Deep learning-based UWB-IMU data fusion for indoor positioning in industrial scenario

Recei ed 14 Ap il 2025; accep ed 29 Ap il 2025. Da e o publica ion 5 May 2025;
da e o cu en e sion 20 May 2025. The e iew o his a icle was coo dina ed by Edi o P ashan Sha ma.
Digi al Objec Iden i ie 10.1109/OJVT.2025.3566888
Deep Lea ning-Based UWB-IMU Da a Fusion
o Indoo Posi ioning in Indus ial Scena io
KARTHIK MUTHINENI 1,2, ALEXANDER ARTEMENKO 3, JOSEP VIDAL 4(Senio Membe , IEEE),
MONTSE NÁJAR4, MARISA CATALAN 5, AND JOSEP PARADELLS6
1Co po a e Sec o Resea ch and Ad ance Enginee ing, Robe Bosch GmbH, 71272 Renningen, Ge many
2Depa men o Signal Theo y and Communica ions, Uni e si a Poli ècnica de Ca alunya (UPC), 08034 Ba celona, Spain
3Co po a e Sec o Resea ch and Ad ance Enginee ing, Robe Bosch GmbH, 71272 Renningen, Ge many
4Depa men o Signal Theo y and Communica ions, Uni e si a Poli ècnica de Ca alunya (UPC), 08034 Ba celona, Spain
5i2CAT Founda ion, 08034 Ba celona, Spain
6Depa men o Ne wo k Enginee ing, Uni e si a Poli ècnica de Ca alunya (UPC), 08034 Ba celona, Spain
CORRESPONDING AUTHOR: KARTHIK MUTHINENI (e-mail: ka [email p o ec ed]).
The wo k o Josep Pa adells was suppo ed in pa by he Spanish MCIU/AEI/10.13039/501100011033/FEDER/UE h ough P ojec PID2023-146378NB-I00 and
in pa by he Sec e a ia d’Uni e si a s i Rece ca del depa amen d’Emp esa i Coneixemen de la Gene ali a de Ca alunya unde G an 2021 SGR 00330. This
wo k was suppo ed in pa by he Eu opean Union’s Ho izon 2020 Resea ch and Inno a ion P og amme h ough he Ma ie Sklodowska-Cu ie unde G an 956670,
in pa by P ojec 6-SENSES unde G an PID2022-138648OB-I00 unded by MCIN/AEI/10.13039/501100011033, and in pa by ERDF A way o making Eu ope.
ABSTRACT Accu a e and p ecise wi eless in as uc u e-based posi ioning sys ems become c ucial as in-
dus ies mo e owa ds lexible, po able, and au onomous anspo a ion sys ems such as Au oma ed Guided
Vehicles (AGVs). Mul ipa h-dominan dynamic en i onmen s like indus ies p esen signi ican challenges
o wi eless signal p opaga ion and a ec wi eless posi ioning accu acy due o he in e play o e lec ed
signals om obs acles. The achie able indoo posi ioning accu acy o he a ge AGV can be enhanced by
using he measu emen s om he wi eless in as uc u e wi h he a ge ’s onboa d senso da a. Ne e heless,
he lack o co espondence be ween he wi eless in as uc u e and he a ge ’s onboa d senso s causes he
measu emen s om hese wo sys ems o a i e a i egula ime s eps. Using asynch onous measu emen s in
he da a usion p ocess can deg ade he o e all posi ioning accu acy o he a ge AGV. This pape p oposes
a no el deep lea ning-based da a usion app oach o deal wi h asynch onous measu emen s om he wi eless
in as uc u e Ul a-Wideband (UWB) and he a ge ’s onboa d Ine ial Measu emen Uni (IMU) senso o
achie e enhanced posi ioning accu acy o he a ge AGV. In pa icula , a wo-s age cascaded Deep Neu al
Ne wo k (DNN) is p oposed o deal wi h he asynch onized measu emen s om UWB and IMU senso s.
The i s s age o he DNN is used o ob ain he ini ial posi ion es ima e o he AGV by p ocessing he
measu emen s om UWB. Subsequen ly, he second s age o he DNN uses he ini ial posi ion es ima e o
he AGV wi h he IMU senso da a o ob ain he inal enhanced posi ion es ima e. The p oposed app oach is
alida ed wi h eal-wo ld expe imen s in an indoo indus ial scena io using UWB echnology in channel
2(3.7–4.2 GHz) and an IMU senso placed on an AGV. Mo eo e , he achie able posi ioning accu acy
and he compu a ional un ime o p o ide he posi ion es ima es wi h he p oposed app oach a e analyzed.
The expe imen al esul s show ha he p oposed app oach achie es a mean absolu e e o o less han
10 cm, ou pe o ming he conside ed baseline me hods, Ex ended Kalman Fil e (EKF) and Long Sho -Te m
Memo y (LSTM).
INDEX TERMS Au onomous anspo a ion sys ems, da a synch oniza ion, deep neu al ne wo ks, indus ies,
ine ial measu emen uni s, ul a-wideband, wi eless in as uc u e-based posi ioning.
I. INTRODUCTION
Wi eless ne wo ks a e becoming he cen al ne ous sys em
o indus ial applica ions, enabling e icien communica-
ions and con ol o manu ac u ing p ocesses [1]. Posi ioning
and/o acking o indus ial asse s using wi eless echnolo-
gies is one such ield o applica ion in he indus y ha is
in es iga ed widely [2]. Howe e , he complex layou o he
indus y wi h hea y me allic obs acles hinde s wi eless signal
© 2025 The Au ho s. This wo k is licensed unde a C ea i e Commons A ibu ion 4.0 License. Fo mo e in o ma ion, see h ps://c ea i ecommons.o g/licenses/by/4.0/
VOLUME 6, 2025 1209
MUTHINENI ET AL.: DEEP LEARNING-BASED UWB-IMU DATA FUSION FOR INDOOR POSITIONING IN INDUSTRIAL SCENARIO
p opaga ion. Especially, he Non-Line-o -Sigh (NLoS) and
mul ipa h phenomenon impede he in e p e a ion o posi ional
in o ma ion om wi eless signals, leading o inaccu a e e-
sul s [3]. O e he yea s, he ocus has been dedica ed o
he accu a e es ima ion o posi ional in o ma ion like Time o
A i al (ToA) o Line-o -Sigh (LoS) pa hs, which could be
used in de e mining he Use Equipmen (UE) posi ions [4],
[5],[6],[7],[8]. These wo ks iden i y NLoS pa hs and elim-
ina e he bias caused by he NLoS p opaga ion. Howe e ,
he e iciency o hese app oaches in a la ge-scale mul ipa h
dominan dynamic changing indus ial en i onmen is ye o
be known. An al e na i e way o enhancing he accu acy o
wi eless posi ioning is o complemen he adio signal mea-
su emen s om he wi eless in as uc u e wi h he eco ded
da a om UE onboa d senso s h ough he da a usion ech-
nique.
