L5IN+: F om an Analy ical Pla o m o Op imiza ion o Deep
Ine ial Odome y
Hossein Shoush a i 1, Fi as Kassawa 2, Do ian Ha de 1, Ko in Venzke 1, Jö g Mülle -
Lie zkow 3, Ha ald S e nbe g 1
1 Ha enCi y Uni e si y, Geodesy and Geoin o ma ics, Hambu g, Ge many
2 Bonn Uni e si y, Compu e Science Ins i u e, Bonn, Ge many
3 Ha enCi y Uni e si y, Economy and Digi iza ion, Hambu g, Ge many
Abs ac
Fi h gene a ion o mobile communica ions (5G) and Deep Neu al Ne wo ks (DNN) a e wo
impo an echnologies, which will enable new unc ions in he ield o indoo posi ioning. This
could be seen as he second majo de elopmen a e he inno a ion o sma phones, as a
GNSS/INS al e na i e o indoo , loca ion based applica ions. Op imiza ion me hods which
wo k as a co ec o , and as he unce ain y assessmen o eal li e applica ions, guided us
h ough he nex le el o challenges. In his pape , we ha e opened a no el in e p e a ion o a
deep ne wo k o ine ial odome y which is obus o noisy labelled da a ha was de ec ed
om a 5G ne wo k. We also designed and de eloped analy ical pla o m, which is conside ed
a da a collec o and cellula posi ioning simula ion. This pla o m was used o p o ide he inpu
o he lea ning and op imiza ion algo i hms. The simula ion websi e is implemen ed and
a ailable online unde simula ion2e alua ion.he okuapp.com o esea che s o gene a e
g ound u h ajec o ies and simula ed cellula measu emen s wi h assigned quali y and exac
e o alues. We ha e p oposed wo app oaches: (1) deep ine ial odome y based on p edic ing
eloci y ec o elemen s o ela i e posi ions and (2) Kalman Fil e ing o use, combine and es
he absolu e posi ions wi h he ela i e ones om he i s app oach. We inally p o ide
nume ical esul s o ou expe imen s and a discussion o he e ec i eness o ou app oaches.
Keywo ds
1
Indoo Localiza ion, 5G Simula ion, 5G Co ec ion, Deep Neu al Ne wo ks, Kalman Fil e ,
Sma phone.
1. In oduc ion
Ine ial Odome y has been a well-known ield o he Geodesy and Geoin o ma ics communi y,
s a ing wi h me hods o de elop a s apdown [1] ine ial na iga ion sys em (INS) o de e mine he
senso s’ posi ion. Combina ion o GNSS and IMU is s ill one o he main localiza ion me hods, o en
based on an ex ended Kalman Fil e (KF). This localiza ion co e plays a signi ican ole in isual
odome y me hods in ou doo scena ios [2], [3] o many applica ions such as au onomous d i ing,
sma acuum cleane s, UAV, and o he obo s. Howe e , absence o GNSS o a compa able al e na i e
in indoo a eas has been a challenge o indoo applica ions.
Exis ing localiza ion me hods ypically ely on Wi-Fi, Blue oo h, isual senso s such as LiDAR o
came as, bu hey a e usually cos ly due o he ins alla ion equi emen s o an accu a e localiza ion
and/o powe -hung y [4]. IMUs could be a solu ion o he abo e p oblems as hey a e ene gy e icien
and en i onmen ally independen . Howe e , hese me hods equi e co ec ion a e a while, o ha e a
obus pe o mance o a longe ime [5]. Combina ion o wo s a e-o - he-a posi ioning echniques
IPIN 2022 WiP P oceedings, Sep embe 5 – 8, 2022, Beijing, China
EMAIL: hossein.shoush a i@hcu-hambu g.de (H.Shoush a i)
©2022 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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IS S N 1 6 1 3 -0 0 7 3
can add ess he en i e challenge, namely i h
gene a ion (5G) posi ioning and deep lea ning
based IMU localiza ion [6].
