MULTI-ANTENNA LOCALIZATION METHOD

International Journal of Wireless & Mobile Networks (IJWMN) Vol. 9, No. 5, October 2017
DOI: 10.5121/ijwmn.2017.9503 23
MULTI-ANTENNA LOCALIZATION METHOD
John R Rankin
Federation University Australia
ABSTRACT
In a dense wireless network where sensor nodes run on batteries it is essential for the continued running of
the network, to be able to accurately locate and identify nodes that need battery replacement. Accurate
localization of nodes is also necessary for the correlation of sensed data with position in the environment
covered by the network. In this paper a new approach to node localization which is fine grained, range-
based, anchor free and GPS free, is presented which is cheap in hardware components and cheap in
software computation. It concerns the localization of cluster nodes relative to the cluster head and is
suitable for cases of stationary or slow moving nodes. The method is demonstrated for a simple one-level
wireless network.
KEYWORDS
WSN (Wireless Sensor Network), sensor node, RSSI, localization.
1. INTRODUCTION
The problem of determining the position of radio sources relative to a given detector location is a
common problem for which several solutions have been proposed and are also in use. The five
most commonly used methods are Lateration, Angulation, Trilateration, Multilateration and
Triangulation [1]. Each of these methods is well described in the review article [1]. Lateration is
based on distance measurements from the inverse square law for EMR signal intensity as are
likewise Trilateration and Multilateration. The distance between sites is determined by RSSI
measurements on the assumption that the signal intensity at the source is a known constant. In
another work [2] a method is given for computing the positions of sites when the distance matrix
(giving the distances between all sites) is known. Triangulation on the other hand involves the use
of directional antennas at points A and B which each point to the radio source at C the third point
of a triangle whose position is then computed trigonometrically. Angulation also uses directional
signal detection to obtain angles to the source which again can be used to compute relative
positions in 2D or 3D. Directional antennas make more efficient use of battery energy [5] but are
not applicable to networks with randomly placed nodes and dynamic connectivity architectures.
In general the use of directional antennas needs the direction of the antenna to rotate about a
vertical axis to sweep around the horizontal plane at constant speed similar to the use of naval
radar systems to search for input signals. However sweeping directional antennas contain
mechanical parts that wear out, consume battery power and require regular maintenance.
Mechanical moving parts are ultimately more expensive in maintenance and not suitable for the
field placement of the wireless nodes of a WSN. Other more complex designs for directional
antennas using electronic switching rather than moving parts have been considered [3, 4, 5, 7] and
these require additional circuitry and node battery power consumption. While a wide variety of
antenna types exist that may be used in WSNs [3, 6] few of the standard types of antenna are
simple, small, low cost and low power consumptive enough to be suitable [1]. A simpler
approach for determining the location of radio sources in the 2D plane using only omnidirectional
antennas and low battery power consumption is presented in this work.

24
2. DISTANCE MEASUREMENT WITH AN OMNI DIRECTIONAL ANTENNA
When a wireless node is transmitting data its antenna produces a signal strength of EMR (Electro-
Magnetic Radiation) which drops off according to the inverse square law. In suitable units for
signal strength , this law is:
where r is the horizontal distance from the node and 0ψ is the signal strength produced by the
node at its antenna which corresponds to r = 1 in suitable distance units. When a source is not
transmitting 0 0ψ = so then ( ) 0rψ = and no signal is detectable. For r < 1 we can assume that
0( )rψ ψ= and as such no anomalous infinities will occur.
An RSSI or signal strength detector is an antenna connected to an amplifier and then fed into an
ADC (analog to digital converter) chip. If the characteristic minimal signal strength differential
detectable by the detector is ψ∆ then the accuracy of the detector or minimum distinguishable
distance measurable is given by
This shows that the error in the distance measurement r∆ increases with the cube of the distance
from the source but that the error is less for stronger sources. For the accurate positioning of radio
sources we therefore need r and ψ∆ small and 0ψ large. The quantity ψ∆ is however a fixed
characteristic of the detector as provided by the manufacturer and so cannot be varied. In the
following discussions it will be assumed that the scale of the network R is much larger than r∆ so
that localization will be accurate. The radius of radio reach ρ of a source occurs at the distance
3. LOCALIZING IN 2D USING OMNIDIRECTIONAL ANTENNAS
Suppose that node A located at the origin in 2D has n fixed omnidirectional antennas for
detecting signal strength at known positions Ai relative to A in 2D for i = 1 to n. Suppose that
node A is required to detect the position of source node S which is within wireless range ρ of
node A. Denote the signal strength of node S detected at each detector antenna Ai by iψ . Then the
distance of node S from each detector antenna Ai is given by
( ) ( )
22 2
S ix S iy ix A y A r− + − =
for i = 1 to n. Subtracting equation 1 from equations 2 to n gives n-1 linear equations in 2
unknowns:
( ) ( ) { }2 2 2 2 2 21
1 1 1 1 12ix x S iy y S ix x iy y iA A x A A y A A A A r r− + − = − + − + −