A. PRIOR ART
1) MODEL-BASED DATA FUSION
The model-based app oach ollows a ecu si e mechanism o
p o ide he posi ion es ima es by combining he mo ion model
o a ehicle wi h he measu emen model. The well-known
algo i hms unde his ca ego y include Kalman Fil e s and
hei non-linea a ian s [9],[10],[11],[12],[13],[14],[15],
[16], Pa icle Fil e s [17],[18],[19],[20],[21],[22], and
Mul i-Be noulli Fil e s [23],[24]. The p io in o ma ion o he
ehicle is o mula ed in he o m o a mo ion model, which
is used o p edic i s ini ial posi ion. On he o he hand, he
senso ’s measu emen s a e used o upda e he ini ial posi ion.
The usion occu s in he upda e s ep by in eg a ing measu e-
men s om mul iple senso s [15].In[9] and [14], in o ma ion
om he ine ial senso s is used wi h he ange measu e-
men s o he wi eless in as uc u e using EKF o achie e a
be e posi ion es ima e o he use loca ion. Enhancing he
Ul a-Wideband (UWB) based posi ioning accu acy wi h in-
e ial senso s in a mixed en i onmen o LoS/NLoS scena ios
and using a non-linea e sion o he Kalman Fil e , UKF
o da a usion was explo ed in [11] and [13] espec i ely.
Au ho s in [12] p oposed an EKF-based posi ioning app oach
by using he Ine ial Measu emen Uni (IMU) measu emen s
o p edic he ehicle’s s a e in ol ing 2D posi ion and he
UWB measu emen s o upda e he ehicle’s s a e. In [20],a
cascaded posi ioning solu ion wi h UKF and Pa icle Fil e
was p esen ed. To sol e he p oblem o pa icle degene acy in
Pa icle Fil e s, au ho s in [22] p oposed a Dynamic Feasible
Region-based Pa icle Fil e (DFRPF). The p oposed me hod
u ilizes IMU measu emen s o p edic he posi ion o he
pe son. The UWB ancho s in LoS a e iden i ied wi h p io
in o ma ion, and he co esponding LoS ange es ima es a e
used o esample he pa icles.
The signi ican d awbacks o hese app oaches a e hei
na u e o handling non-linea measu emen s and assump ions
abou noise. The pe o mance o EKF is limi ed in e ms o
linea izing he non-linea sys em h ough app oxima ions. I
he sys em is highly non-linea , simila o Au oma ed Guided
Vehicle (AGV), wi h complex mo ion pa e ns in he indus ial
en i onmen s, i can lead o inaccu a e esul s. Mo eo e , EKF
assumes he noise model o be Gaussian. The noise a ec ing
he senso measu emen s in he complex mul ipa h-dominan
indus ial en i onmen migh no cons i u e Gaussian. As a
esul , he pe o mance o he EKF can deg ade. On he o he
hand, he UKF equi es well-de ined s a e-space ma hema ical
models o using measu emen s om mul iple senso s, and
using asynch onous measu emen s in he usion could esul
in signi ican e o s. In con as o model-based app oaches,
da a-d i en app oaches can cap u e non-linea ela ionships
om inpu senso da a, lea n o be obus o noisy da a
om aining on noisy da ase s, and be easily in eg a ed wi h
mul iple senso s. The e o e, he dynamic beha io o indoo
en i onmen s wi h obs acles exhibi ing non-linea dynamics,
he unp edic able non-Gaussian noise a ising om he en-
i onmen al ac o s, and he equi emen o e icien da a
usion app oaches in ol ing senso s wi h asynch onous mea-
su emen s mo i a e he s udy o da a-d i en app oaches.
2) DATA-DRIVEN BASED DATA FUSION
The ole o da a-d i en app oaches can be wi nessed ac oss
a ious indus ial applica ions, ha nessing hei capabili y o
sol e complex models and op imiza ion p oblems [25],[26].
The ad ancemen s in machine lea ning inspi ed esea che s
o apply hese app oaches o achie e p ecise posi ioning in
scena ios whe e adi ional echniques do no wo k e icien ly.
The easons a o ing machine lea ning app oaches o posi-
ioning include hei abili y o lea n non-linea ela ionships
di ec ly h ough he aining phase, using mul imodal da a
h ough ea u e ex ac ion laye s, and implemen ing a model-
ee posi ioning sys em [15]. Di e en echniques, including
supe ised, sel -supe ised, and unsupe ised lea ning, ha e
been used o use he measu emen s om mul iple senso s and
achie e p ecise posi ioning. Using supe ised lea ning, au-
ho s in [27] implemen ed a posi ioning solu ion by using he
Wi eless Fideli y (WiFi) signal s eng h measu emen s wi h
he ine ial senso s o a mobile phone using neu al ne wo ks.
The abili y o he neu al ne wo k o model he non-linea
ela ionship was used o co ec he non-linea app oxima-
ion e o s o EKF. In [28], au ho s p oposed a wo-s age
localiza ion amewo k consis ing o coa se localiza ion and
e ined localiza ion modules. The sma phone’s Long-Te m
E olu ion (LTE) signal d aws a egion o he use ’s possible
ini ial loca ion. The eby, he WiFi signals and came a images
a e used h ough neu al ne wo ks o es ima e he inal po-
si ion o he use . The wo k in [29] u ilized isual, IMU, and
UWB senso s o posi ioning and p oposed a DNN-based da a
usion solu ion (VIU-Ne ) o achie e enhanced posi ioning
esul s. Posi ioning wi h UWB ToA measu emen s using deep
lea ning echniques, including he Long Sho -Te m Mem-
o y (LSTM) ne wo ks and Con olu ional Neu al Ne wo ks
(CNN), a e conside ed o achie e be e posi ioning accu acy
in [30] and [31] espec i ely. Techniques o gene a e g ound
u h labels di ec ly om he inpu da a wi h sel -supe ised
1210 VOLUME 6, 2025
lea ning we e also explo ed in he li e a u e. In [32], he
mo ion ea u es o a ehicle ex ac ed om he came a and
IMU senso s a e used wi h Recu en Neu al Ne wo k (RNN)
o p edic he ehicle posi ion. The augmen ed iews o he
came a images and IMU eadings a e used o gene a e pseudo
labels, which a e used o ain he model. Fusing he isual and
ine ial measu emen s using DNNs o achie e p ecise posi-
ioning wi h an unsupe ised lea ning app oach was p esen ed
in [33].