On one hand, adio in as uc u e can play
a i al ole in au onomous indoo na iga ion,
hanks o he inno a i e capabili ies o 5G
wi eless signals. The la es wi eless ne wo k
echnology, 5G, also known as New Radio
(NR), o e s as e da a a es, lowe la ency,
highe capaci y, lowe ansmi ing powe ,
ne wo k slicing and massi e connec i i y
compa ed o p e ious gene a ions [7].
Mo eo e , he ela ed 3 d Gene a ion
Pa ne ship P ojec (3GPP) eleases (i.e.,
elease 16 and 17 [8], [9]), a e suppo ed by 5G
chips embedded in ecen sma phones [10].
Conside ing he 5G as an al e na i e solu ion
o GNSS in indoo a eas, a 5G-based
co ec o can be used o co ec he ajec o y
once an accu a e measu emen is a ailable.
On he o he hand, ecen deep lea ning app oaches such as IONe [11], RoNIN [12], IDOL [4] and
CTIN [13] ha e demons a ed he capabili y o neu al ne wo ks o add ess he p oblem o accumula ing
senso d i and di e en senso placemen s, h ough he use o supe ised lea ning, o di ec ly es ima e
he eloci y ec o when es ima ing he use pose using an IMU. Wi h a close look on he RoNIN
model o ins ance, i has been seen ha hey do no di ec ly use only IMU alues bu also p e-calcula ed
o a ion ec o s om he And oid posi ion senso [14]. Mo eo e , he model s ill seems no o be obus
o unknown use s o senso s, p esen ing pe haps i s high dependency on he s ill limi ed aining da a.
Finally, a lexible co ec ion o long ajec o ies seems o be he nex s ep, ollowing hese wo ks.
The co ec ion can ma hema ically be modeled as an op imiza ion p oblem. Applying he INS
app oaches using a KF di ec ly on he sma phone senso s alues has been es ed in [15]. The esul s
do no seem p omising because o he poo pe o mances o he senso s and he ix sma phone
placemen issue. Au ho s in [16] ied o combine he absolu e posi ion om inge p in ing wi h he
ela i e ones, which a e calcula ed based on ine ial senso s, using a weigh ed leas squa es app oach.
Thei me hod needs he same equency o he absolu e posi ion and he ela i e ones, which would be
ene gy hung y. 5G and odome y combina ion can es ima e a co ec ed posi ion and compa e he
pe o mances. A non-linea s a e es ima ion by a CNN-based deep lea ning model o in e ing he
momen a y speed using an ex ended KF has shown he easibili y o such op imiza ion model [17]. In
gene al, i has been shown ha any odome y ou pu s in o ma s such as del a x and del a y as well as
s ide leng h and s ide di ec ion o human s eps, and he 5G coo dina es wi h an op imum equency,
in a eal ime manne is possible [18].
In esponse o he obse a ions and conce ns aised abo e, a no el in e p e a ion o Deep Neu al
Ne wo ks (DNN) o ine ial odome y which is obus o noisy labelled da a, o example om a 5G
ne wo k has been p oposed (see Fig. 1). We ha e de eloped a esea ch mode o collec mo e aining
da a o ou u u e 5G ne wo k, and in he absence o he 5G ne wo k, we ha e designed a web
applica ion o simula e 5G posi ion in o ma ion. P ac ically, we ex ended he ideas o neu al ne wo ks
and KF, o p o ide a obus combined solu ion. The majo con ibu ion o his pape is summa ized as
ollows:
• De elopmen o a no el combina ion o DNN and KF o he ela i e and absolu e posi ioning.
• Design and de elopmen o an analy ical pla o m o da a collec ion.
• Ex ending ou cellula posi ioning simula ion and e alua ion web applica ion.
The es o his pape is o ganized as ollows. Sec ion 2 gi es backg ound abou he ine ial
odome y. Sec ion 3 e iews he simula ion web applica ion as well as he esea ch pla o m. Ou
de eloped models including he DNN and he KF a e in oduced in Sec ion 4. E alua ion, and la e
conclusion and ou look a e p esen ed in sec ion 5 and sec ion 6.
