# Bayesian Multidimensional Scaling for Location Awareness in Hybrid-Internet
of Underwater Things

Ruhul Amin Khalil, Nasir Saeed, Mohammad Inayatullah Babar, Tariqullah Jan and
Sadia Din Ruhul Amin Khalil, Mohammad Inayatullah Babar and Tariqullah Jan are
with the Department of Electrical Engineering, Faculty of Electrical and
Computer Engineering, University of Engineering and Technology, Peshawar
25120, Pakistan e-mail: [1. ruhulamin, 2. babar, 3.
<EMAIL_ADDRESS>Saeed is with Department of Electrical
Engineering, Northern Border University, Arar 73222, Saudi Arabia e-mail:
<EMAIL_ADDRESS>Din is with the Department of Information and
Communication Engineering, Yeungnam University, Gyeongbuk 38541, South Korea
email<EMAIL_ADDRESS>received X, X X ; revised X, X X, accepted
X, X X.

###### Abstract

Localization of sensor nodes in the Internet of Underwater Things (IoUT) is of
considerable significance due to its various applications, such as navigation,
data tagging, and detection of underwater objects. Therefore, in this paper,
we propose a hybrid Bayesian multidimensional scaling (BMDS) based
localization technique that can work on a fully hybrid IoUT network where the
nodes can communicate using either optical, magnetic induction, and acoustic
technologies. These communication technologies are already used for
communication in the underwater environment; however, lacking localization
solutions. Optical and magnetic induction communication achieves higher data
rates for short communication. On the contrary, acoustic waves provide a low
data rate for long-range underwater communication. The proposed method
collectively uses optical, magnetic induction, and acoustic communication-
based ranging to estimate the underwater sensor nodes’ final locations.
Moreover, we also analyze the proposed scheme by deriving the hybrid Cramer-
Rao lower bound (H-CRLB). Simulation results provide a complete comparative
analysis of the proposed method with the literature.

###### Index Terms:

Internet of Underwater things (IoUT), Bayesian Multidimensional Scaling
(BMDS), hybrid Cramer-Rao lower bound (H-CRLB), signals of opportunity (SOA)
approach.

##  I Introduction

Internet of underwater things (IoUT) has attained much attention because of
their many applications such as navigation, objects localization, detection of
mines, and monitoring of environmental pollution [1, 2, 3, 4]. The growth of
IoUT is in its early phase and faces innumerable challenges. For example, in
terms of communications, the radio frequency (RF) waves do not provide
satisfactory outcomes due to various factors such as scattering and absorption
in an underwater environment. In contrast, acoustic waves are vastly utilized
for underwater communication due to its low-absorption in water [5, 6]. The
acoustic waves can travel for long distances up to tens of kilometers, but
offers a low data rate and have a substantial propagation delay [7].
Therefore, to provide better data rates and a little propagation delay,
optical communication is recently used to develop optical-IoUT networks.
Optical communication is utilized to correspond among the underwater things
for shorter range and consists of high-quality light-emitting diodes (LEDs) or
lasers. Optical communication provides higher data rates compared to its
counterpart technologies [8, 9]. However, propagation of optical light in the
underwater environment is profoundly affected by the inherent properties of
light, type of water, salinity, and turbulence [10]. Nevertheless, magnetic
induction (MI) is also utilized for underwater communication to provide high
data rates. However, MI has a limited transmission range and is also affected
by the conductive nature of the water[11, 12, 13].

Besides communication, localization in IoUT is of significant importance for
tracking various underwater sensor nodes, data tagging, and detection of
underwater targets [1]. Moreover, the classical localization techniques for
terrestrial IoT networks do not function well in marine environments due to
the harsh nature and non-availability of the Global Positioning System (GPS)
system. It is straightforward that GPS works well in terrestrial networks, but
its performance degrades when used in an indoor [14, 15] and underwater
environment [16]. Moreover, the underwater monitoring systems demand accurate
localization techniques as the collected data is only useful if the nodes’
location is estimated accurately [17, 18]. Based on the communication
technology used, underwater localization techniques can be divided into
acoustic, optical, and MI-based systems. Various localization techniques for
acoustic underwater sensor networks’ been investigated in the past. These
techniques consider different aspects of the system such as signal propagation
model, network topology, environmental factors, localization accuracy, number
of anchor nodes, the geometry of anchor nodes, and the sensor node’s relative
location to the anchors [19, 20]. Most of the acoustic-based underwater
localization systems use time difference of arrival (TDoA) ranging. However,
the TDoA measurements for distance estimation in underwater acoustic
communication channels are highly affected by multi-path. Similarly, the RSS-
based distance estimation also suffers from multi-path propagation, making it
hard to compute accurate distance estimation [21]. Nevertheless, the
underwater acoustic channels show good transmission features at certain depths
where RSS-based distance estimation can be a good option [22].

In case of underwater optical wireless communication, the optical light mainly
suffers from attenuation, scattering, and absorption [23, 24]. Based on these
impediments, the existing literature only presents the time of arrival (ToA)
and RSS-based underwater localization schemes. For instance, [24] proposes an
underwater optical positioning system using both ToA and RSS-based ranging,
where optical base stations (OBS) are used as anchor nodes. The sensor nodes
receive the transmitted optical signal from various anchor nodes and locate
themselves by utilizing a linear-least-square solution. In contrast, a
distance estimation technique based on RSS has been presented in [25] for a
given underwater optical communication network. This technique strongly relies
on various parameters that include properties of the optical channel,
transmitted power, angle of divergence of the transmitter, trajectory angle,
and field view of the receiver. Some recent works also use Magnetic Induction
(MI) for underwater communication and localization. [26] proposes a novel MI-
based localization technique that utilizes received magnetic field strength
(RMFS) for measuring RSS. The proposed system considered proper elimination of
multi-path fading and utilization of constant properties of the MI channel.

Hence, many location awareness methods have been developed in the past to
accurately estimate the position of the underwater nodes using different
communication technologies. Likewise, there exist some other localization
techniques that utilize the fusion of acoustic and optical communication
technologies in finding the position of unknown nodes. Recent studies show
that the hybrid approach can achieve better accuracy and have more network
flexibility. Therefore, in this paper, a fully hybrid location awareness
algorithm has been proposed, that considers three different technologies
including MI, acoustic and optical communication. Such an approach where the
system can utilizes any available technology, is also termed as a signals of
opportunity (SOA) based localization. The main contributions of this paper are
summarized as follows:

  * •

A SOA based hybrid approach is introduced for localization of IoUT devices in
the underwater environment, which takes into account acoustic, optical, and
magnetic induction based ranging.

  * •

BMDS-based dimensionality reduction technique, along with Procrustes analysis,
is used to estimate the position of underwater IoUT devices. The proposed
method uses the ranges from the received power using either optical, MI, or
acoustic communication.

  * •

A hybrid Cramer-Rao, lower bound (H-CRLB) is derived for the analysis of the
proposed scheme. Numerical results show the effectiveness of the proposed
method, where it achieves the H-CRLB.

The rest of the paper is characterized as follows. Section II presents a brief
survey of the literature on underwater localization. In Section III, we
present the BMDS based system modeling for localization in an IoUT and study
its effectiveness for a hybrid optical-acoustic-magnetic induction approach.
In Section IV, performance evaluation of the proposed system is carried out,
followed by conclusions in Section V.

##  II Related Work and Challenges

###  II-A Literature background

The localization algorithm’s for wireless networks are divided into three
categories. The first category involves algorithms that are either centralized
or distributed [8]. In centralized algorithms, ranging measurements from all
the nodes are shared with a central node to find their respective location. On
the contrary, in distributive algorithms, each node is capable enough to
locate itself with the help of available anchors. The second category includes
range-based and range-free localization schemes. The range-based localization
methods usually work with the measurements priorly available among the nodes
to accurately locate unknown nodes [8]. In contrast, the range-free schemes
only consider the proximity information and can work effectively without
requiring the actual ranging measurements. Whilst the range-free schemes are
simple and easy in a design perspective, but provide less accuracy in position
estimation as compared to range-based techniques. Range-based location
awareness techniques usually necessitate different ranging measurements such
as angle of arrival (AoA), ToA, TDoA, and RSS [27]. The third category solely
rely on the availability of anchor nodes, i.e., anchor-based and anchor-free
schemes for localization. The anchor-based schemes require the availability of
at least three anchor nodes in a 2D-space for a node to be able enough to
localize itself. Oppositely, the anchor-free methods do not require anchor
nodes for self-localization. It only utilizes the estimated local distances
among the nodes to locate the unknown node effectively. A technique known as
the linear least square solution is applied to further refine the estimated
position of the node.