B. LIMITATIONS OF PRIOR ART
The wo ks in he p io a conside ed mul imodal senso s,
which p o ide dis inc measu emen s a di e en ou pu e-
quencies o sampling a es (we s ick o he wo d sampling
a es o he es o he pape ). As a esul , he e is no ime
co espondence be ween he senso measu emen s, leading o
da a synch oniza ion issues. In addi ion, da a om he senso s
migh no a i e simul aneously due o di e en sampling
a es, especially o wi eless measu emen s, which can be
a ec ed by en i onmen al ac o s. In such cases, using asyn-
ch onous measu emen s in he da a usion p ocess can lead o
inaccu a e posi ioning esul s. Howe e , despi e i s ele ance
in eal-wo ld scena ios, less emphasis has been placed on
mul imodal da a usion wi h asynch onous measu emen s and
i s impac on posi ioning accu acy. Fo ins ance, indus ies
ope a e AGVs wi h mul imodal senso s om di e en man-
u ac u e s. These senso s do no ope a e a he same sampling
a es. The e o e, he indus ial applica ion ha uses he sen-
so y da a om AGVs needs o wo k wi h he exis ing se up,
a oiding adjus ing he sampling a e o each senso .
C. NOVELTY AND CONTRIBUTIONS
In his pape , we imp o e he mobile a ge ’s achie able wi e-
less in as uc u e-based indoo posi ioning accu acy h ough
a da a usion app oach and demons a e he esul s h ough
eal-wo ld expe imen s. To his end, we p esen a de ailed in-
es iga ion in o he applica ion o DNNs as a powe ul ool o
using measu emen s om he wi eless in as uc u e and he
mobile a ge ’s onboa d senso s o achie e enhanced posi ion
es ima es o he a ge . The key ques ions ela ed o DNN-
based mul imodal da a usion o indoo posi ioning a e: (i)
How o p o ide posi ion es ima ions wi h he DNNs, elying
on he ac ha di e en senso s gene a e da a a a ious
sampling a es and manually adjus ing he ou pu sampling
a e o each senso is no possible in he eal-wo ld scena io?
(ii) Wha pe o mance gain in posi ioning accu acy can be
achie ed wi h DNN-based da a usion compa ed o a con en-
ional model-based app oach such as EKF and a da a-d i en
app oach such as LSTM?
This pape answe s he ques ions men ioned abo e by
demons a ing he e iciency o DNN-based da a usion using
UWB and IMU measu emen s, wi h an AGV being he a ge
UE o be posi ioned. The key con ibu ions o his wo k a e
ou lined below.
1) We p opose a no el and e icien da a usion solu ion o
he measu emen s be ween he wi eless in as uc u e
and he UE senso echnology. Opposed o he wo ks o
p io a , which ely on a model-based app oach o da a
usion [12] and assume he unde lying sys em dynamics
o be pa ially known [34], ou p oposed da a-d i en
DNN-based da a usion solu ion lea ns he sys em dy-
namics om he inpu measu emen s. Mo eo e , ou
app oach can use he measu emen s wi hou manually
adjus ing he ou pu sampling a e o each sou ce o
measu emen . We implemen ou p oposed da a usion
solu ion on he applica ion o indoo posi ioning o en-
hance he posi ioning accu acy o an AGV.
2) In addi ion o he DNN-based da a usion solu ion,
we p opose and implemen wo o he solu ions based
on EKF and LSTM app oaches. We alida e he pe -
o mance o ou p oposed da a usion and posi ioning
app oaches in e ms o achie able posi ioning accu acy
and he compu a ional un ime o p o iding posi ion
es ima es h ough eal-wo ld expe imen s in he indus-
ial en i onmen .
The es o he pape is o ganized as ollows. Sec ion II
desc ibes he sys em model, including he de ails o he
wi eless in as uc u e and he UE senso echnology unde
conside a ion. The p oblem unde in es iga ion is elabo a ed
in Sec ion III. The p oposed DNN-based mul imodal da a
usion and posi ioning solu ion o he p oblem is p esen ed in
Sec ion IV. In Sec ion V, we analyze he posi ioning accu acy
achie ed wi h ou p oposed solu ion compa ed o he bench-
ma ks conside ed. The signi ican lea nings a e summa ized
in Sec ion VI. Las ly, Sec ion VII concludes he wo k wi h a
ew ecommenda ions o u u e esea ch.
II. SYSTEM MODEL
In his wo k, we conside he UWB sys em as a wi eless
in as uc u e wi h a se o nodes. Each o he nodes is
con igu ed ei he as an ancho o ag. The ancho s a e de-
ployed in he A ea o In e es (AoI) o pe o ming posi ioning
wi h known posi ion coo dina es {pac =(pxac ,pyac ),pac ∈
R2,ac ∈{1,2, ..., M}}, wi h M being he maximum
numbe o ancho s, which is six. On he o he hand, he
ag is connec ed o he a ge AGV, whose posi ion needs o
be de e mined {p ag =(px ag ,py ag ),p ag ∈R2}. Each o he
nodes in he UWB ne wo k is p o ided wi h a scheduled ime
in e al o ansmi o ecei e messages o/ om neighbo ing
nodes. The scheduling is done using he Time Di ision Mul-
iple Access (TDMA) scheme consis ing o beacons sen a
pe iodic in e als and ames wi h du a ion τas shown in
Fig. 1. The beacons a e sen by he mas e ancho pe iodi-
cally a an in e al o Ts o synch onize o he ancho s in he
ne wo k. The ime du a ion be ween wo beacons de ines a su-
pe ame. Fu he mo e, he supe ame comp ises K TDMA
ames. As shown in Fig. 1, each TDMA ame con ains a
b oadcas slo , allowing he ag o b oadcas a message, ol-
lowed by he esponse slo s o ecei ing messages om he M
ancho s. I is o be no ed ha he mas e ancho alloca es each
esponse slo o a single ancho . In his wo k, only one ag is
used, and he ag is p o ided wi h a ixed slo o b oadcas
VOLUME 6, 2025 1211
MUTHINENI ET AL.: DEEP LEARNING-BASED UWB-IMU DATA FUSION FOR INDOOR POSITIONING IN INDUSTRIAL SCENARIO
FIGURE 1. Time Di ision Mul iple Access (TDMA) scheduling in
Ul a-Wideband (UWB) ne wo k.
he message in a epea ed TDMA ame cycle. P o iding
mo e slo s o he ag in a epea ed TDMA cycle is possible.
