Abstract—In this study, the Time Difference of Arrival
Averaging (TDOAA) method is studied to minimize the
estimation error and increase the accuracy for emitter location
finding using Particle Swarm Optimization (PSO). We combined
TDOAA method with both classic and improved version of PSO
and found out a considerable performance increase on the
location finding of the transmitter. The improved PSO is to
combine different tasks of implementations of PSO for a single
decision. Therefore the improved PSO also means more accuracy
but price is paid for more complexity. However, the increase on
complexity does not prohibit applying the technique, since
coherence time for decision may well tolerate more complexity
when using today’s state of art microprocessors processing
power.
Keywords—Time Difference of Arrival Averaging, Particle
Swarm Optimization, Time Difference of Arrival
I. INTRODUCTION
TDOAA was presented by Ralph O. Schmidt for three
receivers in 1972 and generalized in 1996 [1, 2]. The method
claims that the sum of the TDOAs in a closed loop must be
zero in the absence of TDOA estimation error. The transmitter
can be positioned using at least three or more receivers in two
dimensional planes. Increasing number of the receivers
decreases the positioning error. Variety of positioning
methods has been indexed in the literature so far [3-10].
These methods can be classified in two categories as
geometric and stochastic. Stochastic methods are more
preferred thanks to their nature of being less sensitive to
noise. Determination of the source location is executed using
different source of information such as Received Signal
Strength (RSS), Direction of Arrival (DOA), Time of Arrival
(TOA), Time Difference of Arrival (TDOA), and Frequency
Difference of Arrival (FDOA). Comparing to RSS, DOA and
TOA, determining the location of the transmitter is obtained
with more accurate using the TDOA. Furthermore there is no
necessity to know the transmitter signal. On the other hand
receivers must be synchronized. PSO and TDOAA were used
separately for source localization applications. In this study
Manuscript received February 27, 2012.
O. Cakir, A. Yazgan, O. Cakir, E. Tugcu, and I. Kaya are with the
Karadeniz Technical University, The Faculty of Engineering, 61080,
Trabzon, Turkey (corresponding authors to provide phone: +904623774203;
fax: +904623257405; e-mail: cakir@ktu.edu.tr, ayhanyazgan@ktu.edu.tr,
cakiro@ktu.edu.tr, emintugcu@ktu.edu.tr, ikaya@ktu.edu.tr).
we combined both proposing a new method and obtained a
notable performance increase.
The paper is organized as following. Section II outlines the
emitter location finding and TDOAA. Section III describes
the PSO and IPSO algorithm. Section IV presents the using
PSO and IPSO algorithms for source localization. Section V
presents and discusses the results comparatively.
Consequently, Section VI concludes the paper.
II. EMITTER LOCATION FINDING AND TDOA AVERAGING
A. Emitter Location Finding using TDOA
The number of TDOA for n receivers can be calculated
using (1)
( ) 1
2
nn
m
-
= (1)
Here m shows the number of TDOAs. Only n-1 TDOAs are
independent from each other’s. m TDOAs can be calculated
using n-1 independent TDOAs.
Three receivers positioning system can be seen in Fig. 1.
where x
1
, y
1
, x
2
, y
2
and x
3
, y
3
are the receivers’ positions and
x
t
, y
t
show the transmitter location. To calculate the exact
(error free) TDOAs, first of all, the distances between the
transmitter and the receivers must be obtained. These
distances are given l
1
, l
2
and l
3
for the first, second and third
receiver respectively and calculated in (2-4).
2 2
1 1 1
( ) ( )
t t
l x x y y = - + - (2)
2 2
2 2 2
( ) ( )
t t
l x x y y = - + - (3)
2 2
3 3 3
( ) ( )
t t
l x x y y = - + - (4)
12 1 2
r l l = - (5)
13 1 3
r l l = - (6)
23 2 3
r l l = - (7)
Where r
12
is the distance difference between first and
second receiver; r
13
is the distance difference between first
and third receiver and r
23
is the distance difference between
second and third receiver and calculated in (5-7)
The TDOAs are calculated as given below where c is the
signal velocity in the medium and known exactly and Δ is the
exact TDOA for the related receivers.
Novel Composite Method for Determining the
Location of the Transmitter using Particle Swarm
Optimization
Oguzhan Cakir, Ayhan Yazgan, Omer Cakir, Emin Tugcu, and Ismail Kaya
335 978-1-4673-1118-2/12/$31.00 ©2012 IEEE TSP 2012