INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 15 |NUMBER: 3 |2017 |SEPTEMBER
G ound Recei ing S a ion Re e ence Pai Selec ion
Technique o a Minimum Con igu a ion 3D Emi e
Posi ion Es ima ion Mul ila e a ion Sys em
Abdulmalik Shehu YARO1,2, Ahmad Zu i SHA’AMERI 1, Nidal KAMEL3
1Depa men o Elec onic and Compu e Enginee ing, Facul y o Elec ical Enginee ing,
Uni e si i Teknologi Malaysia, UTM Joho Bah u, 81310 Joho , Malaysia
2Depa men o Elec ical and Compu e Enginee ing, Facul y o Enginee ing,
Ahmadu Bello Uni e si y, Soko o Road, PMB 06 Za ia, Nige ia
3Depa men o Elec ical and Elec onic Enginee ing, Facul y o Enginee ing,
Uni e si i Teknologi Pe onas, 32610 Se i Iskanda , Malaysia
ya [email protected], zu i@ ke.u m.my, nidalk[email p o ec ed]
DOI: 10.15598/aeee. 15i3.2254
Abs ac . Mul ila e a ion es ima es ai c a posi ion
using he Time Di e ence O A i al (TDOA) wi h
a la e a ion algo i hm. The Posi ion Es ima ion (PE)
accu acy o he la e a ion algo i hm depends on se -
e al ac o s which a e he TDOA es ima ion e o , he
la e a ion algo i hm app oach, he numbe o deployed
GRSs and he selec ion o he GRS e e ence used o
he PE p ocess. Using he minimum numbe o GRSs
o 3D emi e PE, a echnique based on he condi-
ion numbe calcula ion is p oposed o selec he sui -
able GRS e e ence pai o imp o ing he accu acy o
he PE using he la e a ion algo i hm. Valida ion o
he p oposed echnique was pe o med wi h he GRSs
in he squa e and iangula GRS con igu a ion. Fo
he selec ed emi e posi ions, he esul shows ha he
p oposed echnique can be used o selec he sui able
GRS e e ence pai o he PE p ocess. A uni y con-
di ion numbe is achie ed o GRS pai mos sui able
o he PE p ocess. Mon e Ca lo simula ion esul , in
compa ison wi h he ixed GRS e e ence pai la e a-
ion algo i hm, shows a educ ion in PE e o o a
leas 70 % o bo h GRS in he squa e and iangula
con igu a ion.
Keywo ds
Condi ion numbe , la e a ion algo i hm, min-
imum con igu a ion, mul ila e a ion, e e ence
selec ion.
1. In oduc ion
Passi e wi eless posi ioning and na iga ion sys ems
u ilize ai c a ansponde emission which is de ec ed
wi h he suppo o an enna o a G ound Recei ing S a-
ion (GRS) o de e mining he posi ion o he ai c a .
De e mining he posi ion o an ai c a is a wo-s age
p ocess [1]. The i s s age in ol es he es ima ion o
he posi ion dependen signal pa ame e om he e-
cei ed ai c a ansponde emission. Some examples
o posi ion dependen signal pa ame e s a e he An-
gle O A i al (AOA), he Time O A i al (TOA),
he Time Di e ence O A i al (TDOA) and Recei e
Signal S eng h (RSS). In he second s age, he posi-
ion dependen signal pa ame e es ima ed a he i s
s age is inpu in o a Posi ion Es ima ion (PE) algo-
i hm o de e mine he posi ion o he ai c a . This
is known as he PE p ocess. Examples o he PE al-
go i hm used a he PE p ocess a e angula ion, inge -
p in ing and la e a ion. Mul ila e a ion sys em is an
example o a wi eless posi ioning sys em. The sys em
es ima es TDOA om he ecei ed ai c a anspon-
de emission as i s posi ion dependen signal pa ame-
e and uses he la e a ion algo i hm o de e mine he
ai c a posi ion [1], [2] and [3]. I consis s o se e al
specially placed GRSs all connec ed o a cen al p o-
cessing uni . Depending on he numbe o GRS de-
ployed, 2-Dimension (2D) o 3-Dimension (3D) posi-
ion o he ai c a is esol ed. Fo 3D PE, he e is a
minimum o ou GRSs needed [3]. Many s udies ha e
desc ibed me hods o TDOA es ima ion [4], [5], [6],
[7] and [8]. Fo example, [4] compa es TDOA es ima-
ion using c oss-co ela ion and as c oss-co ela ion
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o de e mine which me hod is as e o p ac ical and
heo e ical implemen a ion. In [8], Signal- o-Noise Ra-
io (SNR) is used o he benchma k o compa e he
pe o mance o i e di e en TDOA es ima ion ech-
niques.
The PE p ocess is he scope o his wo k. Depending
on he numbe o GRS (N), N−1nonlinea hype bolic
equa ions a e gene a ed [9]. Se e al app oaches de el-
oping he la e a ion algo i hms ha e been p oposed in
a icles [9], [10], [11], [12], [13], [14] and [15] which can
be g ouped in o wo as a linea and nonlinea app oach
[1] and [11]. The non-linea app oach in ol es he use
o linea app oxima ion and i e a i e me hods such as
Taylo ’s se ies expansion o pe o m PE [9], [10] and
[11]. The linea algo i hm in ol es algeb aically ma-
nipula ing he hype bolic equa ions o di ec ly se an
in e se p oblem ha linea ly ela es he unknown ai -
c a posi ion o he known TDOA measu emen s as
desc ibed in [12], [13], [14] and [15]. Due o he con-
e gence issue and he use o ini ial posi ion es ima ed
o he non-linea app oach [10], his s udy ocuses on
using he linea app oach o de eloping he la e a ion
algo i hm.