Howe e , a single slo pe ag in a epea ed TDMA cycle was
used in his wo k o ensu e a con olled and in e e ence- ee
en i onmen , i.e., minimizing he likelihood o in e e ence
wi h o he de ices ope a ing in he same equency ange
o UWB. A he end o each TDMA ame, he ag ob ains
M esponses wi h messages co esponding o each ancho in
he UWB ne wo k. As he ag knows he s a ime o each
esponse slo and he ancho o which i is allo ed, upon
ecei ing messages om M ancho s, he M Times-o -Fligh
(ToF) a e compu ed by he ag. The M ToFs a e, in u n,
used o es ima e M dis ances using Single-Sided Two-Way
Ranging (SS-TWR) as men ioned in [35],[36]. The dis ances
ob ained by he ag a e ela i ely in 3D due o di e ences in
he heigh s o he deployed ancho s and he ag. As he ocus
o ou wo k is 2D posi ioning, he ob ained 3D dis ances need
o be ans o med o 2D as d2D =((d3D)2−(h)2)1
2, whe e
h ep esen s he di e ence in heigh s be ween he ancho s
and ag. We conside 2D posi ioning in his wo k because
he mobile a ge AGV ope a es only in 2D space, equi ing
posi ion es ima es o be ob ained in 2D. Mo eo e , he g ound
u h senso , LiDAR, is designed o p o ide posi ion es ima es
in 2D, making 3D posi ioning alida ion di icul .
Fo UE senso echnology, we use he IMU senso , which
consis s o an accele ome e and a gy oscope and hei co e-
sponding measu emen s. I is o be no ed ha he IMU senso
has a speci ic coo dina e ame called he local ame, and i
mo es ollowing he mo emen o he AGV o which i is
a ached. On he o he hand, he posi ion coo dina es o he
deployed UWB ancho s de ine he global coo dina e ame o
he AoI, which is ixed and does no change wi h he AGV’s
mo emen . We use he global coo dina es as he ame o
e e ence o posi ioning. The measu emen s p o ided by he
IMU senso co espond o he local coo dina e ame, which
needs o be mapped o a global coo dina e ame using a
o a ion ma ix gi en by
R=⎡
⎢
⎣
cos () cos ()−sin () cos ()+sin ()
sin ()sin()−cos ()sin()+cos ()
00 1
⎤
⎥
⎦,
(1)
whe e deno es he yaw angle, which is ob ained by in eg a -
ing he z-axis angula eloci y om he gy oscope o e ime.
Speci ically, he yaw angle a ime s ep is compu ed as
 = −1+ωz · ,(2)
whe e  −1indica es he yaw angle a he p e ious ime s ep,
ωz ep esen s he angula eloci y along z-axis a ime s ep
om he gy oscope, and  e e s o he sampling pe iod.
I is o be no ed ha he yaw angle a he ini ial ime s ep is
al eady known in ad ance. On he o he hand, he in luence
o g a i y imposed on he accele a ion measu emen s in he x
and yaxes needs o be emo ed. To do so, he g a i y in he
global coo dina e ame gG=[0 ,0,−9.8]Tis ans o med o
he local ame by
gL=R−1·gG.(3)
The ea e , he e ec o g a i y is emo ed om he ac-
cele ome e measu emen s by
aco ec ed =ameasu ed −gL,(4)
whe e ameasu ed co esponds o he ac ual measu emen s
eco ded by he accele ome e in he local coo dina e ame.
Las ly, he co ec ed accele ome e measu emen s a e ans-
o med o he global coo dina e ame by
aG=R·aco ec ed (5)
whe e aG=[ax,ay,az]Tindica es he accele a ion measu e-
men s in he global coo dina e ame. The IMU anomalies,
such as accele ome e bias and gy oscope d i , can s ill
be e iden in he IMU measu emen s. Howe e , he p o-
posed deep lea ning-based posi ioning app oach can lea n
he IMU anomalies om he inpu da a. To maximize he
usion pe o mance o ou algo i hm, we ansla e he global
accele a ions in o he dis ance a e sed by AGV as dimu =
 +1
2a( )2, whe e and  e e s o he eloci y and he
ime in e al be ween IMU measu emen s, which a e known
pa ame e s. The e m aindica es he o al accele a ion gi en
by a=((axG)2+(ayG)2)
1
2. The choice o using dimu comes
om he ac ha adding aw accele a ions and o ien a ion
in o ma ion om he IMU senso as inpu o he DNN does
no enhance he posi ioning pe o mance. The accele a ion
measu emen s eco ded by he IMU senso emain cons an
i he AGV does no change i s eloci y du ing i s mo emen
along a ajec o y. Mo eo e , he o ien a ion measu emen s
eco ded by he IMU senso also emain cons an i he AGV
does no make u ns while mo ing along a ajec o y. In ou
speci ic indus ial en i onmen , he AGV main ains cons an
mo emen (mos o he ime in a gi en ajec o y) wi h mini-
mal a ia ions in accele a ion and aking u ns. In such cases,
adding aw IMU senso da a as inpu does no help he DNN
o lea n o p o ide he posi ion es ima es as he ou pu . The e-
o e, o ha e a eliable inpu ea u e h ough which he DNN
can lea n, we ansla e he measu emen s om he IMU senso
o a new measu emen dimu and eed i as inpu o he DNN.
The UWB ag p o ides he measu emen s a an ou pu
sampling a e o 10 Hz app oxima ely. On he o he hand, he
1212 VOLUME 6, 2025
FIGURE 2. Deep Neu al Ne wo k (DNN) based mul imodal da a usion a chi ec u e o indoo posi ioning.
measu emen s om he IMU senso a e ob ained a a much
highe ou pu sampling a e, i.e., 50 Hz. The measu emen s
om hese wo sys ems a e no ob ained a he same imes-
amps, leading o asynch ony and empo al misalignmen o
he measu emen s. In eg a ing asynch onous measu emen s in
he da a usion and posi ion es ima ion p ocess can impac he
achie able posi ioning accu acy o he a ge .