In the range-free localization schemes, the most critical and well-known
methods applied are usually based on the reduction of dimensionality. BMDS is
considered as one of the fundamental dimensionality reduction techniques that
are utilized extensively for localization [28, 29, 30, 31]. Some other
applications of BMDS include socioeconomics, political science, statistical
economics, and behavioral sciences. Besides, BMDS is also used for the
localization of nodes in IoT networks. According to [32], the connectivity
problem between two nodes is addressed by BMDS for the precise geometrical
representation of the connecting nodes. Initially, BMDS is used to calculate
the local maps of the sensor nodes and are then combined to obtain the global
mapping. Manifold learning is another localization technique used for position
estimation in wireless sensor networks [33]. Applying BMDS for the
localization of a hybrid IoUT system is not straightforward since multiple
range measurements are available, which need to be integrated first before
utilizing it for location awareness in the given underwater environment.

In this paper, we have utilized a centralized RSS-based ranging algorithm with
the presence of anchors. First of all, centralized network localization
schemes have better localization accuracy in harsh environments, such as
underwater or underground. In centralized ranging, the end-user does not
require to localize itself due to limited resources. Usually, its location is
computed periodically by either the surface buoy or sink node. Secondly, we
considered a range-based mechanism as it has better accuracy compared to
range-free schemes [34]. Moreover, the logic behind considering the RSS-based
approach is that the received power in communication systems is already
available, and based on the channel, it can be converted into estimated
distances. Since we are considering a hybrid model, time-based or angle-based
ranging can lead to extra complexity and cost of the system [15].

Recently, BMDS-based localization for underwater applications has gained much
importance due to its robustness and accuracy in position estimation. The
marine environment is quite harsh, turbid, and hazy due to which robust
optimization techniques need to be used to locate the position of IoUT devices
accurately. Many variations of BMDS-based localization schemes are used in the
literature, such as unconstrained optimization conjugate gradient method for
multi-hop underwater networks based on optical medium. To the best of authors
knowledge, none of the existing works tackle the problem of a fully hybrid
IoUT network localization. Therefore, this paper provides an BMDS-based
localization scheme for a hybrid Magnetic Induction-Acoustic-Optical (MIAO)
underwater communication system that works on a SOA approach. The proposed
scheme is novel in the context that it is used for the very first time in an
underwater environment to localize IoUT devices. Furthermore, Procrustes
analysis provided in [35] is applied to precisely estimate the final position
of the nodes in the given hybrid system. Later on, an H-CRLB is also derived
to define the lower threshold for position estimation of the proposed system.
Simulation results are carried out in Matlab, to show that the proposed model
is efficient and provides greater accuracy in position estimation using SOA
approach. The next section provides a detailed layout of the network model and
proposed technique for efficient localization in the IoUT.

Figure 1: Proposed model for Hybrid-Internet of Underwater Things (H-IoUT)

###  II-B Challenges in Hybrid-IoUT

Although the hybrid approach brings new opportunities, it also poses many
challenges that need to be considered when performing localization in the
underwater environment. Some of these challenges include variations in
seawater characteristics, misalignment for optical links, latency in acoustic
connections, and coil orientation mismatch in magnetic links [1]. The acoustic
and optical links undergo severe performance degradation when impacted by
seawater’s refractive and composition properties. The refractive index changes
occur due to variation in temperature, turbulence, and salinity, while the
composition of water depends upon changes in the geographic location.
Moreover, in acoustic links, increasing the transmission power can maintain a
certain SNR level; however, several other factors degrade the SNR in optical
links, such as attenuation-and-scattering, misalignment, divergence angle, and
field of view. Analogously, a major issue with acoustic links is higher
latency that can be minimized using multi-hop networking; however, it cannot
be fully eliminated and must be considered when designing a hybrid underwater
model.

On the other hand, MI systems require proper orientation of the transceivers’
coils in the harsh underwater environment. Although this can be achieved at
the deployment stage, however, the transceivers certainly drift with ocean
tides, and currents get rotated to undesired directions. Another critical
factor for underwater MI communication is the eddy current loss due to the
magnetic field. For instance, MI as a carrier in an aquatic environment can
only achieve a range up to 30m at an operating frequency of 500 Hz [5].

Therefore, we propose a hybrid MIAO model where each communication technology
supports the other, resulting in a better communication and localization
performance. Nevertheless, integration of these various technologies in the
underwater environment is quite a daunting task. Integration of multiple
communication systems requires a combination of electronics components, sub-
systems, chip-level assembly with specific system functionality. The proposed
model can foster interaction among numerous disciplines that will impact
electronics, photonics, electromagnetism, and underwater communication
systems. Consequently, there is a need to address the scientific issues and
challenges associated with the underpinnings of systems integration in hybrid
communication networks. The aim here is to achieve effective underwater
communication and localization utilizing these different available underwater
communication systems.

##  III Network Model and Ranging

This section first describes the network model, then introduces the novel
concept of MIAO ranging, and finally discuss the use of BMDS for IoUT
localization.

###  III-A Network Model

Consider an IoUT network that is composed of $M$ anchor nodes and $N$ sensor
nodes. These nodes are presumed to be lying and embedded on the sea bed, and
few of them are suspending sensor nodes. Fig. 1 depicts a generalized overview
of the proposed network where the underwater objects with unknown location are
communicating using various technologies. Note that, the system is hybrid and
can use any of the available optical, magnetic induction, and acoustic
technologies for communication among them and with the surface buoy. Also,
$M<N$, and the location of each anchor node is a well-known prior. According
to the proposed methodology, it is assumed that each underwater object is able
enough to communicate with each other object in the network through at least
one path (connected network). A surface buoy is needed to collect and share
the respective information shared by every node of the network.

The proposed algorithm comprises three major steps defined as follows;

  1. (a)

Each sensor node attempts to search for the overall neighbourhood by utilizing
any of the communication technology and estimate the range to the adjacent
nodes.

  2. (b)

Some sensor nodes are not lying in the communication range of each other and
can utilize the available connectivity information and estimate the missing
pairwise ranges.

  3. (c)

The information from each node is communicated to the surface buoy through SOA
approach. The initial ranging of every node is carried out on SOA approach
that utilizes the characteristic of any available underwater links such as
acoustic, optical, MI or hybrid. This approach enhances the estimation of
distance among available nodes. The surface buoy utilizes the information
provided and calculates the estimated distance matrix in a pairwise manner. It
further applies the dimensionality reduction methodology based on subjective
manifold interpretations to accurately locate each sensor node.

In the following, we describe the different types of ranging methods and show
how can they be integrated into the SOA concept.

###  III-B Underwater Magnetic-Induction Ranging

The exchange of information among various anchor and sensor nodes in a MI-
based IoUT truly rely on the time-varying magnetic field. The time-varying
magnetic field is basically generated by the modulated signal transmitted from
transmitter coil antenna [36, 37]. It is also responsible for the
intercommunication among the anchor and sensor nodes using magnetic induction
(MI) phenomena as a medium in IoUT. As, the fabrication of the time-varying
magnetic field is carried out by transmitter coil antenna through a sinusoidal
modulated signal and induces current in the receiver coil antenna of the
receiver. The induced current is responsible for demodulation of the signal to
retrieve the embedded information. The realization of an MI-based transceiver
is depicted in Fig. 2.

Figure 2: (a) MI link for underwater communication (b)Tri-directional coil
antenna.

