Time Difference of Arrival Localization Study for SAR Systems over LoRaWAN

Abstract

Over the last years we have seen a rapid expansion within the area of Internet of Things (IoT) applications. For many applications’ use cases, such as rescue monitor systems, the problem of localization (i.e. determine the physical location of nodes) is critical. This paper studies and evaluates the usage of mathematical model of multilateration algorithms using Time Difference of Arrival (TDoA) as a solution for positioning over Long Range Wide Area Network (LoRaWAN). The research is carried out using simulations in Python by configuring the constant positions of the Gateways inside an outdoor area. The proposed algorithms can be integrated in application for tracking people at any time and especially routing people from vulnerable groups. Through multilateration and algorithm’s prediction, we can have an accuracy of 40-60m in location positioning ideal for search and rescue use cases.

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ScienceDirect
Available online at www.sciencedirect.com
Procedia Computer Science 175 (2020) 292–299
1877-0509 © 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
10.1016/j.procs.2020.07.043
10.1016/j.procs.2020.07.043 1877-0509
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chair.
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
The 15th International Conference on Future Networks and Communications (FNC)
August 9-12, 2020, Leuven, Belgium
Time Difference of Arrival Localization Study for SAR Systems
over LoRaWAN
Christos Bourasa
*
, Apostolos Gkamasb, Vasileios Kokkinosa, Nikolaos Papachristosa
aComputer Engineering and Informatics Dept., Univ. of Patras, Greece
bUniversity Ecclesiastical Academy of Vella, Greece
Abstract
Over the last years we have seen a rapid expansion within the area of Internet of Things (IoT) applications. For many
applications’ use cases, such as rescue monitor systems, the problem of localization (i.e. determine the physical location of
nodes) is critical. This paper studies and evaluates the usage of mathematical model of multilateration algorithms using Time
Difference of Arrival (TDoA) as a solution for positioning over Long Range Wide Area Network (LoRaWAN). The research is
carried out using simulations in Python by configuring the constant positions of the Gateways inside an outdoor area. The
proposed algorithms can be integrated in application for tracking people at any time and especially routing people from
vulnerable groups. Through multilateration and algorithm’s prediction, we can have an accuracy of 40-60m in location
positioning ideal for search and rescue use cases.
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
Keywords: ΙοΤ; wireless network; lorawan; TDoA; search and rescue application; mulilateration;
1. Introduction
With the emergence of the Internet of Things (IoT), a growing number of low-cost devices intended to operate on
their own for extended periods of time, often far away from WiFi access points. For this reason, Low Power Wide
Area Network (LPWAN) technologies have attracted a lot of research attention from companies and global
* Corresponding author. Tel.: +30 2610 996951;
E-mail address: bouras@cti.gr
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
The 15th International Conference on Future Networks and Communications (FNC)
August 9-12, 2020, Leuven, Belgium
Time Difference of Arrival Localization Study for SAR Systems
over LoRaWAN
Christos Bourasa*, Apostolos Gkamasb, Vasileios Kokkinosa, Nikolaos Papachristosa
aComputer Engineering and Informatics Dept., Univ. of Patras, Greece
bUniversity Ecclesiastical Academy of Vella, Greece
Abstract
Over the last years we have seen a rapid expansion within the area of Internet of Things (IoT) applications. For many
applications’ use cases, such as rescue monitor systems, the problem of localization (i.e. determine the physical location of
nodes) is critical. This paper studies and evaluates the usage of mathematical model of multilateration algorithms using Time
Difference of Arrival (TDoA) as a solution for positioning over Long Range Wide Area Network (LoRaWAN). The research is
carried out using simulations in Python by configuring the constant positions of the Gateways inside an outdoor area. The
proposed algorithms can be integrated in application for tracking people at any time and especially routing people from
vulnerable groups. Through multilateration and algorithm’s prediction, we can have an accuracy of 40-60m in location
positioning ideal for search and rescue use cases.
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
Keywords: ΙοΤ; wireless network; lorawan; TDoA; search and rescue application; mulilateration;
1. Introduction
With the emergence of the Internet of Things (IoT), a growing number of low-cost devices intended to operate on
their own for extended periods of time, often far away from WiFi access points. For this reason, Low Power Wide
Area Network (LPWAN) technologies have attracted a lot of research attention from companies and global
* Corresponding author. Tel.: +30 2610 996951;
E-mail address: bouras@cti.gr
2 Author name / Procedia Computer Science 00 (2018) 000–000
organizations. Practically the above technology allows such devices to communicate across large distances (up to
20km under good conditions), using comparatively low power. The ability to geolocate such device is often on
interest on many use cases such as rescue monitor systems of vulnerable groups in need. In its basic implementation,
it involves the generation of a set of geographic coordinates and is closely related to the use of positioning systems.
Such an application service built-in using LoRaWAN can be useful for area-based location positioning, with the
advantage of requiring fewer and low-cost devices with long-lasting batteries. LoRa operates in various frequencies
depending on the region, such as 868 MHz for Europe and 915 MHz for North America.
Geolocation can also be achieved through Global Positioning System (GPS) [1], but such a module can be enough
costly. Furthermore, a GPS module can also increase power consumption, making some applications unfeasible to be
used in everyday life or in area with buildings or interference factors. In a Search And Rescue (SAR) use case the
goal is to locate people in need such as track them as they move or by creating geo-fences, for example, sending an
alert if the person in need moves outside a defined area, like a child in a neighborhood. For localization of IoT
devices, the state of the art technology, in terms of accuracy, is GPS. In most modern GPS modules, an accuracy of
less than 10m can be observed in an open outdoor environment. Based on this the above solution is quite attractive
for Search and Rescue Systems. Using GPS IoT modules consumes more than 10 times the energy of LoRa, when
localization packets are sent to the same rate [2]. The difference can even be up to 20 times, if LoRa is configured in
an efficient way on both Spreading Factors and Bandwidth Factors. In addition to a GPS module, a device will also
require an extra module for communication. Having this in mind, it would be more appealing to use a Low-Power
Wide-Area Network (LPWAN) for the communication and localization [3].
Two technologies that can be used in a LPWAN are LoRa and Sigfox. Sigfox is an Ultra Narrowband (UNB),
wireless communication technology owned by a company of the same name. Sigfox, is aimed at IoT devices thus,
one of the services it offers is Geolocation. The localization algorithm that it uses is trilateration with RSSI ranging.
Many times, Sigfox use machine learning techniques in order to improve the accuracy of the position. However, this
technology is able to locate devices with an accuracy precision (<500m), using information from nearby Wi-Fi
access points which is compared to crowd-sourced data. In this research, a position accuracy improvement has been
introduced within a radius of 200m. Similar results have been achieved, where LoRa is used for positioning, using
RSSI. They achieve an accuracy of less than 20m in a small area. SigFox and LoRa are both capable of
communication over many kilometers even in Line of Sight (LoS) or not. However, in this research we test
localization algorithms of in terms of multilateration able to be integrated in SAR systems as an extension to
localization methodologies from previous studies.
In this paper, we describe our approach based on IoT devices and on the deployment of various LoRaWAN
gateways from localization perspective. Through the estimation of the behavior of a LoRaWAN channel and using
multilateration, the localization of a person inside an area can be obtained within a small range (about 40-60m). The
proposed approach is a low power and cost solution, and with a good possibility to operate even though in indoors
cases such as universities, playgrounds or even shopping malls [4][5]. Both solutions Triangulation, Trilateration and
Multilateration are presented as a suitable candidate for such systems. In this study, we start by finding the state-of-
the-art tracking algorithms using multilateration that could be integrated in SAR systems. After that these algorithms
are evaluated for position localization in terms of position accuracy as well as per cent distance error on estimation.
The rest of this work is organized as follows: The next section introduces the Localization techniques whereas
Section 3 refers to the SAR topology and algorithms study on multilateration scenario. Section 4 describes the
performance experiments and results analysis. Section 5 includes the conclusions as well as discusses the future
work and remarks on the implemented system.
2. Localization
In the world of real time location systems, a number of loosely woven technologies have been introduced in order
to track people and objects in real time. Location tracking is not at all a recent phenomenon. One major aspect of a
location tracking system is the basic mathematical computation that determines the exact location. These days,
navigation techniques remain relatively similar, replacing stars and landmarks with satellites and radio towers.
Fortunately, there’s not one but three major ways of determining a location - namely, triangulation, trilateration and
multilateration.

Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299 293
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
The 15th International Conference on Future Networks and Communications (FNC)
August 9-12, 2020, Leuven, Belgium
Time Difference of Arrival Localization Study for SAR Systems
over LoRaWAN
Christos Bourasa*, Apostolos Gkamasb, Vasileios Kokkinosa, Nikolaos Papachristosa
aComputer Engineering and Informatics Dept., Univ. of Patras, Greece
bUniversity Ecclesiastical Academy of Vella, Greece
Abstract
Over the last years we have seen a rapid expansion within the area of Internet of Things (IoT) applications. For many
applications’ use cases, such as rescue monitor systems, the problem of localization (i.e. determine the physical location of
nodes) is critical. This paper studies and evaluates the usage of mathematical model of multilateration algorithms using Time
Difference of Arrival (TDoA) as a solution for positioning over Long Range Wide Area Network (LoRaWAN). The research is
carried out using simulations in Python by configuring the constant positions of the Gateways inside an outdoor area. The
proposed algorithms can be integrated in application for tracking people at any time and especially routing people from
vulnerable groups. Through multilateration and algorithm’s prediction, we can have an accuracy of 40-60m in location
positioning ideal for search and rescue use cases.
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
Keywords: ΙοΤ; wireless network; lorawan; TDoA; search and rescue application; mulilateration;
1. Introduction
With the emergence of the Internet of Things (IoT), a growing number of low-cost devices intended to operate on
their own for extended periods of time, often far away from WiFi access points. For this reason, Low Power Wide
Area Network (LPWAN) technologies have attracted a lot of research attention from companies and global
* Corresponding author. Tel.: +30 2610 996951;
E-mail address: bouras@cti.gr
Available online at www.sciencedirect.com
ScienceDirect
Procedia Computer Science 00 (2020) 000–000
www.elsevier.com/locate/procedia
1877-0509 © 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
The 15th International Conference on Future Networks and Communications (FNC)
August 9-12, 2020, Leuven, Belgium
Time Difference of Arrival Localization Study for SAR Systems
over LoRaWAN
Christos Bourasa*, Apostolos Gkamasb, Vasileios Kokkinosa, Nikolaos Papachristosa
aComputer Engineering and Informatics Dept., Univ. of Patras, Greece
bUniversity Ecclesiastical Academy of Vella, Greece
Abstract
Over the last years we have seen a rapid expansion within the area of Internet of Things (IoT) applications. For many
applications’ use cases, such as rescue monitor systems, the problem of localization (i.e. determine the physical location of
nodes) is critical. This paper studies and evaluates the usage of mathematical model of multilateration algorithms using Time
Difference of Arrival (TDoA) as a solution for positioning over Long Range Wide Area Network (LoRaWAN). The research is
carried out using simulations in Python by configuring the constant positions of the Gateways inside an outdoor area. The
proposed algorithms can be integrated in application for tracking people at any time and especially routing people from
vulnerable groups. Through multilateration and algorithm’s prediction, we can have an accuracy of 40-60m in location
positioning ideal for search and rescue use cases.
© 2020 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Peer-review under responsibility of the Conference Program Chairs.
Keywords: ΙοΤ; wireless network; lorawan; TDoA; search and rescue application; mulilateration;
1. Introduction
With the emergence of the Internet of Things (IoT), a growing number of low-cost devices intended to operate on
their own for extended periods of time, often far away from WiFi access points. For this reason, Low Power Wide
Area Network (LPWAN) technologies have attracted a lot of research attention from companies and global
* Corresponding author. Tel.: +30 2610 996951;
E-mail address: bouras@cti.gr
2 Author name / Procedia Computer Science 00 (2018) 000–000
organizations. Practically the above technology allows such devices to communicate across large distances (up to
20km under good conditions), using comparatively low power. The ability to geolocate such device is often on
interest on many use cases such as rescue monitor systems of vulnerable groups in need. In its basic implementation,
it involves the generation of a set of geographic coordinates and is closely related to the use of positioning systems.
Such an application service built-in using LoRaWAN can be useful for area-based location positioning, with the
advantage of requiring fewer and low-cost devices with long-lasting batteries. LoRa operates in various frequencies
depending on the region, such as 868 MHz for Europe and 915 MHz for North America.
Geolocation can also be achieved through Global Positioning System (GPS) [1], but such a module can be enough
costly. Furthermore, a GPS module can also increase power consumption, making some applications unfeasible to be
used in everyday life or in area with buildings or interference factors. In a Search And Rescue (SAR) use case the
goal is to locate people in need such as track them as they move or by creating geo-fences, for example, sending an
alert if the person in need moves outside a defined area, like a child in a neighborhood. For localization of IoT
devices, the state of the art technology, in terms of accuracy, is GPS. In most modern GPS modules, an accuracy of
less than 10m can be observed in an open outdoor environment. Based on this the above solution is quite attractive
for Search and Rescue Systems. Using GPS IoT modules consumes more than 10 times the energy of LoRa, when
localization packets are sent to the same rate [2]. The difference can even be up to 20 times, if LoRa is configured in
an efficient way on both Spreading Factors and Bandwidth Factors. In addition to a GPS module, a device will also
require an extra module for communication. Having this in mind, it would be more appealing to use a Low-Power
Wide-Area Network (LPWAN) for the communication and localization [3].
Two technologies that can be used in a LPWAN are LoRa and Sigfox. Sigfox is an Ultra Narrowband (UNB),
wireless communication technology owned by a company of the same name. Sigfox, is aimed at IoT devices thus,
one of the services it offers is Geolocation. The localization algorithm that it uses is trilateration with RSSI ranging.
Many times, Sigfox use machine learning techniques in order to improve the accuracy of the position. However, this
technology is able to locate devices with an accuracy precision (<500m), using information from nearby Wi-Fi
access points which is compared to crowd-sourced data. In this research, a position accuracy improvement has been
introduced within a radius of 200m. Similar results have been achieved, where LoRa is used for positioning, using
RSSI. They achieve an accuracy of less than 20m in a small area. SigFox and LoRa are both capable of
communication over many kilometers even in Line of Sight (LoS) or not. However, in this research we test
localization algorithms of in terms of multilateration able to be integrated in SAR systems as an extension to
localization methodologies from previous studies.
In this paper, we describe our approach based on IoT devices and on the deployment of various LoRaWAN
gateways from localization perspective. Through the estimation of the behavior of a LoRaWAN channel and using
multilateration, the localization of a person inside an area can be obtained within a small range (about 40-60m). The
proposed approach is a low power and cost solution, and with a good possibility to operate even though in indoors
cases such as universities, playgrounds or even shopping malls [4][5]. Both solutions Triangulation, Trilateration and
Multilateration are presented as a suitable candidate for such systems. In this study, we start by finding the state-of-
the-art tracking algorithms using multilateration that could be integrated in SAR systems. After that these algorithms
are evaluated for position localization in terms of position accuracy as well as per cent distance error on estimation.
The rest of this work is organized as follows: The next section introduces the Localization techniques whereas
Section 3 refers to the SAR topology and algorithms study on multilateration scenario. Section 4 describes the
performance experiments and results analysis. Section 5 includes the conclusions as well as discusses the future
work and remarks on the implemented system.
2. Localization
In the world of real time location systems, a number of loosely woven technologies have been introduced in order
to track people and objects in real time. Location tracking is not at all a recent phenomenon. One major aspect of a
location tracking system is the basic mathematical computation that determines the exact location. These days,
navigation techniques remain relatively similar, replacing stars and landmarks with satellites and radio towers.
Fortunately, there’s not one but three major ways of determining a location - namely, triangulation, trilateration and
multilateration.

