LoRaWAN Finge p in ing wi h K-Means:
he Rele ance o Clus e s Visual Inspec ion
Joaquín To es-Sosped a1, Michiel Ae nou s2, Ad iano Mo ei a1and
Ra ael Be k ens2
1ALGORITMI Resea ch Cen e, Uni e si y o Minho, 4800-058 Guima ães, Po ugal
2IDLab – Facul y o Applied Enginee ing, Uni e si y o An we p – imec, An we p, Belgium
Abs ac
LoRaWAN-based posi ioning is eme ging as an al e na i e posi ioning solu ion o ba e y-cons ained
IoT de ices o GNSS-denied a eas in u ban en i onmen s. The da a collec ed a he LoRaWAN Base
S a ions, such as he RSSI o ecei ed messages, can be me ged o gene a e an RF inge p in . Unsupe ised
c owdsou cing can be le e aged o build a la ge adio map co e ing a u ban a ea a he expense o
in oducing noise o a ound ens o me e s when labelling he e e ence da a. As inge p in ing may
ha e a low e iciency in a such a dense adio map, we p opose o use
𝐾
-Means clus e ing o make
he posi ion es ima ion as e . Du ing ou s udy, we ound ha clus e ing can also be used o de ec
la ge ou lie s in he adio map ha can be subjec o be emo ed. The a ionale is o iden i y hose
samples wi hin he clus e ha a e a om he geome ic cen oid o he clus e . This pape in oduces
he analysis o in oducing
𝐾
-Means clus e ing wi h ou lie de ec ion and he bene i s i migh b ing.
Al hough emo ing ou lie s ha e no had an ou s anding inc ease in he posi ioning accu acy, he
pe o med analysis has enabled a new me ic ha is mode a ely co ela ed wi h he posi ioning e o .
This co ela ion may be use ul o de ec un eliable posi ion es ima es and disca d hem. The esul s
p esen ed in his wo k, based on wo LoRaWAN da ase s, show ha he a e age and median posi ioning
e o can be imp o ed by 5 % o 10 % by disca ding 4 % o 6 % o ope a ional samples.
Keywo ds
Finge p in ing, Clus e ing, Scalabili y, LoRaWAN
1. In oduc ion
The In e ne o Things (
IoT
) aims o in e connec a wide a ie y o objec s, anging om
empe a u e senso s on mobile cooling con aine s o ga bage bins in a ci y. In o de o co ec ly
in e p e he measu emen s o such senso s, i is impo an o co ela e hem wi h loca ion
in o ma ion. In many cases,
IoT
de ices include a
GNSS
ecei e o his pu pose. Howe e ,
his ecei e only p o ides he de ice i sel wi h loca ion da a, an Low Powe Wide A ea
Ne wo k (
LPWAN
) such as LoRaWAN is o en used o ge senso measu emen s and
GNSS
da a
o he use . This wo k low is illus a ed in Fig.1.
ICL-GNSS’22: In e na ional Con e ence on Localiza ion and GNSS, June 07–09, 2022, Tampe e, Finland
$in o@j o .es ( Joaquín To es-Sosped a); Michiel.A[email p o ec ed] ( Michiel Ae nou s);
[email p o ec ed].p ( Ad iano Mo ei a); a ael.be k ens@uan we pen.be ( Ra ael Be k ens)

0000-0003-4338-4334 ( Joaquín To es-Sosped a); 0000-0002-0527-3871 ( Michiel Ae nou s); 0000-0002-8967-118X
( Ad iano Mo ei a); 0000-0003-0064-5020 ( Ra ael Be k ens)
©2021 Copy igh o his pape by i s au ho s. Use pe mi ed unde C ea i e Commons License A ibu ion 4.0 In e na ional (CC BY 4.0).
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ISSN 1613-0073
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Figu e 1: LPWANS a e used o ge senso and loca ion da a o he use . Addi ionally, he use can
access ne wo k me ada a om he LPWAN.
