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A Joint TDOA-PDOA Localization Approach Using Particle Swarm Optimization

TL;DR: This letter proposes a novel approach that incorporates both TDOA and PDOA to achieve improved position estimation and results show that the proposed approach sufficiently, and justifiably, improves localization performance relative to pure TDOA methods.
Abstract: Estimating the location of a target is essential for many applications such as asset tracking, navigation, and data communications. Time-difference-of-arrival (TDOA) based localization has the main advantage that it does not require synchronization between the transmitting and the receiving sides. Phase-difference-of-arrival (PDOA) provides additional information that can be leveraged to enhance localization performance. The combination of TDOA and PDOA for localization has not been reported in the literature. In this letter, we propose a novel approach that incorporates both TDOA and PDOA to achieve improved position estimation. In the proposed approach, an initial location estimate is obtained by optimizing a TDOA cost function. Next, a PDOA, or a hybrid TDOA-PDOA cost function is optimized using a particle swarm optimizer to obtain the final location estimate. Simulation results show that the proposed approach sufficiently, and justifiably, improves localization performance relative to pure TDOA methods.

Summary (2 min read)

Introduction

  • In the first formulation, the authors use only PDOA measurements, whereas in the second formulation, they consider a hybrid cost function using both TDOA and PDOA information.
  • A PSO is a multidimensional optimization technique inspired by the behavior of bird flock searching for food [21].
  • Section II presents the proposed joint TDOA-PDOA localization algorithm.

B. The proposed PDOA Cost Function

  • Practically, the PDOA of two signals can be estimated directly from the cross power spectrum of the signals [15], [25].
  • This method requires the two received signals to be transferred to a central processor.
  • Practical ways of estimating the error variances of TDOA and PDOA are using the SNRs [10], [25].
  • The function cp(p) is non-convex (at least) due to the nonlinearity of the wrapping operation.
  • The proposed PDOA cost function in (6) can be related to the TDOA cost function in (2), also known as Remark 1.

C. The Proposed Joint Cost Function

  • One can consider combining both TDOA and PDOA measurements to form a joint cost function that leverages all the available information.
  • Recalling (6) and (7), the authors observe that cp(p) is already weighted by the TDOA error variance σ2t .
  • The implication of this weighing is to emphasize the contribution from the more precise measurements, TDOA or PDOA.
  • It is also expected to inherit some of the characteristics of the cost function cp(p), especially the large number of local minima.

D. Optimization

  • The authors consider localization based on both cost functions (6) and (9).
  • The target location can be estimated by finding the global minimum by solving p̂p = argmin p cp(p), (10) or p̂j = argmin p cj(p).
  • A plethora of methods, with well-understood performance characteristics, exist to achieve this task.
  • Namely, the authors utilize a quasi-Newton optimizer to solve the optimization problem (2) and initialize the PSO algorithm.
  • By using (12) and (13), the authors can set the boundaries of the search space of the PSO.

E. Summary of the Proposed TDOA-PDOA Localization Approach

  • I Using TDOA measurements, calculate the initial location by solving (2) using a quasi-Newton optimizer [12].
  • Note that, for Algorithm 1, despite the absence of TDOA from the expression of the cost function, it is still essential to use TDOA information for successful initialization of this algorithm.

A. Simulation Setup

  • For simplicity, the authors consider a 2-D localization problem where the target is on the same plane as the anchors.
  • TDOAs are calculated using (1), while wrapped PDOAs are calculated based on (5) for a single acoustic frequency.
  • The results, however, can easily be extended to the multi-frequency/multi-carrier case.
  • The root mean squared error (RMSE) is adopted as the performance metric.

B. Results

  • The proposed approach yields two algorithms, TDOAPDOA-1 and TDOA-PDOA-2, which are summarized in Section II-E.
  • The CRLB for TDOA-based localization (CRLB-T), lower bound for PDOA-based localization (LB-P) [26] and the joint TDOAPDOA lower bound (LB-J) [26] are also used to compare performance.
  • The proposed TDOA-PDOA methods provide superior results which stay close to the LB in many cases.
  • The RMSE of the proposed algorithms tends to converge to the lower bound as the swarm size increases.
  • When σt is small compared to σp, the joint lower bound LB-J is close to the TDOA CRLB.