25
Since we have two unknowns, xS and yS, it follows that a minimum of n = 3 detecting antennas is
sufficient to accurately pinpoint the location (xS,yS) of any source S. The position of the radio
source for n = 3 is then given by
{ }
{ }
{ }
{ }
2 1 3 1 3 1 2 1
2 2 2 2 2 2
1 2 1 2 1 1 2 3 1
2 2 2 2 2 2
2 3 1 3 1 1 3 2 1
2 2 2 2 2 2
1 2 1 3 1 3 1 1 3
2 2 2 2 2 2
2 3 1 2 1 2 1 1 2
( )( ) ( )( )
( )
( )
( )
( )
x x y y x x y y
x x x y y y y
x x x y y y y
y x x x x y y
y x x x x y y
D A A A A A A A A
D A A A A r r A A
D A A A A r r A A
D A A A A A A r r
D A A A A A A r r
x
= − − − − −
= − + − + − −
= − + − + − −
= − − + − + −
= − − + − + −
1 2
1 2
2
2
x x
S
y y
S
D D
D
D D
y
D
−
=
−
=
Such a setup of 3 omnidirectional antennas for a node is herein termed a localizator. The raw data
from the localizator is 1 2 3{ , , }ψ ψ ψ which must be converted to 1 2 3{ , , }r r r and all other
parameters in the above equations are known constants. It is assumed that the three antennas, A1,
A2 and A3, are set at the vertices of an equilateral triangle by the manufacturer and that the
localizator is placed with the orientation relative to the x and y axes as shown in figure 1.
However it does not matter whether the antennas A1, A2 and A3 are rotated about A by any angle
so long as this angle remains constant: the effect is only a rotation of the coordinate system and of
the local x and y axes relative to point A. In the frame of the localizator therefore the constants in
the above equations are
3 1
1 12 2
2 2
3 1
3 32 2
,
0,
,
x y
x y
x y
A b A b
A A b
A b A b
= = −
= =
= − = −
where b is the distance of any antenna from the centre of the node as set by the manufacturer.
This then assumes that we try to orient all placed nodes that have associated localizators such that
A2 always points to a given fixed distant landmark which determines the y direction in the plane.
(Of course we could have alternatively pointed A1 along the x axis and oriented all localizators
with A1 pointing to a specific distant landmark indicating the x direction in the 2D plane and the
triangle in Figure 1 would be rotated anticlockwise by 30 degrees.)