The linea la e a ion algo i hm has been cha ac e -
ized wi h high PE e o . Nume ous esea che s ha e
p oposed echniques such as weigh ing unc ions [16],
o al leas squa es [17] and Tikhono egula iza ion [9]
o imp o ing he PE accu acy o he la e a ion algo-
i hm. These echniques e icien ly o use bu equi e
a leas i e GRSs o be deployed. The minimum GRS
deployed o 3D PE is ou . Thus, hese echniques
canno be used o imp o e PE accu acy o he la e a-
ion algo i hm o 3D minimum con igu a ion.The use
o mo e han one GRS as a e e ence is sugges ed o
imp o ing he accu acy o he la e a ion algo i hm [6]
and [18]. The choice o he e e ence GRS has been
epo ed o imp o e he PE accu acy o he la e a ion
algo i hm [19], [20] and [21]. In [20], a TDOA esidual-
based me hod was p oposed o selec he sui able GRS
as a e e ence o PE wi h la e a ion algo i hm in an
ac i e sys em. I was assumed ha he emi e posi-
ion is known bu he e was he need o con inuously
ack he posi ion o he sys em using ano he sys em.
Using he known emi e posi ion, each o he deployed
GRS is used as a e e ence and he GRS ha esul ed
in he leas TDOA esidual is chosen as a e e ence o
subsequen es ima ion o he emi e posi ion. An SNR
based GRS e e ence selec ion me hod was p oposed in
[21]. Wi h he assump ion ha all noise powe a he
GRS emains cons an , he GRS wi h he highes e-
cei ed SNR is he closes o he emi e and i is he
mos sui able GRS o be used as a e e ence o he PE
wi h he la e a ion algo i hm. Using GRS pai as a e -
e ence o he la e a ion algo i hm, his s udy sugges s
a echnique o choose he sui able GRS e e ence pai
o he la e a ion algo i hm. The la e a ion algo i hm
conside ed is o he 3D minimum con igu a ion mul-
ila e a ion sys em. The sugges ed echnique in ol es
calcula ing he condi ion numbe o a de i ed ma ix
and choosing he GRS pai wi h he leas condi ion
numbe om he de i ed ma ix. The p oposed GRS
e e ence pai selec ion echnique is alida ed by com-
pa ison wi h he ixed GRS e e ence pai la e a ion
algo i hm, used in [12], wi h selec ed emi e posi ion
and he GRSs deployed in squa e and iangula con-
igu a ions.
The es o he pape is o ganized as ollows.
Sec ion 2. p esen s he mul ila e a ion PE me hodol-
ogy and PE condi ion numbe analysis. The p oposed
GRS e e ence pai selec ion echnique is desc ibed in
Sec. 3. The esul and discussion a e p esen ed in
Sec. 4. ollowed by he conclusion in Sec. 5.
2. Mul ila e a ion PE
Me hodology and Condi ion
Numbe Analysis
This sec ion desc ibes he a iable GRS e e ence pai
PE la e a ion algo i hm ollowed by he condi ion num-
be analysis o he mul ila e a ion PE ma hema ical
model o di e en GRS e e ence pai .
2.1. Va iable GRS Re e ence Pai
Mul ila e a ion PE
Me hodology
Le x= (x, y, z)be he coo dina e o a s a iona y emi -
e in 3D Euclidean space and Si= (xi, zi, zi). he co-
o dina e o he i- h GRS The dis ance a elled by he
elec omagne ic emission om he emi e posi ion o
he i- h GRS is calcula ed as:
di=c·τi=q(x−xi)2+ (y−yi)2+ (z−zi)2,(1)
whe e c= 3 ·108m·s−1is he speed o ligh and τiis
he p opaga ion ime o he signal om he emi e o
he i- h GRS.
The Pa h Di e ence (PD) be ween i- h and m- h
GRS pai is ob ained as:
di,m =q(x−xi)2+ (y−yi)2+ (z−zi)2−
+q(x−xm)2+ (y−ym)2+ (z−zm)2.
(2)
GRS pai is used as a e e ence o he la e a-
ion algo i hm. Le he i- h and j- h GRSs o be
chosen as e e ence pai wi h coo dina es (xi, ji, ki)
and (xj, jj, kj) espec i ely while he non- e e ence
GRSs a e labelled he m- h and n- h wi h coo dina es
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(xm, jm, km)and (xn, jn, kn) espec i ely. Using he
i- h GRS as a e e ence, wo independen PD equa-
ions a e ob ained [12] and exp essed in he ollowing:
di,n =di−dn,(3)
di,m =di−dm,(4)
while o he j- h e e ence GRS, he wo independen
PD equa ions a e ob ained as:
dj,n =dj−dn,(5)
dj,m =dj−dm.(6)
Combining Eq. (3) and Eq. (4) a e u he simpli i-
ca ion esul s in o 3D plane equa ion which is p esen ed
in [12] as ollows:
Ai,n,m =xBi,n,m +yCi,n,m +zDi,n,m,(7)
whe e he coe icien s o Eq. (7) a e:
Ai,n,m = 0.5di,m −di,n +ki,m
di,m
−ki,m
di,n ,(8)
Bi,n,m =Xn,i
di,n
−Xm,i
di,m
,(9)
Ci,n,m =Yn,i
di,n
−Ym,i
di,m
,(10)
Di,n,m =Zn,i
di,n
−Zm,i
di,m
,(11)
ki,w =x2
i+y2
i+z2
i−x2
w+y2
w+z2
w,(12)
Xi,w =xi−xw, Yi,w =yi−yw,(13)
Zi,w =zi−zw, w ∈[m, n].(14)
In addi ion, combining Eq. (5) and Eq. (6) a e u -
he simpli ica ion esul s in o ano he 3D plane equa-
ion as ollows:
Aj,n,m =xBj,n,m +yCj,n,m +zDj,n,m,(15)
whe e he coe icien s o Eq. (15) a e:
Aj,n,m = 0.5dj,m −dj,n +kj,m
dj,m
−kj,m
dj,n ,(16)
Bj,n,m =Xn,j
dj,n
−Xm,j
dj,m
,(17)
Cj,n,m =Yn,j
dj,n
−Ym,j
dj,m
,(18)
Dj,n,m =Zn,j
dj,n
−Zm,j
dj,m
,(19)
kj,w =x2
j+y2
j+z2
j−x2
w+y2
w+z2
w,(20)
Xj,w =xj−xw, Yj,w =yj−yw,(21)
Zj,w =zj−zw, w ∈[m, n].(22)
Equa ion (7) and Eq. (15) when ep esen ed in ma-
ix o m is:
Bi,n,m Ci,n,m Di,n,m
Bj,n,m Jj,n,m Dj,n,m·

x
y
z
=Ai,n,m
Aj,n,m,(23)
Qij ·x=aij.(24)
Equa ion (23) is known as he mul ila e a ion 3D
PE ma hema ical model o minimum GRS con igu-
a ion. The subsc ip “i,n,m” and “j,n,m” o
he en ies o he ma ices Qij and aij indica e ha
he en y is ob ained using he i- h and j- h GRS as
a e e ence espec i ely wi h he m- h and n- h GRS
as non- e e ence. The loca ion o he ai c a (x,y,z)
is ob ained by inding he in e se ma ix solu ion o
Eq. (23) wi h TDOA o PD measu emen s and GRSs
coo dina es as inpu .
