presence of
additive white Gaussian noise (AWGN) $n_{\rm
G}\sim\mathcal{N}(0,\,\sigma^{2}_{\rm n})\,$ can be written as

$\displaystyle S/n_{\rm G}=\frac{P^{\rm(RX)}(r^{(\rm
RX)},d_{i,j})}{\sigma^{2}_{n}}.$ (7)

(a)

(b)

Figure 5: Estimated area and shape of the target based on the blocked laser
beams at mesh positions. (a) Blocked laser beam intersections are shown in red
at respective mesh, (b) estimated area at each blockage. Algorithm 1
Extraction of shape features of the target.

1:procedure Shape-Features-Extraction

2:% Consider that we are at $j^{\rm th}$ laser mesh at the $i^{\rm th}$
steering position (see Fig. 5), and each intersection of the laser beams are
unique in the $(x,y,z)$ coordinate plane

3: for $i=-N:N$ do

4: for $j=1:L$ do

5: if there is blockage at an intersection of the laser beams at $(x,y,z)$
detected using $S/n_{\rm G}<\gamma$ at respective RXs then

6: Assign area $A(x,y,z)$ to each blocked laser mesh intersection position as
shown in Fig. 5(b)

7: if blockage at same $(x,z)$ position at different $j$ mesh then

8: Extend a 3D area using length $l_{\rm e}^{c}$ (where $l_{\rm e}^{c}=\Delta
y$) across the $j$ mesh where the blocked positions have the same $(x,z)$.
Label this 3D area as the central section as shown in Fig. 6

9: After a central section has been identified, the area on the sides of it
(i.e. different $x$ values) is labeled as wings section (discussed in Section
IV)

10: if the area of the wings decreases more than or equal to half at a later
$j^{\rm th}$ mesh then

11: It is identified as the tail section.

12: The 3D area of wings and tail section is obtained by extending the 2D area
of the plane shown in Fig. 6 by $l_{\rm e}^{\rm w}$, and $l_{\rm e}^{\rm t}$,
respectively, on both sides of the plane.

13: The 3D area for wings and tails is extended to later $j$ mesh, only if
later mesh positions have same $(x,z)$ coordinates

14: end if

15: end if

16: end if

17: end for

18: end for

19:return Estimated shape features of the target section-wise (if the target
is detected)

20:end procedure

If there is a blockage to the path of a single laser beam or a bunch of beams
due to a potential target, the received intensity, $I^{(\rm RX)}(r^{(\rm
RX)},d_{i,j})$ of each beam is reduced and a subsequent reduction occurs in
the SNR, $S/n_{\rm G}$. This reduction is due to the reflection and absorption
of the incident intensity from a target given in 4. Let $\gamma$ be the
threshold for minimum SNR. The detection threshold $\gamma$ is obtained using
Neyman-Pearson decision rule and square law detection function for a given
probability of false alarm (pfa). If $S/n_{\rm G}<\gamma$, then, this is
perceived as the presence of a target at that particular RX position. The
material of the target does not significantly change the blockage
characteristics.

Figure 6: The estimated 3D shape of the target based on blocked laser mesh
intersections in Fig. 5.

##  IV Target Features

In this section, details of the features, i.e. 3D shape, maximum velocity,
pitch, and drift angles, and maximum altitude, obtainable by the proposed
approach are provided.

###  IV-A Features Associated with Target Shape

Depending on the distance between consecutive beams, the blockage at the
intersection position of laser beams on a mesh due to a target has a
corresponding blocked area. Fig. 5(a) shows laser beams blocked at different
positions on laser meshes, $j=1,2,3$, due to a target. The area of each
blocked position (i.e., blocked intersection of two beams) is represented as
$A(x,y,z)=s^{2}(x,y,z)$, where $s$ is one edge of the squares shown in Fig.
5(b). An example blockage of four neighboring intersections, their
corresponding areas, and area of elements are illustrated in Fig. 5(b), where
$s\approx\Delta x$ (see Fig. 2). There is a single blocked intersection at
$j=1$ laser mesh, whereas, five and three blocked intersections at $j=2$ and
$j=3$, respectively. A 3D area of the target based on the blocked laser beams
at $j=1,2,3$ can be approximately calculated (Fig. 6). The overall procedure
for 3D area calculation and extraction of shape features of the target are
given in Algorithm 1.

At lines $2$, and $3$ of Algorithm 1, we traverse over all the steering
positions and laser mesh at these steering positions. We will focus on the
$i^{\rm th}$ steering position and corresponding $j={1,2,3}$, laser mesh,
shown in Fig. 5 for the explanation of the algorithm. At lines $5$ and $6$, if
there is a blockage due to the presence of a target and the condition
$S/n_{\rm G}<\gamma$ is true (see Section III-B), a fixed area $A(x,y,z)$ is
assigned to each blocked laser mesh intersection position. The area assignment
due to blockage is shown in Fig. 5(b). On line $7$ it is checked whether the
blockage is present at same points in the $xz$ plane at different $j^{\rm th}$
laser mesh. To understand that, consider that we have blockages at the same
points in the $xz$ plane at $j=1,2,3,$ laser mesh shown in Fig. 5(a) and (b),
then we can draw a straight line passing through these points (along the
$y$-axis) at $j=1,2,3,$ laser mesh and the line will be perpendicular to the
laser mesh $xz$ plane. If instead of a line, we consider blockage area
$A(x,y,z)$ extension across the laser mesh positions along the $y$-axis, a 3D
central section is formed shown in Fig. 6. The length of the central section
between any two laser mesh is $l_{\rm e}^{c}=\Delta y$ given at line $8$.
After the central section has been identified, any laser mesh intersections
that are blocked and not part of the central section and extend along the $x$
or $z$-axes only is considered either as wing or tail section. The 3D area and
lengths of the wings and tail sections are provided at lines $9$ to $13$ of
Algorithm 1.