Figu e 1: O e iew o he p oposed me hod.
2. Backg ound
2.1. Ine ial Odome y
Technically, 3D angula eloci y and 3D
accele a ion p o ided by IMUs a e he basis
measu emen s. These a e subjec ed o bias and
whi e noises, bu ou obse a ion shows ha
calib a ion o hese pa ame e s canno sol e he
p oblem, due o he non-s able and poo
pe o mance o such senso s. Howe e , he
dynamic accele a ion (wi hou g a i y) and he
angula a e in he na iga ion coo dina e sys em
is essen ial o each ine ial odome y me hod.
We ha e used he Madgwick [19] o calcula e
he dynamic accele a ion and o he senso
alues in he na iga ion ame. The esul s can
be seen in Figu e 2. Qua e nions a e one o he
easies ways o es ima e hese alues:
(0,𝑥!)=𝑞⊗(0,𝑥")⊗𝑞#$
(1)
Whe e
𝑥!,𝑥"
a e qua e nions wi h pu e ec o s i.e., he scale alue is se o be ze o since he
qua e nion p oduc mus be applied.
𝑞#$
is he in e se o he qua e nion. These qua e nions p oduc s
a e also easy o implemen using he well-known ma ix below, which would be used o do a qua e nion
p oduc wi hou any qua e nion ep esen a ions.
C(q)=+1
|𝑞|.−𝑞$
𝑞%
𝑞&
−𝑞'
−𝑞'
−𝑞&
𝑞%
𝑞$
−𝑞&
𝑞'
−𝑞$
𝑞%0,𝒙!=C(q).𝒙"
(2)
2.2. Deep Neu al Ne wo k
Wi h he p esence o IMU senso s eading and eco ding o he esul ed eloci ies which c ea es a
ajec o y ac oss ime, he use o machine lea ning and supe ised lea ning is now possible. DNN is
one o he mos adop ed app oaches o supe ised lea ning due o he ad an ages o ha ing high
accu a e p edic ions and he abili y o deduce ela ions be ween he da a ac oss ime which canno be
deduced by a no mal human. Despi e no being able o show he de e mined ela ions, DNN can be
es ed o accu acy un il we a e sa is ied wi h he esul . The main objec i e o using a DNN model o
ine ial odome e y o p edic s accu a ely he eloci y and ajec o y o a mo ing subjec (e.g.,
pedes ian) based on he his o y o he IMU measu emen s. This is possible due o New onian
mechanics as shown in [20].
DNNs a e di e en om no mal neu al ne wo ks by he numbe o hidden laye s, as i s dep h
inc eases wi h mo e laye s. Fo some neu al ne wo ks, i was obse ed ha i makes sense o a i m ha
“ he deepe he be e ”. Howe e , when deep neu al ne wo ks s a con e ging, deg ada ion p oblems
appea as he accu acy s a s o sa u a e wi hou eaching he s a e o o e i ing. A his poin adding
mo e laye s o he ne wo ks leads o highe aining e o [21]. Au ho s in [22] ha e in oduced he
Residual lea ning neu al Ne wo k (ResNe ) o add ess such p oblems. The idea o his ne wo k is o le
he non-linea laye s i a esidual mapping, ins ead o hoping each s acked laye (dep h) i s he desi ed
unde lying mapping. I means, he ne wo k should app oxima e he iden i y unc ion in which, he
ou pu
𝐻
(
𝑥
) become he inpu
𝑋
i sel .
𝐹(𝑋)=𝑋
(3)
Figu e 2: IMU alues in he na iga ion coo dina e
sys em.