2.2. Mul ila e a ion PE
Ma hema ical Condi ion
Numbe Analysis
In he p ac ical applica ion, he PD measu emen s a e
ob ained wi h e o s which a ec he solu ion ob ained
using ma ix Eq. (23). The e ec o he PD measu e-
men e o on he solu ion o ma ix Eq. (23) is de-
e mined by he sensi i i y o ma ix Qij de ined by
he condi ion numbe alue. The condi ion numbe o
a squa e ma ix indica es on how he e o in he in-
pu a iables is ampli ied o he solu ion ob ained us-
ing he sys em. Ma ix Qij in Eq. (24) is a ec angula
ma ix whose condi ion numbe canno be de e mined.
Assuming ha he GRSs ha e insigni ican heigh di -
e ence, ha is:
Zi,w =zi−zw≈0,(25)
Zj,w =zj−zw≈0,(26)
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Tab. 1: Ma ix Aij condi ion numbe o di e en GRS pai as e e ence. Yellow shade indica es he GRS pai wi h he leas
K(Aij ).
Range
(km)
Bea ing
(◦)
Al i ude
(km)
GRS e e ence pai condi ion numbe
i= 1
&
j= 2
i= 1
&
j= 3
i= 1
&
j= 4
i= 2
&
j= 3
i= 2
&
j= 4
i= 3
&
j= 4
560 1 17 21 4 19 10 30
50 1 87 59 17 64 50 99
5120 7 37 21 31 8 30 49
50 7 89 50 66 17 60 101
o all 1≤i≤4,1≤j≤4,1≤w≤4and i6=j6=w,
ma ix Qij can be educed o a squa e ma ix w i en
as:
Aij =Bi,n,m Ci,n,m
Bj,n,m Cj,n,m,(27)
whe e Di,n,m =Dj,n,m = 0.
Using he ma ix Aij, he condi ion numbe can be
ob ained and used in de e mining he e ec o PD mea-
su emen e o on he PE accu acy o he la e a ion
algo i hm. The condi ion numbe o ma ix Aij in
Eq. (27) deno ed as K(Aij)is ob ained as:
K(Aij) = kAijk2·
A−1
ij 
2,(28)
whe e kAijk2and 
A−1
ij 
2a e he 2-no m o ma ix
Aij and i s in e se espec i ely.
The 2-no m o he ma ix Aij and i s in e se a e
de ined wi h espec o en ies in Eq. (27) which ha e
been exp essed in [22].
kAijk2=
=q|Bi,m,n|2+|Ci,m,n|2+|Bj,m,n|2+|Cj,m,n|2,(29)

A−1
ij 
2=
=q|Bi,m,n|2+|Ci,m,n|2+|Bj,m,n|2+|Cj,m,n|2
de (Aij),
(30)
whe e de (Aij)is a de e minan o ma ix Aij ex-
p essed ma hema ically as:
de Aij = (Bi,m,n ·Cj,m,n)−(Bj,m,n ·Ci,m,n).(31)
Subs i u ing Eq. (29) and Eq. (30) in o Eq. (28),
he condi ion numbe he ma ix Aij as unc ion o i s
en ies can be w i en as Eq. (32).
Equa ion (32) ep esen s he condi ion numbe o
ma ix Aij in Eq. (27) whose en ies a e ob ained
using he i- h and j- h GRS pai as a e e ence wi h he
m- h and n- h as non- e e ence GRSs. Fo an emi e
a a s a iona y posi ion wi h a ixed GRS con igu a ion,
di e en GRS pai (i, j)will p oduce di e en en ies
o ma ix Aij. This will esul in di e en condi ion
numbe alue in Eq. (32). Highe condi ion numbe
alues indica e g ea e e o in he solu ion ob ained
using Eq. (23). Table 1 shows he condi ion numbe
o he ma ix Aij using Eq. (32) o di e en GRS
pai (i, j)a ou emi e posi ions wi h GRS in he
squa e con igu a ion. Emi e posi ions a e gi en in
cylind ical coo dina e sys em. The condi ion numbe
di e s o di e en emi e posi ions and GRS e e -
ence pai s. A ixed emi e posi ion, di e en GRS
pai p oduces di e en condi ion numbe s. A emi -
e posi ion (5 km, 60◦, 1 km), GRS pai i= 1 and
j= 4 has he leas condi ion numbe alue while GRS
pai i= 3 and j= 4 has he highes condi ion numbe
alue. A emi e posi ion (50 km, 120◦, 7 km), GRS
pai i= 2 and j= 3 has he leas condi ion numbe
alue while i= 3 and j= 4 has he highes condi ion
numbe alue. Fo each emi e posi ion, he pai wi h
he leas condi ion numbe alue,used as a e e ence o
he la e a ion algo i hm, will esul in he emi e po-
si ion es ima ed wi h he leas e o . This means ha
o emi e posi ions (5 km, 60◦, 1 km) and (50 km,
60◦, 1 m), he sui able GRS pai as a e e ence a e he
i= 1 and j= 4. Fo emi e posi ions (5 km, 120◦,
7 km) and (50 km, 120◦, 7 km), he sui able GRS pai s
as a e e ence a e i= 2 and j= 3.