Assume that the current flowing through the transmitter coil antenna is
represented by

$\displaystyle I=I_{0}\text{exp}^{-j\omega t}$ (1)

where $I_{0}$ is termed as the direct current, the term $\omega$ in the
superscript represents the angular frequency, where $t$ shows the
instantaneous time. The direct current $I_{0}$ is responsible for inducing the
current in the neighboring coil antenna by a phenomenon known as mutual
induction. It should be noted that mutual induction phenomena do not result
well if the transmitter and receiver coil antennas are not accurately coupled.
As, the underwater environment is harsh; therefore the assumption of a tri-
directional coil is used [38]. The tri-directional coil antenna can receive
strong induced signals if there comes little variation in the coupling
formation and thus making it omnidirectional.

The coils in the tri-directional antenna are mutually orthogonal, and hence,
do not interfere with the reception of each other. The signals received at any
of these mutually orthogonal coils are combined at the receiver to demodulate
the required information. This technique of using tri-directional antenna
essentially reduces the misalignment factor that affect the overall
communication [38]. According to [39], the MI-based relationship between the
power transmitted $P_{MI_{t_{m}}}$ and power received $P_{MI_{r_{n}}}$, for
some high range of frequencies and large number of turns $Z_{t_{m}}$ in coil
antenna of the transmitter is expressed by

$\displaystyle P_{MI_{r_{n}}}=\frac{\omega\mu
P_{MI_{t_{m}}}Z_{r_{n}}Z_{t_{m}}{d_{t_{m}}^{3}{d_{r_{n}}^{3}\sin^{2}{\vartheta_{mn}}}}}{16D_{0}r_{MI_{mn}}^{2}},$
(2)

in (2), the term $\mu$ provides the permeability of water, where $d_{t_{m}}$
is characterized as diameter of the transmitter coil antenna. Also, the term
$Z_{r_{n}}$ shows the number of turns in the receiver coil, and $d_{r_{n}}$ is
the respective diameter of the receiver coil antenna. $\vartheta_{mn}$ is the
angle between the axis of transmitter and receiver coil antennas, $D_{0}$ is
the impedance of unit length loop, and
$r_{MI_{mn}}={||}\alpha_{m}-\alpha_{n}{||}$ is the Euclidean distance between
the transmitting and receiving coil antennas. It should be noted that path
loss in (2) do not consider the phenomena of skin depth. According to [40,
41], the received power for MI channel is defined as

$\displaystyle
10^{\frac{P_{{MI}_{r_{n}}}}{10}}=10^{\frac{(P_{MI_{t_{n}}}-L_{MI})}{10}}+S,$
(3)

where $\ell_{MI}$ [dB] is the path loss and $S$ is the Gaussian distributed
random variable with zero mean and standard deviation of $\phi$. In case of
$N$ number of received magnetic field strength measurements, i.e.,
$P_{{MI}_{r_{1}}},\cdots,P_{{MI}_{r_{N}}}$, which are identical and
independent Gaussian variable with mean ${\Theta}_{MI}$ and variance
$\phi^{2}$. Then, the likelihood function $\ell(\cdot)$ be can written as

$\begin{aligned}
\ell(\Theta_{MI}|P_{{MI}_{r_{1}}},\cdots,P_{{MI}_{r_{N}}})\hskip 108.405pt\\\
=\prod_{n=1}^{N}\frac{\exp(-(P_{{MI}_{r_{n}}}-\hat{\Theta}_{MI})^{2}/2\phi^{2})}{\sqrt{2\pi\phi^{2}}}\end{aligned},$
(4)

where $\hat{\Theta}_{MI}=\frac{1}{N}\sum_{n=1}^{N}P_{MI_{r_{n}}}$. By using
the unbiased estimator $\hat{\Theta}_{MI}$, $r_{MI_{mn}}$ is estimated as [41]

$\displaystyle\tilde{r}_{MI_{mn}}=f(P_{MI_{r_{n}}})$ (5)
$\displaystyle=\operatorname*{arg\,min}\Bigg{\\{}r_{MI_{mn}}\Bigg{|}\bigg{(}10^{\frac{(P_{MI_{t_{m}}}-\hat{\Theta}_{MI})}{10}}-1\bigg{)}\Bigg{\\}}.$

Solving (5) yields

$\begin{aligned}
\tilde{r}_{MI_{mn}}=\frac{16D_{0_{t}}D_{0_{r}}r_{MI_{mn}}^{3}}{{\omega^{2}{\mu^{2}Z_{t_{m}}Z_{r_{n}}{d_{t_{m}}^{3}{d_{r_{n}}^{3}}G^{2}(\sigma,\omega,r_{MI_{mn}})}}}}\end{aligned}.$
(6)

the term $G^{2}(\sigma,\omega,r_{MI_{mn}})$ represents the loss occurred due
to skin depth, where $\sigma$ gives the electrical conductivity of water. It
is observed that the values of $\sigma$ changes with the types of water. For
instance, the value of $\sigma$ = 0.01 S/m for clean water, but it goes to a
higher value of $\sigma$ = 4 S/m for turbid sea water. These performance
degrading factors of the MI technique in different types of underwater
environment needs the coil configuration to be selected carefully in order to
avoid the losses.

###  III-C Underwater Acoustic Ranging

Acoustic ranging works well even for a larger distance in an underwater
environment as compare to MI. The acoustic channel in underwater medium
experiences two types of losses during propagation: delay spreading and path
loss attenuation [42]. The delay spread is caused by the combined effect of
cylindrical and spherical losses, while the path loss attenuation occurs due
to multiple effects such as absorption, scattering, leakage from ducts and
diffraction [43]. Usually, the path loss function in an underwater environment
between any two nodes $m$ and $n$ can be computed using the following equation

$\displaystyle\upsilon_{t}=\upsilon_{c}+\upsilon_{s}+10^{-3}\phi r_{A_{mn}},$
(7)

where $\upsilon_{c}$ is the cylindrical loss, $\upsilon_{s}$ is the spherical
loss, $\phi$ is respective coefficient of absorption, and $r_{A_{mn}}$ is the
corresponding euclidean distance between the two nodes for acoustic
communication. According to Thorp model for absorption given in [44], the
factor $\phi$ only depends on the frequency $f$ of the transmitted signal
given by

$\begin{aligned}
\phi=\frac{0.11f^{2}}{1+f^{2}}+\frac{44f^{2}}{4100+f^{2}}\end{aligned}.$ (8)

The spherical spread loss works effectively in underwater environment and;
therefore, ignoring the loss due to cylindrical spreading, we achieve

$\begin{aligned}
\upsilon_{t}=20\log(r_{A_{mn}})+10^{-3}\left[\frac{0.11f^{2}}{1+f^{2}}+\frac{44f^{2}}{4100+f^{2}}\right]r_{A_{mn}}\end{aligned}.$
(9)

using (9), the distance is estimated from $\tilde{r}_{A_{mn}}$ by utilizing
only the real term of the Lambert function $W_{0}$ as follows [45]

$\displaystyle\tilde{r}_{A_{mn}}=\left[\frac{(2\times 10^{4})\hskip
1.084ptW_{0}(1.15\text{exp}^{-4}\hskip 1.084pt\phi\hskip
1.084pt\text{exp}^{0.11\upsilon_{t}})}{2.3\hskip 1.084pt\phi}\right]$ (10)

###  III-D Underwater Optical Ranging

Optical communication in underwater mostly suffers from a number of parameters
such as scattering, absorption, angular attenuation, and widening [46]. It has
been noticed that angular attenuation and widening of the optical signals
during underwater communication is purely dependent on the wavelength of the
transmitting signal. Conferring to [47], the loss coefficient $l(\lambda)$ is
based on the coefficient for scattering $s(\lambda)$ and absorption
$a(\lambda)$, which is given by

$\begin{aligned} l(\lambda)=s(\lambda)+a(\lambda)\end{aligned}.$ (11)

also, the loss occurrence $L_{mn}$ during underwater propagation depends upon
the euclidean distance $r_{O_{mn}}$ and loss coefficient $l(\lambda)$. Their
mutual relationship is expressed by

$\begin{aligned} L_{mn}=\text{exp}^{-l(\lambda)r_{O_{mn}}}\end{aligned}.$ (12)