When he inpu o he i s laye o he model is
a oided o be he ou pu o he las laye o he model,
he ne wo k should be able o p edic wha e e
unc ion i was lea ning be o e wi h he inpu added o
i as ollows.
ins ead o
𝐻(𝑥)=+𝐹(𝑥)
(5)
The in ui ion is ha
𝐹
(
𝑥
)
=0
is easily lea nable,
so ha he lea ning is om di e ences be ween ou pu
and inpu . The block shown in Figu e 3 is adop ed o
e e y ew s acked laye s. The esidual mapping o be lea ned is gi en as
𝐹
(
𝑥,{𝑊(}
) which can be
iden i ied in case o wo laye s, simila o Figu e 3, as
+𝐹
(
𝑥
)
=𝑊'+𝜎+(𝑊$+𝑥)
.
The con olu ional laye s mos ly ha e 3x3 il e s and a e es ic ed o ha e he same ou pu ea u e
map size as he numbe o il e s. Finally, he ne wo k ends wi h a global a e age pooling and a ully
connec ed laye wi h a So max [22] which p o ides he inal max p edic ed p obabili y o he possible
candida es.
2.3. Kalman Fil e ing
KF is an applica ion o Bayesian es ima ion me hod. I ob ains op imal es ima es using he
de e minis ic and s ochas ic p ope ies o he sys em model and measu emen s o execu e ecu si e s a e
es ima ion. The cu en es ima e is upda ed by using he p e ious bes es ima es as inpu s. The sys em
model p o ides a p edic ion o he cu en s a e. Measu emen s a e used o co ec he p edic ed s a e
and he measu emen s a e combined by assigning weigh s o he p edic ion and he measu emen s. The
new es ima e is he weigh ed mean o he p edic ed s a e and he measu emen s [23]. In kinema ic mul i
senso sys ems, which a e usually equipped wi h gy oscopes and accele ome e s, KF is o en used o
he ajec o y de e mina ion o he mo ing pla o m by using he mo ion model as well as he
obse a ion model.
3. I is all abou Da a
The human beha io pa e ns a e no limi ed o a ew ca ego ies. Fo a obus posi ion es ima ion,
we ha e ied o combine he da ase s om IONe [11] and RoNIN [12] including he ones om RIDI
[24]. We ha e also conside ed ou new da ase wi h g ound u h labels o na u al human mo ions
including bo h eal and simula ed 5G coo dina es. We mainly ha e used 1 use , e o o 1 me e as well
as a equency o 1 Hz as se ings, o collec he aining da a. The da a collec ion is s ill a wo k in
p ocess un il using he de eloped esea ch mode in eal 5G wi eless ne wo ks. Howe e , he simula ion
allows esea che o gene a e noisy label da a in absence o a eal 5G ne wo k o u he algo i hm
de elopmen .
3.1. Analy ical Pla o m
Du ing he de elopmen o he L5IN app, an analysis o he expec ed use g oups was ca ied ou a
he beginning. In he backg ound, he app collec s all ele an senso da a om he sma phone and
con e s i in o a posi ion in an analy ical pla o m so called esea ch mode. Based on he use 's own
posi ion and a p e iously selec ed des ina ion, ou e guidance o he use is possible. The collec ed
𝐻
(
𝑥
)
=+𝐹
(
𝑥
)
+𝑥
(4)
Figu e 3: Two laye s example o a ResNe .
senso da a is a ailable o u he
de elopmen o he posi ioning
algo i hms (see Fig. 4). An
independen posi ion
de e mina ion o he mobile
de ice in he 5G ne wo k is
cu en ly unde es and
de elopmen . As soon as his is
locally possible, his way o
posi ion de e mina ion will be
a o ed.
The L5IN app was de eloped
using he Uni y amewo k o
ha e a common code base o
And oid and iOS. The abs ac ion
laye , which is used by Uni y, in
con as o apps de eloped
na i ely o mobile de ices, he
app only indi ec ly communica es
wi h he base ope a ing sys em,
which o e s special challenges
wi h ex emely high sampling
a es o he senso s, as can be seen
in Figu e 4.