GRS e e ence selec ion o PE is ca ied ou p io
o he ac ual PE p ocess. The a ailable pa ame e s
ela ed o he emi e posi ion which can be used o
selec ing he sui able GRS pai as a e e ence a e he
PD measu emen s only. Thus, he condi ion numbe
ob ained om ma ix Aij in Eq. (27) canno be used
since i is a unc ion o bo h PD measu emen s and
GRS coo dina e. In nex sec ion, he app oach is de-
eloped o de e mine he sui able GRS e e ence pai
o be selec ed o he PE p ocess.
3. P oposed GRS Re e ence
Pai Selec ion Technique
In his sec ion, he echnique o selec ion o he sui -
able GRS e e ence pai o he PE p ocess is p e-
sen ed. In Subsec. 2.2. , i was concluded ha us-
ing ma ix Aij o de e mine he sui able GRS pai as
a e e ence o PE is no possible. Ma ix Aij can
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K(Aij) = |Bi,m,m|2+|Ci,m,m|2+|Bj,m,m|2+|Cj,m,m|2
(Bi,m,m ·Cj,m,m)−(Bj,m,m ·Ci,m,m).(32)
Aij =



Xm,i
di,m
−Xn,i
di,n  Ym,i
di,m
−Yn,i
di,n 
Xm,j
dj,m −Xn,j
dj,n Ym,j
dj,m
−Yn,j
dj,n 



=



(Xm,idi,n −Xn,idi,m)
di,mdi,n
(Ym,idi,n −Yn,idi,m)
di,mdi,n
(Xm,jdj,n −Xn,jdj,m)
dj,mdj,n
(Ym,jdj,n −Yn,jdj,m)
dj,mdj,n




=
=(di,m ·di,n)−10
0 (dj,m ·dj,n)−1·(Xm,idi,n −Xn,idi,m) (Ym,idi,n −Yn,idi,m)
(Xm,jdj,n −Xn,jdj,m) (Ym,j dj,n −Yn,j dj,m),
(33)
be spli in o wo ma ices while one o he ma ices
is ha ing only he PD measu emen s as i s en ies.
F om Eq. (27), he ma ix Aij is w i en as Eq. (33).
Le
Mij =(di,m ·di,n)−10
0 (dj,m ·dj,n)−1.(34)
Nij =
(Xm,idi,n −Xn,idi,m) (Ym,idi,n −Yn,idi,m)
(Xm,j dj,n −Xn,j dj,m) (Ym,j dj,n −Yn,j dj,m).(35)
Then
Aij =Mij ·Nij.(36)
Ma ix Mij and Nij a e bo h squa e ma ices. The
ma ix Mij is ha ing only PD measu emen s ob ained
using any possible GRS pai (i, j)as i s en ies. This
ma ix can be used ins ead o ma ix Aij o condi ion
numbe calcula ion o de e mine he sui able GRS pai
as a e e ence o he PE p ocess. The condi ion num-
be o ma ix Mij as a unc ion o he PD measu emen
is ob ained as Eq. (37).
Fu he simpli ica ion o Eq. (37) will esul in:
K(Mij) = dj,m ·dj,n
di,m ·di,n +di,m ·di,n
dj,m ·dj,n .(38)
Using Eq. (38), he condi ion numbe s o all he
possible GRS pai s a e ob ained. The pai wi h he
leas condi ion numbe is chosen as a e e ence o he
PE p ocess wi h he la e a ion algo i hm. The sum-
ma y o he p ocedu e o selec ion o GRS e e ence
pai o ou numbe s o GRSs is desc ibed as ollows:
•Ob ain he PD measu emen se using Eq. (39) o
each o he possible GRS pai (i, j)as e e ences
as shown below.
di,j,m,n = [di,m, di,n, dj,m, dj,n].(39)
•Using he PD measu emen se om (i) o each
GRS pai , subs i u e in o Eq. (38) and sol e o
K(Mij).
•Choose he GRS pai wi h he leas K(Mij) alue
om s ep (ii) as he e e ence pai o he PE p o-
cess wi h he la e a ion algo i hm.
4. Resul s and Discussion
In his sec ion, he echnique o he selec ing he sui -
able GRS e e ence pai based on he condi ion numbe
which is calcula ed using Eq. (38) o he PE using he
la e a ion algo i hm is alida ed. This is done wi h a
compa ison o he condi ion numbe which has been
ob ained using Eq. (38) wi h he suppo o Eq. (32).
Valida ion is ca ied ou o some selec ed emi e po-
si ions wi h GRSs in he squa e and iangula con-
igu a ion as shown in Fig. 1. I has been es ablished
−15 −10 −5 0 5 10 15
−15
−10
−5
0
5
10
15
X−coo dina e (km)
Y−coo dina e (km)
GRS−1
GRS−2
GRS−3
GRS−4
(a) Squa e GRS con igu a ion.
−15 −10 −5 0 5 10 15
−15
−10
−5
0
5
10
15
X−coo dina e (km)
Y−coo dina e (km)
GRS−1
GRS−2
GRS−3
GRS−4
(b) T iangula GRS con igu a ion.
Fig. 1: Squa e and iangula GRS con igu a ion wi h GRS sep-
a a ion o 10 km.
c
2017 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 395

INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 15 |NUMBER: 3 |2017 |SEPTEMBER
KMij =1
de (Mij)· kMijk2
2=


(di,m ·di,n)−10
0 (dj,m ·dj,n)−1



2
2
de (di,m ·di,n)−10
0 (dj,m ·dj,n)−1=
=q(di,m ·di,n)−2+ (dj,m ·dj,n)−22
(di,m ·di,n ·dj,m ·dj,n)−1= (di,m ·di,n ·dj,m ·dj,n)· 1
(di,m ·di,n)2+1
(dj,m ·dj,n)2!.
(37)
ha he GRS pai wi h he leas condi ion numbe is
he sui able GRS pai as a e e ence o he la e a ion
algo i hm.
Fo each o he GRS con igu a ions, he alida ion o
he p oposed GRS e e ence pai selec ion echnique is
ca ied ou o he emi e posi ions which a e de ined
in Tab. 2.