IV. CONCLUSION

  • A localization approach that jointly uses time-differenceof-arrival (TDOA) and phase-difference-of-arrival (PDOA) measurements has been presented.
  • Two cost functions were proposed; one using only PDOA information, and the other using a joint function that takes advantage of both TDOA and PDOA measurements.
  • A particle swarm optimizer (PSO) is employed to minimize the proposed cost functions and obtain the final location of the target.
  • The proposed methods also stay close to the estimation lower bound for moderate SNR values.
  • The performance of the proposed approach depends on the TDOA estimation result, and the PSO swarm size which dictates the computational complexity of the proposed approach.

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A Joint TDOA-PDOA Localization Approach
Using Particle Swarm Optimization
Item Type Article
Authors Chen, Hui; Ballal, Tarig; Saeed, Nasir; Alouini, Mohamed-Slim;
Al-Naffouri, Tareq Y.
Citation Chen, H., Ballal, T., Saeed, N., Alouini, M.-S., & Al-Naffouri, T. Y.
(2020). A Joint TDOA-PDOA Localization Approach Using Particle
Swarm Optimization. IEEE Wireless Communications Letters, 1–
1. doi:10.1109/lwc.2020.2986756
Eprint version Post-print
DOI 10.1109/LWC.2020.2986756
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Journal IEEE Wireless Communications Letters
Rights (c) 2020 IEEE. Personal use of this material is permitted.
Permission from IEEE must be obtained for all other users,
including reprinting/ republishing this material for advertising or
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components of this work in other works.
Download date 09/08/2022 17:49:09
Link to Item http://hdl.handle.net/10754/662503

1
A Joint TDOA-PDOA Localization Approach Using
Particle Swarm Optimization
Hui Chen, Student Member, IEEE , Tarig Ballal, Member, IEEE, Nasir Saeed, Senior Member, IEEE ,
Mohamed-Slim Alouini, Fellow, IEEE and Tareq Y. Al-Naffouri, Senior Member, IEEE
Abstract—Estimating the location of a target is essential
for many applications such as asset tracking, navigation, and
data communications. Time-difference-of-arrival (TDOA) based
localization has the main advantage that it does not require
synchronization between the transmitting and the receiving sides.
Phase-difference-of-arrival (PDOA) provides additional informa-
tion that can be leveraged to enhance localization performance.
The combination of TDOA and PDOA for localization has not
been reported in the literature. In this paper, we propose a
novel approach that incorporates both TDOA and PDOA to
achieve improved position estimation. In the proposed approach,
an initial location estimate is obtained by optimizing a TDOA
cost function. Next, a PDOA, or a hybrid TDOA-PDOA cost
function is optimized using a particle swarm optimizer to obtain
the final location estimate. Simulation results show that the pro-
posed approach sufficiently, and justifiably, improves localization
performance relative to pure TDOA methods.
Index Terms—Localization, TDOA, PDOA, particle swarm
optimizer
I. INTRODUCTION
Existing and future wireless communication technologies
require accurate real-time localization and tracking methods.
Location information is important for numerous applications
such as target monitoring [1], wireless sensor network [2],
navigation [3], drones localization [4] and connected vehi-
cles [5]. A survey of positioning techniques and systems can
be found in [6], [7].
Time-difference-of-arrival (TDOA) based localization algo-
rithms [8] are mainly used because no synchronization is