An impo an cons ain on
IoT
communica ion and localiza ion echnologies is ha hey
mus be as ene gy-e icien as possible, because
IoT
de ices gene ally ope a e o mul iple
yea s using small ba e ies. This, and he ac ha
GNSS
can no mally only be used in ou doo
en i onmen s, has mo i a ed esea che s o omi powe -hung y
GNSS
ecei e s and ins ead
le e age he exis ing
LPWAN
link and senso da a o localiza ion pu poses. Fo example,
me ada a such as he Recei ed Signal S eng h Indica o (
RSSI
), phase o iming in o ma ion
om mul iple
LPWAN
ecei e s can be ansla ed o dis ance es ima ions be ween each ecei e
and a ansmi ing
IoT
de ice. Howe e , hese me hods s ongly depend on he
LPWAN
ne wo k
deploymen and gene ally lead o high loca ion es ima ion e o s. A p e ious analysis on he
choice be ween
GNSS
and
LPWAN
localiza ion shows ha he la e should only be a o ed
o e
GNSS
when a la ge loca ion e o is jus i iable and when he ene gy budge o an
IoT
de ice is ex emely limi ed [
1
]. In p ac ice, his means ha implemen ing
GNSS
ecei e s on
low-powe
IoT
de ices is o en easible. Tha being said,
LPWAN
localiza ion can ce ainly s ill
p o e i s use, because no all applica ions equi e loca ion da a wi h
GNSS
-like accu acy. Fo
example, a cons uc ion company migh only wan o know a which o i s building si es i s
asse s a e loca ed, which implies ha an e o o hund eds o me e s can be accep ed.
LPWAN
localiza ion can also play an impo an ole in mul imodal localiza ion, o example as a allback
solu ion when a acking de ice is mo ing in o
GNSS
-denied a eas such as unnels o indoo
en i onmen s [2]. Mo eo e , i may ac as a e i ica ion mechanism o de ec GNSS spoo ing.
In 2019, Ae nou s e al. published an ex ended e sion o he LoRaWAN da ase desc ibed
in [
3
]. O e a cou se o h ee mon hs, 20 pos al se ices ca s ca ied LoRaWAN de ices
ha pe iodically ansmi ed hei la es
GNSS
loca ion. As a esul , he collec ed da ase
con ains
130430
en ies wi h a g ound u h loca ion, he LoRa Sp eading Fac o (
SF
) used
by he ansmi e , iming da a and Recei ed Signal S eng h (
RSS
) da a o each ecei ing
LoRaWAN ga eway. I should be no ed ha he g ound u h in o ma ion was collec ed om
GNSS
ecei e s and, he e o e, wi h po en ial e o s o ens o me e s. Fi s , u ban canyoning
can dec ease he
GNSS
accu acy, since he da ase is collec ed in a dense u ban a ea. Second,
he ecei ed
GNSS
coo dina es o he ansmi ing de ice could di e om he ac ual de ice
coo dina es a ecei ing ime because he o al ansmission ime o a LoRa signal can ake up
o a ew seconds, depending on he payload size and he
SF
. This e ec becomes e en mo e
p ominen when he ansmi e a els a highe speeds.
RSS
da a enables posi ioning wi h ila e a ion and inge p in ing. While he o me equi es
knowing he loca ion o he LoRaWAN Base S a ions (
BS
s), he p opaga ion model and he
en i onmen obs uc ions; he la e only equi es a se o e e ence da a a known posi ions, also
known as he adio map. In his pape , we ocus on passi e inge p in ing, whe e a inge p in
is he se o
RSSI
measu emen s o a pa icula LoRaWAN message ansmi ed by a de ice and
measu ed in he a ailable LoRaWAN BSs in he ope a ional a ea.
This echnique equi es wo phases: he o line phase ocuses on geo- e e enced
RSSI
da a
collec ion (see adio map collec ion in [
3
]), whe eas he online phase es ima es he posi ion o
new inge p in s a unknown posi ions wi h, o ins ance, a
𝑘
-Nea es Neighbou (
𝑘-NN
)-based
algo i hm and he adio map.