26
Figure 1 showing the positions of the antennas at A1, A2 and A3 relative to the node at A.
4. APPLICATION WSN
In this work we are concerned with a WSN which is structured as a mains powered base station
wirelessly connected to a number N1 of clusters (or “subnets”). The whole WSN is considered to
lie in a plane. Each cluster consists of an aggregator node as cluster head and N2 sensor nodes
surrounding the aggregator node [8]. The sensor nodes in a cluster send data to the aggregator
node of that cluster and the aggregator node relays the data on to the base station. For example in
the case of a subnet consisting of N2 = 4 sensor nodes, A, B, C and D, they will be arranged
roughly at the corners of a square of side length a and the aggregator node E is roughly at the
centre of the square and we want to establish accurate positioning of these nodes. This is the
process of localization. The base station should initiate the localization process and thereby tell
all nodes of the WSN to cease transmissions resulting in radio silence except for commands from
the base station. The base station then sends a signal to the first aggregator node telling it to
localize all N2 sensor nodes in its cluster. The aggregator node, say node E, is assumed to be at
the origin of 2D coordinates for its cluster. To do the localization task, node E sends a radio
signal to tell all its sensor nodes A, B, C … to cease transmissions until localization is finalized
and then node E asks each sensor node in its cluster in turn to transmit long enough for node E to
locate it using the localizator at E. Once all locations relative to E are known to E, then node E
sends the data to the base station. The base station also has a localizator and uses its own multi-
antenna RSSI detector to determine the coordinates of E relative to the base station. The base
station now has the coordinates of E and the sensors A, B, C … of the E subnet and then proceeds
to repeat this process for the second aggregator node in the WSN and so on. Once all nodes of the
WSN are located relative to the base station, the sensor nodes can return to their normal
operational transmission mode. Of course any node, in a subnet could do the localization process
but it is convenient if the task is undertaken by the aggregator for then only aggregator nodes and
not sensor nodes need to have multi-antenna RSSI detectors to save costs. If the aggregator nodes
are not all exactly oriented with their three antennas in the same orientations as the base station
then an adjustment in the code of the base station can compensate for this. To achieve this, each
aggregator should not only localize the sensor nodes of its own subnet, but it should also localize
the base station relative to the aggregator’s rotated coordinate system. When the aggregator sends
the base station the coordinates of the base station relative to the
aggregator, the base station can compare these coordinates with its own determination of the
aggregator’s coordinates relative to the base station. Let the coordinates of the aggregator relative
to the base station be ' ( ' , ' )x yu u u=
r
and the coordinates of the base station relative to the

27
aggregator in the aggregator’s rotated frame be ( , )x yu u u=
r
. If the aggregator’s frame of
reference is un-rotated relative to the base station’s frame of reference then 'u u= −
r r
otherwise
the base station computes the angle between the two vectors by
1
2
' '
cos
x x y yu u u u
r
θ π −
+ 
= −  
 
where r is the distance between the base station and the aggregator (according to either
localizator). The coordinates of any node A of the aggregator’s subnet in the base station’s frame
of reference is therefore:
' ' cos sin
' ' sin cos
x x x y
y y x y
A E A A
A E A A
θ θ
θ θ
= + −
= + +
where (Ax,Ay) are the coordinates of A relative to the aggregator E and (E’x,E’y) are the
coordinates of the aggregator E relative to the base station. The double (A’x,A’y) is the
coordinates of node A relative to the frame of reference of the base station. There is no problem
having the base station compute all node coordinates in its own frame of reference and store all
node positions in both the aggregator relative frame of reference and in the base station’s own
frame of reference because the base station is a full powered mains connected PC with large
memory, disk capacity and fast CPU. To deal with networks containing slow moving nodes, this
whole process of network localization as described above needs to be scheduled to be repeated at
regular intervals.
5. DISCUSSION
It is worth now considering the relative costs of this approach to localization. For the localization
scheme described here we need just 3 simple omnidirectional antennas with an amplifier and one
ADC (analog to digital converter) chip. The ADC chip is multiplexed between the 3 antennas so
that one rather than 3 ADC chips is required per detector/localizator. The antennas and amplifier
are of negligible cost compared with the ADC chip. Therefore in this design we only need to pay
for one ADC chip per subnet (since only the aggregator node requires an RSSI detector) and
therefore N1+1 ADC chips in total. By comparison in other schemes, every node and the base
station has a detector so requiring considerably more, namely 3N1N2+3, ADC chips without
multiplexing. Since battery life is an essential consideration in any WSN, we must also look at the
costs of on-board voltmeters for providing the battery level to the software of every node. The
digital voltmeter is essentially an ADC chip and so it adds to the cost of the node. The ADC chip
like other circuitry takes low power to run but also in sampling the input analog signal to convert
it to a digital signal the ADC consumes power from this input signal. In the case of taking power
from the antenna signal as input for a localizator this is negligible but in the case of an inbuilt
battery level meter the ADC is continually drawing power from and thus draining the battery.
Thus the ADC as a voltmeter continuously runs down the node’s battery (as with mobile phones
needing regular recharging even if not used). Battery operated computers regularly come with
battery level meters inbuilt as standard and so the recommendation here for extending the
working life of a WSN is to disable or remove this part of the hardware for the construction of all
nodes. Additionally digital voltmeters show hysteresis so that the State of Charge is not accurate
until long periods of use after which the batteries have also been run down. Also note that when a