Tab. 2: Emi e posi ions o alida ion.
No. Emi e
posi ion
Range
(km)
Al i ude
(km)
Bea ing
(◦)
1 A
5 7
30
2 B 120
3 C 220
4 D 320
Table 3 shows he condi ion numbe compa ison o
he ma ix Aij in Eq. (27) and Mij in Eq. (34) us-
ing Eq. (32) and Eq. (37) espec i ely o he squa e
GRS con igu a ion. Fo he selec ed emi e posi ions
conside ed, i is seen ha he GRS pai wi h he leas
KAij also has he leas KMij. A emi e posi ion
A, he GRS pai wi h he leas KAij = 8 and leas
KMij = 1 is he pai i= 1 and j= 4. A emi e
loca ion B, he GRS pai wi h he leas Aij = 8 and
leas KMij = 1 is he pai i= 2 and j= 3. I is also
seen ha he GRS pai wi h he leas Aij will ha e
KMij = 1. This means ha he GRS pai sui able as
a e e ence o PE p ocess wi h he la e a ion algo i hm
a any gi en emi e posi ion will ha e KMij = 1.
Table 4 shows he condi ion numbe compa ison o
ma ix Aij in Eq. (27) and ma ix Mij in Eq. (34)
using Eq. (32) and Eq. (37) espec i ely o he ian-
gula GRS con igu a ion. The same conclusion o he
squa e GRS con igu a ion is deduced o he iangula
con igu a ion. E en hough , a he emi e posi ions
A and D he leas K(Aij)is ob ained by mo e han one
GRS e e ence pai . One o he GRS pai s was chosen
as he mos sui able o he PE p ocess o he emi e
a he selec ed posi ion which has K(Mij) = 1.
4.1. PE Accu acy Imp o emen
In his sec ion, he PE accu acy o he la e a ion algo-
i hm wi h he p oposed e e ence selec ion echnique
in Sec. 3. is compa ed wi h he ixed GRS e e -
ence pai app oach (GRS 1 and GRS 2) used in [12].
PE Roo Mean Squa e E o (RMSE) is used as he
pe o mance measu e o he compa ison. Ma hema i-
cally, he PE RMSE is ob ained as:
P E mse =
=
u
u
u
u
N
X
i=1 h(ˆx−x)2+ (ˆy−y)2+ (ˆz−z)2i
N,
(40)
whe e (x, y, z)a e he known emi e coo dina es and
(ˆxi,ˆyi,ˆzi)a e he es ima ed emi e coo dina es a he
i- h Mon e Ca lo simula ion ealiza ion. The Mon e
Ca lo simula ion esul s we e ob ained a e 500 eal-
iza ions. The PD Es ima ion (PDE) e o was mod-
elled as N(0, σ2)and i was assumed o be he same a
all he spa ially placed GRSs.
By a ying he PDE e o s anda d de ia ion om
0 m o 2 m, he PE RMSE o he la e a ion algo i hm
wi h he p oposed e e ence selec ion echnique and
ha o he ixed GRS e e ence pai we e ob ained and
compa ed. Figu e 2 and Fig. 3 show he PE RMSE
compa ison be ween wo app oaches o emi e a po-
si ion B using he squa e and iangula con igu a-
ion espec i ely. The PE RMSE inc eases wi h in-
c ease in he PDE e o s anda d de ia ion om 0 m
o 2 m. Compa ison be ween he PE RMSE o he la -
e a ion algo i hm wi h he p oposed e e ence selec ion
echnique o bo h squa e and iangula con igu a ion
shows ha he e is an imp o emen in he PE accu-
acy by he educ ion in he PE RMSE. F om Fig. 2,
a PDE e o s anda d de ia ion o 1 m, he PE RMSE
o he la e a ion algo i hm wi h he p oposed echnique
is 6.25 m and ha o using he ixed GRS e e ence pai
is 21.78 m. This means a educ ion in he PE RMSE
o abou 15.53 m (∼71 %) was achie ed wi h he p o-
posed echnique a emi e posi ion A wi h he GRS in
he squa e con igu a ion. Ex ending he analysis o he
iangula con igu a ion, a PDE e o s anda d de i-
c
2017 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 396
INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 15 |NUMBER: 3 |2017 |SEPTEMBER
Tab. 3: Squa e GRS con igu a ion condi ion numbe compa ison. Yellow shade indica es he GRS pai wi h he leas KAij alue
while g een shade indica es he GRS pai wi h he leas KMij alue.
GRS e e ence pai
Emi e
posi ion
i= 1
&
j= 2
i= 1
&
j= 3
i= 1
&
j= 4
i= 2
&
j= 3
i= 2
&
j= 4
i= 3
&
j= 4
K(Aij )21 49 8 31 37 30
AK(Mij )351236
K(Aij )37 21 31 8 30 49
BK(Mij )332165
K(Aij)85 73 7 80 98 60
CK(Mij )17 9 1 2 16 9
K(Aij )85 98 80 7 73 60
DK(Mij )17 16 2 1 9 9
Tab. 4: T iangula GRS con igu a ion condi ion numbe compa ison. Yellow shade indica es he GRS pai wi h he leas K(Aij)
alue while g een shade indica es he GRS pai wi h he leas K(Mij) alue.