Wi h ocus on he cu en s a e o he app, which is suppo ed in he backg ound by he p e iously
men ioned se ices, i is possible a e he ins alla ion o he app o s o e a s a ing posi ion in a
pa icipa ing building. A e wa ds, he use can mo e eely, o by en e ing his des ina ion, guided in
he en i e building, e en o e se e al loo s. A 2D o 3D map o he building is displayed, depending
on he use 's p e e ence. A use login and he use o he esea ch mode is only possible o he esea ch
eam. I will be soon a ailable as an AWS [25], which can help analyzing a high amoun o posi ioning
da a.
In explo e mode, p e iously con igu ed es ou es can be loaded and un. In addi ion, so-called
waypoin s can be se a p ominen poin s o be able o assign hese poin s du ing a la e analysis o he
collec ed senso da a. An example o a eco ded ou e is shown in Figu e 5. The indi idual senso alues
as well as all o he eco ded da a can be downloaded as an expo . The s anda dized da a can hen be
e alua ed in subsequen sys ems.
Figu e 5: The esea ch Mode es ou e (abo e) and da a access (down).
Figu e 4: Da a collec ion in he L5IN app (le ) and
adjus able sampling a e o he senso s ( igh ).

3.2. Simula ion
To enable he esea ch and de elopmen o 5G posi ioning app oaches wi hou an exis ing 5G
ne wo k, he ollowing simula ion has been de eloped. The simula ion no only pe mi s he gene a ion
o measu emen da a and o add noise o i wi h he desi ed measu emen equency, i also uses
e e ence poin s and u ns hem in o a g ound u h ajec o y. The measu emen s ha can be simula ed
include signal sending and ecei ing ime, angle and posi ion coo dina es. The accu acy o simula ion
alues, as well as he g anula i y o he e o in o ma ion can be adjus ed. In addi ion o he whi e noise
e o , seman ic e o ha esul s om en i onmen al condi ions can be speci ied as well.
The main ask o he Simula o is o gene a e da a o esea che s. I no 5G ne wo k is a ailable, his
pa b ings all he ools o simula e di e en an enna placemen s and quali y scena ios. This equi es
e e ence poin s and senso da a (accele a ion and gy oscope). A e gene a ing g ound u h da a, he
measu emen s can be simula ed and downloaded (see Fig. 6).
Figu e 6: O e iew o he simula ion web applica ion.
The websi e is hos ed on He oku's ee cloud se ices [26], which can be connec ed o a Gi Hub
eposi o y. He oku au oma ically upda es he si e, and he la es upda es can be iewed online
immedia ely. Unlike adi ional websi es, Py hon is no only used o all unc ions and calcula ions, bu
also o he layou and he en i e websi e using Dash, an open-sou ce amewo k o da a isualiza ion
in e aces and p edic i e analysis [27]. The gene al wo k low includes ou main s eps: upload, g ound
u h gene a ion, simula ion, and expo , as i can be seen in Figu e 7. The uploaded da a can be iewed
on he map. The p e e ed o ma is GeoJSON espec i e o i s coo dina e e e ence sys em. I is
impo an o ensu e ha he geo e e enced coo dina es a e used o bo h maps and waypoin s.
Figu e 7: O e iew o he simula ion web applica ion.
The nex pa consis s o g ound u h gene a ion ollowed by he simula ion o measu emen s. The
g ound u h calcula ion mainly uses he accele a ion and gy oscope da a as well as some e e ence
poin s. The waypoin s can be indi idually selec ed and displayed on he map. The ajec o y can also
be iewed on he map. To simula e measu emen s, g ound u h da a and alues o equency, e o
and he numbe o use s is equi ed as inpu . The se ings bu on in he simula ion sec ion allows o
change de aul pa ame e s o u he cus omize he seman ic e o s.
The websi e also o e s he possibili y o upload an enna coo dina es. Simula ing measu emen s such
as he dis ance and azimu h o all an ennas a e also calcula ed and can be seen in he ou pu ile. In
addi ion, a ious shapes such as lines, polygons and ma ke s can be d awn di ec ly on he map and be
expo ed. The ou pu ile will be downloaded as a comp essed ile.