294 Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299
Author name / Procedia Computer Science 00 (2018) 000–000 3
2.1. Triangulation
In out of the three techniques, triangulation is the only one that measures angles rather than distance, and it is a
preferred technique by the surveyors and researches. Building a SAR system through triangulation starts by initiate
two points (point 1 and point 2) with a known distance between them, which is established as the baseline. From
these two points, the researchers measure the angle made by lines from distant points intersecting with the base line
using a device called Theodolite. These angles are then used to determine the unknown distances and thus locate the
distant points.
Fig. 1 Geolocation based on triangulation
If the known points are replaced with anchors in terms of a SAR system, at least 2 anchors are required to
determine a location in a Two-dimensional (2D) space and at least three anchors would be required to determine a
location in a Three-dimensional (3D) space. Triangulation as a methodology, mostly finds use in Navigation,
Metrology and Astrometry. It is also an ideal candidate when surveying a hilly area due to the ease of establishing
stations at appropriate distances and areas, the LoS (Line of Sight) is hugely impacted and can only be overcome by
the use of towers, which escalates the cost to a high degree [6].
2.2. Trilateration
Trilateration is a more popular technique that is also used by the traditional GPS. Trilateration pinpoints a
location by measuring distance. The general idea is that a satellite broadcast a signal for a GPS receiver to pick up.
This is how the distance between a satellite and a GPS receiver is known. Similarly, when 3 such satellites come
into contact with the GPS receiver, the exact location is determined. In Fig. 2, it can be seen that each satellite is at
the center of a circle. The intersection of the circles gives the location of the GPS receiver. As the GPS receiver
moves, so does the point of intersection of the circles.
Fig. 2 Geolocation based on trilateration
4 Author name / Procedia Computer Science 00 (2018) 000–000
In real-world scenario, the circles become spheres, and thus 4 satellites are required to pinpoint the location with
better accuracy. Following our previous research on trilateration for a SAR system, we used the multiple
associations that a LoRaWAN node establishes with surrounding GWs. The GWs in our area receive a packet from
a LoRaWAN IoT device and forward it to the network server. This leads the network server to have multiple copies
of the same package. Next step was to filter the duplicate copies and send a unique copy to the application service.
The above data can be extracted through the application service by developing a simple API. Message Queuing
Telemetry Transport (MQTT) [7] can be used to obtain the above information. The basic concept is the deployment
of a broker, publishers / subscribers and topic creation. The critical condition in a SAR system is that in any position
inside an area the client has connectivity with a minimum of three GWs so that we can benefit of trilateration. The
locations of the GWs inside a SAR system are to be installed and the total number of required GWs is strongly
dependent on the context in which the localization process has to take place. The setup of the LoRaWan GWs has to
be done into consideration of factors like the size of the area that we want to cover, the number of devices that can
be tracked and any buildings that may be inside [8].
2.3. Multilateration through TDoA
Multilateration relies on the time difference in the arrival of signals to various base stations. Through the
literature on positioning systems this technique used for indoor and also outdoor positioning in confined regions [9].
For this reason, we extend our previous research about trilateration by integration Multilateration in a SAR system.
The popular positioning methodology known as Time Difference of Arrival (TDoA) uses multilateration in which
the base stations (LoRa GWs) need to be synchronized. In this method, the end-nodes (people in need) send out data
packets with their information that are received by the established GWs. The difference in the time of reception
between the GWs is the basis of the distance calculation and, ultimately, the calculation to locate the object. The
principle behind multilateration is similar to trilateration, except that there’s no circle or sphere here; TDoA is
known as one of the most accurate and power-optimized technique for localization. This method does not require the
exact distance from an end-node to each GW but rather, only the differences in distance from each gateway to the
device. The difference in distances can be calculated with the TDoA of a signal from a device to the GWs. [10].
TDoA is a popular technique for localization as it does not require the transmitter to be synchronized with the
receivers. This is because TDoA only requires the differences between the timestamps of a transmission. Let us give
a SAR scenario where we have to locate an end-node (person in need) in a unknown distance from our established
GWs. When a LoRa signal is transmitted from a device, it is received by n gateways (where n is the number of
established GWs). These gateways will be our anchor points because we know their exact locations (longitude and
latitude). Each gateway will be at a slightly different distance to the device therefore, they will receive the LoRa
transmission at different instances in time. Because TDoA uses the difference in time, there is one measurement for
each possible pair of GWs. The total number of possible pairs is a binomial coefficient:
2
n