Here, we assume line-of-sight (LOS) underwater optical communication, where
the node $m$ directly communicate with node $n$ using the optical light.
According to [48], the power received $P_{O_{r_{n}}}$ at node $n$ as a result
of LOS communication with node $m$ is given by

$\begin{aligned}
P_{O_{r_{n}}}=P_{O_{t_{m}}}\eta_{m}\eta_{n}L_{mn}\left[\frac{A_{n}\cos{\theta}}{2\pi
r_{O_{mn}}^{2}(1-\cos\theta_{0})}\right]\end{aligned},$ (13)

where $P_{O_{t_{m}}}$ represents the total power transmitted by node $m$,
whereas $\eta_{m}$ and $\eta_{n}$ are the optical efficiencies of node $m$ and
$n$, respectively. The aperture area of the $n$ is given by $A_{n}$. Also,
there exists various angles such as the angle of aperture between the
trajectories of node $m$ and node $n$, that is represented by $\theta$,
moreover the angle of divergence of the transmitted signal is given by
$\theta_{0}$. In literature, many modulation techniques are used for optical
wireless communication, but intensity modulation with direct detection (IM-DD)
is most commonly used method. The expression for bit-error-rate (BER) for
performance evaluation of IM-DD with ON/OFF shift-keying model is calculated
using Poisson model that is basically given by the number of photons reached
at the photon counter. In order to compute the number of photons arrived at
the node $n$ in the time duration $T$, can be expressed as follows

$\begin{aligned}
\rho=\frac{P_{O_{r_{n}}}\eta_{n}\lambda}{T{D_{r}}h\hat{c}}\end{aligned},$ (14)

where $D_{r}$ is the data transmission rate, $h$ is the Planck’s constant, and
$\hat{c}$ is the respective speed of light in water. The BER for photons
arriving at node $n$ can be computed as

$\begin{aligned}
g_{n}=\frac{1}{2}\text{erfc}\left[\sqrt{\frac{T}{2}}(\sqrt{d_{1}}-\sqrt{d_{0}})\right]\end{aligned},$
(15)

where $d_{1}=d_{r}+d_{n}+d_{g}$ and $d_{0}=d_{r}+d_{g}$ symbolize the number
of photons essential for binary transmission 0 and 1, respectively.
$\text{erfc}(.)$ is the complementary error function for the photons arriving
at node $n$. Also, $d_{r}$ is the dark count noise, while $d_{g}$ refer to the
noise added as result of contextual enlightenment. According to [49], by
substituting the values of $d_{1}$ and $d_{0}$ in (15) and solving for $d_{n}$
we get

$\displaystyle
d_{n}=\left(\sqrt{d_{r}+d_{g}}+\sqrt{\frac{2}{T}}\text{erfc}^{-1}(2g_{n})\right)^{2}-d_{r}-d_{g}$
(16)

Now, putting (14), and (15) in (16), and solving it yields the optical
distance $\tilde{r}_{O_{mn}}$ between node $m$ and node $n$ as

$\begin{aligned}
\tilde{r}_{O_{mn}}=\frac{2\cos{\theta}}{l(\lambda)}W_{0}\left[\frac{l(\lambda)}{2\cos{\theta}\sqrt{\frac{2\pi
Th\hat{c}D_{r}d_{n}(1-\cos{\theta_{0}})}{\eta_{n}\lambda
P_{O_{t_{m}}}\eta_{m}\eta_{n}A_{n}\cos{\theta}}}}\right]\end{aligned},$ (17)

where $W_{0}(\cdot)$ is known as the real part of Lambert $W_{0}$ function.

###  III-E Hybrid MIAO Ranging Model

The noisy range measurements $\tilde{r}_{MI_{mn}}$, $\tilde{r}_{A_{mn}}$, and
$\tilde{r}_{O_{mn}}$, are calculated using (6), (10), and (17), respectively.
In order to define the matrix for all the noisy range measurements, consider
that

$\tilde{r}_{mn}\approx\begin{cases}\tilde{r}_{MI_{mn}}\;\;\text{for MI
link},\\\ \tilde{r}_{A_{mn}}\;\;\;\;\text{for acoustic link},\\\
\tilde{r}_{O_{mn}}\;\;\;\;\text{for optical link}.\end{cases}$ (18)

Now combining them all together we get

$\begin{aligned}
\boldsymbol{\aleph}=\left\\{\tilde{r}_{mn}\right\\}_{m,n=1,m\neq
n}^{K}\end{aligned},$ (19)

where $K=M+N$ represents the total number of anchor and sensor nodes. In order
to formulate the define problem for total number of nodes $K$, all dimensional
spaces $\tilde{r}_{mn}$ are well approximated as ${r}_{mn}$. A cost function
can be defined as follows which minimizes the error between the actual range
and measured range

$\displaystyle\text{min}_{L}\sum_{m<n}\gamma_{mn}\left({\tilde{r}_{mn}}-r_{mn}(\textbf{{L}})\right)^{2},$
(20)

where
$\textbf{{L}}=\\{\textbf{{l}}_{1},\textbf{{l}}_{2},\cdots,\textbf{{l}}_{K}\\}$
are the respective 3D coordinates of all $K$ number of nodes. Also,
$\gamma_{mn}$ is the weight between any two nodes $m$ and $n$, and is defined
based on the ranging error variance, i.e.,
$\gamma_{mn}=\frac{1}{\sigma_{mn}^{2}}$, where the noisy range measurements
are down-weighted by the large noise variance and vice-versa. Note that If
there is no range measurement available between $m$-th and $n$-th node, then
$\gamma_{mn}=0$. Also, we assume that ${\textstyle\sum}\gamma_{mn}=1$,
$\gamma_{mn}\geq 0$, $\gamma_{mm}=0$, and $\gamma_{mn}=\gamma_{nm}$, i.e.,
symmetric weights. In literature, many techniques have been presented to
tackle the optimization problem, but none of those techniques uses more than
one ranging measurement. Here, we propose a hybrid MIAO model that utilizes
multiple input ranging measurements. For the hybrid MIAO ranging, the
objective function is characterized as follows

$\begin{aligned}
\text{min}_{\eth^{(w)},L}\sum_{w=1}^{D}\eth^{(w)^{\tau}}\sum_{m<n}\gamma_{mn}\left({\tilde{r}_{mn}}-r_{mn}(L)\right)^{2}\end{aligned},$
(21)

where $\eth^{(w)}$ shows the importance of $w$-th iteration such that
$\sum_{w=1}^{D}\eth^{(w)}=1$. Also, the term $\tau$ is the controlling factor
and $D$ represent the total number of dimensions. The controlling factor for
weighting is assumed to be $(\tau>1)$, in order to define the overall
distribution of multiple observations. Selecting only one view is not optimum
in any case while ignoring the rest. Therefore, the proposed model assumes the
combination of weights for each iteration view.

##  IV Proposed Localization Technique

Utilizing the BMDS technique and Procrustes analysis, the proposed method is
characterized as follows:

  1. (a)

The MIAO based single hop ranging is used to find the shortest path distances
among all pair of anchor and sensor nodes in the given network. Once all the
pairwise distances are obtained, the completion of distance information matrix
$\textbf{R}=\\{\rho_{mn}^{2}\\}_{m,n=1}^{K}$ is achieved, i.e.,

$\textbf{R}=\begin{bmatrix}0&\ldots&\rho_{1K}^{2}\\\ \vdots&\ddots&\vdots\\\
\rho_{K1}^{2}&\ldots&0\end{bmatrix}.$ (22)

Matrix R is a square symmetric matrix.

