1530-437X (c) 2021 IEEE. Pe sonal use is pe mi ed, bu epublica ion/ edis ibu ion equi es IEEE pe mission. See h p://www.ieee.o g/publica ions_s anda ds/publica ions/ igh s/index.h ml o mo e in o ma ion.
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2017 1
En i onmen -Awa e Reg ession o Indoo
Localiza ion based on WiFi Finge p in ing
Ge m´
an Mendoza-Sil a, Ana C is ina Cos a, Joaqu´
ın To es-Sosped a, Ma co Painho and Joaqu´
ın Hue a
Abs ac —Da a en ichmen h ough in e pola ion o eg ession is
a common app oach o deal wi h sample collec ion o Indoo Lo-
caliza ion wi h WiFi inge p in ing. This pape p o ides guidelines
on whe e o collec WiFi samples , and p oposes a new model o
ecei ed signal s eng h eg ession. The new model c ea es ec o s
ha desc ibe he p esence o obs acles be ween an access poin
and he collec ed samples. The ec o s, he dis ance be ween he
access poin and he posi ions o he samples, and he collec ed,
a e used o ain a Suppo Vec o Reg ession. The expe imen s
included some ele an analyses and showed ha he p oposed
model imp o es ecei ed signal s eng h eg ession in e ms o
eg ession esiduals and posi ioning accu acy.
Index Te ms—Indoo Posi ioning, WiFi Finge p in ing, WiFi Samples Collec ion, RSS Reg ession
I. INTRODUCTION
The demand o Indoo Posi ioning Sys ems (IPS) has al-
eady d i en academic and comme cial esea ch, i is expec ed
ha i will d ama ically ise in he yea s o come [1]. Despi e
he la ge di e si y on ela ed posi ioning echnologies o
indoo scena ios, WiFi is one o he mos o en used. Sma -
phones and applica ions elying on Loca ion Based Se ices
(LBS) made WiFi a cos -less app oach a he expense o
posi ioning e o s a ound a ew me e s [2].
Finge p in ing is commonly used wi h WiFi o p o ide
posi ion indoo s. A WiFi inge p in is a ec o wi h he Re-
cei ed Signal S eng h (RSS) o each WiFi access poin (AP)
de ec ed in a gi en posi ion and ime. I equi es a calib a ion
s age, whe e samples a e collec ed a well-known posi ions o
c ea e a e e ence da ase ( adio map). In he ope a ional s age,
gi en a new inge p in measu ed a an unknown posi ion, he
inge p in me hod usually p o ides he cen oid o he mos
simila e e ence inge p in s as posi ion es ima e [3].
Samples collec ion is known as one o he main challenges
o WiFi inge p in ing [4], gi en ha he collec ion e o
Manusc ip ecei ed xx Decembe 2019; e ised xx Ap il 2020; ac-
cep ed xx xxxx 2020. Da e o publica ion xx xxxx 2020; (Co esponding
au ho : J. To es-Sosped a.). G. M. Mendoza-Sil a g a e ully acknowl-
edges unding om g an PREDOC/2016/55 by Uni e si a Jaume I.
J. To es-Sosped a g a e ully acknowledges unding om Minis e io de
Ci´
encia, Inno aci´
on y Uni e sidades (PTQ2018-009981).
G. M. Mendoza-Sil a and J. Hue a a e wi h he Ins i u e o New
Imaging Technologies, Uni e si a Jaume I, 12071 Cas ell´
on, Spain. (e-
mail: {gmendoza,hue a}@uji.es)
J. To es-Sosped a (co esponding au ho ), is wi h UBIK Geospa ial
Solu ions, 12006 Cas ell´
on, Spain. (e-mail: [email p o ec ed])
A. C. Cos a and M. Painho a e wi h he NOVA IMS, Uni e sidade No a
de Lisboa, Campus de Campolide, 1070-312 Lisboa, Po ugal. (e-mail:
{c is ina,painho}@@no aims.unl.p )
Co esponding au ho : J. To es-Sosped a ([email p o ec ed])
Digi al Objec Iden i ie : 10.1109/JSEN.202x.xxxxxxx
can be signi ican o la ge a eas. The li e a u e sugges s o
educe he equi ed e o ei he by c owdsou cing he collec-
ion o olun ee s [5], es ima ing he RSS alues applying a
p opaga ion model, o applying an in e pola ion echnique o
densi y an ini ial educed adio map [4], [6], [7]. Despi e
being e y aluable, he eliabili y o posi ion ags and he
imp ope dis ibu ion sample posi ion a e usual conce ns wi h
c owdsou ced signal da a [8].
This pape add esses he adio map en ichmen by applying
eg ession echniques on a p ope signal cha ac e iza ion o
he en i onmen . Also, h ough expe imen s pe o med on
wo publicly a ailable da abases, we add ess he p oblem o
choosing he mos con enien posi ions o collec ing WiFi
inge p in s o adio map c ea ion. Fu he mo e, we e alua e
a new model ha applies en i onmen knowledge o Suppo
Vec o Reg ession (SVR), which imp o es he eg ession es i-
ma es co esponding o ex apola ion poin s in compa ison o
o he ex apola ion wo k shown in WiFi posi ioning li e a u e.
The main con ibu ions o his pape can be summa ized as
ollows: i) a no el eg ession model awa e o he en i onmen
ea u es; ii) a comp ehensi e analysis o e e ence posi ion
selec ion o build e ec i e adio maps; and iii) alida ion in a
eal-wo ld scena io independen o he esea ch objec i es.
II. BACKGROUND AND RELATED WORKS
A WiFi Access Poin (AP) is a ne wo king de ice ha
b oadcas s one o mo e wi eless ne wo ks. A se o RSS alues
om a ailable APs measu ed a a speci ic loca ion h oughou
a sho ime in e al is called a inge p in , which can be used
o posi ioning as desc ibed in Sec ion I. The quali y o he
adio map depends on he loca ion o he e e ence poin s,
he e e ence poin densi y, he numbe o samples o each
e e ence poin s, among many o he pa ame e s [9], [10].
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This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
2 IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2017
Howe e , collec ing samples o a adio map equi es a
no able amoun o ime [11]. To ackle his p oblem, wo
al e na i es a e usually conside ed: c owdsou cing and spa se
collec ion. C owdsou cing has been p aised o adio map
collec ion and upda e [12] a he expense o su e ing om
low quali y o posi ion ags o une en dis ibu ions o he
collec ed samples, whe eas spa se collec ion educes he col-
lec ion e o s a he expense o poo e cha ac e iza ions o
he en i onmen s. The la e app oach (spa se collec ion wi h
eg ession, in e pola ion and/o ex apola ion models) has been
applied o syn he ically en ich he adio map o mo e han 15
yea s [13], [14], and me hods all in one o he nex g oups:
•Spa se eco e y includes, o example, comp essed sens-
ing using Singula Value Decomposi ion (SVD) [15], and
adio map in e pola ion using spa se eco e y [6].
•In e pola ion me hods includes adi ional in e pola ion
me hods [16]–[19]; me hods capable o deli e ing bo h
in e pola ion and ex apola ion like Nea es Neighbo
and In e se Dis ance Weigh ing (IWD) [20]; and o he
in e pola ion heu is ics [21].
•Ex apola ion me hods applied a ian s based on log-
dis ance pa h loss model [21]–[23]; on he ay acing
model [24], [25] o he adiosi y model [26]–[28].
•Reg ession me hods la gely includes he applica ion o
Gaussian P ocess Reg ession (GPR) [29]–[33], al hough
o he s ha e also applied K iging [14], [34]–[36], Ge-
og aphy Weigh ed Reg ession (GWR) [37] and Suppo
Vec o Reg ession (SVR) [38].