Howe e , inge p in ing is compu a ionally demanding i he da ase con ains housands o
samples, e.g. LoRaWAN da ase s in [
3
]. In hose da ase s, e e y single ope a ional inge p in
has o be compa ed wi h all he e e ence samples in he adio map, e en i hey signi ican ly
di e , o ob ain he mos simila ones and compu e he inal posi ion es ima e. Thus, clus e ing
echniques ha e been applied o spli he adio map in o se e al smalle e sions [
4
,
5
,
6
,
7
,
8
,
9
,
10
,
11
,
12
,
13
,
14
]. In he ope a ional s age, he iden i ica ion o he mos ele an clus e is done
i s (coa se sea ch). Then, he posi ion is es ima ed using he co esponding educed adio map
( ine-g ained sea ch). This wo-s ep p ocedu e is signi ican ly as e ha egula inge p in ing,
specially in la ge da ase s [15].
In his pape we p opose a e sion o
𝐾
-Means clus e ing wi h ou lie de ec ion whe e noisy
inge p in s a e emo ed. We hypo he ise ha he clus e s gene a ed wi h
𝐾
-Means o e he
ea u e
RSSI
space can be de-noised by emo ing he e e ence samples which a e signi ican ly
a o he clus e geome ic cen oid. I is wo h no ing ha he p oposed algo i hmic solu ion is
pe o med a e gene a ing he clus e s wi h
𝐾
-Means.
𝐾
-Means clus e ing is an unsupe ised
model ha g oups simila da a wi hou , in his case, he loca ion in o ma ion (i.e., he labels).
Thus, we conside ha
𝐾
-MEANS basic p inciples canno be signi ican ly e- o mula ed o
make i mo e obus . The main con ibu ions o his wo k include:
•
Modi ica ion o
𝐾
-Means o emo e ou lie s om clus e s acco ding o he geome ic
in o ma ion;
•
Comp ehensi e compa ison be ween applying
𝐾
-Means wi hou and wi h ou lie de ec-
ion;
•A new me ic which is co ela ed wi h he posi ioning e o unde some cases;
•A p ocedu e o disca d un eliable posi ion es ima ions.
The emainde o his wo k is o ganised as ollows. Sec ion 2in oduces he ela ed wo k on
LoRaWAN, inge p in ing and clus e ing. Sec ion 3desc ibes he ma e ials and me hods used
in his wo k. Sec ion 4de ails he expe imen al se up and shows he empi ical esul s. Sec ion 5
p o ides he inal discussion and conclusions abou his wo k.
2. Rela ed wo k
2.1. LoRaWAN and inge p in ing
LoRaWAN’s ela i ely wide bandwid h o
125 kHz
o
250 kHz
makes i a sui able candida e
o bo h
RSS
-based and ime-based localiza ion. Thanks o he widesp ead a ailabili y o
LoRaWAN ne wo ks and da ase s, many esea che s ha e e alua ed he pe o mance o a ious
localiza ion me hods. Fo ins ance, Pospisil e al. e alua ed he pe o mance o i e Time
Di e ence o A i al (
TDoA
) algo i hms h ough simula ion and alida ed wo o hem wi h
ield measu emen s. They achie ed a mean loca ion e o o
543 m
in a es a ea o
4.58 km2
[
16
].
The a o emen ioned LoRaWAN da ase by Ae nou s e al. enabled many esea che s o e alu-
a e inge p in ing and machine lea ning app oaches o localiza ion. Pandangan e al. gene a ed
a hyb id da ase con aining
RSS
and
TDoA
in o ma ion based on he LoRaWAN da ase . Thei
hyb id da ase was hen used o e alua e
𝑘-NN
and Random Fo es algo i hms which esul ed in
a median e o o
333 m
and
194 m
espec i ely [
17
]. This is a sligh imp o emen compa ed o
ela ed esea ch on Neu al Ne wo k localiza ion wi h he LoRaWAN da ase [
18
,
19
]. Pu ohi e
al. also used his da ase o hei esea ch on Neu al Ne wo k localiza ion. In hei in es iga ion
o h ee di e en lea ning models, he Long Sho -Te m Memo y (LSTM) model wi h 64 neu ons
came ou on op wi h a mean e o o
191 m
[
20
]. Janssen e al. compa ed he loca ion accu acy,
𝑅2
sco e and e alua ion ime o en Machine Lea ning algo i hms using he LoRaWAN da ase .