28
node is receiving a signal from another node it does not need an ADC chip for this because the
signal is binary rather than having an arbitrary amplitude as in an analog signal. Thus it is
recommended here to remove all ADCs used for batteries in WSN nodes and only use one ADC
chip per localizator and only on the base station and on all aggregator nodes.
We can also optimize the WSN by adjusting the initial signal strength 0ψ if the nodes allow this
flexibility. There is no need to waste energy with 0ψ initially higher than necessary for the given
size of the WSN. The minimum necessary value of 0ψ for communication over a distance r is
2
m rψ ψ= ∆ so we only need 0 mψ ψ> . If 0ψ attenuates during operation due to battery depletion
then controlling 0ψ could extend the longevity of the WSN. Since distance measurement depends
crucially on knowing 0ψ and there is the possibility of 0ψ attenuating due to battery depletion we
adopt the following assumptions. Firstly the transmission hardware attempts to send signals of the
same constant intensity at the source 0ψ so far as the battery level permits. Secondly if the WSM
has non-moving nodes then the distances between nodes need only be measure once at the start of
the WSN: the localization process is only required at the start-up of the WSN. Thirdly if the
WSM has moving nodes or 0ψ is different for each node, then each node needs a localizator to
read its own local signal strength 0ψ and then it must broadcast this value so that other nodes will
make correct distance measurements.
A dense WSN can be defined as one where full connectivity is initially possible. If the whole
WSN fits into a circle of radius R and R ρ< then we have a dense WSN. The dense WSNs have
the advantage that the architecture and connectedness of the WSN can be dynamically changed:
nodes can be moved in and out of clusters as desired. So when a node has failed a replacement
can be swapped in to the subnet. With such density it is possible to have many nodes dormant (an
perhaps recharging with attached solar cells) and only becoming active when a cluster head has
removed a sensor node from the cluster because its radio radius ρ has dropped below the
distance between the sensor and its aggregator node: roughly 1 2/R N Nρ < . Even when 0ψ
for a node has dropped below the critical ψ∆ value there is still residual battery life left in its
battery and this could be used to light a flashing LED on the node whose rate of flashing slows
down to zero as the battery dies. In removing a dying sensor node from its cluster, the aggregator
should shut down all its functions and leave the battery only driving the flashing LED. The
flashing LED immediately lets the network manager know exactly which sensor node needs a
battery replacement.
6. CONCLUSIONS
Rather than using directional antennas to determine angles, the cheaper and simpler
omnidirectional antennas can be used for network localization provided each localizator has at
least 3 omnidirectional antennas in manufacturer fixed positions relative to the node. The
antennas should be spaced evenly at the corners of an equilateral triangle around the node which
will detect the relative locations of other nodes. The equations for the position (xS,yS) of a radio
source are linear and therefore quick to compute. The formulas for computing (xS,yS) can also be
put into the hardware circuitry for the localizator to speed up the localization process and reduce
the computational burden and energy consumption of a battery-based node. Alternatively the
aggregators can send their raw data 1 2 3{ , , }ψ ψ ψ to the base station and the calculation of (xS,yS),
the coordinates of a node relative to an aggregator and the calculation of (x’S,y’S), the coordinates
of that same node relative to the base station, are then all done on the more powerful base station