Figure 7: Four categories of the targets based on the shape.

The 3D shape of a target can have a minimum of one section and a maximum of
three sections. These are central, wing, and tail sections as shown in Fig. 6.
The total length of the central section of a target is given as $l^{(\rm
c)}=l_{\rm e}^{\rm c}\times(N_{\rm B}-1)$, where $l_{\rm e}^{\rm c}=\Delta y$,
and $N_{\rm B}$ is the number of meshes that have blocked beam or beams. Four
shape categories recognizable by the proposed method are shown in Fig. 7. The
width of the central section at the $j^{\rm th}$ mesh is
$w_{j}^{\rm(c)}=s\times N_{j,\rm B}^{(\rm c)}$, where $N_{j,\rm B}^{(\rm c)}$
are the number of the blocked laser beams at the center section of the $j^{\rm
th}$ mesh. The coordinates of the blocked positions at the $j^{\rm th}$ mesh
constituting the width of the central section are $\big{(}x_{j}^{(\rm
c)},y_{j,\rm o}^{(\rm c)},z_{j,\rm o}^{(\rm c)}\big{)}$, where $y_{j,\rm
o}^{(\rm c)}$, and $z_{j,\rm o}^{(\rm c)}$ are the constant coordinates in the
$y$ and $z$ planes, respectively, whereas $x_{j}^{(\rm c)}$ varies. The height
of the central section at the $j^{\rm th}$ mesh is obtained similarly as
$h_{j}^{(\rm c)}=s\times N_{j,\rm B}^{(\rm c)}$. The coordinates of the
blocked positions at the $j^{\rm th}$ mesh contributing to the height of the
central section are $\big{(}x_{j,\rm o}^{(\rm c)},y_{j,\rm o}^{(\rm
c)},z_{j}^{\rm(c)}\big{)}$ where $z_{j}^{\rm(c)}$ only varies and the other
two coordinate values are constant. The width and height of the central
section are shown in Fig. 6 for a particular target and in Fig. 7 for
different categories of the targets. In Fig. 6, the length, width, and height
of the central section is $2l_{\rm e}^{\rm c}$, $s$, and $s$, respectively.

TABLE I: Training data of 3D shape, maximum velocity, pitch and drift angles,
and maximum altitude of targets and their respective categorization based on
shape.

Target Type |  |  Given target |  Multi-rotor UAVs |  Heli-copters |  Fixed-wing UAVs |  Small fixed-wing planes |  Large fixed-wing planes |  Fighter jets |  Cruise missiles |  Birds |  Ballastic missiles |  Rockets and artillery shells |  HGVs
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Category |  |  cat. 3 |  cat. 1 |  cat. 2 |  cat. 3 |  cat. 3 |  cat. 3 |  cat. 3 |  cat. 3 |  cat. 3 |  cat. 4 |  cat. 4 |  cat. 4
Central part |  Length (m) |  $\mu=5.65,\sigma=0.05$ |  $\mu=1.94,\sigma=1.3$ |  $\mu=21.4,\sigma=16.2$ |  $\mu=7.8,\sigma=6.15$ |  $\mu=13.63,\sigma=9.3$ |  $\mu=56.8,\sigma=14.6$ |  $\mu=20.26,\sigma=6.2$ |  $\mu=6.48,\sigma=2.6$ |  $\mu=0.69,\sigma=0.4$ |  $\mu=14.1,\sigma=11.1$ |  $\mu=3.3,\sigma=2.5$ |  $\mu=5.3,\sigma=4.5$
|  Width (m) |  $\mu=0.52,\sigma=0.03$ |  $\mu=2.15,\sigma=1.6$ |  $\mu=21.4,\sigma=16.2$ |  $\mu=0.73,\sigma=0.5$ |  $\mu=2.17,\sigma=1.04$ |  $\mu=4.4,\sigma=1.32$ |  $\mu=3.36,\sigma=1.1$ |  $\mu=0.7,\sigma=0.2$ |  NA |  $\mu=1.54,\sigma=0.91$ |  $\mu=0.33,\sigma=0.09$ |  $\mu=0.75,\sigma=0.2$
|  Height (m) |  $\mu=0.52,\sigma=0.03$ |  $\mu=0.6,\sigma=0.36$ |  $\mu=5.35,\sigma=2.26$ |  $\mu=2.1,\sigma=1.89$ |  $\mu=3.5,\sigma=1.28$ |  $\mu=14.6,\sigma=5.9$ |  $\mu=4.5,\sigma=1.5$ |  $\mu=0.7,\sigma=0.2$ |  NA |  $\mu=1.5,\sigma=0.91$ |  $\mu=0.23,\sigma=0.21$ |  $\mu=0.75,\sigma=0.2$
Wings and tail sections span and width |  Wing span (m) |  $\mu=2.67,\sigma=0.04$ |  NA |  $\mu=21.35,\sigma=13.99$ |  $\mu=20.7,\sigma=17.36$ |  $\mu=15.2,\sigma=7.9$ |  $\mu=59.4,\sigma=17.4$ |  $\mu=12,\sigma=4.44$ |  $\mu=2.5,\sigma=0.52$ |  $\mu=1.4,\sigma=0.7$ |  NA |  NA |  NA
|  Wing width (m) |  $\mu=0.75,\sigma=0.02$ |  NA |  NA |  $\mu=1.03,\sigma=0.62$ |  $\mu=1.93,\sigma=0.94$ |  $\mu=7.15,\sigma=2.36$ |  $\mu=3.7,\sigma=1$ |  $\mu=0.8,\sigma=0.4$ |  $\mu=0.8,\sigma=0.5$ |  NA |  NA |  NA
|  Tail span (m) |  $\mu=0.89,\sigma=0.035$ |  NA |  $\mu=3.1,\sigma=1.2$ |  $\mu=6.56,\sigma=5.5$ |  $\mu=4.7,\sigma=2.8$ |  $\mu=22,\sigma=8$ |  $\mu=4.6,\sigma=2.02$ |  $\mu=0.9,\sigma=0.2$ |  $\mu=0.41,\sigma=0.2$ |  NA |  NA |  NA
|  Tail width (m) |  $\mu=0.27,\sigma=0.022$ |  NA |  $\mu=1,\sigma=0.7$ |  $\mu=1.85,\sigma=1.6$ |  $\mu=1.9,\sigma=2.2$ |  $\mu=8.33,\sigma=5.5$ |  $\mu=1.87,\sigma=0.9$ |  $\mu=0.3,\sigma=0.15$ |  $\mu=0.18,\sigma=0.12$ |  NA |  NA |  NA
$v^{(\rm max)}$ (m/s) |  |  $\mu=350.2,\sigma=7.5$ |  $\mu=20.2,\sigma=8.5$ |  $\mu=65.9,\sigma=28.14$ |  $\mu=76.8,\sigma=62.3$ |  $\mu=154.5,\sigma=87$ |  $\mu=266.5,\sigma=17.8$ |  $\mu=636,\sigma=99.2$ |  $\mu=800,\sigma=750$ |  $\mu=32.2,\sigma=29.5$ |  $\mu=3500,\sigma=3000$ |  $\mu=937.5,\sigma=593$ |  $\mu=4000,\sigma=2500$
$\alpha^{\circ}$ |  |  $\mu=12,\sigma=8$ |  $\mu=10,\sigma=5$ |  $\mu=15,\sigma=25$ |  $\mu=20,\sigma=30$ |  $\mu=10,\sigma=20$ |  $\mu=8,\sigma=15$ |  $\mu=20,\sigma=45$ |  $\mu=12,\sigma=30$ |  $\mu=10,\sigma=30$ |  $\mu=5,\sigma=30$ |  $\mu=5,\sigma=15$ |  $\mu=10,\sigma=60$
$\beta^{\circ}$ |  |  $\mu=7,\sigma=5$ |  $\mu=15,\sigma=10$ |  $\mu=10,\sigma=15$ |  $\mu=15,\sigma=20$ |  $\mu=8,\sigma=15$ |  $\mu=7,\sigma=15$ |  $\mu=15,\sigma=40$ |  $\mu=8,\sigma=10$ |  $\mu=5,\sigma=15$ |  $\mu=5,\sigma=20$ |  $\mu=5,\sigma=8$ |  $\mu=8,\sigma=45$
$h^{\rm G}$ (km) |  |  $\mu=30,\sigma=25$ |  $\mu=4.62,\sigma=2.21$ |  $\mu=4.7,\sigma=1.9$ |  $\mu=11.5,\sigma=6.9$ |  $\mu=9.95,\sigma=5.31$ |  $\mu=14,\sigma=1.15$ |  $\mu=17.2,\sigma=1.3$ |  $\mu=20,\sigma=17.5$ |  $\mu=2.8,\sigma=2$ |  $\mu=721,\sigma=829$ |  $\mu=13.2,\sigma=14.63$ |  $\mu=23,\sigma=10.5$