Thei expe imen s show ha he weigh ed
𝑘-NN
and Random Fo es algo i hms esul in he
bes accu acy and
𝑅2
sco e, bu Random Fo es has a signi ican ly as e compu a ion ime [
21
].
In a subsequen s udy, he au ho s ex ended hei compa ison wi h ange-based localiza ion
using eigh di e en pa h loss models and six weigh unc ions. Thei bes pa h loss model -
weigh unc ion combina ion yielded an es ima ion e o o
700 m
, which is signi ican ly highe
han he
340 m
ob ained wi h inge p in ing. Fu he mo e, his wo k p o ides a comp ehensi e
o e iew o he ade-o s ha mus be made be ween ange-based and inge p in ing-based
localiza ion, including accu acy, complexi y, cos , e c. [22].
2.2. Clus e ing in inge p in ing
Clus e ing has been widely applied in Wi-Fi and BLE inge p in ing o educe he compu a-
ional cos and keep simila accu acy, being
𝐾
-Means [
4
,
5
], including
𝐾
-Medoids [
6
,
7
] and
Fuzzy 𝑐-Means (FCM) [8,9,10] a ian s, he mos popula . O he app oaches, such as A ini y
P opaga ion Clus e ing (
APC
) [
11
,
12
] o Densi y-based spa ial clus e ing o applica ions wi h
noise (
DBSCAN
) [
13
,
14
], ha e also been explo ed bu hei easibili y may depend on he
da ase acco ding o some p elimina y expe imen s we pe o med.
The e o e, his wo k is ocusing in
𝐾
-Means clus e ing, ying o ake bene i om he
posi ion in o ma ion o he e e ence da a o emo e hose e e ence samples ha may poison
he adio map. To enhance he pe o mance o
𝐾
-Means, we ha e used he Manha an dis ance
o dis ances compu a ions in he ea u e (
RSSI
) space and he cen oid ini ializa ion p oposed
in [23].
3. Ma e ials and Me hods
3.1. 𝐾-Means in inge p in ing
The co e o he passi e inge p in ing echnique equi es wo phases: he o -line and on-line
phases as explained be o e. In he o -line phase, e e ence inge p in s (
𝑠𝑡
) a e gene a ed om
a se o ecei ed LoRaWAN messages ( ha include hei posi ion om GPS) by he a ailable
LoRaWAN
BS
, gene a ing hus a adio map (
𝒯
). In he on-line phase, he ope a ional inge p in s
( om unknown posi ions) a e compa ed o he inge p in s s o ed in he adio map. Thei
posi ion is es ima ed using he loca ions o he mos simila inge p in s in he adio map,
usually compu ing hei cen oid.
A e gene a ing he adio map
𝒯
, simila inge p in s in he ea u e
RSSI
space a e g ouped
by
𝐾
-Means clus e ing algo i hm. I is expec ed ha inge p in s wi hin a clus e would be
also close in he geome ical space. The ou pu o
𝐾
-Means p o ides he
𝐾
clus e cen oids,
𝒞𝑖,∀𝑖∈[1, . . . , 𝐾]
, and he educed adio map o e e y clus e
𝒯𝑖,∀𝑖∈[1, . . . , 𝐾]
. The
cen oids and e e ence inge p in s a e bo h ec o s ep esen ing he ea u e
RSSI
space, hus
ha ing as many alues as LoRaWAN BSs.
As an illus a i e example, a ew clus e s o e he LoRaWAN 2017/18 da ase a e shown
in Fig. 2. The g ay do s ep esen he e e ence inge p in s in he adio map, whe eas he
colou ed ones ep esen he samples in he clus e . The numbe o e e ence inge p in s and
hei dispe sion in he geome ic space depends on he clus e .