. For each GW pairs,
the TDoA can be presented by
,ij j i
t tt
, where 1

i < j

n and,
i
t
and
j
t
are the timestamps of the GWs.
By using the time difference from all the possible gateway pairs, we can calculate the position of the transmitter if
the signal was received by at least three GWs. The time differences can be referred as the TDoA measurement and
the distance as TDoA distance. The distance is extracted from the mathematical formula below:
,,ij ij
d ct
,
where c is the speed of light through air. By using TDoA for distance calculation we can create a hyperbola
consisting of all the possible points of where the end-node (person in need) could be. The general 3D range
equations for source localization using TOA and TDOA are: TOA:
2 2 2 1/ 2
[( )( )( )]
ii i i
st x x y y z z   
(1)
and TDOA:
2 2 2 1/ 2
2 2 2 1/2
[( )( )( )]
[( )( )( )],
, 1,...,
ij i i i
j jj
st x x y y z z
xx yy zz
ij N
     
    

(2) where s is the signal propagation velocity,
i
t
is the signal
traveling time from the source to GW, and
ij

the time difference as described above. The terms x,y,z are the

Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299 295
Author name / Procedia Computer Science 00 (2018) 000–000 3
2.1. Triangulation
In out of the three techniques, triangulation is the only one that measures angles rather than distance, and it is a
preferred technique by the surveyors and researches. Building a SAR system through triangulation starts by initiate
two points (point 1 and point 2) with a known distance between them, which is established as the baseline. From
these two points, the researchers measure the angle made by lines from distant points intersecting with the base line
using a device called Theodolite. These angles are then used to determine the unknown distances and thus locate the
distant points.
Fig. 1 Geolocation based on triangulation
If the known points are replaced with anchors in terms of a SAR system, at least 2 anchors are required to
determine a location in a Two-dimensional (2D) space and at least three anchors would be required to determine a
location in a Three-dimensional (3D) space. Triangulation as a methodology, mostly finds use in Navigation,
Metrology and Astrometry. It is also an ideal candidate when surveying a hilly area due to the ease of establishing
stations at appropriate distances and areas, the LoS (Line of Sight) is hugely impacted and can only be overcome by
the use of towers, which escalates the cost to a high degree [6].
2.2. Trilateration
Trilateration is a more popular technique that is also used by the traditional GPS. Trilateration pinpoints a
location by measuring distance. The general idea is that a satellite broadcast a signal for a GPS receiver to pick up.
This is how the distance between a satellite and a GPS receiver is known. Similarly, when 3 such satellites come
into contact with the GPS receiver, the exact location is determined. In Fig. 2, it can be seen that each satellite is at
the center of a circle. The intersection of the circles gives the location of the GPS receiver. As the GPS receiver
moves, so does the point of intersection of the circles.
Fig. 2 Geolocation based on trilateration
4 Author name / Procedia Computer Science 00 (2018) 000–000
In real-world scenario, the circles become spheres, and thus 4 satellites are required to pinpoint the location with
better accuracy. Following our previous research on trilateration for a SAR system, we used the multiple
associations that a LoRaWAN node establishes with surrounding GWs. The GWs in our area receive a packet from
a LoRaWAN IoT device and forward it to the network server. This leads the network server to have multiple copies
of the same package. Next step was to filter the duplicate copies and send a unique copy to the application service.
The above data can be extracted through the application service by developing a simple API. Message Queuing
Telemetry Transport (MQTT) [7] can be used to obtain the above information. The basic concept is the deployment
of a broker, publishers / subscribers and topic creation. The critical condition in a SAR system is that in any position
inside an area the client has connectivity with a minimum of three GWs so that we can benefit of trilateration. The
locations of the GWs inside a SAR system are to be installed and the total number of required GWs is strongly
dependent on the context in which the localization process has to take place. The setup of the LoRaWan GWs has to
be done into consideration of factors like the size of the area that we want to cover, the number of devices that can
be tracked and any buildings that may be inside [8].
2.3. Multilateration through TDoA
Multilateration relies on the time difference in the arrival of signals to various base stations. Through the
literature on positioning systems this technique used for indoor and also outdoor positioning in confined regions [9].
For this reason, we extend our previous research about trilateration by integration Multilateration in a SAR system.
The popular positioning methodology known as Time Difference of Arrival (TDoA) uses multilateration in which
the base stations (LoRa GWs) need to be synchronized. In this method, the end-nodes (people in need) send out data
packets with their information that are received by the established GWs. The difference in the time of reception
between the GWs is the basis of the distance calculation and, ultimately, the calculation to locate the object. The
principle behind multilateration is similar to trilateration, except that there’s no circle or sphere here; TDoA is
known as one of the most accurate and power-optimized technique for localization. This method does not require the
exact distance from an end-node to each GW but rather, only the differences in distance from each gateway to the
device. The difference in distances can be calculated with the TDoA of a signal from a device to the GWs. [10].
TDoA is a popular technique for localization as it does not require the transmitter to be synchronized with the
receivers. This is because TDoA only requires the differences between the timestamps of a transmission. Let us give
a SAR scenario where we have to locate an end-node (person in need) in a unknown distance from our established
GWs. When a LoRa signal is transmitted from a device, it is received by n gateways (where n is the number of
established GWs). These gateways will be our anchor points because we know their exact locations (longitude and
latitude). Each gateway will be at a slightly different distance to the device therefore, they will receive the LoRa
transmission at different instances in time. Because TDoA uses the difference in time, there is one measurement for
each possible pair of GWs. The total number of possible pairs is a binomial coefficient:
2
n