III. PROBLEM FORMULATION
We conside an AGV equipped wi h h ee di e en senso s
S∈{s1,s
2,s
3}: UWB ag, IMU, and Ligh De ec ion and
Ranging (LiDAR), which p o ide measu emen s a di e -
en sampling a es. The measu emen s om he senso s a e
ep esen ed by (S) ={(S)
1,
(S)
2, ..., 
(S)
N}, whe e (S)
i
ep esen s he measu emen om he senso s S a i- h ime,
wi h N being he maximum. The measu emen is de ined
by (S)
i={ ,x}, whe e is he imes amp o he mea-
su emen and xis he s a e ec o . Fo he UWB ag, he
s a e ec o includes he 2D dis ances ob ained h ough SS-
TWR be ween he UWB ag and a o al o M UWB ancho s
x ag =[d1,d2, ..., dM]T. Fo he IMU senso , he s a e ec-
o includes accele a ions om he accele ome e and angula
eloci ies om gy oscope ximu =[ax,ay,az,gx,gy,gz]T.
Las ly, he s a e ec o o LiDAR includes he posi ion co-
o dina es o he AGV xlida =[px,py]T, which is used as a
g ound u h. The LiDAR senso p o ides posi ion es ima es
o he AGV as he ou pu using he LiDAR-Simul aneous Lo-
caliza ion and Mapping (SLAM) algo i hm [37]. The p oblem
o in e es is gi en he measu emen s (S) a disc e e imes
{ i}N
i=1wi h asynch onized samples om UWB and IMU sen-
so s, how o use he measu emen s om bo h senso s o
p o ide he posi ion es ima ions o AGV o e a con inuous
ajec o y? We o mula e his as
(S)
i, iN
i=1→{pi}N
i=1,(6)
whe e {pi}N
i=1=[ˆpx,ˆpy]T ep esen s he es ima ed posi ion o
he AGV in 2D coo dina es a ime i.
IV. DEEP LEARNING-BASED MULTIMODAL DATA FUSION
The a chi ec u e o enhancing he indoo posi ioning accu-
acy o he AGV by using he measu emen s om UWB
and IMU senso s using DNNs is illus a ed in Fig. 2.In he
subsequen sec ions, we go h ough Fig. 2, in oducing he
s eps in ol ed in he da a usion p ocess and p ocedu es o
aining.
A. DEEP CASCADED POSITIONING
The DNNs a e he specialized a chi ec u es in deep lea n-
ing wi h mul iple laye s o neu ons, allowing he ne wo k
o lea n complex da a ep esen a ions. The p oposed deep-
lea ning-based da a usion and posi ioning solu ion uses wo
DNNs cascaded oge he , allowing he in o ma ion o low
om he i s DNN o he second DNN. This a chi ec u e
is mo i a ed by he indus ial equi emen o ha e a high
posi ioning upda e a e o he AGV and sol e he p oblem
o using measu emen s om senso s wi h di e en sampling
a es. In addi ion, he cascaded DNNs o e modula i y, lex-
ibili y, and pe o mance bene i s. (i) The complex p oblem
can be spli in o subp oblems, ocusing on lea ning posi ional
ea u es om each senso and hei espec i e measu emen s.
(ii) O e ing plug-and-play design, allowing modi ica ion o
he pa ame e s o one o he DNNs wi hou a ec ing he
o e all a chi ec u e. (iii) The a chi ec u e enables p og es-
si e e inemen , whe e he coa se ou pu p oduced by he
i s DNN can be e ined in he second DNN o imp o e he
p ecision.
Fi s s age o DNN: The i s s age o he DNN is used
o p ocess he measu emen s om he UWB ne wo k. We
use he dis ances (2D) compu ed by he ag o he M an-
cho s in he AoI using SS-TWR as inpu s. Mo eo e , o
VOLUME 6, 2025 1213

MUTHINENI ET AL.: DEEP LEARNING-BASED UWB-IMU DATA FUSION FOR INDOOR POSITIONING IN INDUSTRIAL SCENARIO
enable he ne wo k o lea n he empo al dependencies, we
also add he p e ious posi ion o he AGV in xand yco-
o dina es as addi ional inpu s o he i s DNN. To his end,
he inpu ec o o he i s DNN (D1) a ime comp ises
xD1
=[px −1,py −1,d1, ... , dM]Tas shown in Fig. 2.The
i s DNN is ained o es ima e he ini ial posi ion o he
AGV. The g ound u h posi ions o he AGV ob ained om
he LiDAR senso a e used o supe ised lea ning du ing he
aining p ocedu e. Each neu on in he laye limplemen s
an ac i a ion unc ion o in oduce non-linea i y and lea n
complex pa e ns. In pa icula , i x s
de ines he inpu ec o
o he - h neu on in s- h hidden laye , hen he ou pu o
he espec i e neu on is in e p e ed as y s = s(wT
sx s
+b s),
whe e w s and b s indica es weigh s and bias associa ed wi h
he neu on. The ac i a ion unc ion is ep esen ed by s(·).
The inpu ec o is passed h ough all he hidden laye s o
p o ide he ini ial posi ion o he AGV [ ˆpini ial
x,ˆpini ial
y]Tas he
ou pu o he i s DNN, illus a ed in Fig. 2.