The wingspan at a $j^{\rm th}$ mesh from Fig. 6 and Fig. 7 is given as
$l^{\rm(w)}=s\times N_{j,\rm B}^{(\rm w)}$, where $N_{j,\rm B}^{(\rm w)}$ are
the number of blocked laser beam positions of the $j^{\rm th}$ mesh at the
wings section. The coordinates of the blocked positions at the $j^{\rm th}$
mesh for the wingspan are $\big{(}x_{j}^{(\rm w)},y_{j,\rm o}^{(\rm
w)},z_{j,\rm o}^{(\rm w)}\big{)}$. For example in Fig. 6, the wingspan is
$5s$. The width of the wings section at the $j^{\rm th}$ mesh is $w^{(\rm
w)}=l_{\rm e}^{\rm(w)}\times N_{j,\rm B}^{(\rm w)}$, where $l_{\rm
e}^{\rm(w)}$ is a constant value, and for simplicity can be taken as $l_{\rm
e}^{\rm(w)}=s$, and coordinates of the blocked positions corresponding to the
width of the wings at the $j^{\rm th}$ mesh are $\big{(}x_{j,\rm o}^{(\rm
w)},y_{j}^{(\rm w)},z_{j,\rm o}^{\rm(w)}\big{)}$. The height of the wings
section at the $j^{\rm th}$ mesh is given as $h^{(\rm w)}=sN_{j,\rm B}^{(\rm
w)}$. The coordinates of the blocked mesh positions forming the height of the
wings are represented as $\big{(}x_{j,\rm o}^{(\rm w)},y_{j,\rm o}^{(\rm
w)},z_{j}^{\rm(w)}\big{)}$. The width and height of the wings section for a
given target is shown in Fig. 6, and for Category 3 in Fig. 7. In Fig. 6, the
width and height of the wings section is $l_{\rm e}^{\rm(w)}$, and $s$,
respectively. The dimensions of the tail section are obtained similarly as for
the wings section.

###  IV-B Velocity, Pitch and Drift Angles, and Altitude of the Target

The motion characteristics of a target at a given time depends on the
velocity, and pitch and drift angles. These three features of a target can be
estimated using the proposed framework and can be utilized to classify a
target. Let $\Delta d_{i,i+1}$ represents the distance between any two
steering positions, $i$ and $i+1$, which have one or more blocked
intersections due to a target, and $\Delta t_{i,i+1}$ is the corresponding
time difference for a target to move between mesh locations at $i^{\rm th}$
and $(i+1)^{\rm th}$ steering positions. The instantaneous velocity is
represented as $v(t)=\frac{\Delta d_{i,i+1}}{\Delta t_{i,i+1}}$. Over the
steering positions, we can write the maximum velocity as

$v^{(\rm max)}=\max\bigg{(}\frac{\Delta d_{i,i+1}}{\Delta
t_{i,i+1}}\bigg{)},~{}\forall~{}i=-N,-N+1,\ldots,N-1,N.$ (8)

TABLE II: Size, velocity, and flying altitude of popular rotary and fixed-wing
UAVs.