  2. (b)

BMDS technique is applied to matrix R for the estimation of relative
coordinates. According to [50], Kruskal outlined a stress function that
basically minimizes the loss function to estimate the relative coordinates,
i.e.,

$\zeta(\rho_{mn}|\textbf{Y})=\frac{\sqrt{\sum_{m\neq
n=1,\cdots,K}(\rho_{mn}-r_{mn})^{2}}}{{\sum_{m\neq
n=1,\cdots,K}(\rho_{mn})^{2}}}$ (23)

Minimizing the above loss functions yields the estimated positions of all the
nodes that is expressed as $\hat{}\textbf{Y}=\\{{\alpha}_{m}\\}_{m=1}^{K}$.
The minimization is achieved by first double centering matrix R, i.e.,

$\mathbf{\Gamma}=-{\frac{1}{2}}(\textbf{ARA}),$ (24)

where
$\textbf{A}=\textbf{I}_{K}-(\frac{1}{K})\textbf{1}_{K}\textbf{1}_{K}^{T}$ is
termed as operator for centering, where as $\textbf{I}_{K}$ is a $K\times K$
identity matrix. Also, $\textbf{1}_{K}$ is considered as the vector of ones
with size of $k$. Eigen value decomposition of R yields

$\text{EV}(\mathbf{\Gamma})=\textbf{u}\textbf{v}\textbf{u}^{T}.$ (25)

The relative coordinates of all available nodes are measured utilizing the two
largest eigenvalues provided by v, and the corresponding eigenvectors u as
follows

$\hat{\textbf{Y}}=\textbf{u}\sqrt{\textbf{v}},$ (26)

which can also be written as

$\hat{\textbf{Y}}=\\{\hat{\alpha}_{m}\\}_{m=1}^{K}.$ (27)

The terms $\hat{\alpha}_{m}=\\{\hat{x}_{m},\hat{y}_{m},\hat{z}_{m}\\}$ depicts
the relative coordinates of node $m$ in the given network. Note that
$\hat{\textbf{Y}}$ consists of relative coordinates of both the anchor nodes
and sensor nodes. This is because the difference between the actual and
estimated location of anchors is used to transform the map generated via BMDS
in the next stage. This way, we can find out the values of optimal
translation, rotation, and scaling factors that are used to find out the
global coordinates of other sensor nodes. The translation, rotation, and
scaling factors can be estimated using various linear transformation
techniques, such as Procrustes analysis and principal component analysis.

  3. (c)

Once BMDS calculates the initial estimated coordinates of the nodes. Then
global transformation method is utilized to transform these initial estimated
coordinates to their absolute equivalent coordinates. This method essentially
finds out different parameters such as the scaling, rotation and translation.
These parameters should be able enough to best maps the actual underlying
coordinates. Assume that there exist $M$ number of anchor nodes in a 3D space,
with actual coordinates equal to $\alpha_{j}=\\{x_{j},y_{j},z_{j}\\}$, and
lies in range of $1\leq j\leq M$. It should be noted that the relative
coordinates $\hat{\alpha}_{j}=\\{\hat{x}_{j},\hat{y}_{j},\hat{z}_{j}\\}$ must
match the actual coordinates $\alpha_{j}=\\{x_{j},y_{j},z_{j}\\}$ for all the
$M$ anchor nodes. Also, the relationship between the actual and relative
coordinates is computed by

$\Upsilon=\sum_{j=1}^{M}{(\hat{\alpha}_{j}-\alpha}_{j})^{T}(\hat{\alpha}_{j}-\alpha_{j}).$
(28)

This relationship can also be expressed in terms of an objective function
$q(\xi,\nu,\kappa)$, where $\xi$ is the scaling factor, $\nu$ is the rotation
factor, and $\kappa$ is the respective translational factor. According to
linear transformation, the objective function can be written as

$q(\xi,\nu,\kappa)=\sum_{j=1}^{M}{(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}}-\nu)^{T}\times(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}-\nu),$
(29)

The objective function in (29) can be minimizes by determining the optimum
values of $\xi$, $\nu$, and $\kappa$, i.e.,

$\\{\bar{\xi},\bar{\nu},\bar{\kappa}\\}=\arg_{\xi,\nu,\kappa}\text{min}\hskip
1.8063ptq(\xi,\nu,\kappa).$ (30)

For anchor nodes, assuming that $\textbf{b}_{0}$ and $\textbf{c}_{0}$ are the
centroids for the actual and estimated locations, respectively. These
centroids are represented as

$\textbf{b}_{0}=\frac{1}{M}\sum_{j=1}^{M}\alpha_{j},$ (31)

and

$\textbf{c}_{0}=\frac{1}{M}\sum_{j=1}^{M}\hat{\alpha}_{j}.$ (32)

In order to achieve optimum translation, the objective function is expressed
as

$\displaystyle q(\xi,\nu,\kappa)=$ (33)
$\displaystyle\sum_{j=1}^{M}{\bigg{(}(\hat{\alpha}_{j}-\textbf{c}_{0})-\xi\kappa^{T}(\alpha_{j}-\textbf{b}_{0})}+\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}-\nu\bigg{)}^{T}$
$\displaystyle\times\bigg{(}(\hat{\alpha}_{j}-\textbf{c}_{0})-\xi\kappa^{T}(\alpha_{j}-\textbf{b}_{0})+\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}-\nu\bigg{)}$

After seprating the term $\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}-\nu$ from
equation (33), we get

$\displaystyle
q(\xi,\nu,\kappa)=\sum_{j=1}^{M}\Bigg{\\{}{\bigg{(}(\hat{\alpha}_{j}-\textbf{c}_{0})-\xi\kappa^{T}(\alpha_{j}-\textbf{b}_{0})\bigg{)}^{T}}$
(34)
$\displaystyle\times\bigg{(}(\hat{\alpha}_{j}-\textbf{c}_{0})-\xi\kappa^{T}(\alpha_{j}-\textbf{b}_{0})\bigg{)}$
$\displaystyle+M(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j}-\nu)^{T}(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha{j}-\nu)\Bigg{\\}}.$

Now using (34), the optimum translation factor $\overline{\nu}$ that minimizes
the above objective function, can be expressed as

$\overline{\nu}=(\hat{\alpha}_{j}-\overline{\xi}\overline{\kappa}^{T}\alpha_{j}).$
(35)

In terms of the centroids $\textbf{c}_{0}$ and $\textbf{b}_{0}$, (35) can be
written as

$\overline{\nu}=\textbf{c}_{0}-\overline{\xi}\overline{\kappa}^{T}\textbf{b}_{0}.$
(36)

By considering the condition of $\textbf{b}_{0}=\textbf{c}_{0}=0$ and
substituting (36) into (34), the objective function can be simplified as
follows

$\displaystyle
q(\xi,\nu,\kappa)=\sum_{j=1}^{M}{(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j})^{T}(\hat{\alpha}_{j}-\xi\kappa^{T}\alpha_{j})}.$
(37)

The above objective function obtained is convex and differentiating it with
respect to $\xi$, the optimum value $\overline{\xi}$ that minimizes the
overall function $q(\xi,\nu,\kappa)$ and is calculated as

$\overline{\xi}=\frac{\text{Tr}(\alpha_{j}\overline{\kappa}\hat{\alpha}_{j}^{T})}{\text{Tr}(\alpha_{j}\hat{\alpha}_{j}^{T})},$
(38)

where $\text{Tr}({\cdot})$ is known as the trace operator. The optimum
rotation matrix $\overline{\kappa}$ is expressed in terms Eigen-decomposition
of the factors $\alpha_{j}\hat{\alpha}_{j}$ as

$\overline{\kappa}=u{v}^{\prime}$ (39)

whereas $u$ and ${v}^{\prime}$ are the respective eigenvectors and eigenvalues
of $\alpha_{j}\hat{\alpha}_{j}$. Likewise, the term $\overline{\kappa}$ can be
inscribed in terms of

$\overline{\kappa}=\frac{\sqrt{(\alpha_{j}^{T}\hat{\alpha}_{j}\hat{\alpha}_{j}^{T}\alpha_{j}})}{(\hat{\alpha}_{j}^{T}\alpha_{j})}.$
(40)

Finally, with the use of optimum parameters $\overline{\xi}$,
$\overline{\nu}$, $\overline{\kappa}$, the actual positions of all nodes in
the given network can easily to be computed by

$\tilde{\textbf{Y}}=\overline{\xi}\overline{\kappa}^{T}({\hat{\textbf{Y}})}+\overline{\nu}.$
(41)

  4. (d)

Energy Consumption Vs. Localization Accuracy: The IoUT network comprises
battery-operated sensor nodes with a limited amount of onboard energy
operating in a harsh environment. Therefore, these IoUT networks require the
designing of energy-efficient protocols to improve the lifetime of the
network. In the case of our proposed MIAO model, we can express the total
energy consumed by all $M+N$ nodes as