I is common ha adio map en ichmen wo ks p o ide
he p opo ions be ween poin s used o i ing and hose
used o es ima ions. Tal i ie e al. [20] concluded ha he
posi ions whe e samples a e selec ed we e mo e impo an
han how many o hem we e selec ed. Khalajmeh abadi e
al. [6] sugges ed a andom selec ion o e e ence poin s and
discou age a uni o m placemen o hose poin s. Ezpele a e
al. [16] suppo ed he di ision in zones a guing ha a zone
wi h highe quali y o RF signals han o he zones equi ed
less aining poin s. The impo ance o he dis ibu ion o
samples o adio map cons uc ion is almos in ui i e and
acknowledged [39]. Howe e , some wo ks pe o m andom
selec ion o sample posi ions o adio map cons uc ion [6],
[23], [32]. Kana is e al. [40], de e mined he sample size
gi en a small p elimina y se o measu emen s, sugges ing
o andomly choose posi ions om a g id in he numbe
de e mined by he sample size calcula ion.
Some adio map en ichmen solu ions ha e conside ed he
en i onmen ’s in luence on he signals in ensi ies. The in e -
pola ion in Bong e al. [41] p ese ed signals discon inui y
o e he wall. Ali e al. [23] used a pa h loss wi h wall
a enua ion ac o ha in oduced an image o coun he
numbe o in e e ing walls. Mogh adaiee e al. [21] i ed a
log-dis ance model independen ly o each a chi ec u al zone
and c ea ed an in e pola ion ha conside ed only sample a
simila dis ances o he a ge AP. Some au ho s [14], [34]–[36]
used K iging, bu only conside ed he Euclidean dis ance o
desc ibing he spa ial dependency, which does no hold ue o
indoo en i onmen s. [39] i ed a log dis ance pa h loss model
o each a ge posi ion, gi ing o he samples used o i ing
dis inc weigh s (using a ke nel densi y es ima ion) based on
hei dis ances o he a ge posi ion. Du e al. [37] applied
GWR, which compu ed se e al local models ins ead a single
global one. They used he dis ance be ween he emi e s and
he sample poin s as p edic o a iables.
The dis ibu ion o samples necessa ily should ake he
layou o he en i onmen in o accoun , no only ega ding
whe e i is possible o collec samples, bu whe e is con enien
o collec hem. The indoo en i onmen s s ongly in luence
he WiFi and BLE signals, and he decision on he collec ion
dis ibu ion should be awa e o i . The adio map en ichmen
me hod should ideally be also awa e o he a ge en i onmen ,
i.e., o he obs acles and he posi ions o he emi e s.
III. MATERIALS AND METHODS
A. Selec ed da ase s
This wo k is buil on op o wo public WiFi inge p in -
ing da ase s: he Lib a y da ase [42] and he Mannheim
da ase [43]. Pa ial e sions o bo h da ase s will be used o
analyse he in luence o posi ion dis ibu ion and he in luence
o AP s eng h on posi ion accu acy. Mo eo e , hey will
be used o analyse he in luence o AP s eng h on RSS
eg essions. Fo he e alua ion o ou p oposed en i onmen -
awa e eg ession model only he Lib a y da ase will be used.
The Lib a y da ase was collec ed in wo loo s o he Li-
b a y building o Uni e si y Jaume I (UJI) and he sys ema ic
da a collec ion was epea ed mul iple imes in a ime span o
25 mon hs. The e a e six WiFi inge p in s pe each e e ence
poin and each o he wo di ec ions a which he collec ion
subjec was acing. Also, as he da a con ained in o ma ion
abou a 620 AP, a selec ion o he 52 mos ele an APs
was pe o med (as done in To es-Sosped a e al. [44]) o
ease he analyses and and educe he noise c ea ed by a la ge
numbe o in e mi en APs. The collec ion a ea is a ela i ely
small en i onmen ha co e ed abou 15 ×10 m. The a e age
dis ance be ween e e ence poin s is abou 2 m.
The Mannheim da ase was collec ed in he Mannheim
Uni e si y. The collec ion a ea comp ises a medium-scale
en i onmen , co e ing abou 50 ×36 m o co ido s o a
uni e si y depa men . The inge p in s a e on a 1.5 m g id
[43], [45] and he posi ions o 10 APs a e known. The da ase
con ained 110 inge p in s pe e e ence poin . Ou o 110
samples, we andomly selec ed 10 o ease he analyzes and
ha e a numbe o samples ha is close o ha o he Lib a y
da ase . Bo h he o iginal Mannheim and he Lib a y da ase s
p o ided hei posi ion ags using a local coo dina e sys em
ha allows dis ance compu a ion using he Euclidean dis ance.
Figu e 1 shows he ope a ional a ea o he wo e alua ion
en i onmen s. The s uc u al ba ie s we e manually c ea ed
om loo plans. Thick walls we e d awn in black colo and
hin walls we e d awn wi h a ligh shade o g ay in he
image, whose in ensi y alues a e used by eq.(2). Figu e 1 also
p esen s he dis ibu ion o aining and es e e ence poin s,
as well as he posi ion o some APs. The highe he densi y
o APs and e e ence poin s in he ope a ional a ea, he lowe
expec ed posi ioning e o . In bo h cases, some APs lay ou
he loo map o ha e an unknown loca ion.
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1530-437X (c) 2021 IEEE. Pe sonal use is pe mi ed, bu epublica ion/ edis ibu ion equi es IEEE pe mission. See h p://www.ieee.o g/publica ions_s anda ds/publica ions/ igh s/index.h ml o mo e in o ma ion.
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Jou nal
MENDOZA-SILVA e al.: ENVIRONMENT-AWARE REGRESSION FOR INDOOR LOCALIZATION BASED ON WIFI FINGERPRINTING 3
Fig. 1: Lib a y 5 h loo (le ) and Mannheim ( igh )
loo maps. Blue and magen a do s ep esen aining and es
e e ence poin s, espec i ely. APs posi ions a e d awn wi h
o ange ci cles. O he APs may lay ou o he a eas.
B. En i onmen -Awa e Reg ession on WiFi adio maps
This wo k p esen s a eg ession model ha in eg a es he AP
e e ence posi ion and a loo plan o he a ea. The e e ence
posi ion is used as a aw indica ion o whe e he AP is. The
posi ion o APs inside o e y close o he collec ion a ea
can be de e mined wi h, o ins ance, he weigh ed cen oid
o he me hod p oposed in [46]. The app oxima e posi ion
o an AP can be also manually ob ained by measu ing he
signal in ensi y wi h a sma phone applica ion walking in he
a ea. Howe e , he accu acy o AP loca ion is low o hose
APs ha a e away om he ope a ional a ea and an indica o
o he ela i e di ec ion is ob ained ins ead. Those a APs
a e ypically de ec ed wi h a maximum in ensi y weake han
−60 dBm. De e mining whe he an AP is wi hin he collec ion
a ea could be done, o ins ance, using he Si ua ion Goodness
es p esen ed in [46] i a ela i ely dense sample collec ion is
a ailable.
Figu e 2 in oduces an example in he Lib a y en i onmen
(5 h loo ). I shows he mean RSS alues pe e e ence poin
o 3APs, which will la e be used o e alua e he p oposed
eg ession model. The APs wi h IDs 15 and 49 a e inside he
collec ion a ea. Thei posi ions shown in he igu e a e abou
hal a me e and mo e han a me e away om he ac ual
de ice posi ions, espec i ely. The posi ion o he de ice ha
emi ed he AP wi h ID 8was unknown. The posi ion shown
in he igu e is anyway a use ul es ima ion o he ac ual AP
di ec ion.