Target Type | Type | Total area | $v^{(\rm max)}$ (m/s) | Max. altitude (km)
---|---|---|---|---
|  | Length of central part (m) | Wing span (m) | Height of central part (m) |  |
Phantom 4 [22] | Multi-rotor UAV | $0.4$ |  $0.15$, propellers dia | $0.19$ | $20$ | $0.5$
Matrice 600 [23] | Multi-rotor UAV | $1.18$ |  $0.5$, propellers dia | $0.5$ | $18$ | $2.5$
Amazon Prime Air [24] | Multi-rotor UAV | $9.1$ |  $2.5$, frame and propellers | $1.5$ | $22.2$ | $0.15$
MQ-8B [25]] | Helicopter UAV | $7.3$ |  $8.4$, propellers dia | $2.9$ | $59.2$ | $6.1$
Sky Surfer [26] | Fixed-wing UAV | $0.91$ | $1.4$ | $0.32$ | $13.8$ | $0.2$
Eclipse 2.0 [27] | Fixed-wing UAV | $1.1$ | $5.5$ | $0.25$ | $28$ | $0.13$
MQ-9A [28] | Fixed-wing UAV | $11$ | $20$ | $3.6$ | $123.5$ | $15.24$
Global Hawk [29] | Fixed-wing UAV | $14.5$ | $35.4$ | $4.7$ | $175$ | $19.8$

The trajectory variations of a target in the elevation and azimuth planes can
be represented using pitch and drift angles, respectively. Let $\alpha(t)$,
and $\beta(t)$ represent the pitch and drift angles of a target, respectively.
If $h_{i+1}(t)$ and $h_{i}(t)$ are the estimated heights of the target at
$i+1$ and $i$ steering positions, $x_{i+1}(t)$ and $x_{i}(t)$ are the
$x$-coordinates of the target at $i+1$ and $i$ steering positions at time $t$,
and $\Delta P$ is the distance between two consecutive steering positions
shown in Fig. 3, then $\alpha(t)$ and $\beta(t)$ are given as [30, 31]

$\displaystyle\alpha(t)=\tan^{-1}{\Bigg{(}\frac{h_{i+1}(t)-h_{i}(t)}{\Delta
P}}\Bigg{)},$ (9)
$\displaystyle\beta(t)=\tan^{-1}{\Bigg{(}\frac{x_{i+1}(t)-x_{i}(t)}{\Delta
P}}\Bigg{)}.$ (10)

The maximum altitude of an aerial target contains valuable information
characterizing the target. This feature can also be determined using our
proposed setup. The maximum z-coordinate value at the intersection pair of
blocked beams provides the maximum altitude of the target at that location.
The maximum altitude of the target from the ground is represented as $h^{(\rm
G)}$. The maximum altitude, velocity, pitch and drift angles, and 3D shape
features for different types of targets are given in Table I. The data in
Table I is used for creating the training set that is utilized developing the
ML models for classification. Another Table II is provided that contains the
size, maximum velocity and flight altitude of popular rotary and fixed-wing
UAVs.

##  V Classification, Localization, and Target Tracking

In this section, details of the classification, localization, and target
tracking models used in our approach are provided.

###  V-A Classification of a Target using Training Data

(a)

(b)

Figure 8: PDFs of length of central section and maximum velocity of the
training targets.

Any flying object that disrupts the path of the laser beams is considered as a
potential target in the proposed approach. These objects can be man-made or
birds. Flying objects are classified based on the features discussed in
Section IV, i.e., shape, maximum velocity, pitch and drift angle
characteristics, and maximum flight altitude by developing ML models using
training data details provided in Table I. Target types are grouped into four
categories based on the 3D shape (Fig. 7), i.e., drone-like objects, chopper-
like objects, fixed-wing type objects, and missile-like objects. The
dimensions of the 3D shapes are provided in Table I. The first category is
assigned to multi-rotor UAVs that have either a square or rectangular central
section from the mainframe and mounted rotors onboard the mainframe. The 3D
shape of the first category is shown in Fig. 7(a). The second category for
helicopters with a square central section due to the rotor blades followed by
a tail section shown in Fig. 7(b). The tail section is not present in some
cases for Category 2. Central sections of objects in Category 2 are expected
to be larger than central sections of objects in Category 1. In Fig. 7(c), a
third category is shown that covers all the aerial targets with central,
wings, and tail sections. These include fixed-wing UAVs and planes, cruise
missiles, and birds. The fourth category represents targets with only a long
main central section without any significant wings and tail spans (Fig. 7(d)).
The fourth category includes ballistic missiles, rockets and artillery shells,
and hypersonic glide vehicles (HGVs).

The parameters of the training data in Table I consist of the length, width,
and height of the central section of eleven different targets (i.e., classes),
grouped into four categories. The wingspan, wing width, tail span, and tail
width values are also provided. The height of the wings and tail sections have
small variances among different types of targets, hence, these two features
are not included in the training set to decrease the statistical noise as low
as possible. Other features used while creating the training set are maximum
velocity, pitch and drift angles, and maximum altitude values of eleven
different types. Each and every feature that are used creating the training
data assumed to have a Gaussian distribution with the mean and standard
deviations provided in Table I. The NA entries in Table I indicate that there
are no values present for the training features of that particular target
type.