$\displaystyle\mathcal{E}_{T}=\sum_{m=1}^{M+N}E_{F_{m}}+(M+N)\sum_{m=1}^{M+N}E_{R_{m}},$
(42)

where $E_{F}=\sum_{m=1}^{M+N}E_{F_{m}}$ is the $m$-th node system’s electronic
circuitry for fundamental operation, and
$E_{R}=(M+N)\sum_{m=1}^{M+N}E_{R_{m}}$ represents the energy consumed during
the transmission. The $E_{R_{m}}$ for the $m$-th node can be written as

$\displaystyle E_{R_{m}}=E_{B}\left(\frac{4\pi R_{m}}{\lambda}\right)^{2},$
(43)

where $E_{B}$ is the energy required for a single bit transmission and $R_{m}$
is the achievable transmission range of $m$-th node. It is clear from (43), as
energy consumption is proportional to the square of the transmission range for
each node in the given hybrid network. Both communication energy consumption
and localization accuracy rely on the transmission range $R_{m}$. Therefore,
we introduce the following energy error product as a benchmark to confer the
trade-off between energy consumption and localization accuracy

$\displaystyle C(R)=E_{R}\times\text{(RMSE)},$ (44)

where RMSE represents the average root-mean-square-error of all nodes in the
given network. The RMSE as a function of estimated and actual nodes locations
can be written as

$\displaystyle\text{RMSE}=$ (45)
$\displaystyle\sum_{m=1}^{M+N}\frac{\sqrt{(\hat{x}_{m}-x_{m})^{2}+(\hat{y}_{m}-y_{m})^{2}+(\hat{z}_{m}-z_{m})^{2}}}{M+N}.$

Now substituting (43) and (45) in (44) results in

$\displaystyle
C(R)=E_{B}\left(\frac{4\pi}{\lambda}\right)^{2}\sum_{m=1}^{M+N}R_{m}^{2}$ (46)
$\displaystyle\times\sum_{m=1}^{M+N}\frac{\sqrt{(\hat{x}_{m}-x_{m})^{2}+(\hat{y}_{m}-y_{m})^{2}+(\hat{z}_{m}-z_{m})^{2}}}{M+N}.$

Simplifying (46) yields

$\displaystyle C(R)=E_{B}\left(\frac{4\pi}{\lambda\sqrt{M+N}}\right)^{2}$ (47)
$\displaystyle\times\sum_{m=1}^{M+N}R_{m}^{2}\sqrt{(\hat{x}_{m}-x_{m})^{2}+(\hat{y}_{m}-y_{m})^{2}+(\hat{z}_{m}-z_{m})^{2}}.$

According to (47), the energy-error product can be optimized by finding the
minimum of $C(R)$ function.

  5. (e)

Computational Complexity: The fundamental step in finding a sensor node’s
location in network localization schemes is measuring the pairwise distances.
Afterward, an optimization method needs to be followed to minimize the
inconsistency between the estimated pairwise distances and actual Euclidean
distances. Usually, single-hop distances among the neighbors are measured
using ranging methods [51, 52]. The complexity to estimate the pairwise
distances from these single-hop distances is $C(K^{3})$, where $K=M+N$ (total
number of nodes). Moreover, the computational complexity for global
transformation, i.e., from local coordinates to global using anchor nodes is
$C(M^{2})+C(K)$. Therefore, the total time complexity can be expressed as

$\displaystyle\text{Complexity}=C(K^{3})+C(M^{2})+C(K),$ (48)

in (48), the term $C(K^{3}$) represents the total complexity which is
dominated by $C(K^{3})$.

##  V Performance Evaluation of the Proposed Model

Gaussian noise usually effect the performance of the ranging measurements
$\rho_{mn}$. As, the noise is probabilistic in nature, hence affecting the
overall ranging measurements. Therefore, the probability density function
(PDF) of the ranging measurements $\rho_{mn}$ with specified locations of the
anchor node $m$ and sensor node $n$ can be expressed by
$s(\rho_{mn}|\alpha_{m},\alpha_{n})$ in terms of

$s(\rho_{mn}|\alpha_{m},\alpha_{n})=\frac{1}{\psi_{d}\sqrt{2\pi}}\exp^{\left({-\frac{(\rho_{mn}-r_{mn})^{2}}{2\psi_{d}^{2}}}\right)}.$
(49)

It should be noted that variance of the calculated measurements for range
estimation are correlated to the distance by $\psi_{d}^{2}=\varepsilon
r_{mn}^{\delta_{mn-1}}$. The consequent ratio of log likelihood is depicted as
$E_{mn}=\log(s(\rho_{mn}|\alpha_{m},\alpha_{n}))$. The same when converted to
decibel (dB) scale can be written as follows

$\displaystyle
E_{mn}\text{[dB]}=-\text{log}\sqrt{2\pi\varepsilon}-\frac{\delta_{mn}}{4}\text{log}({||}\alpha_{m}-\alpha_{n}{||}^{2})$
(50)
$\displaystyle-\frac{1}{2\varepsilon}\frac{(\rho_{mn}-{||}\alpha_{m}-\alpha_{n}{||})^{2}}{{{(||}\alpha_{m}-\alpha_{n}{||}^{2})}^{\frac{\delta_{mn}}{2}}}$

It is further anticipated that $\rho_{mn}$ is degraded by the environmental
noise, independent in nature. So, considering the effect of noise with joint
ratio of log-likelihood to estimate the range of almost each set of pairwise
measurements.

$\begin{aligned}
\mathbf{\Psi}_{mn}=\sum_{m=1}^{M}\sum_{n=m+1}^{M+N}\log(s(\rho_{mn}|\alpha_{m},\alpha_{n}))\end{aligned},$
(51)

where $M+N$ shows the total number of anchor and sensor nodes. Further solving
(51) yields

$\displaystyle\mathbf{\Psi}_{mn}=\sum_{m=1}^{M}\sum_{n=m+1}^{M+N}\\{-\text{log}\sqrt{2\pi\varepsilon}-\frac{\delta_{mn}}{4}\text{log}{({||}\alpha_{m}-\alpha_{n}{||}^{2})}$
(52)
$\displaystyle-\frac{1}{2\varepsilon}\frac{(\rho_{mn}-{||}\alpha_{m}-\alpha_{n}{||})^{2}}{{{(||}\alpha_{m}-\alpha_{n}{||}^{2})}^{\frac{\psi_{mn}}{2}}}\\}$

Based on this log-likelihood ratio, the Hybrid Cramer-Rao lower bound (H-CRLB)
is derived. The H-CRLB is basically a lower threshold on the estimator
variance that is unbiased [53], and thus, providing a benchmark to accurately
evaluate the designed algorithms in terms of performance. The H-CRLB technique
is based on Fisher Information Matrix (FIM) [54] represented by
$\mathbf{\Phi}$ and expressed as

$\begin{aligned}
\mathbf{\Phi}=-\mathbb{C}_{\alpha_{m},\alpha_{n}}(\Delta_{\alpha_{m},\alpha_{n}}(\Delta_{\alpha_{m},\alpha_{n}}(\mathbf{\Psi}_{mn})))\end{aligned},$
(53)

where $\mathbb{C}_{\alpha_{m},\alpha_{n}}$ is termed as the expected value for
second order derivative of the ratio of log-likelihood $\mathbf{\Psi}_{mn}$.
The FIM can further be inscribed in terms of sub-matrices as follows

$\mathbf{\Phi}=\begin{bmatrix}\mathbf{\Phi}_{xx}&\mathbf{\Phi}_{xy}&\mathbf{\Phi}_{xz}\\\
\mathbf{\Phi}_{xy}^{T}&\mathbf{\Phi}_{yy}&\mathbf{\Phi}_{yz}\\\
\mathbf{\Phi}_{xz}^{T}&\mathbf{\Phi}_{yz}^{T}&\mathbf{\Phi}_{zz}\\\
\end{bmatrix}$ (54)