500
1000
1500
2000
2500
3000
200
400
600
800
1000
1200
1400
1600
1800
2000
200
400
600
800
1000
1200
1400
1600
1000
1500
2000
2500
3000
3500
4000
4500
500
1000
1500
2000
2500
3000
3500
4000
Figu e 2: Example o six illus a i e clus e s gene a ed by
𝐾
-Means in LoRaWAN 2017/18 da ase .
Colo indica es dis ance [m] o geome ic cen oid.
In he ope a ional phase, he sea ch o mos simila e e ence inge p in s is done in a wo-s ep
p ocess. Fi s , he ope a ional inge p in is compa ed o all he clus e cen oids (
RSSI
space)
o e ie e he one epo ing he lowes Euclidean dis ance. Second, he sea ch o mos simila
e e ence inge p in s is done o e he co esponding educed adio map, 𝒯𝑖.

3.2. Analysis o clus e ing wi h 𝐾-Means
P e ious esul s in he li e a u e show ha
𝐾
-Means in inge p in ing educes he compu a ional
cos a he expense o a sligh ly highe posi ioning e o . This educ ion on ime is specially
ele an in la ge da ase s [24].
In his pape , he same clus e ing model has been applied o bo h LoRaWAN da ase s, being
𝐾 he squa ed oo o he samples in he adio map as sugges ed in [24]. These esul s, which
a e shown in Sec ion 4.2, we e in phase wi h he esul s epo ed in he li e a u e.
Howe e , o a oid he adop ion o a black box app oach while using
𝑘
-Means, an addi ional
o e all analysis on he clus e s was pe o med. In pa icula , he loca ion (longi ude and la i ude
in WGS84 o ma ) o he e e ence samples in he educed adio map was isually inspec ed o
each clus e , showing a ele an ou pu in many clus e s.
Fig. 2shows six illus a i e examples o he clus e s gene a ed wi h
𝐾
-Means. Despi e hei
size and dispe sion depend on he clus e , mos o hem epo cases whe e he inge p in s a e
e y a ( eddish poin s in he igu e) om he cu en geome ic cen oid and close o o he s
geome ic cen oids. Those ou lie s sha e simila
RSSI
alues wi h espec o he e e ence
inge p in s in he clus e , bu he geog aphically a om hem. Among o he ac o s, his
e ec may be caused by he posi ioning e o s in oduced by he GNSS ecei e s.
3.3. Remo ing noisy samples om clus e s
The idea o emo e noisy samples om he adio map is simple. Gi en he samples ( inge p in s)
o a clus e , hei geome ic cen oid (in he WGS84 space) is calcula ed. All samples whose
dis ance o he geome ic cen oid is highe han wice he median alue a e emo ed. This is
only applied o hose clus e s whe e he maximum dis ance is highe han
5
imes he median
alue. i.e., i is only applied o hose clus e s ha ing signi ican ou lie s. The p oposed model
is desc ibed in Algo i hm 1, which has 3 s ages: clus e s gene a ion (line 2), clus e s cleaning
(ln. 3–12) and posi ion es ima ion (ln.15–22). Fi s and second s age can be pe o med once pe
da ase , so hei iming can be neglec ed when p o iding he compu a ional cos s o p o iding
a posi ion es ima e in he online phase.
𝒯
is he adio map,
𝒱
is he se wi h he es /e alua ion samples,
𝑘
is he numbe o nea es
neighbo s o
𝑘-NN
. A sample ( inge p in ) is ep esen ed wi h
s
and has
𝑁𝑏𝑠
elemen s (one o
each LoRaWAN
BS
), whe eas i s posi ion is ep esen ed and i s posi ion (longi ude and la i ude
in WGS84) wi h
pos
. Fo
𝐾
-Means,
𝐾
is he numbe o clus e s (
𝐾=√︀|𝒯 |
as sugges ed
in [
15
]),
𝒞
ep esen s he clus e s
RSSI
cen oids and
𝒢
ep esen s he clus e s geome ic la /lon
cen oids. ˙
𝒯𝑐s ands o he clean educed adio map o clus e 𝑐.
The o he pa ame e s o he ou lie de ec ion we e se based on he esea che s expe ience.
e.g., he h eshold used o emo e he noisy samples,
2
imes he median dis ance, has been
selec ed as he dis ances o he geome ic cen oid usually inc ease g adually.