Fig. 8 shows the probability density functions (PDFs) of the length of the
central section and maximum velocity of different types of training targets
based on the parameters provided in Table I. Even though the PDFs of different
training targets overlaps, the used ML models take several other features into
account that yields to high classification accuracy. Visual boundaries among
the different types of targets for length of the central section and maximum
velocity are given in Fig. 9. It is observed that even with only two features,
target classes become quite separable. Let $\textbf{M}^{(\rm Tr)}$ represent
the matrix containing training data of eleven targets that is given as

$\textbf{M}^{(\rm Tr)}=\\!\begin{aligned} &\left[\begin{matrix}l_{1}^{(\rm
c,C_{1})}&w_{1}^{(\rm c,C_{1})}&h_{1}^{(\rm c,C_{1})}&l_{1}^{(\rm
w,C_{1})}&w_{1}^{(\rm w,C_{1})}&l_{1}^{(\rm t,C_{1})}\\\ l_{2}^{(\rm
c,C_{1})}&w_{2}^{(\rm c,C_{1})}&h_{2}^{(\rm c,C_{1})}&l_{2}^{(\rm
w,C_{1})}&w_{2}^{(\rm w,C_{1})}&l_{2}^{(\rm t,C_{1})}\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\ l_{k}^{(\rm c,C_{1})}&w_{k}^{(\rm
c,C_{1})}&h_{k}^{(\rm c,C_{1})}&l_{k}^{(\rm w,C_{1})}&w_{k}^{(\rm
w,C_{1})}&l_{k}^{(\rm t,C_{1})}\\\ l_{1}^{(\rm c,C_{2})}&w_{1}^{(\rm
c,C_{2})}&h_{1}^{(\rm c,C_{2})}&l_{1}^{(\rm w,C_{2})}&w_{1}^{(\rm
w,C_{2})}&l_{1}^{(\rm t,C_{2})}\\\ l_{2}^{(\rm c,C_{2})}&w_{2}^{(\rm
c,C_{2})}&h_{2}^{(\rm c,C_{2})}&l_{2}^{(\rm w,C_{2})}&w_{2}^{(\rm
w,C_{2})}&l_{2}^{(\rm t,C_{2})}\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\ l_{k}^{(\rm c,C_{2})}&w_{k}^{(\rm
c,C_{2})}&h_{k}^{(\rm c,C_{2})}&l_{k}^{(\rm w,C_{2})}&w_{k}^{(\rm
w,C_{2})}&l_{k}^{(\rm t,C_{2})}\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\ l_{1}^{(\rm c,C_{K})}&w_{1}^{(\rm
c,C_{K})}&h_{1}^{(\rm c,C_{K})}&l_{1}^{(\rm w,C_{K})}&w_{1}^{(\rm
w,C_{K})}&l_{1}^{(\rm t,C_{K})}\\\ l_{2}^{(\rm c,C_{K})}&w_{2}^{(\rm
c,C_{K})}&h_{2}^{(\rm c,C_{K})}&l_{2}^{(\rm w,C_{K})}&w_{2}^{(\rm
w,C_{K})}&l_{2}^{(\rm t,C_{K})}\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\ l_{k}^{(\rm c,C_{K})}&w_{k}^{(\rm
c,C_{K})}&h_{k}^{(\rm c,C_{K})}&l_{k}^{(\rm w,C_{K})}&w_{k}^{(\rm
w,C_{K})}&l_{k}^{(\rm t,C_{K})}\end{matrix}\right.\\\
&\qquad\qquad\left.\begin{matrix}w_{1}^{(\rm t,C_{1})}&v_{1}^{(\rm
C_{1})}&\alpha_{1}^{(\rm C_{1})}&\beta_{1}^{(\rm C_{1})}&h_{1}^{(\rm
G,C_{1})}\\\ w_{2}^{(\rm t,C_{1})}&v_{2}^{(\rm C_{1})}&\alpha_{2}^{(\rm
C_{1})}&\beta_{2}^{(\rm C_{1})}&h_{2}^{(\rm G,C_{1})}\\\
\vdots&\vdots&\vdots&\vdots&\vdots\\\ w_{k}^{(\rm t,C_{1})}&v_{k}^{(\rm
C_{1})}&\alpha_{k}^{(\rm C_{1})}&\beta_{k}^{(\rm C_{1})}&h_{k}^{(\rm
G,C_{1})}\\\ w_{1}^{(\rm t,C_{2})}&v_{1}^{(\rm C_{2})}&\alpha_{1}^{(\rm
C_{2})}&\beta_{1}^{(\rm C_{2})}&h_{1}^{(\rm G,C_{2})}\\\ w_{2}^{(\rm
t,C_{2})}&v_{2}^{(\rm C_{2})}&\alpha_{2}^{(\rm C_{2})}&\beta_{2}^{(\rm
C_{2})}&h_{2}^{(\rm G,C_{2})}\\\ \vdots&\vdots&\vdots&\vdots&\vdots\\\
w_{k}^{(\rm t,C_{2})}&v_{k}^{(\rm C_{2})}&\alpha_{k}^{(\rm
C_{2})}&\beta_{k}^{(\rm C_{2})}&h_{k}^{(\rm G,C_{2})}\\\
\vdots&\vdots&\vdots&\vdots&\vdots\\\ \vdots&\vdots&\vdots&\vdots&\vdots\\\
w_{1}^{(\rm t,C_{K})}&v_{1}^{(\rm C_{K})}&\alpha_{1}^{(\rm
C_{K})}&\beta_{1}^{(\rm C_{K})}&h_{1}^{(\rm G,C_{K})}\\\ w_{2}^{(\rm
t,C_{K})}&v_{2}^{(\rm C_{K})}&\alpha_{2}^{(\rm C_{K})}&\beta_{2}^{(\rm
C_{K})}&h_{2}^{(\rm G,C_{K})}\\\ \vdots&\vdots&\vdots&\vdots&\vdots\\\
w_{k}^{(\rm t,C_{K})}&v_{k}^{(\rm C_{K})}&\alpha_{k}^{(\rm
C_{K})}&\beta_{k}^{(\rm C_{K})}&h_{k}^{(\rm
G,C_{K})}\end{matrix}\right]\end{aligned}$ (11)