required between the target and the anchors. The anchors share
the same timing so that the TDOA information of the signal
between different anchors can be estimated, and hence the
location can be obtained. There are two main types of methods
to solve the nonlinear localization problems using the TDOA
measurements. One solution is linearization, followed by a
least-squares (LS) estimation. Despite the obvious advantage
of linearization in simplifying these algorithms, the same
linearization operation makes these algorithms more sensitive
to noise [9], [10]. Formulating the localization task as a non-
convex optimization problem is another way that can be solved
by using, for example, iterative optimization methods [11],
[12], or convex relaxation methods [13], [14].
PDOA information is customarily used in far-field scenarios
where anchor separations are small [15], [16]. For large
The authors are with the Division of Computer, Electrical and Mathematical
Science & Engineering, King Abdullah University of Science and Technol-
ogy (KAUST), Thuwal, 23955-6900, KSA. e-mail: ({hui.chen; tarig.ahmed;
nasir.saeed; slim.alouini; tareq.alnaffouri}@kaust.edu.sa).
inter-anchor distance, the actual phase difference of a signal
between a pair of anchors cannot be computed in a direct
way. This is due to the phase wrapping problem [15], which
results in an observed wrapped phase difference that cannot
be directly used. Despite the phase wrapping issue, PDOA
provides high measurement precision compared to TDOA [15],
[17]–[19].
To leverage the high precision of PDOA, we propose a
localization technique that combines both TDOA and PDOA
measurements. We consider two problem formulations. In the
first formulation, we use only PDOA measurements, whereas
in the second formulation, we consider a hybrid cost function
using both TDOA and PDOA information. In both cases,
the resulting cost functions suffer from the presence of large
numbers of local minima. To obtain a feasible solution, we
utilize a particle swarm optimizer (PSO) [20] to solve the
two optimization problems. A PSO is a multidimensional
optimization technique inspired by the behavior of bird flock
searching for food [21]. It has the advantages of simple
implementation, high-quality solutions to global optima, and
quick convergence [22]. For the PSO to work well, the
optimizer needs to start from a good initial guess of the target’s
location and to have sufficient swarms to search for a global
optimum. To provide such a good initialization, we rely on
the pure TDOA approach whose cost function is much easier
to optimize than our proposed cost functions.
Numerical simulations were carried out to evaluate the
performance of the proposed joint TODA-PDOA localization
method using PSO. The proposed method is compared to
pure TDOA localization implemented using a linear closed-
form, and using a semidefinite programming (SDP) convex
relaxation optimization method.
The remainder of this paper is organized as follows. Sec-
tion II presents the proposed joint TDOA-PDOA localization
algorithm. Section III discusses simulation setup and presents
the results, while Section IV, states the conclusion of the paper.
II. THE PROPOSED LOCALIZATION ALGORITHM
A. The TDOA Approach
Consider a 2-D or 3-D space with a system of N anchors
R
1
, R
2
, ..., R
N
located at r
i
, i = 1, ..., N, and a target located
at a point p. For any signal, the time difference of arrival
between anchor R
i
and anchor R
j
at point p is given by
τ
ij
(p) =
||p r
i
||
2
||p r
j
||
2
v
, i, j = 1, ..., N, (1)