. For each GW pairs,
the TDoA can be presented by
,ij j i
t tt
, where 1

i < j

n and,
i
t
and
j
t
are the timestamps of the GWs.
By using the time difference from all the possible gateway pairs, we can calculate the position of the transmitter if
the signal was received by at least three GWs. The time differences can be referred as the TDoA measurement and
the distance as TDoA distance. The distance is extracted from the mathematical formula below:
,,ij ij
d ct
,
where c is the speed of light through air. By using TDoA for distance calculation we can create a hyperbola
consisting of all the possible points of where the end-node (person in need) could be. The general 3D range
equations for source localization using TOA and TDOA are: TOA:
2 2 2 1/ 2
[( )( )( )]
ii i i
st x x y y z z   
(1)
and TDOA:
2 2 2 1/ 2
2 2 2 1/ 2
[( )( )( )]
[( )( )( )],
, 1,...,
ij i i i
j jj
st x x y y z z
xx yy zz
ij N
     
    

(2) where s is the signal propagation velocity,
i
t
is the signal
traveling time from the source to GW, and
ij

the time difference as described above. The terms x,y,z are the

296 Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299
Author name / Procedia Computer Science 00 (2018) 000–000 5
coordinates for the position of the person in need in the SAR system. The possible location of the person in a SAR
system is given by a hyperbolic Line Of Position (LOP) in which the focal points of the hyperbola are the positions
of the two receivers used in the TDOA computation. Because TOA and TDoA have measurements errors, the
location of a person in need in a SAR scenario may be estimated by propagating the errors through the computation
and estimating the location along with errors in the estimates. In the 3D case, where we build our simulation, a
hyperboloid is defined by each TDoA, and at least three TDoAs need to intersect at a unique point to identify a
person in SAR system. Intersection of LOPs, a geometric construct is the most basic and intuitive method for
position estimation. Our research is based on the well-known methods that have been studied, developed, validated
and published in literature [11].
3. SAR Topology and Algorithm Literature
3D localization and tracking of people in a SAR system, requires at least four different GWs to form the
necessary nonlinear localization equations. From TDoA equation described above, the precision of the estimation of
a person can be estimated as a function of the errors in the measurements of GWs locations, TDoA, and signal
velocity [12]. In our research on the above algorithms we start by configure four different LoRa GWs in a specific
area of Western Greece (view positions in Fig. 3). The position of the person in SAR scenario was at (38.282200,
21.787980). The above locations that we view in Fig. 3 were used in the performance analysis that we studied in
which we try to estimate the position of a person using the algorithms in Table 1.
Fig. 3 Actual position of GWs and Wearable in SAR scenario
Table 1. Summary of TDoA Localization Algorithms in LoS Condition
Author, Year
Algorithm
Advantages/Disadvantages
Schmidt, 1972
LOCA: Location on the conic axis,
an alternative geometry to the
hyperbolic intersection plane (PX).
Provide a plane in 3 dimensions of
people position in SAR system
The GWs appear on the conic rather than at foci and thus the person’s
location appears at foci rather than on a hyperbola.
Friedlander, 1987
Weighted LS method
Derived a linearization algorithm to estimate person’s velocity from TDOA.
S. Robinson, 1987
Spherical Intersection (SX) method
Requires a priori solution for the actual position range.
Foy, 1976
Taylor-series, an iterative Gauss-
Newton method, gives LS solution
Requires an initial guess, not a start in application Convergence is not
proved. Is computationally expensive. Useful in solving multiple-
measurement, mixed-mode problems
4. Performance analysis and Results
The technique used in our research uses TDoA data measured at 4 synchronized GWs with known locations.
Following Schmidt algorithm introduced in 1972, appears person’s location at foci rather than a hyperbola [13].
6 Author name / Procedia Computer Science 00 (2018) 000–000
From the other hand Friedland introduced a Least Squares (LS) method, where a linearization algorithm is used to
estimate person’s position from TDoA [14]. Solutions like Robinson’s and Foy using Taylor Series, require a priori
solution or guess in order to estimate the actual position of an object or a person. Using the above algorithms we
start by studying the positioning accuracy and error as it emerged from the simulations in Python [15][16].
4.1. Positioning Accuracy
Table 2 includes the prediction of position estimation using the algorithms from Table 1. For the whole
simulation the position of the GWs is fixed. Using the mathematical model of each algorithm we are tried to
estimate the position of an IoT device in SAR use case.
Table 2. Results of Algorithms estimation about the position of person in SAR system.
Algorithm
Calculated
Longitude
Calculated Latitude
Actual Position
38,28220
21,78798
schauAndRobinson3
38,18953
21,86329
schauAndRobinson
38,32114
21,74945
friedlander3
38,26205
21,79862
friedlander
38,28242
21,78848
taylorSeries
38,27241
21,78800
schmidt
38,26232
21,78856
Via the Friedlander algorithm the calculated position of the person in need in the SAR use case as we can see is
(38.282424, 21.788484). The calculated position seems to be very close to the actual position. The other algorithms
seem to calculate the position of the IoT device with a deviation from the actual position. The worst accuracy with
the biggest deviation from the actual position is the prediction of the schauAndRobinson3 algorithm (38.18953,
21.86329).
Fig. 4 TDoA Position estimation based on algorithms
The natural significance of the above results is that the method of calculating the position using multilateration
in the case of the friedlander3 and taylorSeries calculates the position of a person more accurately. The location of
base stations or better GWs must be fixed in order to be accurate. Upon improving positioning accuracy, LoRa
shields offer great energy efficiency and make them an ideal choice for quick transmitters that can continuously
operate for over a week on a small battery bank. This is very useful in emergency situations such as people with
high probability to get lost as the accuracy of the position should be as high as possible.
4.2. Positioning Error
Fig. 5 depicts the distance error as calculated in our simulation using the algorithms from Table 1. The results in

Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299 297
Author name / Procedia Computer Science 00 (2018) 000–000 5
coordinates for the position of the person in need in the SAR system. The possible location of the person in a SAR
system is given by a hyperbolic Line Of Position (LOP) in which the focal points of the hyperbola are the positions
of the two receivers used in the TDOA computation. Because TOA and TDoA have measurements errors, the
location of a person in need in a SAR scenario may be estimated by propagating the errors through the computation
and estimating the location along with errors in the estimates. In the 3D case, where we build our simulation, a
hyperboloid is defined by each TDoA, and at least three TDoAs need to intersect at a unique point to identify a
person in SAR system. Intersection of LOPs, a geometric construct is the most basic and intuitive method for
position estimation. Our research is based on the well-known methods that have been studied, developed, validated
and published in literature [11].
3. SAR Topology and Algorithm Literature
3D localization and tracking of people in a SAR system, requires at least four different GWs to form the
necessary nonlinear localization equations. From TDoA equation described above, the precision of the estimation of
a person can be estimated as a function of the errors in the measurements of GWs locations, TDoA, and signal
velocity [12]. In our research on the above algorithms we start by configure four different LoRa GWs in a specific
area of Western Greece (view positions in Fig. 3). The position of the person in SAR scenario was at (38.282200,
21.787980). The above locations that we view in Fig. 3 were used in the performance analysis that we studied in
which we try to estimate the position of a person using the algorithms in Table 1.
Fig. 3 Actual position of GWs and Wearable in SAR scenario
Table 1. Summary of TDoA Localization Algorithms in LoS Condition
Author, Year
Algorithm
Advantages/Disadvantages
Schmidt, 1972
LOCA: Location on the conic axis,
an alternative geometry to the
hyperbolic intersection plane (PX).
Provide a plane in 3 dimensions of
people position in SAR system
The GWs appear on the conic rather than at foci and thus the person’s
location appears at foci rather than on a hyperbola.
Friedlander, 1987
Weighted LS method
Derived a linearization algorithm to estimate person’s velocity from TDOA.
S. Robinson, 1987
Spherical Intersection (SX) method
Requires a priori solution for the actual position range.
Foy, 1976
Taylor-series, an iterative Gauss-
Newton method, gives LS solution
Requires an initial guess, not a start in application Convergence is not
proved. Is computationally expensive. Useful in solving multiple-
measurement, mixed-mode problems
4. Performance analysis and Results
The technique used in our research uses TDoA data measured at 4 synchronized GWs with known locations.
Following Schmidt algorithm introduced in 1972, appears person’s location at foci rather than a hyperbola [13].
6 Author name / Procedia Computer Science 00 (2018) 000–000
From the other hand Friedland introduced a Least Squares (LS) method, where a linearization algorithm is used to
estimate person’s position from TDoA [14]. Solutions like Robinson’s and Foy using Taylor Series, require a priori
solution or guess in order to estimate the actual position of an object or a person. Using the above algorithms we
start by studying the positioning accuracy and error as it emerged from the simulations in Python [15][16].
4.1. Positioning Accuracy
Table 2 includes the prediction of position estimation using the algorithms from Table 1. For the whole
simulation the position of the GWs is fixed. Using the mathematical model of each algorithm we are tried to
estimate the position of an IoT device in SAR use case.
Table 2. Results of Algorithms estimation about the position of person in SAR system.
Algorithm
Calculated
Longitude
Calculated Latitude
Actual Position
38,28220
21,78798
schauAndRobinson3
38,18953
21,86329
schauAndRobinson
38,32114
21,74945
friedlander3
38,26205
21,79862
friedlander
38,28242
21,78848
taylorSeries
38,27241
21,78800
schmidt
38,26232
21,78856
Via the Friedlander algorithm the calculated position of the person in need in the SAR use case as we can see is
(38.282424, 21.788484). The calculated position seems to be very close to the actual position. The other algorithms
seem to calculate the position of the IoT device with a deviation from the actual position. The worst accuracy with
the biggest deviation from the actual position is the prediction of the schauAndRobinson3 algorithm (38.18953,
21.86329).
Fig. 4 TDoA Position estimation based on algorithms
The natural significance of the above results is that the method of calculating the position using multilateration
in the case of the friedlander3 and taylorSeries calculates the position of a person more accurately. The location of
base stations or better GWs must be fixed in order to be accurate. Upon improving positioning accuracy, LoRa
shields offer great energy efficiency and make them an ideal choice for quick transmitters that can continuously
operate for over a week on a small battery bank. This is very useful in emergency situations such as people with
high probability to get lost as the accuracy of the position should be as high as possible.
4.2. Positioning Error
Fig. 5 depicts the distance error as calculated in our simulation using the algorithms from Table 1. The results in