where $l_{1}^{(\rm c,C_{1})},w_{1}^{(\rm c,C_{1})}$, and $h_{1}^{(\rm
c,C_{1})}$ are the first points representing length, width, and height of the
central section, respectively, belonging to the first class. $l_{1}^{(\rm
w,C_{1})},w_{1}^{(\rm w,C_{1})}$ are first points of the wingspan and wing
width of the first class, respectively, and the first points of the tail span
and width are represented with $l_{1}^{(\rm t,C_{1})},w_{1}^{(\rm t,C_{1})}$.
Moreover, the first points of maximum velocity, pitch and drift angles, and
maximum flight altitude are represented, respectively, with $v_{1}^{(\rm
C_{1})},\alpha_{1}^{(\rm C_{1})},\beta_{1}^{(\rm C_{1})},h_{1}^{(\rm
G,C_{1})}$, for the first class. Each class has $k$ number of samples and
there are $K=11$ classes in our training set.

Figure 9: Visualization of the length of the central section and maximum
velocity of training targets.

Similar to the training data, the feature values for a given target is given
in the form of a matrix, $\textbf{M}^{(\rm eval)}$ as

$\textbf{M}^{(\rm eval)}=\\!\begin{aligned} &\left[\begin{matrix}l_{1}^{(\rm
c)}&w_{1}^{(\rm c)}&h_{1}^{(\rm c)}&l_{1}^{(\rm w)}&w_{1}^{(\rm
w)}&l_{1}^{(\rm t)}\\\ l_{2}^{(\rm c)}&w_{2}^{(\rm c)}&h_{2}^{(\rm
c)}&l_{2}^{(\rm w)}&w_{2}^{(\rm w)}&l_{2}^{(\rm t)}\\\
\vdots&\vdots&\vdots&\cdots&\vdots&\vdots\\\ l_{k^{\prime}}^{(\rm
c)}&w_{k^{\prime}}^{(\rm c)}&h_{k^{\prime}}^{(\rm c)}&l_{k^{\prime}}^{(\rm
w)}&w_{k^{\prime}}^{(\rm w)}&l_{k^{\prime}}^{(\rm t)}\end{matrix}\right.\\\
&\qquad\qquad\left.\begin{matrix}w_{1}^{(\rm
t)}&v_{1}&\alpha_{1}&\beta_{1}&h_{1}^{(\rm G)}\\\ w_{2}^{(\rm
t)}&v_{2}&\alpha_{2}&\beta_{2}&h_{2}^{(\rm G)}\\\
\vdots&\vdots&\vdots&\vdots&\vdots\\\ w_{k^{\prime}}^{(\rm
t)}&v_{k^{\prime}}&\alpha_{k^{\prime}}&\beta_{k^{\prime}}&h_{k^{\prime}}^{(\rm
G)}\end{matrix}\right]\end{aligned}$ (12)

where the number of samples for the target are $k^{\prime}$. The target data
is interpolated to adjust the size of the target’s data equal to the training
data that can be formulated as

$\displaystyle\textbf{M}^{(\rm eval)}=$ $\displaystyle{\rm
interpolate}\bigg{(}\textbf{M}^{(\rm eval)},k\bigg{)}.$ (13)

Let $\textbf{C}^{(\rm Tr)}$ represents an array that contains the target
classes. In 14, the size of this vector corresponding to 11 are $k\times K$,
given as

$\textbf{C}^{(\rm Tr)}=\\!\begin{aligned}
&\left[\begin{matrix}C_{1,1}~{}~{}C_{1,2}~{}~{}\ldots
C_{1,k}~{}~{}C_{2,1}~{}~{}C_{2,2}~{}~{}\ldots\end{matrix}\right.\\\
&\qquad\qquad\left.\begin{matrix}C_{2,k}~{}~{}\ldots\ldots~{}C_{K,1}~{}~{}C_{K,2}~{}~{}\ldots
C_{K,k}\end{matrix}\right]^{T}\end{aligned}$ (14)

where $T$ is the transpose operation.

Algorithm 2 Simultaneous Detection, Classification, Localization, and Tracking
of the Aerial Target.

1:procedure SDCLT

2:% The total coverage of a single virtual door is $M\Delta xh$ and the total
area spanned at all the steering positions is $M\Delta x\Delta y(2N+1)Lh$

3:% Considering that we have $j$ laser mesh at the $i^{\rm th}$ steering
position (see Fig. 3 )

4: for i = -N:N do

5: if there are laser beams with $S/n_{\rm G}<\gamma$ then for a given pfa

6: Obtain the estimated features of the target given in Table I, (and
discussed in Section IV)

7: Categories and classify the target (see Section V)

8: if a positive threat identified then

9: Obtain the localization and tracking of the target and update at every
$i^{\rm th}$ steering position (see Section V-B)

10: end if

11: else

12: Steering positions only

13: end if

14: end for

15:return Estimated coordinates, and features of the target (if detected)

16:end procedure

In this study, four different types of classifiers, i.e., Naive Bayes (NB),
Linear Discriminant Analysis (LDA), K-nearest Neighbor (KNN), and Random
Forest (RF), are used for classification. With $f$ representing the modeling
function of a classifier, $\mathcal{M}_{1}$, $\mathcal{M}_{2}$,
$\mathcal{M}_{3}$, and $\mathcal{M}_{4}$ expresses the corresponding models as
given below