Second s age o DNN: The second DNN is used o use he
measu emen s om he UWB and IMU senso s. The second
DNN akes he es ima ed posi ion o he AGV in xand yco-
o dina es as well as he measu emen con eying he dis ance
a e sedby heAGVdimu, compu ed om he IMU mea-
su emen s (discussed in Sec ion II) as he inpu s. To his end,
he inpu ec o o he second DNN (D2) comp ises xD2
=
[ˆpx,ˆpy,dimu]T. The second DNN is ained o es ima e he
inal posi ion o he AGV, which is he esul o he da a
usion. The selec ed inpu s can con ibu e o DNN lea ning
in eliable ajec o y es ima ion e en when he ajec o ies a e
no s aigh (e.g., ci cula ajec o ies). Since he accele a ions
in he local coo dina e ame om he IMU senso a e ans-
o med in o he global coo dina e ame using he yaw angle,
i helps co ec ly align he AGV’s mo emen in he global
coo dina e ame. The ans o med accele a ions in he global
coo dina e ame a e hen used o compu e dimu. The e o e,
he sequences o dis ances ob ained o e mul iple ime s eps
gi e insigh s in o he mo ion o he AGV in a ci cula ajec-
o y. The g ound u h posi ions o he AGV ob ained om
he LiDAR senso a e used o supe ised lea ning du ing he
aining p ocedu e. The ac i a ion unc ion s(·) cap u es he
non-linea dependencies. The ea e , he inpu ec o is passed
h ough all he hidden laye s o p o ide he inal posi ion o
he AGV [ ˆ
ˆp inal
x,ˆ
ˆp inal
y]Tas he ou pu o he second DNN,
depic ed in Fig. 2.
Cascading he DNNs: The i s and second DNNs a e cas-
caded h ough a ga e, which con ols he low o in o ma ion
o he second DNN as shown in Fig. 2. I is impo an o e-
call ha he IMU senso p o ides mo e ou pu measu emen s
pe ime uni (50 Hz) han he UWB ag (app ox. 10 Hz).
The e o e, he key idea is ha whene e he measu emen
om he UWB ag is a ailable, we use i wi h he IMU
measu emen o enhance he posi ion es ima ion o he AGV.
In hose ime ins ances when he measu emen om he UWB
ag is no a ailable, we ely on he IMU o es ima e he
posi ion o he AGV. Fo example, le ’s assume ha a he
cu en ime s ep , we ob ain he measu emen om he UWB
Algo i hm 1: P oposed Algo i hm o he P oblem (6).
ag (s1)
. This measu emen co esponds o dis ances o a
se o M ancho s, which a e gi en o he i s DNN along
wi h he p e ious posi ion o he AGV as inpu s. Based on
i s lea ning expe ience, he i s DNN es ima es he ini ial
posi ion o he AGV [ ˆpini ial
x,ˆpini ial
y]T o he cu en ime
s ep . The ea e , he ini ial es ima ed posi ion is gi en as
inpu o he second DNN along wi h he IMU measu emen
(s2)
, i.e., dis ance a e sed by he AGV dimu. Subsequen ly,
he second DNN p o ides he inal es ima ed posi ion o he
AGV [ ˆ
ˆp inal
x,ˆ
ˆp inal
y]T. Howe e , a he cu en ime s ep ,i
he measu emen om he UWB ag is una ailable, he i s
DNN becomes inac i e, and only he second DNN is used o
he AGV posi ion es ima ion. None heless, he second DNN
equi es he posi ion o AGV as one o he inpu s. Thus, he
inal posi ion es ima ed by he cascaded DNNs du ing he
p e ious ime s ep −1, [ ˆ
ˆp inal
x −1,ˆ
ˆp inal
y −1]Tis used as he inpu
o he second DNN along wi h dimu. The en i e p ocess is
summa ized in Algo i hm 1. To his end, he ga e is used
o selec he la es a ailable posi ion o AGV, which can be
om he i s DNN o he cascaded DNNs ( om he p e ious
ime s ep −1), and p o ide i as inpu o he second DNN
acco ding o he ollowing condi ion.
(ˆpx,ˆpy)=⎧
⎨
⎩ˆpini ial
x,ˆpini ial
y,i UWB da a is a ailable,
ˆ
ˆp inal
x −1,ˆ
ˆp inal
y −1,o he wise .
(7)
B. TRAINING PROCEDURE
We conside an o line aining p ocedu e desc ibed in
Algo i hm 1, whe e he da a equi ed o aining he cascaded
DNNs a e collec ed be o ehand h ough a measu emen cam-
paign. The key s eps in he aining p ocedu e include da a
collec ion and model aining.
1214 VOLUME 6, 2025
FIGURE 3. Run 1−T aining ajec o y o he Au oma ed Guided Vehicle
(AGV) o da a collec ion. In addi ion, he igu e shows he su ounding
objec s de ec ed by he Ligh De ec ion and Ranging (LiDAR) senso
onboa d he AGV.
1) DATA COLLECTION
The UWB ancho s a e ins alled in he AoI o posi ioning, and
he UWB ag is connec ed o he AGV. In addi ion, he AGV
is also equipped wi h IMU and LiDAR senso s, is con olled
by Robo Ope a ing Sys em 2 (ROS2), and is p o ided wi h
a p e-de ined ajec o y o a e se in he gi en AoI as shown
in Fig. 3. As he AGV ollows he aining ou e, he UWB
ag, IMU, and LiDAR senso s collec hei espec i e mea-
su emen s and a e logged in o he AGV’s con ol compu e .
Subsequen ly, he IMU measu emen s a e ansla ed in o dimu
as desc ibed in Sec ion II. I is o be no ed ha he aining da a
also in ol es asynch onous measu emen s om he UWB and
IMU senso s. The measu emen s a e di ided in o aining
(80%) and alida ion se s (20%).
2) MODEL TRAINING
The measu emen s collec ed by he AGV along he aining
ajec o y a e used o ain each o he DNNs sepa a ely. The
inpu s o he i s DNN include he p e ious posi ion o he
AGV and dis ances om he AGV o M ancho s. The LiDAR
posi ion es ima es a e used as he g ound u h labels. We
adop he Mean Squa e E o (MSE) as he loss unc ion,
which is de ined as
LMSE()=E{||p−ˆ
p||2
2},(8)
whe e pis he ec o con aining he g ound u h posi ion
o AGV in xand ydi ec ions. The es ima ed posi ion is ˆ
p.
The ainable pa ame e s con aining weigh s and biases o
he neu al ne wo k a e ep esen ed by . The deep lea ning
model is implemen ed in Py hon wi h he Ke as amewo k,
which consis s o i e laye s wi h {8,128,64,32,2}neu ons
pe laye . The Rec i ica ion Linea Uni (ReLu) unc ion is
used as he ac i a ion unc ion, and Adap i e Momen Es i-
ma ion (ADAM) is used as he op imize wi h a lea ning a e
o 10−3. The DNN is ained wi h a ba ch size o 32 o 100
epochs. The numbe o laye s, neu ons pe laye , ba ch size,
and epochs a e decided based on expe imen a ion. The second
DNN akes he es ima ed posi ion o AGV and he dis ance
a e sed by AGV as inpu s. The LiDAR posi ion es ima es
FIGURE 4. AGV moun ed wi h UWB, Ine ial Measu emen Uni (IMU), and
LiDAR senso s (le ). The conside ed indus ial scena io ( igh ).
a e used as g ound u h labels wi h MSE as he loss unc ion
de ined as
LMSE()=E{||p−ˆ
ˆ
p||2
2},(9)
whe e ˆ
ˆ
pis he ec o con aining he es ima ed posi ion o
AGV, which is he esul o he da a usion. The DNN com-
p ises i e laye s wi h {3,128,64,32,2}neu ons pe laye .