International Journal of Wireless & Mobile Networks (IJWMN)
PC. Note that not all nodes in the WSN need a localizator: only the base station and aggregator
nodes require a localizator thereby reducing equipment costs. However if nodes in the WSN can
move freely or is ad hoc, or if node radio signals are subject to considerable attenuation as the
battery discharges, then all nodes should have localizators. Furthermore the ADCs for batter
level readings should be disabled or removed from the nodes. This reduces the cost of the WSN
considerably. Further savings in the battery life of the aggregators can be achieved by less
frequent execution of the localization process when nodes are slow
optimizing 0ψ for all nodes also saves battery life.
REFERENCES
[1] N Alrajeh, M Bashir, B Shams, “Localization Techniques in Wireless Sensor Networks”,
International Journal of Distributed Sensor Networks, vol
Publishing Corporation.
[2] J Rankin, “Map Making From Tables”, International Journal of Computer Graphics and Animation,
April 2013, Vol 3, Nr 2.
[3] M Nilsson, “Directional Antennas for Wireless Sensor Networks”, Mart
P.O.B.1263, SE-164 29 Kista, Sweden from DOT adhoc09 AT drnil DOT com, 2009.
[4] L Mottola, T Voigt, G Picco, “Electronically
Networks: A Full-Stack Evaluation”, Sensor, Mesh and Ad Hoc Co
(SECON), 2013 10th Annual IEEE Communications Society Conference, June 2013.
[5] G Tarter, L Mottola, G Picco, “Directional Antennas for Convergecast in Wireless Sensor Networks:
Are They A Good Idea?”, University of Trento Italy,
[6] G Whyte, “Antennas for Wireless Sensor Network Applications”, PhD thesis, Department of
Electrical and Electronic Engineering, University of Glasgow, 2008.
[7] Q Wang, H Dai, Z Zheng, M Imran, A Vasilakos,
with Directional Antennas”, Sensors Journal, 17, 134, 22pp, 2017.
[8] J Rankin “Optimal Data Collection for a 2
and Mobile Networks, Vol 9, No 3, 2017.
AUTHOR
Dr J Rankin has undertaken research over 45 years starting with General Relativity and
Mathematical Physics at the University of Adelaide followed by Computer Graphics,
Fuzzy Logic Systems and Games Technology at La Trobe University and most recentl
Wireless Sensor Networks with Charles Sturt University Study Group Melbourne.
thereby reducing equipment costs. However if nodes in the WSN can
battery discharges, then all nodes should have localizators. Furthermore the ADCs for batter
frequent execution of the localization process when nodes are slow moving or static and
for all nodes also saves battery life.
N Alrajeh, M Bashir, B Shams, “Localization Techniques in Wireless Sensor Networks”,
International Journal of Distributed Sensor Networks, vol 2015, art 304628, 9 pp,2013 Hindawi
J Rankin, “Map Making From Tables”, International Journal of Computer Graphics and Animation,
M Nilsson, “Directional Antennas for Wireless Sensor Networks”, Martin Nilsson. SICS,
164 29 Kista, Sweden from DOT adhoc09 AT drnil DOT com, 2009.
L Mottola, T Voigt, G Picco, “Electronically-switched Directional Antennas for Wireless Sensor
Stack Evaluation”, Sensor, Mesh and Ad Hoc Communications and Networks
(SECON), 2013 10th Annual IEEE Communications Society Conference, June 2013.
G Tarter, L Mottola, G Picco, “Directional Antennas for Convergecast in Wireless Sensor Networks:
Are They A Good Idea?”, University of Trento Italy, http://disi.unitn.it/~picco/papers/mass16.pdf
G Whyte, “Antennas for Wireless Sensor Network Applications”, PhD thesis, Department of
Electrical and Electronic Engineering, University of Glasgow, 2008.
Q Wang, H Dai, Z Zheng, M Imran, A Vasilakos, “On Connectivity of Wireless Sensor Networks
with Directional Antennas”, Sensors Journal, 17, 134, 22pp, 2017.
J Rankin “Optimal Data Collection for a 2-Level Balanced WSN”, International Journal of Wireless
and Mobile Networks, Vol 9, No 3, 2017.
Dr J Rankin has undertaken research over 45 years starting with General Relativity and
Mathematical Physics at the University of Adelaide followed by Computer Graphics,
Fuzzy Logic Systems and Games Technology at La Trobe University and most recently
Wireless Sensor Networks with Charles Sturt University Study Group Melbourne.
, No. 5, October 2017
29
thereby reducing equipment costs. However if nodes in the WSN can
battery discharges, then all nodes should have localizators. Furthermore the ADCs for battery
moving or static and
N Alrajeh, M Bashir, B Shams, “Localization Techniques in Wireless Sensor Networks”,
2015, art 304628, 9 pp,2013 Hindawi
J Rankin, “Map Making From Tables”, International Journal of Computer Graphics and Animation,
in Nilsson. SICS,
switched Directional Antennas for Wireless Sensor
mmunications and Networks
G Tarter, L Mottola, G Picco, “Directional Antennas for Convergecast in Wireless Sensor Networks:
http://disi.unitn.it/~picco/papers/mass16.pdf
G Whyte, “Antennas for Wireless Sensor Network Applications”, PhD thesis, Department of
“On Connectivity of Wireless Sensor Networks
Level Balanced WSN”, International Journal of Wireless

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