2
where || · ||
2
denotes the L
2
norm, and v is the signal
propagation speed. This formula gives the exact (true) TDOA.
Practically, we have to rely on estimates, ˆτ
ij
, of TDOA. With
time synchronization maintained between receivers, TDOA
can be estimated using one of two approaches. By transferring
the received signals to a central processor, a cross-correlation
based method can be used to obtain TDOA estimates [8]. An
alternative approach is based on estimating the times of arrival
of signal at each anchor independently. The differences of
these times give the required TDOA estimates [13].
With TDOA information acquired through any of the
aforementioned or other methods, the target location can
be estimated. Among the candidate methods are the linear
closed-form method [9] where a linearization is performed to
simplify the problem, which results in exacerbating the noise
effect. Other techniques are based on combining weighted least
squares and firefly algorithm [23], and `
1
minimization [24].
In this paper, we adopt a maximum likelihood approach which
can be pursued as follows [13]:
ˆ
p = arg min
p
c
t
(p) = arg min
p
N
X
i=1
N
X
j=1
j6=i
[ˆτ
ij
τ
ij
(p)]
2
.
(2)
To have an idea of the properties of the function c
t
(p) in (2),
we expand its expression using (1) to obtain
c
t
(p) =
N
X
i=1
N
X
j=1
j6=i
1
v
2
||p r
i
||
2
2
+
1
v
2
||p r
j
||
2
2
2
v
2
||p r
i
||
2
||p r
j
||
2
2ˆτ
ij
v
||p r
i
||
2
+
2ˆτ
ij
v
||p r
j
||
2
+ ˆτ
2
ij
.
(3)
Based on (3), we can see that c
t
(p) can be convex (only)
for certain choices of ˆτ
ij
. However, in the general case,
the function c
t
(p) has to be dealt with in the non-convex
optimization framework. To this end, convex relaxation [13],
[14] represents one of the effective tools.
An example of c
t
(p) for a target at [0, 0]
T
m, with the
target and anchors all lying in the plane z = 2, is shown
in Fig. 1 (a-1, a-2). A global minimum can be observed at
[0, 0]
T
, the true target location. It is observed that the function
is relatively flat around the global minimum, which makes the
localization accuracy more susceptible to TDOA estimation
errors. Existing methods for TDOA estimation are limited
in their accuracy by the effect of noise, the sampling rate,
time resolution and other factors [15], [17]–[19]. To enhance
localization accuracy, our proposed approach leverages, in
addition to TDOA, the more accurate estimates of PDOA.
B. The proposed PDOA Cost Function
Given signal frequencies f = [f
1
, ..., f
M
]
T
, PDOA is related
to TDOA through
φ
ij,m
(p) = 2πf
m
τ
ij
(p). (4)
Here, φ
ij,m
is the PDOA between the received signals at
anchors R
i
and R
j
at frequency f
m
. Due to the way PDOA is
(a-1) c
t
(p) (a-2) c
t
(p)
(b-1) c
p
(p) (b-2) c
p
(p)
(c-1) c
j
(p) (c-2) c
j
(p)
Fig. 1. Example plots of the TDOA, PDOA, and the joint cost functions. The
second column plots are obtained by zooming in around the global minimum.
usually estimated, mostly, we only have access to a wrapped
version of it that is given by [25]
ψ
ij,m
(p) = wrap(φ
ij,m
(p)) = mod(φ
ij,m
(p) + π, 2π) π,
(5)
where ψ
ij,m
[π, π) is the wrapped PDOA, and mod(a, b)
returns the remainder of dividing a by b.
Practically, the PDOA of two signals can be estimated
directly from the cross power spectrum of the signals [15],
[25]. This method requires the two received signals to be
transferred to a central processor. Another method to estimate
the PDOA is by recording the phase of arrival of the signal
at each anchor independently and subtracting the two phases
to obtain the PDOA [18], [19]. The method proposed in this
paper does not depend on how the PDOA is obtained.
Given the estimated (wrapped) PDOA, we create the fol-
lowing cost function:
c
p
(p) =
1
M
M
X
m=1
b
m
N
X
i=1
N
X
j=1
j6=i
{wrap[
ˆ
ψ
ij,m
ψ
ij,m
(p)]}
2
.
(6)
In (6), the wrapped PDOA ψ
ij,m
(p) can be computed using
(5). The scalars b
m
are weighting coefficients given by
b
m
=
σ
2
t
σ
2
p,m
=
σ
2
t
γ
2
p,m
(2πf
m
)
2
; (7)