In he p oposed model, he p edic o a iables include
he a ge poin ’s posi ion componen s, he AP’s e e ence
posi ion and in o ma ion om he en i onmen loo map.
Mo eo e , we applied a da a ans o ma ion be o e and a e
he applica ion o he eg ession me hod, so ha he alues
o he esponse a iable a e de e mined as log10(−RSS)(as
a dis ance indica o ) and he RSS es ima e is compu ed as
−(10es )i es is an es ima e p o ided by he eg ession
model. The posi ions o poin s used o aining and es ing
he model a e exp essed in he local coo dina e sys em. Thus,
hei coo dina es need o be ans o med in o image coo di-
na es (cell posi ions o pixels) be o e applying he p oposed
model. The ollowing de ini ions assume posi ions in image
coo dina es (i.e. pixels no me e s).
4 6 8 10 12
Eas ing (m)
16
18
20
22
24
26
28
30
No hing (m)
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
(a) AP ID 15
4 6 8 10 12
Eas ing (m)
16
18
20
22
24
26
28
30
No hing (m)
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
(b) AP ID 49
4 6 8 10 12 14 16 18 20 22
Eas ing (m)
16
18
20
22
24
26
28
30
No hing (m)
-100
-90
-80
-70
-60
-50
dBm
(c) AP ID 8
Fig. 2: Mean RSS alues pe e e ence poin and de ice
e e ence posi ions o h ee APs (Lib a y, 5 h loo ). The de ice
posi ion is indica ed wi h a s a . Ci cles highligh he e e ence
poin s whose alues whe e used o ain eg ession models.
Le p = ( px; py)be he posi ion o a e e ence poin
used o aining he model. Le ap = (apx;apy)be he
posi ion o he AP a ge ed o eg ession. Le B p =
{(x1, y1), . . . , (xk, yk)}be he line ha connec s p and ap.
The cell posi ions ha cons i u e he line a e de e mined using
he B esenham’s line algo i hm [47]. The alues o p edic o
a iables o p a e:
P p ={ px, py,d p + 1
2, F p},(1)
whe e F p ={ 1, . . . , k, . . . , n}and d p is he Euclidean
dis ance be ween p and ap. The alue iis compu ed as:
i=(log2(2 + 255 −Im(xi, yi)) o 1 ≤i≤k
0 o k < i ≤n(2)
whe e xiand yia e he posi ion componen s o he i h poin in
B p,Im is he image ep esen a ion o he en i onmen , and
Im(xi, yi)is he cell alue in he image Im whose posi ion
is (xi, yi). The alue o nis he maximum numbe o poin s
ha may ha e a line connec ing he posi ions o he AP and a
poin in he en i onmen ep esen a ion. I ap lies beyond he
en i onmen ep esen ed by Im, he image is enla ge applying
a padding o ze os. In o he wo ds, Im(x, y)=0 o all (x, y)
ha lies beyond he en i onmen ep esen a ion.
Algo i hm 1 esumes he p ocess o aining he p oposed
eg ession model. I s inpu s a e he en i onmen image Im, he
posi ions (exp essed in a local coo dina e sys em) o collec ion
poin s RP L ={ plj}and hei espec i e RSS alues SI =
{sij}measu ed o an AP. Once he model Mis eady, i
se es o p edic ing he RSS alues SO ={soj} o a se o
posi ions TPL ={ plj}using he Algo i hm 2.
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1530-437X (c) 2021 IEEE. Pe sonal use is pe mi ed, bu epublica ion/ edis ibu ion equi es IEEE pe mission. See h p://www.ieee.o g/publica ions_s anda ds/publica ions/ igh s/index.h ml o mo e in o ma ion.
This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
4 IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2017
Algo i hm 1: Reg ession model aining o an AP
Inpu : Im,RP L,SI,apl Ou pu : The ained
eg ession model M
1Compu e ap = (apx, apy), he posi ion o apljin Im
2 o each pljin RP L do
3Ge p = ( px, py), he posi ion o pljin Im
4Ge B p, as s a ed p e iously
5Ge P p, as s a ed in Equa ion 1
6Se pj=P p
7Ge espj= log10(−sij)
8end
9Build Mby aining SVR using {pj}as p edic o s
da a and { espj}as esponses da a
Algo i hm 2: Signal p edic ion o an AP
Inpu : Im,TPL,apl,M
Ou pu : The p edic ed in ensi ies SO
1Compu e ap = (apx, apy), he posi ion o apljin Im
2 o each pljin TPL do
3Ge p = ( px, py), he posi ion o pljin Im
4Ge B p, as s a ed p e iously
5Ge P p, as s a ed in Equa ion 1
6Se pj=P p
7Ge es jusing Mwi h {pj}as p edic o s alues
8Se soj=−(10es j)
9end
10 Se SO ={soj}
The se F p in Equa ion 1 is a ep esen a ion o he obs acles
be ween p and ap using he in o ma ion o he image’s cells
ha lie in ha pa h. The cell alues in he image Im ep esen
ei he ee space o an obs acle (black o whi e). Thus, he
model is ained o lea n he in luence o an obs acle cell alue
a a gi en dis ance om an AP in he signal p opaga ion. This
wo k did no di e en ia e among dis inc ypes o obs acle
ma e ials o simplici y, despi e Equa ion 2 allows he ange
[1, . . . , 255] o obs acle ep esen a ion. Se ing app op ia e
opaqueness o each ma e ial equi es addi ional conside a ion
and measu emen s. Equa ion 1 includes hal o he dis ance
be ween p and ap. Using he ac ual alue o he dis ance
signi ican ly dec eased he obs acles in luences in he model.
The numbe o a iables p esen ed in Equa ion 1 depends on
he en i onmen and he AP posi ion. Finally, acco ding o ou
expe ience, we selec ed he Suppo Vec o Reg ession (SVR)
wi h a linea ke nel unc ion as eg esso .
IV. EXPERIMENTS AND RESULTS
A. In luence o RPs Dis ibu ion on IPS Accu acy
The goal o he adio map in WiFi inge p in ing is o
cha ac e ize he signal p opaga ion in he a ge en i onmen .
As he main inge p in me hods (including k-NN) can only
p o ide posi ion es ima es wi hin he con ex hull o he
e e ence sample loca ions, we hipo e ise ha he numbe
and dis ibu ion o he collec ed samples a e s ongly ela ed
quali y o he adio map and, hence, he accu acy o he IPS.
Fo ha pu pose, we ha e e alua ed he pe o mance o
he adio map in wo en i onmen s and ou di e en cases:
wi h 100%,75%,50% and 25% o RPs. Excep o 100%, we
epea ed he e alua ion 400 imes wi h di e en ini ializa ion
o co e mul iple andom scena ios. In all cases, we epo
he esul s p o ided by he op imal k- alue ( om he se
[1, . . . , 15]). The esul s a e epo ed as a sca e in Figu e
3 o Lib a y 5 h loo (le ) and Mannheim ( igh ).
345678
Q3 e o (m)
20
30
40
50
60
70
80
90
100
110
A ea (m2)
25
50
75
100
2 2.5 3 3.5 4 4.5 5 5.5
Q3 e o (m)
140
150
160
170
180
190
200
210
220
A ea (m2)
25
50
75
100
Fig. 3: Rela ion be ween aining co e ed a ea and posi ioning
accu acy o Lib a y 5 h Floo (le ) and Mannheimm ( igh ).