All he aining se ings emain he same as ha o he i s
DNN.
V. PERFORMANCE EVALUATION
This sec ion p esen s he esul s o ou analysis o he po-
si ioning pe o mance. Fi s , we desc ibe he expe imen al
se up used in he s udy. Nex , we conside and p o ide de-
ails on using measu emen s wi h wo benchma ks: EKF [12]
and LSTM. Las ly, we compa e he achie able posi ioning
accu acy o AGV using ou p oposed solu ion agains he
benchma ks.
A. EXPERIMENTAL SETUP
In his s udy, we ha e used he Ac i eShu le om Bosch
Rex o h as he es AGV [2]. The AGV is con olled by an
onboa d compu e wi h ROS2 and is equipped wi h UWB
ag, IMU, and LiDAR senso s, as shown in Fig. 4.TheUWB
ag employed is Qo o DWM1001C, which wo ks in channel
2 wi h a cen e equency o 3.9 GHz and a bandwid h o
500 MHz. The IMU senso co esponds o STMic oelec on-
ics LSM6DS3, ea u ing a 3-axis digi al accele ome e and a
3-axis digi al gy oscope. The sa e y lase LiDAR scanne on
he AGV is used o ob ain he g ound u h da a, i.e., posi ion
es ima es o he AGV. The LiDAR uses he LiDAR-SLAM
algo i hm o p o ide he posi ion es ima es o he AGV [37].A
de ailed desc ip ion o he LiDAR-SLAM algo i hm is beyond
he scope o his pape . The expe imen al AoI co esponds
o an indus ial scena io wi h dimensions o 9 m ×12 m ×
3.3 m app oxima ely. A conc e e wall, me al cupboa ds, me al
ables, plas ic con aine s, and o he obo s a e p esen a ound
he AoI. Six UWB ancho s we e deployed a ound he AoI
on he aluminum ame a a heigh o 2 m. The UWB ag is
ins alled on he AGV a a heigh o 1 m om he g ound le el.
VOLUME 6, 2025 1215
MUTHINENI ET AL.: DEEP LEARNING-BASED UWB-IMU DATA FUSION FOR INDOOR POSITIONING IN INDUSTRIAL SCENARIO
Algo i hm 2: Ex ended Kalman Fil e Algo i hm.
B. BENCHMARKS
In his s udy, we alida e he pe o mance o ou p oposed
da a usion and posi ioning solu ion agains he ollowing
benchma ks.
1) EXTENDED KALMAN FILTER
We use he app oach in [12] o use he UWB and IMU mea-
su emen s. In he p edic ion s ep o EKF, we ely on he IMU
measu emen s o es ima e he posi ion o AGV. In pa icula ,
he accele a ions in he global coo dina e ame [ax,ay]T
G om
he IMU a e used o p edic he AGV’s posi ion, ollowing he
mo ion model. In he upda e s ep o EKF, we use he UWB
measu emen s o co ec and compu e he posi ion o AGV. To
his end, he s a e ec o o he AGV includes i s posi ion and
eloci y in xand ydi ec ions a ime ,x =[px,py, x, y]T.
The IMU accele a ions a e used as con ol inpu s o p e-
dic he new s a e o u u e s a e o he AGV ˆ
x +1, ollo-
wing he s a e ansi ion equa ion ˆ
x +1=Ax +Bu +w ,
whe e he s a e ansi ion ma ix A, he con ol inpu ma ix
B, and he con ol inpu ec o u a e gi en as
A=⎡
⎢
⎢
⎢
⎣
10 0
01 0 
00 1 0
00 0 1
⎤
⎥
⎥
⎥
⎦
,B=⎡
⎢
⎢
⎢
⎣
 2
20
0 2
2
 0
0
⎤
⎥
⎥
⎥
⎦
,u =ax
ayG
,
(10)
whe e  is he in e al be ween wo consecu i e IMU mea-
su emen s. In addi ion, he p ocess noise w ∼N(μ, σ 2)
is assumed o be Gaussian wi h mean μand a iance σ2.
The ea e , he e o in he s a e p edic ion known as s a e
co a iance is compu ed as ˆ
ϒ +1=Aϒ AT+Cx, wi h Cx
being he p ocess noise co a iance ep esen ing unce ain ies
in IMU eadings. The Cxis pa ame e ized as
Cx=Cmo ion +Cw,(11)
whe e Cmo ion and Cw ep esen s he noise due o unce aini-
ies in IMU measu emen s and p ocess noise w , gi en as
Cmo ion =⎡
⎢
⎢
⎢
⎢
⎣
 4
4σ2
ax0 3
2σ2
ax0
0 4
4σ2
ay0 3
2σ2
ay
 3
2σ2
ax0 2σ2
ax0
0 3
2σ2
ay0 2σ2
ay
⎤
⎥
⎥
⎥
⎥
⎦
,(12)
whe e σ2
axand σ2
ay ep esen s he a iance o IMU accele a ion
noise in xand y, espec i ely.
Cw=diag σ2
px,σ2
py,σ2
x,σ2
y,(13)
whe e σ2
pxand σ2
pydesc ibes posi ion noise a iance in xand
y, espec i ely. Fu he mo e, σ2
xand σ2
yindica es eloci y
noise a iance in xand y, espec i ely. The UWB measu e-
men s a e used o upda e he s a e ec o . In pa icula , he
dis ances compu ed by he ag o each o he M ancho s a e
used in he obse a ion ec o z +1. The dis ance o ancho M
can be ma hema ically ep esen ed as dM=((px−pxM)2+
(py−pyM)2)1
2, whe e (px,py) indica es he posi ion o he
AGV and (pxM,pyM) ep esen s he known posi ion o he an-
cho M. The EKF compu es esidual +1=z +1−h(ˆ
x +1),
ep esen ing he di e ence be ween he obse a ion ec o
z +1and he p edic ed measu emen s a ime +1, h(ˆ
x +1).