3
where σ
2
t
and σ
2
p,m
are the TDOA and PDOA estimation error
variances in squared second; and γ
2
p,m
are PDOA variances
given in squared radians. Practical ways of estimating the
error variances of TDOA and PDOA are using the SNRs [10],
[25]. Note that the inclusion of σ
2
t
in the weights b
m
has no
effect on the locations of the minima of c
p
(p). The purpose
of scaling the weights by this factor will be explained in the
next subsection.
The function c
p
(p) is non-convex (at least) due to the
nonlinearity of the wrapping operation. Since wrapping occurs
in a periodic fashion at an interval of 2π, we expect c
p
(p) to
be highly non-convex with many local minima. The purpose of
the wrap operation in (6) is to allow us to compute the residual
errors on a circle rather than computing them on a line. For
example, when
ˆ
ψ = π , ψ = π + , and 0 < < π/2,
we have
ˆ
ψ ψ = 2π 2 and wrap(
ˆ
ψ ψ) = 2. The
latter result show that the two PDOA values are closer than
what their difference indicates. An example visualization of
c
p
(p) is shown in Fig. 1 (b-1, b-2) for the same setup used in
Fig. 1 (a-1, a-2).
Remark 1: The proposed PDOA cost function in (6) can be
related to the TDOA cost function in (2). From the definition
of the wrap function, it is to easy to see that
wrap[
ˆ
ψ
ij,m
ψ
ij,m
(p)] = wrap[
ˆ
φ
ij,m
φ
ij,m
(p)]
= wrap{2πf
m
[ˆτ
ij,m
τ
ij,m
(p)]}.
(8)
Based on (8), it can be said that (6) represents another form
of TDOA localization where the residuals undergo a nonlinear
transformation through the wrap function. This transformation
is not unique, which makes the cost function difficult to
optimize. Note that the main merit of (6) is based on the
relatively high quality of the PDOA measurements, and by
extension, the corresponding TDOA estimates.
C. The Proposed Joint Cost Function
One can consider combining both TDOA and PDOA mea-
surements to form a joint cost function that leverages all the
available information. We propose a simple way to achieve
this by using a composite function given by
c
j
(p) = c
t
(p) + c
p
(p), (9)
where c
t
(p) and c
p
(p) are defined in (3) and (6), respectively.
It is important to note here that the cost function c
j
(p)
does not combine the contributions of TDOA and PDOA
equally. Recalling (6) and (7), we observe that c
p
(p) is already
weighted by the TDOA error variance σ
2
t
. In addition, the
contributions of different frequencies to c
p
(p) are weighted by
the inverse of the corresponding PDOA error variances. The
implication of this weighing is to emphasize the contribution
from the more precise measurements, TDOA or PDOA.
The joint function in c
j
(p) is non-convex in p by definition.
It is also expected to inherit some of the characteristics of
the cost function c
p
(p), especially the large number of local
minima. An example plot of c
j
(p) is shown in Fig. 1 (c-1, c-2)
which corresponds to the same scenario depicted in Fig. 1 (a-1,
a-2).
D. Optimization
In this paper, we consider localization based on both cost
functions (6) and (9). The target location can be estimated by
finding the global minimum by solving
ˆ
p
p
= arg min
p
c
p
(p), (10)
or
ˆ
p
j
= arg min
p
c
j
(p). (11)
To avoid picking up a local minimum as the final result,
a PSO (particle swarm optimizer) is used [20], [22]. PSO
initializes a set of candidate solutions (swarm size s) around
an initial point p
0
. However, it is not always guaranteed for
the PSO to find the global minimum as the swarm size and
searching area decide the performance. Two key processes to
achieve good performance are 1) to judiciously set the initial
point for the PSO algorithm, and 2) to set the boundaries of
the search space.
To provide a good initial point to the PSO, we rely on
solving the classical (pure) TDOA problem (2) as a means to
acquire a good initialization point. A plethora of methods, with
well-understood performance characteristics, exist to achieve
this task. Namely, we utilize a quasi-Newton optimizer to solve
the optimization problem (2) and initialize the PSO algorithm.
We define the search space of the PSO as
S
lb
= max(p
0
δ, p
lb
)
S
ub
= min(p
0
+ δ, p
ub
)
, (12)
where p
lb
, p
ub
are the lower and upper bound of the space
covered by the anchors, and δ is a vector of the same
dimensionality as p
0
. We propose the following choice of the
parameter δ:
δ = α σ
t
1, (13)
where σ
t
is the standard deviation of the TDOA error, 1 is an
all-ones vector, and α is a scaling factor. We use α = 0.8 in
all our tests.
By using (12) and (13), we can set the boundaries of the
search space of the PSO. Defining the boundaries this way
improves the chances of the solutions of (10) and (11) to
converge to global optima while reducing the overall com-
putational complexity.
E. Summary of the Proposed TDOA-PDOA Localization Ap-
proach
i Using TDOA measurements, calculate the initial loca-
tion by solving (2) using a quasi-Newton optimizer [12].
ii Define the lower bound, S
lb
, and the upper bound, S
ub
,
of the search space using (12) and (13).
iii Algorithm 1 (TDOA-PDOA-1): Perform (i) and (ii); then
solve (10) using PSO.
iv Algorithm 2 (TDOA-PDOA-2): Perform (i) and (ii); then
solve (11) using PSO.
Note that, for Algorithm 1, despite the absence of TDOA
from the expression of the cost function, it is still essential
to use TDOA information for successful initialization of this
algorithm.