E e y poin in he igu e ep esen he a ea o he educed
adio map’s con ex hull and he bes accu acy epo ed by he
k-NN me hod wi h ha da a se . The accu acy co esponds
o he Q3 alue, i.e., he 75 h pe cen ile as done in IPIN
Compe i ion. The colo indica es he size o he adio map case
(100%,75%,50% and 25%). A clea end can be obse ed
in he wo en i onmen s, he la ge he a ea co e ed, he bes
posi ioning accu acy. In con as , he wo s posi ioning esul s
came when he con ex hull o he e e ence adio map was
small. This is because he kNN me hod can p o ide posi ion
es ima es only wi hin he con ex hull o he e e ence poin s.
Good accu acy can be eached wi h a educed adio map i
he e e ence poin s co e he ull ope a ional a ea.
The igu e also shows ha he dis ibu ion o e e ence
poin s is ele an . E en o a high co e ed a ea, he posi ioning
accu acy can a y up o mo e han 2 m in he h ee cases.
The la ges di e ences in posi ioning a e obse ed o cases
wi h low RPs densi y (i.e. 25%). To e alua e he ela ion
be ween co e ed a ea and accu acy, we calcula ed he Pea son
co ela ion be ween he a ea and he Posi ioning e o in he
hi d qua ile in he 1201 poin s. The co ela ion ac o (ρ)
o Mannheim is −0.77, whe eas i is −0.89 o Lib a y. In
bo h cases, he signi icance (p- alue) is much lowe han 0.05
showing ha he in e se co ela ion is s a is ically signi ican .
Ou hypo hesis is ha placing e e ence poin s nea he inne
bounda y o he collec ion a ea would maximize he co e ed
a ea and assu e ha es posi ions a e loca ed inside he con ex
o he aining posi ions. Finding hose posi ions is a i ial
ask and can be p o ided by, o ins ance, alpha-shape [48].
Thus empi ical da a collec ion can be op imized o ele an
places acco ding o he imposed es ic ions. The es ic ions
will somehow will be an indica o o he densi y and dis ibu-
ion o he empi ical e e ence poin s, which will be loca ed
only a easible loca ions (e.g. he e a e no samples inside a
wall). I he adio map needs o be en ich ed, eg ession can be
used o syn he ically gene a e new e e ence samples in hose
posi ions ha lack o empi ically collec ed da a.
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Jou nal
MENDOZA-SILVA e al.: ENVIRONMENT-AWARE REGRESSION FOR INDOOR LOCALIZATION BASED ON WIFI FINGERPRINTING 5
One s a egy o c ea ing he se o e e ence poin s is o
i s add e e ence poin s lying close o en i onmen bounda y
and la e add a numbe o poin s mp ha maximize he mean
minimum dis ance among he poin s in he se . In kNN, he
es ima ed posi ion is commonly compu ed as he cen oid
o he posi ions o he mos simila samples in he aining
da ase . Thus, maximizing he minimum dis ance among he
e e ence poin s educes he a eas wi hou posi ion es ima es
p oduced by kNN. Such an e en dis ibu ion o poin also
bene i s eg essions as i p o ides in e media e posi ions ha
help explain non-linea beha io s. The alue o mp may be
dic a ed by he a o dable collec ion e o . Fo low alues
o mp, like hose below 20, a b u e o ce app oach may be
applied o de e mine he mp posi ions o he e e ence poin s.
Fo la ge mp alues, a Mon e Ca lo app oach [49] can be used.
This wo k used an op imiza ion app oach based on agen s
mo ing unde epulsion o ces [50].
To explo e he con enience o using he p e ious aining
poin s dis ibu ion, he Pea son co ela ion es was applied
be ween he mean minimum dis ance and he posi ioning
e o o se e al dis ibu ions o aining poin s. The es s
we e pe o med 400 independen imes (wi h andom se s o
e e ence poin s ha included he shape bounda y) sepa a ely
o each o he wo en i onmen s. The posi ion es ima ions
we e ob ained wi h kNN, using he bes k o he aining se .
Table I p esen s he co ela ion esul s. The nega i e co ela-
ion be ween he mean minimum dis ance and he posi ioning
accu acy is no s a is ically signi ican . Fo he Lib a y en i-
onmen , he nega i e weak o mode a e co ela ion appea s
only o la ge se s, and i is s a is ically signi ican o hem.
The co ela ion is consis en ly nega i e o all se sizes in he
Mannheim en i onmen . Howe e , i s s a is ical signi icance
does no show a clea pa e n. The esul s om Table I sugges
ha he dis ibu ion o he inne e e ence poin s p oposed
abo e is bene icial o en i onmen s ha a e la ge o ha e
ela i ely dense collec ions. Despi e i is desi able o a oid he
exis ence o non-posi ionable zones, al e na i e dis ibu ions
may be p e e able o o he en i onmen s.
TABLE I: Co ela ion (ρ) and s a is ical signi icance (p- alue)
be ween he mean minimum dis ance among aining poin s
and he Thi d qua ile o he posi ioning e o (Q3) o
di e en sizes o he adio map ( om 25% o 90% o RPs).
Lib a y Mannheim
%RPs mean k ρ p- alue Q3 (m) mean k ρ p- alue Q3 (m)
25 2 0.004 0.932 4.740 3 -0.144 0.004 3.898
30 2 0.075 0.135 4.480 3 -0.069 0.167 3.562
35 2 0.122 0.015 4.390 3 -0.120 0.016 3.403
40 2 0.091 0.068 4.171 3 -0.086 0.086 3.319
45 2 0.024 0.628 3.971 3 -0.146 0.003 3.193
50 2 0.060 0.233 3.661 3 -0.131 0.009 3.146
55 2 0.036 0.470 3.576 3 -0.130 0.010 3.071
60 3 -0.036 0.471 3.576 3 -0.077 0.122 2.990
65 3 -0.124 0.013 3.505 3 -0.085 0.088 2.966
70 3 -0.200 0.000 3.466 3 -0.075 0.134 2.926
75 4 -0.313 0.000 3.428 4 -0.152 0.002 2.900
80 4 -0.395 0.000 3.390 4 -0.138 0.006 2.874
85 4 -0.302 0.000 3.322 4 -0.056 0.267 2.864
90 4 -0.279 0.000 3.318 4 -0.131 0.009 2.833
B. In luence o AP S eng h on Posi ioning Accu acy
I is known ha he signal s eng h om an AP loga i hmicly
dec eases as he dis ance o he AP inc eases. Thus, i is
expec ed ha he close o he emi e he la ge he expec ed
a ia ions in he signals. A adio map should g asp as much
as he signal a ia ions in he en i onmen as possible. Ha ing
e e ence poin s close o he emi e inc eases he likelihood
o inco po a ing much o hose a ia ions.
This subsec ion explo es he co ela ion be ween AP p ox-
imi y o he collec ion a ea and he posi ioning accu acy
o a kNN me hod. De e mining he dis ance o an AP e-
qui es knowing he ac ual posi ion o he AP. Gi en ha he
knowledge o AP posi ions is commonly no assumed o
inge p in ing, we in e ed p oximi y om he RSS alues.
The RSS alues o an AP measu ed in an a ea should be
s ong i he AP is close o ha a ea o inside i .
Le us assume a adio map RM ( aining se ) and a es
se . Le maxa=max({ p,i,a})be he s onges RSS alue
o he a h de ec ed AP in RM, wi h 1≤a≤mand mbeing
he numbe o APs. Le qap (median in e ed p oximi y) be
he Q2 alue o {maxa}. Le qpe (posi ioning accu acy) be
he Q3 alue o posi ioning e o s ob ained by a kNN me hod
using he abo e aining and es se s.