4. Models Implemen a ion
4.1. Simula ion
In gene al, a g ound u h ajec o y including he imes amps and coo dina es is he basis o he
simula ion models. The use can hen de ine an e o ange and measu emen equency. In he absence
o a g ound u h ajec o y, his can be done wi hin he web applica ion. The simula ed esul wi h he
same o ma o he imes amps and he co esponding coo dina es and measu emen s, acco ding o he
chosen equency, a e hen calcula ed om he g ound u h by linea eg ession. Fo e e y coo dina e
pai a no mal dis ibu ed andom e o is gene a ed, using a andom alue om he speci ied e o ange
as s anda d de ia ion. This e o alue is hen added o he coo dina e alues. He e he gene a ed e o
is assigned o a quali y class, based on he g anula i y o he in o ma ion abou he measu emen quali y
ha is expec ed om he simula ed ne wo k. The simula ion hen e u ns he imes amps and noisy 5G
posi ion measu emen s such as coo dina es, dis ances, and angles, as well as he chosen e o alue and
he assigned quali y class, o each gene a ed measu emen .
Fo he seman ic e o s, he use can speci y a ange o ime in e al leng hs, a ange o he amoun
o ime in e als and an e o ange o he seman ic e o s (see Fig. 7). The numbe o ime in e als
wi h seman ic e o s, as well as he du a ion o each in e al and he assigned e o s alue is hen
andomly chosen om he speci ied anges. The s a imes o he in e als a e dis ibu ed andomly
along he gi en g ound u h ajec o y. Du ing he simula ion p ocess, he e o s o each posi ion a e
de e mined as explained abo e, un il he s a ime o a seman ic e o in e al is eached. Du ing he
seman ic e o in e al, o each measu emen he e o is andomly gene a ed om a no mal
dis ibu ion, using he seman ic e o alue assigned o he in e al as s anda d de ia ion o he e o
dis ibu ion.
Fu he , he numbe o use s eques ing a posi ion om he ne wo k can be speci ied. This way, he
po en ial loss o accu acy due o he lowe equency o ecei ed posi ion in o ma ion can be
examined. The lowe equency o ecei ed posi ion in o ma ion is he esul o he numbe o use s
being g ea e han he possible numbe o que ies o each posi ion measu emen . Fo his, he du a ion
be ween wo ecei ed posi ions o a use is de e mined by di iding he numbe o use s by he que y
equency. The use ecei es he posi ion acco ding o he ime s amp om he las measu emen plus
he es ima ed delay. I his calcula ed du a ion exceeds he du a ion be ween wo measu emen s a ime
lag accumula es, esul ing in a highe inaccu acy o he simula ed es ima ion o he p opaga ion o he
use . In his way, one can oughly model he numbe o use s. Howe e , u he in es iga ion needs o
p o ide an accu a e e ec o he numbe o use s on he posi ioning pe o mance.
4.2. Deep Neu al Ne wo k
IMU alues end o be a ec ed by bias and noise. This may lead o a majo d awback o he whole
p edic ion e icacy o he DNN model. We ackle his d awback, pa ially inspi ing om he ResNe
model om [12], by 1) imp o ing he model’s obus ness o noise. Tha is by p o iding la ge and spa se
da a o be e gene alize he model and educe he e ec s o noise measu emen s. 2) keeping ack o
he p edic ed eloci ies and de ec ing he e o di e ence and aul y measu emen s and inally
compensa ing hem while p edic ing, conside ing he men ioned imp o emen abo e.
In ou ResNe 18 model, one ully connec ed laye wi h 512 uni s is added a he end o eg ess a 2D
ec o . The ne wo k akes IMU alues and c ea es a ea u e ec o o size 6 o e e y imes amp and
calcula es he eloci y o a lexible ime window o [ -n, ]. The ne wo k inpu s enso would ha e he
shape o 6x200 and p edic s he eloci y enso a . F om he p edic ed eloci ies we p edic he cu en
posi ion based on he ini ial posi ion p o ided by eloci y in eg a ion. Figu e 8 shows selec ed
isualiza ions o he econs uc ed ajec o ies agains he g ound u h.