4
III. SIMULATIONS
A. Simulation Setup
To simplify the presentation of the results, we use a specific
anchor configuration with N = 8 receivers to test our proposed
method. The receivers are located at [d, d], [d, 0], [d, d],
[0, d], [0, d], [d, d], [d, 0], [d, d] forming a 2d × 2d m
2
square. In all simulations, d = 2.5 meters is used.
For simplicity, we consider a 2-D localization problem
where the target is on the same plane as the anchors. All
the simulation results presented in the following subsection
are obtained for a target at [1, 1]
T
(all coordinates measured
in meters). TDOAs are calculated using (1), while wrapped
PDOAs are calculated based on (5) for a single acoustic
frequency. f = 21 kHz (e.g., M = 1). The results, however,
can easily be extended to the multi-frequency/multi-carrier
case. TDOA and PDOA errors are simulated as Gaussian
noises with zero mean and standard deviations σ
t
and σ
p
,
respectively. We set σ
p,m
= σ
p
, m {1, · · · , M}. The root
mean squared error (RMSE) is adopted as the performance
metric. For each simulation case, the RMSE is calculated from
5000 trials.
B. Results
The proposed approach yields two algorithms, TDOA-
PDOA-1 and TDOA-PDOA-2, which are summarized in
Section II-E. The performance of the proposed approach is
compared to that of the linear closed-form method (TDOA-
Linear) [9], the SDP relaxation method (TDOA-SDP) [13]
and the iterative optimization method (TDOA-Iter) [12]. The
CRLB for TDOA-based localization (CRLB-T), lower bound
for PDOA-based localization (LB-P) [26] and the joint TDOA-
PDOA lower bound (LB-J) [26] are also used to compare
performance.
The simulation results are shown in Fig. 2 to Fig. 5. We can
see from the figure that TDOA-Iter performs the best amongst
the pure TDOA-based localization algorithm. The proposed
TDOA-PDOA methods provide superior results which stay
close to the LB in many cases.
In Fig. 2, we study the impact of the number of PSO swarms
on the performance of the two proposed algorithms. The setup
considers a TDOA error standard deviation σ
t
= 2 mm
(normalized by multiplying the signal propagation speed), a
PDOA error standard deviation σ
p
= 0.32 mm (0.1265 rad),
and a search space of size 40 × 40 mm
2
. The RMSE of the
proposed algorithms tends to converge to the lower bound as
the swarm size increases. This means a high probability to
find the global minimum. However, with the help of TDOA
information, TDOA-PDOA-2 requires less swarms to reach the
lower bound. The results in Fig. 2 shows a significant advan-
tage using our proposed joint method in location estimation.
Fig. 3 plots the RMSE against the TDOA error standard
deviation σ
t
for σ
p
= 0.32 mm and s = 500 swarms. When
σ
t
is small compared to σ
p
, the joint lower bound LB-J is close
to the TDOA CRLB. On the contrary, when σ
t
is relatively
large, LB-J is closer to LB-P. However, when σ
t
is excessively
large, an erroneous TDOA position will not facilitate the
initialization of the proposed algorithm. Fig. 3 emphasizes that,
10
1
10
2
10
3
Swarm size
10
-1
10
0
10
1
RMSE [mm]
TDOA Linear
TDOA SDP
TDOA Iter
TDOA-PDOA-1
TDOA-PDOA-2
CRLB-T
LB-P
LB-J
Fig. 2. Performance versus number of swarms s for σ
t
= 2 mm and σ
p
=
0.32 mm.
for sufficiently small σ
p
, the proposed approach yield results
with RMSE close to the lower bounds.
10
-2
10
-1
10
0
10
1
10
2
TDOA standard deviation [mm]
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
RMSE [mm]
TDOA Linear
TDOA SDP
TDOA Iter
TDOA-PDOA-1
TDOA-PDOA-2
CRLB-T
LB-P
LB-J
Fig. 3. Performance versus TDOA error standard deviation σ
t
for σ
p
=
0.32 mm and s = 500 swarms.
In Fig. 4, we vary the PDOA error standard deviation σ
p
,
while fixing σ
t
= 5 mm and s = 500 swarms. When σ
p
is large, with an accurate initial position estimation, TDOA-
PDOA-2 has the performance close to the CRLB-T. However,
TDOA-PDOA-1 has a worse performance because the TDOA
information is not utilized in the optimization procedure.
TDOA-PDOA-2 outperforms the rest of the methods, which
highlights the benefit of the joint cost function (9).
10
-2
10
-1
10
0
10
1
10
2
PDOA standard deviation [mm]
10
-3
10
-2
10
-1
10
0
10
1
10
2
RMSE [mm]
TDOA Linear
TDOA SDP
TDOA Iter
TDOA-PDOA-1
TDOA-PDOA-2
CRLB-T
LB-P
LB-J
Fig. 4. Performance versus PDOA error standard deviation σ
p
for σ
t
=
50 mm and s = 500 swarms.
In Fig. 5, we vary both σ
t
and σ
p
while maintaining