The subscripts $xx$, $yy$ and $zz$ denotes the diagonal sub-matrices for the
considered FIM. On the other hand, the $xy$, $xz$, $yz$, ${xy}^{T}$,
${xz}^{T}$ and ${yz}^{T}$ denotes the sub-matrices that are non-diagonal.
Furthermore, the diagonal elements for each sub-matrix ranges from
$m=1,2,3,\cdots,K$ are given as

$\begin{aligned} \mathbf{\Phi}_{xx(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(55) $\begin{aligned} \mathbf{\Phi}_{xy(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}(y_{m}-y_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(56) $\begin{aligned} \mathbf{\Phi}_{yy(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(y_{m}-y_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(57) $\begin{aligned} \mathbf{\Phi}_{yz(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(y_{m}-y_{n})^{2}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(58) $\begin{aligned} \mathbf{\Phi}_{xz(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(59)

and

$\begin{aligned} \mathbf{\Phi}_{zz(m,m)}=\sum_{n\in
H(m)}\frac{1}{\psi_{d}^{2}}\frac{\beta_{mn}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(60)

respectively. Similarly, the non-diagonal sub-matrices, where $m\neq n$ for
$m,n=1,2,\cdots,K$ are given as

$\begin{aligned}
\mathbf{\Phi}_{xx(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(61) $\begin{aligned}
\mathbf{\Phi}_{xy(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}(y_{m}-y_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(62) $\begin{aligned}
\mathbf{\Phi}_{yy(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(y_{m}-y_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(63) $\begin{aligned}
\mathbf{\Phi}_{yz(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(y_{m}-y_{n})^{2}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(64) $\begin{aligned}
\mathbf{\Phi}_{xz(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(x_{m}-x_{n})^{2}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(65)

and

$\begin{aligned}
\mathbf{\Phi}_{zz(m,n)}=\frac{-1}{\psi_{d}^{2}}\frac{\beta_{mn}(z_{m}-z_{n})^{2}}{{||}\alpha_{m}-\alpha_{n}{||}^{2}}\end{aligned},$
(66)

The term $\beta_{mn}$ in the above expressions is known as the scaling factor
that is dependent on the distance estimated among the nodes and can be written
as

$\begin{aligned}
\beta_{mn}=1+\frac{\delta_{mn}^{2}\varepsilon}{2}{r_{mn}^{\delta_{mn}-2}}\end{aligned},$
(67)

On the basis of $\mathbf{\Phi}$, the H-CRLB for position estimation of the
sensor nodes can be specifically expressed as

$\begin{aligned}
\text{H-CRLB}=\text{Tr}\\{\mathbf{\Phi}^{-1}\\}\end{aligned},$ (68)

The term $\mathbf{\Phi}^{-1}$ is the inverse of FIM. The relationship between
the Root-Mean-Square-Error (RMSE) (given by (45))and derived H-CRLB is given
as

$\begin{aligned} \text{RMSE}\geq\text{H-CRLB}\end{aligned}.$ (69)

##  VI Simulation Results and Discussion

MATLAB is used as a simulation tool for performance evaluation of the proposed
MIAO ranging and localization technique for a given IoUT network. The
parameters used for the simulations are summarized in Table I.

TABLE I: Parameters used for simulations. Parameters |  Values
---|---
Simulation Area |  100m $\times$ 100m $\times$ 100m
Permeability $\mu$ |  4 $\pi\times$ 10-7 H/m
Ocean water conductivity $\sigma$ |  4 S/m
Clean water conductivity $\sigma$ |  0.01 S/m
Noise Power $P_{n}$ |  $2\times 10^{-6}$ W
Noise variance |  0-1 m
Number of anchor nodes $M$ |  4 to 20
Number of sensor nodes $N$ |  96 to 150
Number of relay nodes |  4

###  VI-A MIAO-based position estimation

We mainly consider the RMSE as a performance metric to test various parameters
of the proposed model. Utilizing (45), where
{$\hat{x}_{m},\hat{y}_{m},\hat{z}_{m}$} and {$x_{m},y_{m},z_{m}$} are the
respective estimated and actual coordinates of the anchor node $m$. We
consider a 3D IoUT network setup with sensor nodes, anchors nodes, and relay
nodes. Based on recent literature [55, 56, 57], it is efficient to consider
relay nodes in three-dimensional underwater networks. Therefore, in our
simulation setup, we considered four relay nodes. The relay nodes can be AUVs
or suspended sensors to collect the data from other sensor nodes efficiently.
For performance analysis of the proposed method, we have considered two
scenarios, as shown in Fig. 3 and 4. The first scenario consists of sparsely
distributed nodes in a 100m $\times$100m $\times$100m cubic area with four
anchor nodes. In contrast, the second scenario comprises densely populated
nodes in the same observation area. Both figures depict that increasing the
number of nodes improves the location awareness accuracy mainly due to the low
shortest path estimation error in dense networks. It should be noted that
simulations are restricted to 100m $\times$ 100m $\times$ 100m cubic area.
This is mainly due to the centralized nature of the algorithm, which requires
a connected network. If we increase the network area with the same number of
nodes, it will result in a disconnected graph, and Bayesian multidimensional
scaling (BMDS) fails to operate on disconnected graphs.

Figure 3: MIAO-based position estimation of sparsely deployed nodes in a cubic
area of 100m $\times$ 100m $\times$100m. Figure 4: MIAO-based position
estimation of densely deployed nodes in a cubic area of 100m $\times$ 100m
$\times$100m.

###  VI-B RMSE Vs. Ranging noise variance

We carried out the comparative analysis of the proposed method in terms of
various parameters such as noise variance, network density, and number of
anchors. Also, the results are compared to some well-known network
localization techniques such as compressive sensing and weighted centroid
localization (WCL) [58]. Intuitively, it is observed that the RMSE increases
with an increase in the noise variance, as shown in Fig. 5. Indeed, the
estimation of missing distances and noise variance affects the overall
accuracy of location awareness in the hybrid IoUT network. We have examined
the results for proposed MIAO model in the presence of Gaussian noise
distribution with zero mean and variance. For simulation results, values of
the noise variance are set to approximately 0-1m. Further, it has been noted
that the proposed model is robust to error variance as compared to WCL and
compressive sensing. The reason behind is better distance approximation of the
pair-wise missing distances.

Figure 5: RMSE vs. Ranging noise variance.

The ranging noise variance is proportionate to the accurate Euclidean distance
$r_{mn}$ between the anchor node $m$ and sensor node $n$. Moreover, the
proposed method outperforms the literature because the WCL is center-biased in
nature and is not robust to noise. Similarly, the compressive sensing
technique requires signal reconstruction from raw data and gets affected by
the noisy underwater environment. Hence, the proposed method outperforms both
WCL and compressive sensing techniques and is approximately equal to the
H-CRLB, as shown in Fig. 5. The improvement in the proposed method is because
of the availability of the accurately estimated missing distances among the
various nodes.

###  VI-C RMSE Vs. Number of nodes

To show the impact of the number of nodes on the localization accuracy, we
consider the same setup of 100 nodes distributed nodes in a 100m $\times$100m
$\times$100m cubic area with four anchor nodes. Fig. 6 shows that increasing
the number of nodes for location awareness in hybrid IoUT network results in
an improved RMSE. This is mainly due to the improved connectivity of the
network. Increasing the number of nodes provides a better shortest path
estimation of the range measurements in dense networks than sparsely populated
networks.

Figure 6: RMSE vs. Increasing number of nodes.

For performance evaluation of the proposed hybrid technique in accordance with
the number of anchor nodes, we have considered 96 sensor nodes and 4 anchor
nodes in the same 100m $\times$ 100m $\times$ 100m cubic area. It can be
observed from Fig. 7, that if the anchor nodes are increased up to 15, the
hybrid IoUT network become saturated. No further increment in number of anchor
nodes enhances the network localization capability, and hence, no improvement
in RMSE. Therefore, it is important to model these parameters in a much more
accurate way for the practical deployment of Hybrid-IoUT network.

Figure 7: RMSE vs. Increasing number of anchors.