Figu e 8: Selec ed isualiza ions om he deep ine ial odome y model on he L5IN+ da ase including
he handheld ( op-le ) and bag placemen s (bo om-le ) as well as on he RoNIN ( op- igh ) and RIDI
(bo om- igh ).
4.3. Kalman Fil e ing
In he KF used o he s a e es ima ion o he de ice, he absolu e and ela i e posi ions a e used as
he obse a ion a iables. To make he model simple and lexible, we ha e calcula ed he displacemen
ou side he model. The mo emen model is de ined as ollows.
.𝑋)
𝑌)
∆𝑋
∆𝑌0=.1 0 10
010 1
011 0
000 10.𝑋)#$
𝑌)#$
∆𝑋
∆𝑌0
(6)
The obse a ion model is as ollows.
𝑍!=#
⎣
⎢
⎢
⎢
⎢
⎡
𝑋!
𝑌!
)∆𝑋
)∆𝑌⎦
⎥
⎥
⎥
⎥
⎤
(7)
whe e
𝑋,𝑌
a e he absolu e posi ioning and he
+∆𝑋,∆𝑌+
a e he ine ial odome y ou pu . The ini ial
alues o he s a e ec o ha e been achie ed om he label da a. We assume no co ela ion be ween
he ou -s a e componen . The ini ial co a iance ma ix o he p ocess noise is
𝑃%=𝜎'𝐼*×*.
(8)
The co a iance o he sys em s a e is
𝑃,=𝐸[(𝑋−𝑋A)(𝑋−𝑋A)-]
(9)
The noise o he obse ed 5G coo dina es and he ine ial odome y could also be modeled as whi e
Gaussian Noise. The e o e, he ini ial obse a ion co a iance ma ix is
𝑃.=+𝜎'+𝐼*×*.
(10)
Implemen a ion esul s seems o be p omising and ha e been illus a ed in Figu e 9.
Figu e 9: Selec ed isualiza ions o absolu e Posi ioning in UTM 32 coo dina e sys em (WGS 84) wi h
he KF op imiza ion.
5. E alua ion
We conduc e alua ions on h ee asks. Fi s he DNN model compa ison wi h he benchma k, using
he same me ics as p oposed in [12]. Absolu e T ajec o y E o (ATE), de ined as he Roo Mean
Squa ed E o (RMSE) be ween he es ima ed and g ound u h ajec o ies and Rela i e T ajec o y
E o (RTE), de ined as he a e age RMSE o e a ixed ime in e al o 1 minu e, ha e been used.
Table 1 illus a es ou model pe o mance on ou es da ase . We belie e ha ou ne wo k pe o mance
can be e en be e , due o he lexibili y o he inpu da a windows and he inc eased amoun o aining
da ase . We also ound ou he es ima ed o ien a ions and senso alues a e se e ely co up ed on he
abo e-men ioned da ase s. Howe e , ou obse a ions show ha i is no ela ed o he senso
calib a ion, bu poo s abili y o he sma phone senso alues.
Table 1
The Model pe o mance in compa ison
Model
Losses
ATE
RTE
RONIN
0.040185, 0.040000
2.776
3.227
L5IN +
0.021484, 0.020613
2.741
2.524
The pe o mance o he simula ion web applica ion wi h de aul seman ic e o adjus men including
he ne wo k capaci y o 500 eques pe second has been shown in Figu e 10 using no mal Cumula i e
Dis ibu ion Func ions (CDFs). We ha e also conside ed he no el e alua ion me ics as poin in
polygons (pip) pe cen age, ini ially de ined by us in [5]. The simula ion pa ame e s a e lis ed as e o ,
equency and he numbe o use s in he igu e legend. One can use he e alua ion sec ion in he web
applica ion, o u he online in es iga ion.
Figu e 10: CDF o he simula ion on RMSE