He e, we also c ea ed 400 andom subse s con aining he
25% o an o iginal aining se (ei he o he Lib a y o
Mannheim). Fo each subse RMs, he qapsand qpeswe e
compu ed. Fo qpes, he kNN me hod used RMsas aining
se and he o iginal es se . Then, he Pea son co ela ion es
was applied on he se s {qaps}and {qpes}, wi h 1≤s≤400.
The es esul s a e shown in Table II. Fo he wo en i-
onmen s, he co ela ion esul s we e s a is ically signi ican .
The low o mode a e nega i e co ela ion indica es ha high
accu acy is associa ed wi h low p oximi y alues (weak RSS).
Thus, he esul s sugges he con enience o dis ibu ing some
e e ence poin s in zones o he collec ion a ea whe e nea by
APs a e may esul in la ge signal a ia ions.
TABLE II: Co ela ion es esul s be ween qap (median in-
e ed p oximi y) and qpe (posi ioning accu acy).
En i onmen ρ p- alue
Lib a y -0.37 ≈0
Mannheim -0.28 ≈0
C. In luence o AP S eng h on RSS Reg essions
The ollowing expe imen s add essed he no ion o he
con enience o ha ing mo e e e ence poin s close o nea by
APs in ela ion o he eg ession o in e pola ion esul s.
The goodness o a eg ession o an in e pola ion applied o
adio map densi ica ion is no mally assessed by he di e ence
be ween he es ima ed RSS and hei ac ual alues. The
in e pola ion me hods used in he expe imen s we e Na u al
Neighbou s [51], (Bi)Cubic In e pola ion [52], [53] and In-
e se Dis ance Weigh ing [54]. The eg ession me hods used
in he expe imen s we e Suppo Vec o Machines (SVM)
[55], Gaussian P ocess [56], Gene alized Linea Models [57],
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This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
6 IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2017
Decision T ees (DT) [58], and Ensembles o Decision T ees
[59]. The in e pola ion and eg ession me hods, he eina e
only called eg ession me hods, we e applied using aining
poin s o i he model and es s poin o compu e RSS
es ima es. The mean RSS alue o an AP and a e e ence
poin was used o ain he eg ession model o an AP and o
la e compu e he eg ession esiduals. The esiduals a e he
AP-wise absolu e di e ence be ween RSS es ima es p o ided
by he eg ession and he ac ual RSS used o aining.
Table III shows he co ela ion alues be ween signal
s eng h and eg ession esiduals o each en i onmen . Le
Sj={s1, . . . , sn}and Rj={ j,1, . . . , j,n}be wo se s,
whe e nis he numbe o APs de ec ed in ha en i onmen .
The alue siwas compu ed as he mean RSS alue o he
i h AP in he en i onmen , conside ing all e e ence poin s.
The alue j,i was compu ed as he mean o he esidual
alues ob ained o he i h AP applying he j h eg ession
me hod in he en i onmen . The alues o he signal s eng h
and eg ession esiduals used o he co ela ion es in an
en i onmen a e he se s {S1, . . . , Sm}and {R1, . . . , Rm},
whe e mis he numbe o eg ession me hods.
TABLE III: Co ela ion be ween mean alues o signal s eng h
in he en i onmen and mean alues o eg ession esiduals.
En i onmen ρ p- alue
Lib a y 0.88 ≈0
Mannheim 0.24 ≈0
The co ela ion is s a is ically signi ican o he wo
en i onmen s. The co ela ion magni ude is weak o he
Mannheim en i onmen bu no able o he Lib a y en i on-
men . The highe he median alue o he signal s eng h in he
en i onmen , he la ge he esiduals o he eg essions. The
co ela ion di e ence be ween he wo en i onmen s is a likely
esul o he dimensions o he en i onmen s. The Mannheim
en i onmen is la ge, and hus he de ec ed signal in ensi ies
o an AP can be e y s ong in some a eas and e y weak a
some o he a eas. Ve y s ong and e y weak signal in ensi ies
a e no de ec ed o he same AP in he Lib a y en i onmen .
Figu e 4 shows he ela ion be ween he s eng h wi h which
an AP is seen in an en i onmen and he eg ession goodness.
The in es iga ion was pe o med o wo APs in he Lib a y
en i onmen (one wi h weak and one wi h s ong RSS alues).
The cha s om Figu e 4 p esen o each AP includes he
median alue o he RSS alues o he AP a each e e ence
poin and he median alue o he eg ession esiduals a
each e e ence poin . In pa icula , igu e 4a shows eg ession
esiduals o mode a e alues o he weak AP, while Figu e 4b
shows eg ession esiduals o he s ong AP ha a e no only
no ably la ge han hose o he weak AP bu also mainly
si ua ed in a speci ic zone o he en i onmen .
The cha s sugges ha o weak, a away APs, he e-
g ession equi es only a ew samples o ain a model, as
he APs signals a e only weakly a ec ed by he en i onmen .
Howe e , he s eng h alues o signals om APs nea he
a ge en i onmen hea ily depend on he Line o Sigh (LOS)
and Non Line o Sigh (NLOS) si ua ions.
5 6 7 8 9 10 11 12
Eas ing (m)
18
20
22
24
26
28
No hing (m)
Signal in esi y
-100
-90
-80
-70
-60
-50
-40
dBm
5 6 7 8 9 10 11 12
Eas ing (m)
18
20
22
24
26
28
No hing (m)
In e pola ion esiduals
2
3
4
5
6
7
8
9
10
dBm
(a) Weak AP
5 6 7 8 9 10 11 12
Eas ing (m)
18
20
22
24
26
28
No hing (m)
Signal in esi y
-100
-90
-80
-70
-60
-50
-40
dBm
5 6 7 8 9 10 11 12
Eas ing (m)
18
20
22
24
26
28
No hing (m)
In e pola ion esiduals
2
3
4
5
6
7
8
9
10
dBm
(b) S ong AP
Fig. 4: Mean alue o esiduals dis ibu ion compa ed o mean
alue o RSS o he Lib a y en i onmen .
Table IV p esen s he spa ial au o-co ela ion es as ob-
ained by Mo an’s I [60] o he wo an ennas add essed
in Figu e 4. The able sugges s ha o APs s ongly seen
ac oss he en i onmen he dis ibu ion o eg ession esiduals
is no andom and ends o o ganize in clus e s; while o APs
weakly seen in he en i onmen he dis ibu ion o esiduals is
likely andom. As s a ed in he li e a u e [61], he en i onmen
in luence is less signi ican o weak han o s ong signals.
Fu he mo e, he signal in ee space ollows a loga i hmic
decay, i.e., he a he om he AP he slowe he decay
a e. The es ed eg ession models ail o accoun o a spa ial
p ocess induced by he en i onmen o s ong signals. Thus,
samples a e equi ed in zones o LOS and NLOS wi h espec
o nea by APs, gi en ha he RSS alues in hose wo
si ua ions can be signi ican ly di e en .
TABLE IV: Spa ial au o-co ela ion (Mo an’s I) o eg ession
esiduals.
Beha io Q2o RSS Q2o esiduals z-sco e p- alue
Weak AP -83 4 0.920 0.357
S ong AP -74 6 7.702 ≈0
Gi en he mode a e co ela ion ob ained in some o he
analyses, and ha he expe imen s we e only pe o med in wo
en i onmen s, a e e ence poin posi ion de e mina ion me hod
is no p oposed. Howe e , such de e mina ion me hod may
ha e he ollowing s eps:
1) Place some e e ence poin s in he bounda ies.
2) Dis ibu e he es o poin maximizing he mean mini-
mum dis ance among e e ence poin s.
3) Adjus he dis ibu ion o ha e some poin s close o
nea by APs.