298 Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299
Author name / Procedia Computer Science 00 (2018) 000–000 7
this research vary based on factors used such as initial guesses, base stations positions, etc. As we can see from the
diagram below, the Distance Error of Friedlander is some meters from the actual position of the IoT device (50.6
meters). Next, taylorSeries estimation had a distance error of ~200 meters, while Friedlander3 and Schmidt
approached the error on about 1Km relative to the actual position. The worst cases seem to be schauAndRobinson3,
schauAndRobinson where the distance error is increasing to 6-7km.
Fig. 5 Distance statistical error on meters
As we mentioned in the case of position accuracy, our goal here is to reduce the margin of error in calculating
the position of a person or an IoT device. Fig. 6 shows the percent distance error in each different algorithm. As we
can see friedlander calculates the distance with the minimum error in comparison with schauAndRobinson and
friedlander3 whose error per cent is about 95-99%. This is very important in SAR cases while the accurac y of the
position must be a few metres, for familiar but also police or emergency services, fire brigades which must be
immediately called to the site [17].
Fig. 6 Percent Distance error
The above research is based on mathematical models and algorithms, so a practical study with real time
information could be also beneficial for our next steps. Some improvements on GWs positions, interferences from
close devices or improvements at transmission power, and improved path-loss model with similar LOS could lead to
better results. The above solutions could achieve even better localization accuracy as well as reduce the distance
error.
5. Conclusions and Future Work
This research has reviewed localization algorithms that apply TDoA in transmitter and receiver technologies for
a SAR case study. Compared with other signal source localization approaches and triangulation and trilateration,
TDoA is appropriate for applications that require high accuracy. For this reason, we focus on the simulation and
research study of some of the most known algorithms. We came to the result that many factors can influence the
8 Author name / Procedia Computer Science 00 (2018) 000–000
performance of localization algorithms in specific applications like SAR. Among these are the GWs positions,
actual size of the person in need, IoT limitations (lost connection to GWs, synchronization, channel structure,
battery life), mobility in network, environmental conditions as well as uncertainties in propagations (e.g Non Line
Of Sight (NLOS), multipath, sound speed variation and etc.). Despite that companies and research studies focus on
the development and improvements on both software and hardware the challenges on location estimation still exist
as they try to achieve high performance and accuracy with economical solutions on both hardware and software.
Next steps in our research study are the integration of the above algorithms on the development of the hardware
running on the SAR end-node so as to verify our research in practical experiments.
Acknowledgements
This research has been co-financed by the European Union and Greek national funds through the Operational
Program Competitiveness, Entrepreneurship and Innovation, under thecall RESEARCH - CREATE - INNOVATE
(project code:T1EDK-01520).
References
[1] Rashmi Bajaj, Samantha L. Ranaweera and Dharma Agrawal, “GPS: location-tracking technology,” in Computer, vol. 35, no. 4, pp. 92-94,
March 2002.
[2] Christophe Adrados, Irene Girard, Jean.P Gendner, and Georges Janeau.(2002) “Global positioning system (gps) location accuracy
improvement due to selective availability removal”, Comptes Rendus Biologies: 165–170.
[3] Ioannis Daramouskas, Vaggelis Kapoulas and Theodoros Pegiazis.(2019) “A survey of methods for location estimation on Low Power
Wide Area Networks,” 10th International Conference on Information, Intelligence, Systems and Applications (IISA): 1-4.
[4] Christos Bouras, Apostolos Gkamas,, Vassileios Kokkinos,, and Nikolaos Papachristos.(2019)“Using LoRa Technology for IoT Monitoring
Systems”, 10th International Conference on the Network of the Future (NoF 2019): 134-137.
[5] Federico Bonafini, Dhiego Fernandes Carvalho, Alessandro Depari, Paolo Ferrari, Alessandra Flammini, Marco Pasetti, Stefano Rinaldi,
and Emiliano Sisinni, “Evaluating indoor and outdoor localization services for LoRaWAN in Smart City applications”,II Workshop on
Metrology for Industry 4.0 and IoT (MetroInd4.0&IoT): 300-305.
[6] Wenjian Yan ; Ke Wang ; Ruifeng Li.(2019) “A Method for Position Estimation of Mobile Robot Based on Data Fusion” Chinese Control
And Decision Conference (CCDC): 5568-5572
[7] https://docs.oasis-open.org/mqtt/mqtt/v5.0/mqtt-v5.0.html
[8] Andrew Mackey and Petros Spachos.(2019) “LoRa-based Localization System for Emergency Services in GPS-less Environments,” IEEE
INFOCOM 2019 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS): 939-944.
[9] Wikipedia. http://en.wikipedia.org/wiki/Multilateration.
[10] Harvey C. Schau and A. Z. Robinson.(1987) “Passive source localization employing intersecting spherical surfaces from time-of-arrival
differences,” IEEE Trans. Acoust. Speech (35):1223–1225.
[11] Kai Yang, Jianping An, Xiangyuan Bu, and Gangcan Sun.(2010) “Constrained total least-squares location algorithm using time-difference-
of-arrival measurements,” IEEE Transactions on Vehicular Technology, (59):1558-1562.
[12] Zhu Guo-hui and Wang Yang.(2018) “An approximately efficient estimator for moving source localization using multiple-time TDOA
measurements,” 14th IEEE International Conference on Signal Processing (ICSP):934-938.
[13] Ralph Schmidt. (1972) “A new approach to geometry of range difference location,” IEEE Trans. Aerosp. Electron. Syst. (8):821–835.
[14] Benjamin Friedlander.(1987) “A passive localization algorithm and its accuracy analysis,” IEEE J. Oceanic Eng. (12):234–245.
[15] Foy, Wade.(1976) “Position-location solutions by Taylor-series estimation,” IEEE Trans. Aerosp. Electron. Syst, (12):187–194.
[16] James Smith and Jorge Abel.(1987) “The spherical interpolation method of source localization,” IEEE Journal of Oceanic Engineering:.
246-252.
[17] Bardia Alavi and Kaveh Pahlavan.(2006) “Modeling of the TOA-based distance measurement error using UWB indoor radio
measurements,” IEEE Communications Letters, 10 (4): 275-277.