$\displaystyle\mathcal{M}_{1}=f^{(\rm NB)}\bigg{(}\textbf{M}^{(\rm
Tr)},\textbf{C}^{(\rm Tr)}\bigg{)},$ (15)
$\displaystyle\mathcal{M}_{2}=f^{(\rm LDA)}\bigg{(}\textbf{M}^{(\rm
Tr)},\textbf{C}^{(\rm Tr)}\bigg{)},$ (16)
$\displaystyle\mathcal{M}_{3}=f^{(\rm KNN)}\bigg{(}\textbf{M}^{(\rm
Tr)},\textbf{C}^{(\rm Tr)}\bigg{)},$ (17)
$\displaystyle\mathcal{M}_{4}=f^{(\rm RF)}\bigg{(}\textbf{M}^{(\rm
Tr)},\textbf{C}^{(\rm Tr)}\bigg{)}.$ (18)

The interpolated target’s data and the classifier models are used to estimate
the particular class of the target using the prediction function given as

$\displaystyle C^{(\rm{est},\mathcal{M}_{q})}=$ $\displaystyle{\rm
predict}\bigg{(}\mathcal{M}_{q},\textbf{M}^{(\rm eval)}\bigg{)},$ (19)

where $q={1,2,3,4}$ stands for the model used, and
$C^{(\rm{est},\mathcal{M}_{q})}$ is the estimated class from the $q^{\rm th}$
model. The predictions are made using the relevant predict functions specific
to the models deployed.

###  V-B Localization and Tracking of the Target

The $(x,y,z)$ coordinates of the intersection of the laser beams are unique as
shown in Fig. 5(a). If one or more laser intersections are blocked by a
target, the coordinates of the blocked intersection positions provide the
localization of the target at a given time instance. As the target moves, the
localization information is also updated in time. The center of the target is
the center position of the blocked laser intersections and mesh. For example
in Fig. 5(b), the center of the target is at the third blocked intersection of
$j=2$ laser mesh. The tracking and mapping of the target’s trajectory are
obtained as the blocked laser intersection positions are updated as the target
moves. Overall SDCLT process of a target is given in Algorithm 2. In Algorithm
2 at lines $4$ and $5$, a detection test is carried out $S/n_{\rm G}<\gamma$
to determine the presence of a target for each steering position. Once a
target is detected, the shape features of the target are extracted (that are
provided in Table I). Next, the target is classified and categorized based on
the extracted features. The localization and tracking of the target are also
carried out at different steering positions (discussed inSection V-B). The
extraction of features, classification, and localization, and tracking of the
target are provided at lines $6$ to $9$ of Algorithm 2.

(a)

(b)

Figure 10: (a) Reflected laser beams to provide spatial diversity, (b) laser
beam transmitted and reflected towards the source. Figure 11: An example laser
mesh scenario using a low-altitude satellite network. The laser beams from
satellites are directed toward the ground at an angle $\Theta$ with the unit
normal (of the satellite). The laser beams are reflected at an angle $\Theta$
with the unit normal (of the ground) towards the nearby satellite in the
network. Using this configuration, and a large number of satellites in the
network, the change in the shape of the laser mesh at a given location due to
the motion of the satellites can be significantly reduced.

##  VI Limitations of the Proposed Approach and Solutions

In this section, limitations of our proposed approach are discussed and
possible solutions are provided.

###  VI-A Laser Beams Transmission and Reception

A limitation of the proposed approach is the difficulty in the deployment of
airborne laser TXs and a large number of laser RXs on the ground. There can be
different options for the deployment of laser TXs and RXs. The TXs of the
uniformly spaced array of laser beams can be placed on high-altitude platforms
(using tethered hot air balloons) or low-altitude satellites e.g. Starlink
satellite network. The RXs of the laser beams can be either located near the
TX or co-located with the TX using the reflection of laser beams from the
ground as shown in Fig. 10(a), and (b), respectively. This can eliminate the
need for the placement of RXs on/near the ground. Similar to Starlink
Satellite Constellation, a dense network of satellites can be used carrying
TXs and RXs of laser beams shown in Fig. 11. In Fig. 11, an example laser mesh
setup using a network of low-altitude satellites and laser reflection from the
ground is shown. The transmitted and reflected laser beams form an angle
$\Theta$ with the unit normal at the satellite and ground, respectively. The
transmitted laser beams are reflected from the ground and received at a nearby
satellite. Using the configuration in Fig. 11, and a large number of
satellites in the network, the change in the shape of the laser mesh at a
given geographic location due to the motion of the satellites is minimum.
Moreover, a large coverage area is possible at an affordable cost.

Figure 12: The sequence of laser beams for multiple target detection. The
sequence of laser beams is activated sequentially starting from the center.
The center of the sequence is the estimated center of the detected target’s
position.

The classification and localization accuracy of a target depend on the
distance between consecutive laser beams in a mesh. To obtain greater
accuracy, we require a mesh of closely spaced and spatially diverse laser
beams that is challenging. The generation of spatially diverse laser beams can
be realized through the use of lens, and mirrors [32], or using multiple
reflectors at different spatial positions in the path of the transmitted laser
beams. Fig. 10(a) shows an example scenario of transmitted and reflected laser
beams for a given reflector orientation. These techniques, together with the
use of multiple hierarchical TXs, and RXs of the laser beams, can create a
dense mesh of laser beams that are spatially diverse and in close formation.