###  VI-D RMSE Vs. Transmission range:

We performed simulations to look for the relationship between RMSE and
transmission range for the scenario of 100 nodes (96 sensor nodes and 4 relay
nodes) deployed in a 100m $\times$100m $\times$100m cubic area. The anchor
nodes are equal to four, and the noise variance is 0.1m. Fig. 8 shows that the
RMSE decreases with an increase in transmission range $R$. As the node’s
transmission range increases, the network’s average connectivity increases and
decreases the RMSE up to a particular value, after which it saturates. For
example, we can see that the RMSE decreases with an increase in the
transmission range up to 7m, after which it almost saturates, and further
increase in transmission range will only increase the energy consumption.

Figure 8: RMSE vs. Transmission Range.

Fig. 8 also illustrates that the proposed approach outperforms WCL [58] and
compressive sensing because both WCL and compressive sensing consider a fully
connected network where an increase in the transmission range does not improve
the localization accuracy.

Fig. 8 shows only the impact of transmission range on the localization
accuracy; we further evaluate the energy error product as a function of the
transmission range. For this, we consider three different scenarios with 50,
100, and 200 IoUT nodes in 100m $\times$100m $\times$100m cubic area. Fig. 9
shows that the energy error product depends on both the number of nodes and
the transmission range.

Figure 9: Energy error product vs. Transmission Range.

For a dense network such as 200 nodes, the optimal transmission range with
minimum energy error product is towards the lower end, i.e., 4m. For a sparse
network, the minimum energy error product is around 8m. This is because
increasing the transmission range improves the accuracy up to a specific
value, after which the saturation occurs, and a further increase in range will
only result in high energy consumption. Fig. 9 deduce that a larger
transmission range reduces the localization error but leads to increased
energy consumption. Hence, it is crucial to select a proper transmission range
for IoUT nodes to maintain energy efficiency. Besides optimizing the above
function, energy-harvesting techniques have recently attracted the researchers
for improving the network lifetime of underwater communications systems [17].
As the underwater nodes are not capable to survive on the battery-operation
for larger time, thus, energy harvesting methods including microbial fuel
cells [59] and acoustic piezo-electric harvesters [60] can be a promising
solutions.

##  VII Conclusion

This paper introduces a hybrid MIAO ranging technique that utilizes a SOA
approach for accurate localization. Based on the SOA method, nearest-neighbour
distances are measured. This method leads to better localization accuracy than
a stand-alone single underwater communication technology due to the
availability of many single-hop ranges in IoUT networks. Moreover, Bayesian
MDS is introduced to calculate the network graph from the computed single-hop
distances. The output graph from the BMDS is fed to the Procrustes analysis
technique to estimate the underwater IoUT devices’ unknown location
accurately. Furthermore, the hybrid Cramer Rao lower bound is derived for
analyzing the performance of the proposed method. Simulations are performed
for sparse and dense IoUT networks to see the effectiveness of the proposed
scheme. The results show the superior performance of the proposed method with
respect to the literature in terms of different system parameters, such as
ranging error variance, network density, and the total number of anchors. The
simulation results depict that the proposed MIAO scheme achieves a sub-meter
level of accuracy in even sparse IoUT networks.

In future work, we will perform in-situ measurements in a real underwater
setup and compare the simulation and practical results both in terms of
computational complexity, energy efficiency, and error performance.

## Acknowledgement

The authors would like thank the anonymous reviewers for their fruitful
comments which further improved the scope of this manuscript.

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|  RUHUL AMIN KHALIL (Member, IEEE) received the bachelor’s, master’s, and
Ph.D. degrees in electrical engineering from the Department of Electrical
Engineering, Faculty of Electrical and Computer Engineering, University of
Engineering and Technology, Peshawar, Pakistan, in 2013, 2015, and 2021,
respectively. He has been serving as a Lecturer with the Department of
Electrical Engineering, Faculty of Electrical and Computer Engineering,
University of Engineering and Technology, Peshawar. His research interests
include audio signal processing and its applications, machine learning, the
Internet of Things (IoT), routing, network traffic estimation, software
defined networks, and underwater wireless communication.
---|---
|  NASIR SAEED (Senior Member, IEEE) received the bachelor’s degree in
telecommunication from the University of Engineering and Technology, Peshawar,
Pakistan, in 2009, the master’s degree in satellite navigation from the Polito
di Torino, Italy, in 2012, and the Ph.D. degree in electronics and
communication engineering from Hanyang University, Seoul, South Korea, in
2015. He was an Assistant Professor with the Department of Electrical
Engineering, Gandhara Institute of Science and IT, Peshawar, from August 2015
to September 2016. He has worked as an Assistant Professor with IQRA National
University, Peshawar, from October 2016 to July 2017. From July 2017 to
December 2020, he was a Postdoctoral Research Fellow with the Communication
Theory Laboratory, King Abdullah University of Science and Technology (KAUST).
He is currently an Associate Professor with the Department of Electrical
Engineering, Northern Border University, Arar 73222, Saudi Arabia. His current
research interests include cognitive radio networks, non-conventional wireless
communications, aerial networks, dimensionality reduction, and localization.
---|---
|  MOHAMMAD INAYATULLAH BABAR received his Bachelor of Science Degree in
Electrical Engineering from University of Engineering and Technology (UET),
Peshawar, Pakistan in 1997. He received his Masters and Doctorate Degrees in
2001 and 2005 respectively from School of Engineering and Applied Sciences,
George Washington University, Washington DC USA. He is a member of IEEE USA
and ACM USA. He also taught a number of Telecommunications Engineering Courses
at Graduate Level in School of Engineering, Stratford University, Virginia USA
as Adjunct faculty. Currently, he is working as Professor in Department of
Electrical Engineering, supervising postgraduate Scholars in the field of
Wireless Communications Network.
---|---
|  TARIQULLAH JAN did his PhD in the field of Electronic Engineering from the
University of Surrey, United Kingdom in 2012. He did his Bachelor in
Electrical Engineering from the University of Engineering and Technology
Peshawar, Pakistan in 2002. Currently he is serving as Associate Professor at
Department of Electrical Engineering, Faculty of Electrical and Computer
Systems Engineering, University of Engineering and Technology Peshawar,
Pakistan. His Research interest includes Blind signal processing, machine
learning, blind reverberation time estimation, speech enhancement, multimodal
based approaches for the blind source separation, compressed sensing, and Non-
negative matrix/tensor factorization for the blind source separation.
---|---
|  SADIA DIN is currently working as an Assistant Professor in the Department
of Information and Communication Engineering, Yeungnam University, South
Korea. Dr. Sadia is also working as a senior researcher in University of
Milano, Milan, Italy. Previously, she was working as a Post-Doctoral
Researcher in Kyungpook National University, South Korea (Mar 2020 Aug 2020).
She received her Ph.D. in Data Science and Masters in Computer Science from
Kyungpook National University, South Korea, and Abasyn University, Islamabad
Pakistan in 2020 and 2015, respectively. During her Ph.D., she was working on
various projects including Demosaicking and Denoising using Machine/Deep
Learning, Artificial Learning. Furthermore, she extended her research toward
Internet of Things, 5G, and Big Data Analytics. At the beginning of her
research career, she has published highly more than 60 journals and
conferences including IEEE IoT, IEEE TII, IEEE Wireless Communication, IEEE
Globecom, IEEE LCN, IEEE Infocom, etc. In addition, she is the recipient of
two Korean patents in 2019 and 2020. In 2015, she was visiting researcher at
CCMP Lab, Kyungpook National University, South Korea, where she was working on
Big Data and Internet of Things. Moreover, she is the recipient of two
international awards, i.e., research Internship at CCMP Research Lab,
Kyungpook National University, S. Korea (June 2015), and CSE Best Research
Award at Kyungpook National University, S. Korea (October 29, 2019). She was
also the chair for the IEEE International Conf. on Local Computer Networks
(LCN’18). She is serving as a Guest Editor in journal of Wiley, Big Data, and
Microprocessor and microsystem. In IEEE LCN 2017 in Singapore, she has chair
couple of sessions. Her area of research is Demosaicking and Denoising using
Machine/Deep Learning, Artificial Learning, Big Data analytics, 5G, and IoT.
Moreover, she got CSE Best Research Award at Kyungpook National University, S.
Korea (October 29, 2019.
---|---