To ob ain he p edic ed measu emen s, he obse a ion ec o
needs o be linea ized a ound he s a e ec o ˆ
x +1.Todo his,
he Jacobian H +1is compu ed as
H +1=∂h
∂ˆ
x +1
=⎡
⎢
⎢
⎣
px−px1
d1
py−py1
d100
.
.
..
.
..
.
..
.
.
px−pxM
dM
py−pyM
dM00
⎤
⎥
⎥
⎦
,(14)
Subsequen ly, he s a e is upda ed as ˆ
x∗
+1=ˆ
x +1+K +1
(z +1−h(ˆ
x +1)), whe e K +1=ˆ
ϒ +1HT
+1(H +1ˆ
ϒ +1HT
+1+
C )−1is he Kalman gain and C is he measu emen
noise co a iance ep esen ing he unce ain y in he UWB
measu emen s. The C is a diagonal ma ix, ep esen ing he
unce ain y in UWB dis ance measu emen o each ancho
and is gi en by
C =diag(σ2
1,σ2
2,...,σ2
M) (15)
Las ly, he e o in he s a e es ima ion is also upda ed as
ϒ∗
+1=(I−K +1H +1)ˆ
ϒ +1. The en i e p ocess is summa-
ized in Algo i hm 2.
2) LONG SHORT-TERM MEMORY
The second benchma k conside ed in his wo k is LSTM. We
use an app oach simila o he cascaded DNNs (discussed
1216 VOLUME 6, 2025
Algo i hm 3: Long Sho -Te m Memo y Algo i hm.
in Sec ion IV) o using UWB and IMU measu emen s. To
his end, a wo-s age cascaded LSTM is used o es ima e he
posi ion o he AGV. The i s s age o he LSTM ne wo k
is used o map he inpu s o UWB SS-TWR dis ances o
he ini ial posi ion o he AGV. A e ha , he second LSTM
ne wo k is used o use AGV’s ini ial posi ion wi h he IMU
measu emen s o ob ain he enhanced posi ion es ima ion o
he AGV.
The i s s age o he LSTM (LS1) ne wo k consis s o ou
laye s, including one inpu laye , wo LSTM laye s, and one
dense laye . The inpu laye akes UWB SS-TWR dis ances
compu ed by he ag o M ancho s xLS1
=[d1,d2,...,dM]T
a imes ep as he inpu s. The inpu s o he LSTM a e p o-
ided in he o m o s uc u ed da a sequences. Each da a
sequence con ains measu emen s co esponding o di e en
imes amps. In his wo k, we conside he da a sequence
leng h o 2, ep esen ing he LSTM laye ha akes 2 con-
secu i e ime s eps o inpu measu emen s o p o ide he
ou pu . Fo ins ance, he i s da a sequence con ains seq1=
[x 1,x 2]Tas he inpu measu emen s o imes eps 1and 2,
ed o he i s s age o he LSTM ne wo k. Consequen ly, he
ini ial es ima ed posi ion o he AGV is ob ained as he ou pu .
Nex , he second da a sequence con ains seq2=[x 3,x 4]Tas
he inpu measu emen s, ed o he i s s age o he LSTM
ne wo k o ob ain he ini ial posi ion es ima e. The cycle
con inues ill all he da a sequences ha e been p ocessed.
The s uc u e o he LSTM laye is shown in Fig. 5, which
p o ides he cell s a e cs and he hidden s a e hs as he ou -
pu s. The cell s a e cs ep esen s he long- e m o he LSTM
ne wo k. Speci ically, i moni o s he inpu measu emen s a
each imes ep and upda es i s memo y by emo ing i ele-
an in o ma ion o adding ele an in o ma ion. In sho , he
cell s a e holds he cumula i e in o ma ion om he da a se-
quence. On he o he hand, he hidden s a e hs ep esen s he
FIGURE 5. The Long Sho -Te m Memo y (LSTM) cell s uc u e wi h o ge ,
inpu , and ou pu ga es.
sho - e m memo y o he LSTM ne wo k. I holds he in-
o ma ion co esponding o he cu en imes ep, which is
necessa y o gene a e he cu en ou pu . Th ee ga es, he
o ge ga e, inpu ga e, and ou pu ga e, ha e been used in he
LSTM ne wo k o enable he ne wo k o con ol he in o ma-
ion low. The o ge ga e akes he inpu x 1and decides how
much o he in o ma ion has o be e ained by compu ing
1=σ(wT
x 1+b ),(16)
whe e σis he ReLu ac i a ion unc ion, w and b a e he
weigh s and bias o he o ge ga e. The inpu ga e decides how
much o he in o ma ion om he inpu x 1has o be added o
he cell s a e by compu ing
i 1=σ(wT
ix 1+bi),(17)
whe e wiand bia e he weigh s and bias o he inpu ga e.
Subsequen ly, he cell s a e cs is upda ed based on he p e i-
ous cell s a e cs 0and he inpu ga e i 1as
cs 1= 1cs 0+i 1˜
cs 1,(18)
˜
cs 1= anh(wT
csx 1+bcs),(19)
whe e ˜
cs 1is he inpu o he cell s a e. Finally, he ou pu ga e
o 1and he hidden s a e hs 1a e compu ed as
o 1=σ(wT
ox 1+bo),(20)
hs 1=o 1 anh(cs 1).(21)
The e o e, he hidden s a e holds he ini ial posi ion es ima e
o he AGV, which is gi en as inpu o he second s age o he
LSTM. In pa icula , he second s age o he LSTM also con-
ains one inpu laye , wo LSTM laye s, and one dense laye
wi h he same p ocessing s eps as he i s LSTM. Howe e ,
he inpu s o he second s age o he LSTM (LS2) ne wo k a e
xLS2
=[ˆpini ial
x,ˆpini ial
y,dimu]Twi h a da a sequence leng h
o 2. In addi ion, simila o he cascaded DNNs, he ga e is
used o selec he la es a ailable posi ion o he AGV as inpu
o he second s age o LSTM based on (7). The da a collec ed
du ing he measu emen campaign is di ided in o aining
(80%) and alida ion (20%) da ase s. The LSTM model is
implemen ed in Py hon, and MSE is used as he loss unc ion.
The en i e p ocedu e is summa ized in Algo i hm 3.
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