Algo i hm 1 𝑘-NN o posi ioning wi h 𝐾-Means and ou lie de ec ion
1: inpu 𝒯,𝒱,𝑘,𝐾
2: 𝒞𝑖,𝒯𝑖←Apply 𝐾-Means o 𝒯
3: o 𝑖= 1 o 𝐾do
4: 𝒢𝑖←Compu e geome ic cen oid o samples in 𝒯𝑖
5: 𝐺←{︀𝑔𝑒𝑜𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (︀pos𝑗,𝒢𝑖)︀,∀𝑗∈ 𝒯𝑖}︀
6: i 𝑚𝑎𝑥 (𝐺)>(5 ·𝑚𝑒𝑑𝑖𝑎𝑛 (𝐺)) hen
7: // Remo e samples a om geome ic cen oid
8: ˙
𝒯𝑖←{︁s𝒯𝑖
𝑗∈ 𝒯𝑖:𝐺𝑗≤(2 ·𝑚𝑒𝑑𝑖𝑎𝑛 (𝐺))}︁
9: else
10: ˙
𝒯𝑖← 𝒯𝑗// No cleaning o clus e 𝑖
11: end i
12: end o
13: o 𝑖= 1 o |𝒱| do
14: Iden i y mos ele an clus e , 𝑐
15: Se he educed adio map ˙
𝒯𝑐
16: o 𝑗= 1 o |˙
𝒯𝑐|do
17: Compu e dis ance be ween s𝒱
𝑖and s
˙
𝒯𝑐
𝑗
18: end o
19: So dis ances in RSS space
20: Selec he 𝑘closes candida es
21: Es ima e posi ion la /lon
22: end o
23: Re u n: Es ima ed posi ions o all samples in 𝒱
4. Expe imen s and Resul s
4.1. Expe imen al Se up
In o de o assess he p oposed clus e ing model wi h ou lie de ec ion, we ha e compa ed
he esul s be ween he plain
𝑘-NN
, he op imiza ion ule p oposed by Mo ei a [
25
],
𝐾
-Means
wi hou ou lie de ec ion and
𝐾
-Means wi h ou lie de ec ion. To es ima e he inal posi ion,
we ha e used he simple
1
-NN algo i hm using he Euclidean dis ance. The models ha e been
un 10 imes o minimise he andom ini ializa ion o 𝐾-Means.
Fo he expe imen s, wo da ase s collec ed in he ci y o An we p be ween end o 2017 and
beginning o 2019 [
3
,
26
] ha e been used, namely LoRaWAN 2017/18 and LoRaWAN 2018/19.
Bo h da ase s we e collec ed o e alua e inge p in localiza ion algo i hms in la ge ou doo
en i onmen s and, acco ding o he da abase au ho s, he
RSSI
o he LoRaWAN messages could
hold an addi ional GPS e o . This ea u e makes hem app op ia e o assessing he p oposed
algo i hm o emo e noise om clus e s. Fo bo h da ase s, he samples ha e been so ed by
imes amp and hen spli o aining and es ing, he i s
≈80%
o samples ha e been used
o aining and he las
≈20%
o samples ha e been used o e alua ion. This di ision has
been pe o med o a oid ha ing da a om he same de ice and day on bo h subse s, 𝒯and 𝒱.
The e alua ion me ics include he A e aged Posi ioning E o (
APE
),
¯𝜖
; he Median Posi-
ioning E o (
MPE
),
˜𝜖
; and he A e aged Ope a ional Time (
AOT
),
¯𝜏𝑓𝑝
, and conside all he
10 execu ion uns. The
APE
and
MPE
a e included in he ISO18305 s anda d, whe eas he
AOT e e s o he a e age ime equi ed o p ocess an ope a ional inge p in and p o ide he
posi ion es ima e. In con as o he plain
𝑘
-NN algo i hm, whe e all inge p in s hold simila
ope a ional ime, he ope a ional ime may signi ican ly a y depending on he clus e . i.e.,
𝐾
-Means clus e ing does no gua an ee ha all clus e s a e equally dis ibu ed, so he ime
equi ed o pe o m he ine-g ained sea ch will depend on he selec ed clus e . The e o e, he
s anda d de ia ion is also epo ed o he ope a ional ime.