Citations
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Journal ArticleDOI
TL;DR: Terahertz (THz) communications are celebrated as key enablers for converged localization and sensing in future 6G wireless communication systems and beyond as discussed by the authors , and localization in 6G is indispensable for location-aware communications.
Abstract: Terahertz (THz) communications are celebrated as key enablers for converged localization and sensing in future sixth-generation (6G) wireless communication systems and beyond. Instead of being a byproduct of the communication system, localization in 6G is indispensable for location-aware communications. Towards this end, we aim to identify the prospects, challenges, and requirements of THz localization techniques. We first review the history and trends of localization methods and discuss their objectives, constraints, and applications in contemporary communication systems. We then detail the latest advances in THz communications and introduce THz-specific channel and system models. Afterward, we formulate THz-band localization as a 3D position/orientation estimation problem, detailing geometry-based localization techniques and describing potential THz localization and sensing extensions. We further formulate the offline design and online optimization of THz localization systems, provide numerical simulation results, and conclude by providing lessons learned and future research directions. Preliminary results illustrate that under the same transmission power and array footprint, THz-based localization outperforms millimeter wave-based localization. In other words, the same level of localization performance can be achieved at THz-band with less transmission power or a smaller footprint.

25 citations

Posted Content
TL;DR: Terahertz (THz) communications are celebrated as key enablers for converged localization and sensing in future 6G wireless communication systems and beyond as discussed by the authors, and localization in 6G is indispensable for location-aware communications.
Abstract: Terahertz (THz) communications are celebrated as key enablers for converged localization and sensing in future sixth-generation (6G) wireless communication systems and beyond. Instead of being a byproduct of the communication system, localization in 6G is indispensable for location-aware communications. Towards this end, we aim to identify the prospects, challenges, and requirements of THz localization techniques. We first review the history and trends of localization methods and discuss their objectives, constraints, and applications in contemporary communication systems. We then detail the latest advances in THz communications and introduce the THz-specific channel and system models. Afterward, we formulate THz-band localization as a 3D position/orientation estimation problem, detailing geometry-based localization techniques and describing potential THz localization and sensing extensions. We further formulate the offline design and online optimization of THz localization systems, provide numerical simulation results, and conclude by providing insight into interdisciplinary future research directions. Preliminary results illustrate that under the same total transmission power and time, THz-based localization is ~5 (~20) times more accurate than mmWave-based localization without (with) prior position information.

24 citations

Journal ArticleDOI
TL;DR: In this paper, a time-of-flight based indoor positioning system for LiFi is presented based on the ITU -T recommendation G.9991, which can reach an average distance error of a few centimeters in three dimensions.
Abstract: Precise position information is considered as the main enabler for the implementation of smart manufacturing systems in Industry 4.0. In this article, a time-of-flight based indoor positioning system for LiFi is presented based on the ITU - T recommendation G.9991. Our objective is to realize positioning by reusing already existing functions of the LiFi communication protocol which has been adopted by several vendors. Our positioning algorithm is based on a coarse timing measurement using the frame synchronization preamble, similar to the ranging, and a fine timing measurement using the channel estimation preamble. This approach works in various environments and it requires neither knowledge about the beam characteristics of transmitters and receivers nor the use of fingerprinting. The new algorithm is validated through both, simulations and experiments. Results in an $\text{1}\;{\rm{m}} \times \text{1}\;{\rm{m}} \times \text{2}\;{\rm{m}}$ area indicate that G.9991-based positioning can reach an average distance error of a few centimeters in three dimension. Considering the common use of lighting in indoor environments and the availability of a mature optical wireless communication system using G.9991, the proposed LiFi positioning is a promising new feature that can be added to the existing protocols and enhance the capabilities of smart lighting systems further for the benefit of Industry 4.0.

23 citations

Journal ArticleDOI
TL;DR: In this article, the authors use difference-of-convex (DC) programming tools to solve the time difference of arrival (TDOA) localization problem, which guarantees convergence to a stationary point of the objective function.
Abstract: A popular approach to estimate a source location using time difference of arrival (TDOA) measurements is to construct an objective function based on the maximum likelihood (ML) method. An iterative algorithm can be employed to minimize that objective function. The main challenge in this optimization process is the non-convexity of the objective function, which precludes the use of many standard convex optimization tools. Usually, approximations, such as convex relaxation, are applied, resulting in performance loss. In this work, we take advantage of difference-of-convex (DC) programming tools to develop an efficient solution to the ML TDOA localization problem. We show that, by using a simple trick, the objective function can be modified into an exact difference of two convex functions. Hence, tools from DC programming can be leveraged to carry out the optimization task, which guarantees convergence to a stationary point of the objective function. Simulation results show that, when initialized within the convex hull of the anchors, the proposed TDOA localization algorithm outperforms a number of benchmark methods, behaves as an exact ML estimator, and indeed achieves the Cramer-Rao lower bound.