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This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
MENDOZA-SILVA e al.: ENVIRONMENT-AWARE REGRESSION FOR INDOOR LOCALIZATION BASED ON WIFI FINGERPRINTING 7
4) Tend o LOS si ua ions, assu ing o place poin s in LOS
and NLOS si ua ions.
This wo k ecommends he p e ious me hod s eps as a se o
guidelines ha ollow a e he esul s o he analyses p o ided
in his sec ion. The mos common app oach o placing he
e e ence poin s on a g id does no ake in o accoun he
en i onmen cha ac e is ics. The guidelines sugges adap ing
he sampling posi ions o he en i onmen and highligh he
impo ance o knowing he posi ion o nea by an ennas. Thus,
he ollowing wo expe imen s add ess he en i onmen awa e
eg ession and i s e alua ion on he Lib a y en i onmen . We
selec ed he Lib a y as he e alua ion en i onmen because
he bene i s om including en i onmen knowledge in o a
eg ession model we e expec ed o be g ea e o he Lib a y
han o Mannheim, as sugges ed by he co ela ions shown in
Table III. Fu he mo e, he Lib a y en i onmen ep esen s a
medium-size open a ea wi h many obs acles (bookshel es), in
which a posi ioning se ice is commonly desi ed.
D. En i onmen Awa e eg ession assessmen
The eg ession models we e gene a ed using he e e ence
poin s ha de ined he bounda y o he collec ion a ea (see
Figu e 2), which ep esen less han 8% o all a ailable
e e ence poin s. The emaining e e ence poin s we e used
o compu e he eg ession esiduals. The expe imen s only
included APs ha had measu emen s o all e e ence poin s.
Figu e 5 p esen s he eg ession es ima es o APs 15,49
and 8p o ided by a baseline ha combines Na u al Neighbou
in e pola ion and G adien Ex apola ion and by he p oposed
eg ession model based on Suppo Vec o Machine. Fo ou
p oposed Model, he images we e smoo hed using 9pixels
squa e windows con olu ion.
Baseline Model Model & Obs acles
AP wi h ID 15
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
AP wi h ID 49
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
AP wi h ID 8
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
dBm
Fig. 5: Reg ession es ima es o APs 15,49 and 8.
Gi en he small numbe o aining poin s, he wo eg es-
sions pe o med ema kably well o he APs loca ed inside
he collec ion a ea, APs 15 and 49. The p oposed eg ession
can clea ly cap u e he in luence o obs acles in he adio
map. Fo an AP ou side he collec ion zone, he di e ence
be ween Baseline and Model eg ession is no signi ican as
he en i onmen has li le impac on he p opaga ion o weak
signals. The p oposed model cap u es such beha io , and hus
i s es ima es mos ly depend on he dis ance o APs.
Figu e 6 p esen s he eg ession esiduals ob ained using he
baseline and ou p oposed model. The esiduals ob ained o
he p oposed model a e consis en ly be e han hose om he
baseline. Fo AP 15, he maximum esidual alue was abou
10 dBm smalle in he p oposed model han in he baseline.
Fo AP 49, he maximum esidual alues we e simila o
he wo app oaches. Howe e , he p oposed model pe o med
no ably be e han he baseline ega ding pe cen iles be ween
he 25 h and 75 h. Fo AP 8, he di e ence in esidual alues
is less no able han o he p e ious wo AP, which is in pa
a esul o no ably lowe esidual alues.
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Empi ical CDF
Model
Baseline
P obabili y
Reg ession Residuals (dB)
(a) AP ID 15
0 5 10 15 20 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Empi ical CDF
Model
Baseline
P obabili y
Reg ession Residuals (dB)
(b) AP ID 49
0 2 4 6 8 10 12 14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Empi ical CDF
Model
Baseline
P obabili y
Reg ession Residuals (dB)
(c) AP ID 8
Fig. 6: Reg ession esiduals CDF o baseline and ou model.
TABLE V:75 h pe cen ile o eg ession esiduals in dB.
AP ID 1 6 8 15 17 49 51 52 54 69
Model 6.7 6.8 4.7 8.8 8.0 7.8 9.5 8.4 8.5 11.5
Baseline 10.7 10.3 6.6 13.6 13.2 12.2 13.2 10.1 11.2 16.2
Di e ence 4 3.5 1.9 4.8 5.2 4.4 3.7 1.7 2.7 4.7
Table V p esen s he 75 h pe cen ile o eg ession esiduals
o he p oposed model and he baseline me hod. The esul s
a e p o ided o some ele an APs, i.e., hose APs wi h
alid measu emen s a ailable o all (106) e e ence poin s.
Addi ionally, we included AP 71 (which had measu emen s
o 105 poin s) and one weakly seen AP (AP 8). The p oposed
me hod pe o ms be e han he baseline o all selec ed APs.
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Jou nal
8 IEEE SENSORS JOURNAL, VOL. XX, NO. XX, XXXX 2017
V. EMPIRICAL VALIDATION
This sec ion includes he empi ical alida ion by applying
oge he he wo main con ibu ions o his pape : he con-
enien posi ions whe e o collec he e e ence samples and
he imp o ed RSS eg esso o enhance he adio map. Fo
ha pu pose, we ha e used he da a collec ed o he i s
mon h om he Lib a y da ase [42]. I co esponds o a eal
en i onmen wi h se e al obs acles (bookshel es and people)
whose da a collec ion was independen o his esea ch wo k.
T adi ional: The se 01 om he aining se was used as
e e ence da a ( adio map), and he se s 02–05 om he
e alua ion se we e used o e alua ion.
Measu emen : Only he es ing da a (se s 01–05) was used o
e e ence and e alua ion. The 8 poin s highligh ed in Figu e 2
a e used as aining da a ( adio map), whe eas he emaining
poin s a e used o e alua ion.
In e pola ion – Baseline: Simila o Measu emen , bu Na -
u al Neighbo s in e pola ion model is applied o inc ease he
densi y o da a in he aining se .
In e pola ion – P oposed model: Simila o Measu emen ,
bu ou p oposed in e pola ion model is applied o inc ease
he densi y o da a in he aining se .
Following he ISO 18305 S anda d o es and e alua ion o
localiza ion and acking sys ems, we epo he esul s using
he mean, median and 95 h pe cen ile (P95) o he posi ioning
e o in Table VI. Addi ionally, we p o ide he Thi d qua ile
(Q3) as done in he IPIN Compe i ion [62] and he 90 h
pe cen ile (P90).
TABLE VI: Resul s o he empi ical e alua ion
Base model. Mean Median Q3 P90 P95
T adi ional 3.41 2.83 4.74 6.63 7.94
Measu emen 4.26 3.71 5.67 7.98 8.43
In e pola ion – Baseline 4.06 3.69 5.67 7.32 8.7
In e pola ion – P oposed model 3.94 3.8 5.38 6.82 7.21
As expec ed, he adi ional app oach, whe e mul iple e -
e ence posi ions (24 in his case) a e equally dis ibu ed in he
ope a ional a ea, is p o iding he bes o e all esul s, excep ,
su p isingly, o he P95 me ic. The measu emen app oach
(wi h 8 e e ence poin s) is, as expec ed, p o iding he wo s
esul s as a ew e e ence poin s a e loca ed in he pe iphe y.
Bo h in e pola ions, he Na u al Neighbo s and ou p oposed
model, imp o e he esul s o he measu emen app oach. In
gene al, ou model is p o iding he bes esul s using he
educed se o e e ence poin s. Wi h a ew e e ence poin s,
we achie ed a mean accu acy below 4 m and pe cen ile e o s
close o he adi ional app oach.