GRS e e ence pai
Emi e
posi ion
i= 1
&
j= 2
i= 1
&
j= 3
i= 1
&
j= 4
i= 2
&
j= 3
i= 2
&
j= 4
i= 3
&
j= 4
K(Aij)14 2 2 2 2 15
AK(Mij )241532
K(Aij )338512
BK(Mij )323312
K(Aij)13 44 13 8 4 7
CK(Mij )15 3 13 5 1 5
K(Aij )10 1 2 1 4 10
DK(Mij )213122
SECTION POLICIES VOLUME: XX | NUMBER: X | 2015| MONTH
© 2015 ADVANCESIN ELECTRICAL AND ELECTRONIC ENGINEERING 7
Fig. 2:PE RMSE compa ison wi h he squa e GRS con igu a ion
Fig. 3: PE RMSE compa ison wi h he iangula GRS con igu a ion
Fu he mo e, compa ing he PE RMSE o he squa e and
iangula GRS con igu a ion, he iangula GRS
con igu a ion esul ed in he leas PE RMSE. This is due
o he low condi ion numbe alues ob ained wi h he
iangula con igu a ion as shown in Tab. 4 compa ed o
he squa e con igu a ion as shown in Tab. 3. Thus, he
iangula GRS con igu a ion will esul in highe PE
accu acy compa ed o he squa e GRS con igu a ion
5. Conclusion
This esea ch has accomplished a me hod o selec he
sui able GRS e e ence pai which is o be used o
imp o ing PE accu acy o he la e a ion algo i hm o a
minimum con igu a ion 3D mul ila e a ion sys em. The
echnique was alida ed by condi ion numbe calcula ion
and PE RMSE es ima ion compa ison wi h a ixed GRS
e e ence pai la e a ion algo i hm. Condi ion numbe
calcula ion esul s indica e ha he mos sui able GRS pai ,
used as a e e ence o he la e a ion algo i hm, has he
leas condi ion numbe alue. PE RMSE Mon e Ca lo
simula ion esul s compa ison shows ha he p oposed
e e ence selec ion echnique imp o ed he PE accu acy o
he la e a ion algo i hm by a educ ion in he PE RMSE o
a leas 70 % o bo h squa e and iangula GRS
con igu a ion. Fu he wo k will ocus on he ex ension o
he echnique o mo e han 4 GRSs.
Acknowledgemen s
The au ho s hank Uni e si i Teknologi Malaysia (UTM)
o p o iding he esou ces and suppo o his esea ch.
Re e ences
[1] FALLETTI, E., M. LUISE and D. DARDARI.
Sa elli e and e es ial adio posi ioning echniques:
A signal p ocessing pe spec i e. Ams e dam:
Academic P ess/Else ie , 2011.
ISBN: 9780123820846
[2] PETROCHILOS, N., G. GALATI and E. PIRACCI.
Sepa a ion o SSR Signals by A ay P ocessing in
Mul ila e a ion Sys ems. IEEE T ansac ions on
Ae ospace and Elec onic Sys ems. 2009, ol. 45, iss.
3, pp. 965-982. DOI: 10.1109/ aes.2009.5259177.
[3] Ne en, W. H. L., T. J. Quil e , R. Weedon, R. A.
Hogendoo n. Wide a ea mul ila e a ion, 2005, NLR,
Repo on EATMP TRS 131.
[4] YAN, H. and W. LIU. Design o Time Di e ence o
A i al Es ima ion Sys em Based on Fas C oss
Co ela ion. In:2nd In e na ional Con e ence on
Fu u e Compu e and Communica ion. Wuhan,
IEEE, 2010, pp 464-466, DOI:
10.1109/ICFCC.2010.5497484.
[5] DOU, H., Q. LEI, W. LI, and Q. XING. A new TDOA
es ima ion me hod in Th ee-sa elli e in e e ence
localisa ion. In e na ional Jou nal o Elec onics,
2015, ol 102, iss. 4, pp 849-854 ISSN 0020-7217,
DOI: 10.1080/00207217.2014.942886.
[6] MARMAROLI, P., X. FALOURD, and H. LISSEK,
A Compa a i e S udy o Time Delay Es ima ion
Techniques o Road Vehicle T acking. In:
P oceedings o he 11 h F ench Cong ess o
Acous ics and 2012 Annual IOA Mee ing,Nan es,
F ance, Socié é F ançaise d'Acous ique, 2012, pp
4136-4140, HAL Id: hal-0081098.
[7] KNAPP, C. and G. CARTER, The gene alized
co ela ion me hod o es ima ion o ime delay. IEEE
T ansac ions on Acous ics, Speech, and Signal
P ocessing, 1976, ol. 24, iss. 4, pp 320 – 327,
ISSN0096-3518, DOI:
10.1109/TASSP.1976.1162830.
[8] ZHANG, Y. AND A. WALEED, A compa a i e s udy
o ime-delay es ima ion echniques using
mic ophone a ays, New Zealand, 2007. Repo .
Depa men o Elec ical and Compu e Enginee ing,
Uni e si y o Auckland, Auckland.
[9] MANTILLA-GAVIRIA, I. A., G. GALATI, M.
LEONARDI, and J. V. BALBASTRE-
TEJEDOR,Time-di e ence-o -a i al egula ised
loca ion es ima o o mul ila e a ion sys ems. IET
Rada , Sona & Na iga ion, 2014, ol 8, iss. 5, pp
479 – 489, ISSN 1751-8784, DOI: 10.1049/ie -
sn.2013.0151
[10] CHAITANYA, D. E., M. N. V. S. S. KUMAR, G. S.
Fig. 2: PE RMSE compa ison wi h he squa e GRS con igu a-
ion.
a ion o 1 m, he educ ion in PE RMSE o abou 3 m
(∼77 %) was ob ained.
Fu he mo e, compa ing he PE RMSE o he
squa e and iangula GRS con igu a ion, he iangu-
la GRS con igu a ion esul ed in he leas PE RMSE.
This is due o he low condi ion numbe alues ob-
ained wi h he iangula con igu a ion as shown in
Tab. 4 compa ed o he squa e con igu a ion as shown
in Tab. 3. Thus, he iangula GRS con igu a ion will
esul in highe PE accu acy compa ed o he squa e
GRS con igu a ion.