13 citations

Journal ArticleDOI
TL;DR: This survey introduces a review of various conventional geolocation techniques, current orientations, and state-of-the-art techniques and highlights some approaches and algorithms employed in wireless and satellite systems for geolocated and target tracking that may be extremely beneficial.
Abstract: A single Radio-Frequency Interference (RFI) is a disturbance source of modern wireless systems depending on Global Navigation Satellite Systems (GNSS) and Satellite Communication (SatCom). In particular, significant applications such as aeronautics and satellite communication can be severely affected by intentional and unintentional interference, which are unmitigated. The matter requires finding a radical and effective solution to overcome this problem. The methods used for overcoming the RFI include interference detection, interference classification, interference geolocation, tracking and interference mitigation. RFI source geolocation and tracking methodology gained universal attention from numerous researchers, specialists, and scientists. In the last decade, various conventional techniques and algorithms have been adopted in geolocation and target tracking in civil and military operations. Previous conventional techniques did not address the challenges and demand for novel algorithms. Hence there is a necessity for focussing on the issues associated with this. This survey introduces a review of various conventional geolocation techniques, current orientations, and state-of-the-art techniques and highlights some approaches and algorithms employed in wireless and satellite systems for geolocation and target tracking that may be extremely beneficial. In addition, a comparison between different conventional geolocation techniques has been revealed, and the comparisons between various approaches and algorithms of geolocation and target tracking have been addressed, including H∞ and Kalman Filtering versions that have been implemented and investigated by authors.

8 citations

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Abstract: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives an explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, spherical-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical-interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >

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"A Joint TDOA-PDOA Localization Appr..." refers methods in this paper

  • ...based method can be used to obtain TDOA estimates [8]....

    [...]

  • ...Time-difference-of-arrival (TDOA) based localization algorithms [8] are mainly used because no synchronization is required between the target and the anchors....

    [...]

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TL;DR: The style of the entries in the Encyclopedia of Machine Learning is expository and tutorial, making the book a practical resource for machine learning experts, as well as professionals in other fields who need to access this vital information but may not have the time to work their way through an entire text on their topic of interest.
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"A Joint TDOA-PDOA Localization Appr..." refers background or methods in this paper

  • ...To avoid picking up a local minimum as the final result, a PSO (particle swarm optimizer) is used [20], [22]....

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  • ...It has the advantages of simple implementation, high-quality solutions to global optima, and quick convergence [22]....

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Proceedings ArticleDOI
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TL;DR: In this paper, the authors give an overview of spatial identification of modulated backscatter UHF RFID tags using RF phase information, and describe three main techniques based on PDOA (phase difference of arrival): TD (Time Domain), FD (Frequency Domain), and SD (Spatial Domain).
Abstract: In this paper, we give an overview of spatial identification (determining position and velocity) of modulated backscatter UHF RFID tags using RF phase information. We describe three main techniques based on PDOA (Phase Difference of Arrival): TD (Time Domain), FD (Frequency Domain), and SD (Spatial Domain). The techniques are illustrated with modeling and simulation example in free space and in presence of multipath using a multi-ray channel model for amplitude and phase of the received tag signal in deterministic environment. We also present and discuss the experiments performed in a real RFID warehouse portal environment.

438 citations


"A Joint TDOA-PDOA Localization Appr..." refers methods in this paper

  • ...estimate the PDOA is by recording the phase of arrival of the signal at each anchor independently and subtracting the two phases to obtain the PDOA [18], [19]....

    [...]

Frequently Asked Questions (1)
Q1. What have the authors contributed in "A joint tdoa-pdoa localization approach using particle swarm optimization" ?

The combination of TDOA and PDOA for localization has not been reported in the literature. In this paper, the authors propose a novel approach that incorporates both TDOA and PDOA to achieve improved position estimation.