Analysing he CDF plo (Figu e 7) we can obse e ha :
i) below 30 h pe cen ile, he adi ional app oach and bo h
in e pola ions pe o m simila ly; ii) be ween 30 h and 80 h
pe cen iles, he adi ional app oach is clea ly he bes me hod
(a he expense o collec ing 3 imes mo e e e ence da a); and
iii) he adi ional app oach and ou p oposed me hod ha e a
simila pe o mance in alues abo e 80 h pe cen ile.
0 2 4 6 8 10 12
0
0.2
0.4
0.6
0.8
1Empi ical CDF
Measu emen
In e pola ion - Baseline
In e pola ion - P oposed Me hod
T adi ional
P obabili y
Posi ioning E o (m)
Fig. 7: Posi ioning accu acy.
VI. CONCLUSIONS
This pape has add essed he educ ion o collec ion e o s
o WiFi inge p in ing wi h wo p oposals. The i s p oposal
is a se o guidelines o de e mine con enien posi ions whe e
o collec WiFi samples. The second p oposal is a model
ha imp o es he RSS eg ession es ima es o APs ha a e
s ongly seen in he collec ion a ea. The guidelines we e
d awn om expe imen s ha analyzed he e ec ha he
dis ibu ion o collec ion poin s and he in ensi y o he APs
in he en i onmen ha e in (1) he accu acy o an IPS and
(2) in he quali y o a eg ession ha could be applied o
en ich he adio map. The guidelines highligh he impo ance
o si ua ing collec ion poin s a ound he bounda ies o he
a ge en i onmen . Also, zones ha a e close o APs equi e
mo e collec ion poin s han o he s. Thus, he posi ion o an
AP was shown o be an impo an piece o in o ma ion o
he de e mina ion o collec ion posi ions. Fu he mo e, he
eg essions and in e pola ion me hods a e shown o p o ide
e y good es ima es o AP weakly seen in he en i onmen .
The p oposed model conside s he in luence o obs acles o
imp o e WiFi RSS eg essions o APs s ongly seen in he
en i onmen . The model equi es an app oxima e e e ence
posi ion o he AP whose RSS a e o be es ima ed. The e -
e ence AP posi ion and aw map in o ma ion o he obs acles
in he en i onmen a e used o c ea e he aining ea u es
o a Suppo Vec o Machine eg ession. The eg ession
p oposal p o ided RSS es ima es be e han o he eg ession
o in e pola ion me hods in he es en i onmen and selec ed
(s ong) APs. The bene i s o he eg ession p oposal we e also
es ed acco ding o he posi ioning accu acy o a kNN me hod.
The kNN was applied (1) using he adio map composed
only by collec ed samples, (2) using he adio map c ea ed
wi h o he eg ession o in e pola ion me hods, and (3) using
he adio map c ea ed wi h ou eg ession p oposal. The bes
posi ioning accu acy was ob ained using he hi d op ion.
The eg ession model p esen ed in his pape could be
conside ed a i s s ep owa ds he de ini ion o mo e gene al
eg ession models o me hods whe e, o ins ance, he ype o
ma e ial could be conside ed. To he bes o his wo k’s knowl-
edge, he e is no in e pola ion me hod, eg ession me hod,
o ool ha allows he di ec modeling o he en i onmen
in luence (p esence o obs acles and walls) on a measu ed
phenomenon.
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This a icle has been accep ed o publica ion in a u u e issue o his jou nal, bu has no been ully edi ed. Con en may change p io o inal publica ion. Ci a ion in o ma ion: DOI 10.1109/JSEN.2021.3073878, IEEE Senso s
Jou nal
MENDOZA-SILVA e al.: ENVIRONMENT-AWARE REGRESSION FOR INDOOR LOCALIZATION BASED ON WIFI FINGERPRINTING 9
The idea behind he eg ession model p oposed in his pape
could inspi e o he s o include he en i onmen cha ac e is ics
in o he exis en me hods ha conside he spa ial ela ion
be ween measu emen s. We acknowledge ha mo e ambi ious
conclusions would ha e eached wi h a mo e comp ehensi e
e alua ion. Howe e , some me hods p oposed in he li e a u e
a e no ully ep oducible (some pa ame e s a e s ill missing)
and he se o di e se da a se s a ailable o posi ioning do
no con ain enough in o ma ion o in eg a e maps. We, he
indoo posi ioning communi y, need o adop and p omo e
ep oducible p ac ices as well as c ea ing ich da a se s ol-
lowing in e na ional s anda ds and ensu ing in e ope abili y.
Fu he esea ch is s ill needed o es he p oposed me hod in
a mo e challenging indus ial en i onmen s and/o using BLE
as posi ioning echnology.
REFERENCES
[1] G. M. Mendoza-Sil a, J. To es-Sosped a, and J. Hue a, “A me a-
e iew o indoo posi ioning sys ems,” Senso s, ol. 19, no. 20, 2019.
[2] R. Mau z, “Indoo posi ioning echnologies,” en, PhD hesis, ETH
Zu ich, Zu ich, 2012.
[3] P. Bahl and V. Padmanabhan, “Rada : An in-building -based use
loca ion and acking sys em,” in P oceedings IEEE INFOCOM 2000.
Con e ence on Compu e Communica ions., IEEE, 2000.
[4] A. P´
e ez-Na a o, J. To es-Sosped a, R. Mon oliu, e al., “Challenges
o inge p in ing in indoo posi ioning and na iga ion,” in Geog aphi-
cal and Finge p in ing Da a o C ea e Sys ems o Indoo Posi ioning
and Indoo /Ou doo Na iga ion, Else ie , 2019, pp. 1–20.
[5] E. S. Lohan, J. To es-Sosped a, H. Lepp¨
akoski, e al., “Wi- i c owd-
sou ced inge p in ing da ase o indoo posi ioning,” Da a, ol. 2,
no. 4, 2017.
[6] A. Khalajmeh abadi, N. Ga sis, and D. Akopian, “S uc u ed g oup
spa si y: A no el indoo wlan localiza ion, ou lie de ec ion, and
adio map in e pola ion scheme,” IEEE T ansac ions on Vehicula
Technology, ol. 66, no. 7, pp. 6498–6510, 2017.
[7] ——, “Mode n wlan inge p in ing indoo posi ioning me hods and
deploymen challenges,” IEEE Communica ions Su eys Tu o ials,
ol. 19, no. 3, pp. 1974–2002, 2017.
[8] X. Zhou, T. Chen, D. Guo, e al., “F om one o c owd: a su ey
on c owdsou cing-based wi eless indoo localiza ion,” F on ie s o
Compu e Science, ol. 12, no. 3, pp. 423–450, 2018.
[9] D. Zou, W. Meng, S. Han, e al., “Use aided sel -g owing app oach
on adio map cons uc ion o wlan based localiza ion,” in P oceedings
o he 26 h In e na ional Technical Mee ing o The Sa elli e Di ision
o he Ins i u e o Na iga ion (ION GNSS+ 2013), 2013, pp. 991–997.
[10] S. Ts uya, R. Dalla To e, D. Aljade , e al.,De ices, me hods, and
sys ems o adio map gene a ion, US Pa en 8,938,255, 2015.
[11] F. Meneses, A. Mo ei a, A. Cos a, e al., “4 - adio maps o inge -
p in ing in indoo posi ioning,” in Geog aphical and Finge p in ing
Da a o C ea e Sys ems o Indoo Posi ioning and Indoo /Ou doo
Na iga ion, Academic P ess, 2019, pp. 69 –95.
[12] Y. Zhuang, Z. Syed, J. Geo gy, e al., “Au onomous sma phone-
based wi i posi ioning sys em by using access poin s localiza ion and
c owdsou cing,” Pe asi e and Mobile Compu ing, ol. 18, pp. 118
–136, 2015.