SECTION POLICIES VOLUME: XX | NUMBER: X | 2015| MONTH
© 2015 ADVANCESIN ELECTRICAL AND ELECTRONIC ENGINEERING 7
Fig. 2:PE RMSE compa ison wi h he squa e GRS con igu a ion
Fig. 3: PE RMSE compa ison wi h he iangula GRS con igu a ion
Fu he mo e, compa ing he PE RMSE o he squa e and
iangula GRS con igu a ion, he iangula GRS
con igu a ion esul ed in he leas PE RMSE. This is due
o he low condi ion numbe alues ob ained wi h he
iangula con igu a ion as shown in Tab. 4 compa ed o
he squa e con igu a ion as shown in Tab. 3. Thus, he
iangula GRS con igu a ion will esul in highe PE
accu acy compa ed o he squa e GRS con igu a ion
5. Conclusion
This esea ch has accomplished a me hod o selec he
sui able GRS e e ence pai which is o be used o
imp o ing PE accu acy o he la e a ion algo i hm o a
minimum con igu a ion 3D mul ila e a ion sys em. The
echnique was alida ed by condi ion numbe calcula ion
and PE RMSE es ima ion compa ison wi h a ixed GRS
e e ence pai la e a ion algo i hm. Condi ion numbe
calcula ion esul s indica e ha he mos sui able GRS pai ,
used as a e e ence o he la e a ion algo i hm, has he
leas condi ion numbe alue. PE RMSE Mon e Ca lo
simula ion esul s compa ison shows ha he p oposed
e e ence selec ion echnique imp o ed he PE accu acy o
he la e a ion algo i hm by a educ ion in he PE RMSE o
a leas 70 % o bo h squa e and iangula GRS
con igu a ion. Fu he wo k will ocus on he ex ension o
he echnique o mo e han 4 GRSs.
Acknowledgemen s
The au ho s hank Uni e si i Teknologi Malaysia (UTM)
o p o iding he esou ces and suppo o his esea ch.
Re e ences
[1] FALLETTI, E., M. LUISE and D. DARDARI.
Sa elli e and e es ial adio posi ioning echniques:
A signal p ocessing pe spec i e. Ams e dam:
Academic P ess/Else ie , 2011.
ISBN: 9780123820846
[2] PETROCHILOS, N., G. GALATI and E. PIRACCI.
Sepa a ion o SSR Signals by A ay P ocessing in
Mul ila e a ion Sys ems. IEEE T ansac ions on
Ae ospace and Elec onic Sys ems. 2009, ol. 45, iss.
3, pp. 965-982. DOI: 10.1109/ aes.2009.5259177.
[3] Ne en, W. H. L., T. J. Quil e , R. Weedon, R. A.
Hogendoo n. Wide a ea mul ila e a ion, 2005, NLR,
Repo on EATMP TRS 131.
[4] YAN, H. and W. LIU. Design o Time Di e ence o
A i al Es ima ion Sys em Based on Fas C oss
Co ela ion. In:2nd In e na ional Con e ence on
Fu u e Compu e and Communica ion. Wuhan,
IEEE, 2010, pp 464-466, DOI:
10.1109/ICFCC.2010.5497484.
[5] DOU, H., Q. LEI, W. LI, and Q. XING. A new TDOA
es ima ion me hod in Th ee-sa elli e in e e ence
localisa ion. In e na ional Jou nal o Elec onics,
2015, ol 102, iss. 4, pp 849-854 ISSN 0020-7217,
DOI: 10.1080/00207217.2014.942886.
[6] MARMAROLI, P., X. FALOURD, and H. LISSEK,
A Compa a i e S udy o Time Delay Es ima ion
Techniques o Road Vehicle T acking. In:
P oceedings o he 11 h F ench Cong ess o
Acous ics and 2012 Annual IOA Mee ing,Nan es,
F ance, Socié é F ançaise d'Acous ique, 2012, pp
4136-4140, HAL Id: hal-0081098.
[7] KNAPP, C. and G. CARTER, The gene alized
co ela ion me hod o es ima ion o ime delay. IEEE
T ansac ions on Acous ics, Speech, and Signal
P ocessing, 1976, ol. 24, iss. 4, pp 320 – 327,
ISSN0096-3518, DOI:
10.1109/TASSP.1976.1162830.
[8] ZHANG, Y. AND A. WALEED, A compa a i e s udy
o ime-delay es ima ion echniques using
mic ophone a ays, New Zealand, 2007. Repo .
Depa men o Elec ical and Compu e Enginee ing,
Uni e si y o Auckland, Auckland.
[9] MANTILLA-GAVIRIA, I. A., G. GALATI, M.
LEONARDI, and J. V. BALBASTRE-
TEJEDOR,Time-di e ence-o -a i al egula ised
loca ion es ima o o mul ila e a ion sys ems. IET
Rada , Sona & Na iga ion, 2014, ol 8, iss. 5, pp
479 – 489, ISSN 1751-8784, DOI: 10.1049/ie -
sn.2013.0151
[10] CHAITANYA, D. E., M. N. V. S. S. KUMAR, G. S.
Fig. 3: PE RMSE compa ison wi h he iangula GRS con ig-
u a ion.
5. Conclusion
This esea ch has accomplished a me hod o selec he
sui able GRS e e ence pai which is o be used o
imp o ing PE accu acy o he la e a ion algo i hm o
a minimum con igu a ion 3D mul ila e a ion sys em.
The echnique was alida ed by condi ion numbe cal-
cula ion and PE RMSE es ima ion compa ison wi h
a ixed GRS e e ence pai la e a ion algo i hm. Condi-
ion numbe calcula ion esul s indica e ha he mos
sui able GRS pai , used as a e e ence o he la e a-
ion algo i hm, has he leas condi ion numbe alue.
PE RMSE Mon e Ca lo simula ion esul s compa ison
shows ha he p oposed e e ence selec ion echnique
imp o ed he PE accu acy o he la e a ion algo i hm
c
2017 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 397
INFORMATION AND COMMUNICATION TECHNOLOGIES AND SERVICES VOLUME: 15 |NUMBER: 3 |2017 |SEPTEMBER
by a educ ion in he PE RMSE o a leas 70 % o
bo h squa e and iangula GRS con igu a ion. Fu -
he wo k will ocus on he ex ension o he echnique
o mo e han 4 GRSs.
Acknowledgmen
The au ho s hank Uni e si i Teknologi Malaysia
(UTM) o p o iding he esou ces and suppo o his
esea ch.
Re e ences
[1] FALLETTI, E., M. LUISE and D. DARDARI.
Sa elli e and e es ial adio posi ioning ech-
niques: A signal p ocessing pe spec i e. 1s ed.
Ams e dam: Academic P ess, 2011. ISBN 978-0-
123-82085-3.