4.2. Resul s
This subsec ion is de o ed o show he empi ical esul s. Fi s , a compa ison wi h adi ional
inge p in models is in oduced. Then, a comp ehensi e analysis abou he consequences o
emo ing noise om he adio map is pe o med. Finally, he possible bene i s o he p oposed
model a e desc ibed.
4.2.1. Compa a i e analysis
Table 1in oduces he main esul s o he compa a i e analysis. I includes he plain
𝑘
-NN
algo i hm (
𝑘= 1
), he op imiza ion ule based on common s onges ancho p oposed in
Mo ei a e al. [
25
], and
𝐾
-Means clus e ing wi hou and wi h he ou lie de ec ion (OD). Fig. 3
in oduces he Empi ical Cumula i e Dis ibu ion Func ion (
ECDF
) plo s o he posi ioning
e o and ope a ional ime o he ou me hods o bo h da ase s.
Table 1
Main esul s: APE, MPE and AOT
Lo awan 2017/18 Lo awan 2018/19
Me hod ¯𝜖[m] ˜𝜖[m] ¯𝜏[ms] ¯𝜖[m] ˜𝜖[m] ¯𝜏[ms]
plain 𝑘-NN 558.3 374.1 2464.0 (13.7 )375.6 169.3 2518.2 (11.0 )
Mo ei a [25] 563.4 377.0 202.9 (149.7 )375.5 167.7 306.4 (223.9 )
𝐾-Means 566.1 379.2 17.1 (7.3 )379.7 174.7 28.2 (16.0 )
𝐾-Means OD 559.3 369.6 16.4 (6.8 )378.8 168.0 26.8 (15.5 )
In gene al, he ou models p o ide simila esul s in e ms o posi ioning e o being he
main di e ence hei compu a ional cos . The wo solu ions based on
𝐾
-Means epo he
lowes compu a ional cos wi h an a e aged execu ion ime below
20 ms
and
30 ms
espec i ely.
Remo ing he ou lie s no only made
𝐾
-Means sligh ly mo e accu a e bu also sligh ly mo e
e icien in he ope a ional s age as he p oposed app oach emo ed
8.6%
and
9.5%
o e e ence
inge p in s on each da ase espec i ely. Howe e , he imp o emen s may be ma ginal.
LoRaWAN 2017 LoRaWAN 2019
Figu e 3: ECDF o posi ioning e o and execu ion ime o bo h da ase s
4.2.2. A comp ehensi e analysis o emo ing noise
Despi e
𝐾
-Means wi hou and wi h ou lie s de ec ion ha ing simila pe o mance acco ding o
he p e ious esul s, posi ioning can be based on wo sou ces, namely a noisy adio map and a
clean adio map. This enables o exploi some addi ional in o ma ion a he ope a ional s age
as he e a e samples whe e bo h app oaches based on
𝐾
-Means (wi hou and wi h ou lie s
de ec ion) do no ag ee in es ima ing he posi ion. This happens in
12%
and
32%
o samples on
each da ase , espec i ely.
Thus, he e alua ion se can be spli in o wo subse s, one whe e bo h es ima o s ag ee and
p o ide he same posi ion es ima ion (“same” in able and igu e), and he o he whe e hey
disag ee (“di ”). Table 2and Fig. 4show he co esponding esul s and ECDFs.
Acco ding o Table 2and he
ECDF
s plo s om Fig. 4, he subse “same” is gene ally be e
han he subse “di ” in bo h me ics, posi ioning e o and execu ion ime, specially in he i s
da ase (LoRaWAN 2017/18). i.e. when he wo es ima o s –wi hou and wi h ou lie de ec ion–
ag ee, he posi ioning esul s a e be e ha when hey disag ee. I bo h es ima o s disag ee,
he posi ioning e o p o ided wi h 𝐾-Means wi h ou lie de ec ion is be e .