[13] J. K umm and J. Pla , “Minimizing calib a ion e o o an indoo
802.11 de ice loca ion measu emen sys em,” Mic oso Resea ch,
No embe , 2003.
[14] B. Li, Y. Wang, H. K. Lee, e al., “Me hod o yielding a da abase
o loca ion inge p in s in wlan,” IEE P oceedings - Communica ions,
ol. 152, no. 5, pp. 580–586, 2005.
[15] Z. Gu, Z. Chen, Y. Zhang, e al., “Reducing inge p in collec ion o
indoo localiza ion,” Compu e Communica ions, ol. 83, pp. 56 –63,
2016.
[16] S. Ezpele a, J. Cla e , J. P´
e ez-Solano, e al., “RF-Based Loca ion
Using In e pola ion Func ions o Reduce Finge p in Mapping,” en,
Senso s, ol. 15, no. 10, pp. 27 322–27 340, 2015.
[17] J. Racko, J. Machaj, and P. B ida, “Wi- i inge p in adio map c ea ion
by using in e pola ion,” P ocedia Enginee ing, ol. 192, pp. 753 –758,
2017, 12 h in e na ional scien i ic con e ence o young scien is s on
sus ainable, mode n and sa e anspo .
[18] M. Zhang and W. Cai, “Mul i a ia e polynomial in e pola ion based
indoo inge p in ing localiza ion using blue oo h,” IEEE Senso s Le -
e s, ol. 2, no. 4, pp. 1–4, 2018.
[19] L. Xie, X. Jin, M. Zhou, e al., “Cos -e icien ble inge p in da abase
cons uc ion app oach ia mul i-quad ic b in e pola ion,” EURASIP
Jou nal on Wi eless Communica ions and Ne wo king, ol. 2019, 2019.
[20] J Tal i ie, M Ren o s, and E. S. Lohan, “Dis ance-Based In e pola ion
and Ex apola ion Me hods o RSS-Based Localiza ion Wi h Indoo
Wi eless Signals,” IEEE T ansac ions on Vehicula Technology, ol. 64,
no. 4, pp. 1340–1353, 2015.
[21] V. Mogh adaiee, S. A. Gho ashi, and M. Gha ami, “New econs uc ed
da abase o cos educ ion in indoo inge p in ing localiza ion,” IEEE
Access, ol. 7, pp. 104 462–104 477, 2019.
[22] J. S. Seybold, Indoo P opaga ion Modeling. Wiley, 2005, ch. 9,
pp. 208–216.
[23] M. U. Ali, S. Hu , and Y. Pa k, “Locali: Calib a ion- ee sys ema ic
localiza ion app oach o indoo posi ioning,” Senso s, ol. 17, 2017.
[24] A. S. Glassne , An in oduc ion o ay acing. Else ie , 1989.
[25] M. Ayadi, N. To jemen, and S. Tabbane, “Two-dimensional de e -
minis ic p opaga ion models app oach and compa ison wi h calib a ed
empi ical models,” IEEE T ansac ions on Wi eless Communica ions,
ol. 14, no. 10, pp. 5714–5722, 2015.
[26] P. S. Heckhe , “Radiosi y in la land,” Compu e G aphics Fo um,
ol. 11, no. 3, pp. 181–192, 1992.
[27] M. F. Cohen, D. P. G eenbe g, D. S. Immel, e al., “An e icien
adiosi y app oach o ealis ic image syn hesis,” IEEE Compu e
g aphics and Applica ions, ol. 6, no. 3, pp. 26–35, 1986.
[28] ´
Osca Belmon e-Fe n´
andez, R. Mon oliu, J. To es-Sosped a, e al.,
“A adiosi y-based me hod o a oid calib a ion o indoo posi ioning
sys ems,” Expe Sys ems wi h Applica ions, ol. 105, pp. 89 –101,
2018.
[29] M. M. A ia, A. Nou eldin, and M. J. Ko enbe g, “Dynamic online-
calib a ed adio maps o indoo posi ioning in wi eless local a ea
ne wo ks,” IEEE T ansac ions on Mobile Compu ing, ol. 12, no. 9,
pp. 1774–1787, 2013.
[30] P. Rich e and M. Toledano-Ayala, “Re isi ing gaussian p ocess eg es-
sion modeling o localiza ion in wi eless senso ne wo ks,” Senso s,
ol. 15, no. 9, pp. 22 587–22 615, 2015.
[31] H. Zou, M. Jin, H. Jiang, e al., “Winips: Wi i-based non-in usi e
indoo posi ioning sys em wi h online adio map cons uc ion and
adap a ion,” IEEE T ansac ions on Wi eless Communica ions, ol. 16,
no. 12, pp. 8118–8130, 2017.
[32] W. Sun, M. Xue, H. Yu, e al., “Augmen a ion o inge p in s o indoo
wi i localiza ion based on gaussian p ocess eg ession,” IEEE T ans-
ac ions on Vehicula Technology, ol. 67, no. 11, pp. 10 896–10 905,
2018.
[33] H. Ai, K. Tang, W. Huang, e al., “Fas inge p in s cons uc ion ia
gp o high spa ial- empo al esolu ion wi h spa se ss sampling in
indoo localiza ion,” Compu ing, 2019.
[34] C. Liu, A. Ki ing, N. Salman, e al., “A k iging algo i hm o loca ion
inge p in ing based on ecei ed signal s eng h,” in 2015 Senso Da a
Fusion: T ends, Solu ions, Applica ions (SDF), 2015, pp. 1–6.
[35] S.-S. Jan, S.-J. Yeh, and Y.-W. Liu, “Recei ed signal s eng h da abase
in e pola ion by k iging o a wi- i indoo posi ioning sys em,” Senso s,
ol. 15, no. 9, pp. 21 377–21 393, 2015.
[36] S. K am, C. Nickel, J. Sei z, e al., “Spa ial in e pola ion o wi- i ss
inge p in s using model-based uni e sal k iging,” in 2017 Senso Da a
Fusion: T ends, Solu ions, Applica ions (SDF), 2017, pp. 1–6.
[37] Y. Du, D. Yang, and C. Xiu, “A no el me hod o cons uc ing a wi i
posi ioning sys em wi h e icien manpowe ,” Senso s, ol. 15, no. 4,
pp. 8358–8381, 2015.
[38] N. He n´
andez, M. Oca˜
na, J. M. Alonso, e al., “Con inuous space
es ima ion: Inc easing wi i-based indoo localiza ion esolu ion wi hou
inc easing he si e-su ey e o ,” Senso s, ol. 17, no. 1, 2017.
[39] L. Li, G. Shen, C. Zhao, e al., “Expe iencing and handling he
di e si y in da a densi y and en i onmen al locali y in an indoo
posi ioning se ice,” in P oceedings o he 20 h Annual In e na ional
Con e ence on Mobile Compu ing and Ne wo king, 2014, pp. 459–470.
[40] L. Kana is, A. Kokkinis, G. Fo ino, e al., “Sample Size De e mi-
na ion Algo i hm o inge p in -based indoo localiza ion sys ems,”
Compu e Ne wo ks, ol. 101, pp. 169–177, 2016.
[41] W. Bong and Y. C. Kim, “Finge p in wi- i adio map in e pola ed by
discon inui y p ese ing smoo hing,” in In e na ional Con e ence on
Hyb id In o ma ion Technology, Sp inge , 2012, pp. 138–145.
Au ho ized licensed use limi ed o: Uni jaume I. Downloaded on July 01,2021 a 07:38:26 UTC om IEEE Xplo e. Res ic ions apply.