###  VI-B Multiple Targets Detection

The detection of multiple targets simultaneously is a complex task. In case
laser beams are blocked due to multiple targets that are close to each other,
a clear decision cannot be made whether it is because of a single large target
or multiple smaller targets. To remove this ambiguity, a sequence of laser
beams can be directed to the next steering position once a target is
identified. The center of the sequences is the estimated center of the target
at the next steering position based on the trajectory of the target. The
sequences are applied sequentially with a delay of $\Delta t_{\rm seq}$. An
example illumination sequence is shown in Fig. 12 where rectangular sequences
are applied. In Fig. 12, $L=13$, and nine mesh are illuminated sequentially
for a delay of $\Delta t_{\rm seq}$ starting from the center outwards for an
$i^{\rm th}$ steering position. Other complex sequences that may help in the
identification of multiple close flying targets are also possible. The
sequential application of the sequences helps in the identification of
boundaries of a target, thus leading to the detection of multiple targets.

Figure 13: Intensity plot of the Gaussian laser beam.

##  VII Simulation Setup and Results

Simulations are carried out to first observe the blockage of a laser beam by a
target (discussed in Section III). In the simulations, a Gaussian beam of
waist radius $2\text{\times}{10}^{-3}$ is generated as shown in Fig. 13. The
intensity of the Gaussian beam shown in Fig. 13 is normalized. The wavelength
is $\lambda=$100\text{\times}{10}^{-9}$$, beam waist radius
$w_{0}=$2\text{\times}{10}^{-3}$$, and Rayleigh range $x_{\rm R}=125.7$ m. An
RX is present at a distance of $d_{i,j}=350$ m, and the radius of the aperture
at the RX is $r^{(\rm RX)}=$1\text{\times}{10}^{-2}$$. The variance of the
AWGN noise is $\sigma^{2}_{\rm n}=$1\text{\times}{10}^{-4}$$. The electric
field amplitude at the origin is $E_{0}=200$, and the received power in 6 is
$3.3\text{\times}{10}^{-4}$ W, and the maximum SNR (from 7 ) is $5.1$ dB when
there is no target present. The threshold $\gamma$ for a pfa of $0.1$ is set
to be $\gamma=3.6$ dB. Now, a target is introduced at a $200$ m distance from
the TX of the laser beam. The value of $\Gamma_{1}$ and $\Gamma_{2}$ are
selected to be $0.7$ and $0.2$, respectively, for the target. The SNR due to
blockage from the target is $-14.7$ dB that is significantly less than the SNR
threshold for target detection. Consequently, the target will be detected.

Figure 14: Simultaneous detection, localization, and tracking of a target
using three laser mesh at each steering position. The red dot shows the
position of the target.

The laser beam in Fig. 13 is used to form meshes at different steering
positions shown in Fig. 14. In the simulations, we used $7$ steering
positions, i.e., $i=-250:25:250$, and each steering position had three 1D
arrays i.e. $L=3$. Each 1D array had 21 RX elements from the two airborne
UAVs. The number of laser intersection positions in each mesh were $21\times
21$. A target highlighted with red dots is shown in Fig. 14. The target lays
over three meshes at each steering position. The estimated features of the
target from Section IV were recorded for the target. The features of the
target are given in Table I under the name Given target. The features of the
given target are similar to a BGM-109 Tomahawk missile [33].

In our dataset, we used 200 samples per class generated from the Gaussian
distribution parameters given in Table I. A target can be classified with the
help of training data of different aerial targets, and using NB, LDA, KNN, and
RF classifiers. The NB, LDA, KNN, and RF classifiers from Statistics and
Machine Learning Toolbox of Matlab are used in the simulations [34].
Hyperparameter optimization in classification is also performed using Matlab.
For this specific target (Tomahawk misile), NB, LDA, and DT models were able
to correctly classify based on its features provided in Table I as a cruise
missile, whereas KNN failed. For a better understanding of the used
classification models, the confusion matrices are also provided for all four
classifiers in Fig. 15. To derive the confusion matrices, $200$ new samples
are created using the parameters given in Table I. The model is optimized
using automated optimized hyperparameter values to minimize the classification
error.

(a)

(b)

(c)

(d)

Figure 15: Confusion matrix for classification of targets at $200$ different
instances using (a) Naive Bayes, (b) K-nearest neighbor, (c) Linear
Discriminant Analysis classifiers, and (d) Random forest classifiers. The
classifications are obtained through automated hyperparameter optimization.

The results given in Fig. 15 show that NB classifier performs the best among
all. There are no misclassifications with NB classifier. The NB classifier
considers the different features given in Table I as independent that helps in
the best classification. The KNN performs poorly compared to the other
classifiers. The classification in KNN is based on nearest distance and values
of many of the features of the targets e.g., length and velocity shown in Fig.
8 are overlapping, therefore, KNN misclassifies different targets. The LDA is
able to correctly classify most of the targets except fixed-wing UAVs and
small fixed-wing planes. The LDA misclassifies fixed-wing UAVs and small
fixed-wing planes as fighter jets, as many of the features are similar.
Similar to LDA, RF classifier misclassifies fixed-wing UAVs and small fixed-
wing planes. However, the total number of misclassifications is smaller for RF
classifier compared to the LDA classifier. Overall performance of the models
proves the viability of our proposed approach.

##  VIII Conclusions and Future Work

In this work, a novel technique called laser mesh for detection,
classification, localization, and tracking of aerial targets that is an
alternative to radars is provided. Mesh of laser beams are proposed to detect,
classify, and localize aerial targets. To create the mesh, at least two
airborne platforms are required. Any aerial object crossing the mesh will
block the path of the laser beams and, subsequently, will be detected and
localized in space. Using our laser mesh setup, we can obtain the 3D shape,
velocity, pitch and drift angles, and a maximum altitude of a target. ML
models for classification are used assuming Gaussian distributed features of
3D shape, maximum velocity, and pitch and drift angles, and a maximum altitude
of 11 different classes. Simulations proved the viability of the proposed
approach. Future work includes carrying out the real-world implementation of
the proposed approach.

## Acknowledgement

This work has been supported by NASA under the Federal Award ID number
NNX17AJ94A.

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