[2] PETROCHILOS, N., G. GALATI and
E. PIRACCI. Sepa a ion o SSR Signals by
A ay P ocessing in Mul ila e a ion Sys ems
Sign In o Pu chase. IEEE T ansac ions
on Ae ospace and Elec onic Sys ems. 2009,
ol. 45, iss. 3, pp. 965–982. ISSN 0018-9251.
DOI: 10.1109/TAES.2009.5259177.
[3] NEVEN, W. H. L., T. J. QUILTER, R. WEEDON
and R. A. HOGENDOORN. Wide a ea mul ila -
e a ion. In: Eu ocon ol [online]. 2005. A ailable
a : h ps://www.eu ocon ol.in /si es/de aul /
iles/publica ion/ iles/su eilllance- epo -wide-
a ea- mul ila e a ion-200508.pd .
[4] YAN, H. and W. LIU. Design o ime di -
e ence o a i al es ima ion sys em based on
as c oss co ela ion. In: 2nd In e na ional
Con e ence on Fu u e Compu e and Com-
munica ion (ICFCC). Wuha: IEEE, 2010,
pp. V2-464–V2-466. ISBN 978-1-4244-5824-0.
DOI: 10.1109/ICFCC.2010.5497484.
[5] DOU, H., Q. LEI, W. LI and Q. XING.
A new TDOA es ima ion me hod in Th ee-
sa elli e in e e ence localisa ion. In e na-
ional Jou nal o Elec onics. 2015, ol. 102,
iss. 5, pp. 839–854. ISSN 1362-3060.
DOI: 10.1080/00207217.2014.942886.
[6] MARMAROLI, P., X. FALOURD and H. LIS-
SEK. A Compa a i e S udy o Time De-
lay Es ima ion Techniques o Road Vehi-
cle T acking. In: 11 h F ench Cong ess o
Acous ics and 2012 Annual IOA Mee ing.
Nan es: IEEE, 2012, pp. 4135–4140. A ailable
a : h ps://hal.a chi es-ou e es. /
hal-00810981/documen .
[7] KNAPP, C. and G. CARTER. The gene -
alized co ela ion me hod o es ima ion o
ime delay. IEEE T ansac ions on Acous-
ics, Speech, and Signal P ocessing. 1976,
ol. 24, iss. 4, pp. 320–327. ISSN 0096-3518.
DOI: 10.1109/TASSP.1976.1162830.
[8] ZHANG, Y. and W. H. ABDULLA. A com-
pa a i e s udy o ime-delay es ima ion ech-
niques using mic ophone a ays: School o
Enginee ing Repo no. 619. In: Seman ic-
schola [online]. 2005. A ailable a : h ps:
//pd s.seman icschola .o g/ 32c/
b5 b2d0205d7c9b35e8d48edee 6c3d354db.
pd
[9] MANTILLA-GAVIRIA, I. A., M. LEONARDI,
G. GALATI and J. V. BALBASTRE-TEJEDOR.
Time-di e ence-o -a i al egula ised loca ion es-
ima o o mul ila e a ion sys ems. IET Rada ,
Sona &Na iga ion. 2014, ol. 8, iss. 5,
pp. 479–489. ISSN 1751-8792. DOI: 10.1049/ie -
sn.2013.0151.
[10] CHAITANYA, D. E., M. N. V. S. S. KUMAR,
G. S. RAO and R. GOSWAMI. Con e gence issues
o aylo se ies me hod in de e mining unknown
a ge loca ion using hype bolic mul ila e a ion.
In: In e na ional Con e ence on Science Engi-
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Abou Au ho s
Abdulmalik Shehu YARO was bo n in Kaduna,
Nige ia. He ecei ed his B.Eng. deg ee in Elec ical
Enginee ing om Ahmadu Bello Uni e si y, Za ia in
2012 and his M.Eng. deg ee in Elec ical-Elec onics
and Telecommunica ions om Uni e si y Teknologi
Malaysia in 2014. He is cu en ly pu suing his Ph.D.
deg ee on Su eillance sys em a he Depa men o
Elec ical and Compu e Enginee ing a Uni e si i
Teknologi Malaysia.
Ahmad Zu i SHA’AMERI ob ained his B.Sc.
in Elec ical Enginee ing om he Uni e si y o
Missou i-Columbia, USA in 1984, and M.Eng. Elec-
ical Enginee ing and Ph.D. bo h om Uni e si i
Teknologi Malaysia in 1991 and 2000 espec i ely.
A p esen , he is an associa e p o esso , Coo dina o
o he Digi al Signal and Image P ocessing (DSIP)
Resea ch G oup and Academic Coo dina o o he
DSP Lab, Elec onic and Compu e Enginee ing
Depa men , Facul y o Elec ical Enginee ing, Uni-
e si i Teknologi Malaysia. His esea ch in e es
includes signal heo y, signal p ocessing o ada and
communica ion, signal analysis and classi ica ion, and
in o ma ion secu i y. The subjec s augh a bo h
unde g adua e and pos g adua e le els include digi al
signal p ocessing, ad ance digi al signal p ocessing,
ad ance digi al communica ions and in o ma ion
secu i y. He has also conduc ed sho cou ses o bo h
go e nmen and p i a e sec o s. A p esen , he has
published 160 pape s in his a eas o in e es a bo h
na ional and in e na ional le els in con e ences and
jou nals.
Nidal KAMIL ecei ed he Ph.D. deg ee (Hons.)
om he Technical Uni e si y o Gdansk, Poland, in
1993. His Ph.D. wo k was ocused on he subspace-
based a ay signal p ocessing o di ec ion-o -a i al
es ima ion. Since 1993, he has been in ol ed in he
esea ch p ojec s ela ed o es ima ion heo y, noise
educ ion, op imal il e ing, and pa e n ecogni ion.
He de eloped SNR es ima o o an enna di e si y
combining and in oduced he da a glo e o online
signa u e e i ica ion. Cu en ly, he is an Associa e
P o esso a he Pe onas Uni e si y o Technology,
T onoh, Pe ak, Malaysia. His esea ch in e es s
include b ain signal p ocessing o epilepsy assessmen
and seizu e p edic ion.
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2017 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 399