Christos Bouras et al. / Procedia Computer Science 175 (2020) 292–299 299
Author name / Procedia Computer Science 00 (2018) 000–000 7
this research vary based on factors used such as initial guesses, base stations positions, etc. As we can see from the
diagram below, the Distance Error of Friedlander is some meters from the actual position of the IoT device (50.6
meters). Next, taylorSeries estimation had a distance error of ~200 meters, while Friedlander3 and Schmidt
approached the error on about 1Km relative to the actual position. The worst cases seem to be schauAndRobinson3,
schauAndRobinson where the distance error is increasing to 6-7km.
Fig. 5 Distance statistical error on meters
As we mentioned in the case of position accuracy, our goal here is to reduce the margin of error in calculating
the position of a person or an IoT device. Fig. 6 shows the percent distance error in each different algorithm. As we
can see friedlander calculates the distance with the minimum error in comparison with schauAndRobinson and
friedlander3 whose error per cent is about 95-99%. This is very important in SAR cases while the accurac y of the
position must be a few metres, for familiar but also police or emergency services, fire brigades which must be
immediately called to the site [17].
Fig. 6 Percent Distance error
The above research is based on mathematical models and algorithms, so a practical study with real time
information could be also beneficial for our next steps. Some improvements on GWs positions, interferences from
close devices or improvements at transmission power, and improved path-loss model with similar LOS could lead to
better results. The above solutions could achieve even better localization accuracy as well as reduce the distance
error.
5. Conclusions and Future Work
This research has reviewed localization algorithms that apply TDoA in transmitter and receiver technologies for
a SAR case study. Compared with other signal source localization approaches and triangulation and trilateration,
TDoA is appropriate for applications that require high accuracy. For this reason, we focus on the simulation and
research study of some of the most known algorithms. We came to the result that many factors can influence the
8 Author name / Procedia Computer Science 00 (2018) 000–000
performance of localization algorithms in specific applications like SAR. Among these are the GWs positions,
actual size of the person in need, IoT limitations (lost connection to GWs, synchronization, channel structure,
battery life), mobility in network, environmental conditions as well as uncertainties in propagations (e.g Non Line
Of Sight (NLOS), multipath, sound speed variation and etc.). Despite that companies and research studies focus on
the development and improvements on both software and hardware the challenges on location estimation still exist
as they try to achieve high performance and accuracy with economical solutions on both hardware and software.
Next steps in our research study are the integration of the above algorithms on the development of the hardware
running on the SAR end-node so as to verify our research in practical experiments.
Acknowledgements
This research has been co-financed by the European Union and Greek national funds through the Operational
Program Competitiveness, Entrepreneurship and Innovation, under thecall RESEARCH - CREATE - INNOVATE
(project code:T1EDK-01520).
References
[1] Rashmi Bajaj, Samantha L. Ranaweera and Dharma Agrawal, “GPS: location-tracking technology,” in Computer, vol. 35, no. 4, pp. 92-94,
March 2002.
[2] Christophe Adrados, Irene Girard, Jean.P Gendner, and Georges Janeau.(2002) “Global positioning system (gps) location accuracy
improvement due to selective availability removal”, Comptes Rendus Biologies: 165–170.
[3] Ioannis Daramouskas, Vaggelis Kapoulas and Theodoros Pegiazis.(2019) “A survey of methods for location estimation on Low Power
Wide Area Networks,” 10th International Conference on Information, Intelligence, Systems and Applications (IISA): 1-4.
[4] Christos Bouras, Apostolos Gkamas,, Vassileios Kokkinos,, and Nikolaos Papachristos.(2019)“Using LoRa Technology for IoT Monitoring
Systems”, 10th International Conference on the Network of the Future (NoF 2019): 134-137.
[5] Federico Bonafini, Dhiego Fernandes Carvalho, Alessandro Depari, Paolo Ferrari, Alessandra Flammini, Marco Pasetti, Stefano Rinaldi,
and Emiliano Sisinni, “Evaluating indoor and outdoor localization services for LoRaWAN in Smart City applications”,II Workshop on
Metrology for Industry 4.0 and IoT (MetroInd4.0&IoT): 300-305.
[6] Wenjian Yan ; Ke Wang ; Ruifeng Li.(2019) “A Method for Position Estimation of Mobile Robot Based on Data Fusion” Chinese Control
And Decision Conference (CCDC): 5568-5572
[7] https://docs.oasis-open.org/mqtt/mqtt/v5.0/mqtt-v5.0.html
[8] Andrew Mackey and Petros Spachos.(2019) “LoRa-based Localization System for Emergency Services in GPS-less Environments,” IEEE
INFOCOM 2019 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS): 939-944.
[9] Wikipedia. http://en.wikipedia.org/wiki/Multilateration.
[10] Harvey C. Schau and A. Z. Robinson.(1987) “Passive source localization employing intersecting spherical surfaces from time-of-arrival
differences,” IEEE Trans. Acoust. Speech (35):1223–1225.
[11] Kai Yang, Jianping An, Xiangyuan Bu, and Gangcan Sun.(2010) “Constrained total least-squares location algorithm using time-difference-
of-arrival measurements,” IEEE Transactions on Vehicular Technology, (59):1558-1562.
[12] Zhu Guo-hui and Wang Yang.(2018) “An approximately efficient estimator for moving source localization using multiple-time TDOA
measurements,” 14th IEEE International Conference on Signal Processing (ICSP):934-938.
[13] Ralph Schmidt. (1972) “A new approach to geometry of range difference location,” IEEE Trans. Aerosp. Electron. Syst. (8):821–835.
[14] Benjamin Friedlander.(1987) “A passive localization algorithm and its accuracy analysis,” IEEE J. Oceanic Eng. (12):234–245.
[15] Foy, Wade.(1976) “Position-location solutions by Taylor-series estimation,” IEEE Trans. Aerosp. Electron. Syst, (12):187–194.
[16] James Smith and Jorge Abel.(1987) “The spherical interpolation method of source localization,” IEEE Journal of Oceanic Engineering:.
246-252.
[17] Bardia Alavi and Kaveh Pahlavan.(2006) “Modeling of the TOA-based distance measurement error using UWB indoor radio
measurements,” IEEE Communications Letters, 10 (4): 275-277.