Actually, wheeled mobile robots(WMR) have applications
in many fields like personal care [1], health [2], and manu-
facturing process [3]. Omnidirectional mobile robots (OMR)
are vehicles are attracting more attention because of his ca-
pability to reach any posture independently of his orientation.
Nowadays, mobile robots seems to be a new trend in Industry
4.0 [4], the control [5], motion analysis [6] and path planning
[7] are common challenges in the design of a robot, but with
the need of cooperative robots the location tasks difficulty is
increasing [8]. The robot needs data to perform a task. Using
several UltraWide band (UWB) ranging sensors, we estimate
the localization of the OMR . UWB technology can achieve
precise localization [9] and is a great option to implement
sensor networks due to its power consumption efficiency and
robustness in harsh environments. Here, we discuss the case
of the three wheeled omnidirectional robot(TWOR) moving
along a UWB sensor network [10]. In [11], [12] the au-
thors present a model for UWB range measurement. Classic
methods of state estimation are in [13]–[16]. Some troubles
in UWB ranging are covered in [17], [18] were the authors
discussed the mitigation of error when the sensors are out of
sight.
Identify applicable funding agency here. If none, delete this.
In this section, we show the geometric modeling of TWOR.
We develop the model in discrete-time and, to apply the
estimation algorithms, we take the kinematic model into its
state-space representation. A TWOR is pictured in Fig. 1.
Because of its kinematic constraints, this kind of robot has the
same number of actuation and degrees of freedom. Therefore,
they can perform translational and rotational motions at the
same time [19].
Fig. 1. Festo Robotino Mobile Robotic Development Platform
We equipped the TWOR with three omnidirectional wheels
(OMW) [20]. They comprise a set of bottom-rollers arranged
around a rotation axis. In our case, the axes of the rollers
and the wheel are perpendicular. In figure 2, we sketch an
Tracking a mobile robot in a UWB-sensor grid
JORGE A. ORTEGA-CONTRERAS, YURIY S. SHMALIY, JOSE A. ANDRADE-LUCIO,
MIGUEL VAZQUEZ-OLGUIN, ELI G. PALE-RAMON, KAREN URIBE-MURCIA
Dept. of Electronics Engineering, Universidad de Guanajuato Salamanca, MEXICO
Abstract: This work presents the development of a tracking system for a three-wheeled omnidirectional mobile
robot. This kind of robot can perform rotation and translation in any pose. The arc-length segment described by
the omni-wheels controls the trajectory of the robot. We present a simplified kinematic model in state-space.
The observation system is based on an UltraWide Band ranging sensor. Finally made the state estimation using
some classic positioning algorithms and compare the results against Finite Impulse Response Filter state
estimators.
Keywords: Kalman Filter, EOFIR Filter, State Estimation, UWB sensor
Received: May 29, 2021. Revised: June 9, 2022. Accepted: July 12, 2022. Published: August 2, 2022.
1. Introduction 2. Kinematic Analysis of the Mobile Robot
2.1. Description of the Mobile Robot
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
134
Volume 21, 2022
OMW with perpendicular rollers. The axes of rotation of the
omni-wheel axis are independent of each other. We consider
that the actuation signal unrepresent the displacement of the
wheel. An omni-directional drive system requires at least three
points of intersection between the axes of the bottom-rollers
to satisfy the full-rank condition for the Jacobian of the wheel
orientation matrix [7].
Fig. 2. Omni-wheel 3D model
For the topology of the robot, we use rotational symmetry
configuration [19]. In order to balance the vertical reaction
in the wheels and, in consequence, get similar longitudinal
friction forces. The TWOR used in our experiment have a
diameter of 60cm and use omnidirectional wheels with radius
of 5cm. Depending on the dynamic constraints, a mobile
wheeled robot can control each DOF independently.
A kinematic diagram of a three-wheeled omnidirectional
robot (TWOR) with perpendicular rollers is shown in Fig. 3.
We use the following notations and symbols to describe the
system model
•World frame coordinates
xn, ynPosition of the robot
x, y World coordinate system
ΦnOrientation of the local frame referred to the
world system
•Local frame coordinates
pnTotal displacement of the robot
ϕnAngle of the displacement vector referred to the
local frame
uiArc-length step of the wheels
xL, yLLocal coordinate system
•Model constants
RRadius of the robot
The robot is driven by the displacement of its wheels. Assum-
ing a pure-roll condition, the displacement ∆ujcan be found
by:
∆uj=
proj ujuxL
+
proj ujuyL
+ ∆ϕ∗R , (1)
u2
u3
u1
pnxn-1
L
yn-1
L
R
y
xn-1 ,yn-1
( )
φ
Φn-1
Fig. 3. Kinematic diagram of TWOR
From (1), the robot kinematics in state-space representation is
as follows:
∆u1
∆u2
∆u3
=
cos π/6 sin π/6R
−cos π/6 sin π/6R
0−1R
∆uxL
∆uyL
∆ϕ
∆Ui=A∆UL
,(2)
Where ∆Uiis the displacements vector, ∆ULis the robot
position vector in the local frame, and Ais the system matrix.
By inverting (2), we have
∆UL=A−1∆Ui
A−1=
√3/3−√3/3 0
1/3 1/3−2/3
1/3R1/3R1/3R
.(3)
And applying a rotation to transform into the world frame, we
get
∆U=R(Φ)UL
∆U=R(Φ)A−1Ui(4)
Then, each coordinate can be written as:
∆ux=√3
3∆u12cos(Φn−1)−1
3∆u123sin(Φn−1),(5)
∆uy=√3
3∆u12sin(Φn−1) + 1
3∆u123cos(Φn−1),(6)
∆ϕ=1
3R∆u1+ ∆u2+ ∆u3,(7)
Where ∆u12 = ∆u1−∆u2and ∆u123 = ∆u1+∆u2−2∆u3.
We can measure the real displacement of the wheel using
incremental encoders, therefore the quantities ∆u1,∆u2, and
∆u3are known. The model can be simplified by considering
2.2. Kinematics of the Transition State Function
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
135
Volume 21, 2022
pnand ∆ϕas exogenous variables. Doing some trigonometric
transformations in (5-6) we can show that:
pn=1
3q3∆u2
12 + ∆u2
123,(8)
ϕn= ∆ϕn+ Φn−1,(9)
By introducing the state vector xn= [x1nx2nx3n]Tof the
global coordinates, with the components
x1n=x1n−1+pncos(x3n−1+ ∆ϕn),
x2n=x2n−1+ +pnsin(x3n−1+ ∆ϕn),
x3n=x3n−1+ ∆ϕn,(10)
We can write the nonlinear state equation as:
xn=fn(xn−1,un,wn),(11)
where wn∼ N(0, Qn)is zero mean white Gaussian noise
with the covariance Qn.
We will derive localization information in UWB based
positioning system through different measurements like RSSI
or ToF, we deploy our setup using the Decawave DW1000
transceiver with a bandwidth of 900MHz and IEEE 802.15.4a
compliant. The distance between anchor and tags will be
calculated using Asymmetric Double sided Two-way ranging
(AltDS-TWR) [21], [22]. Basically, AltDS-TWR derive the
range estimation based on the round-trip delay between two
data bursts. This algorithm has the smallest error due to clock
drift [23] even if the error increase with the distance, the
order is less than 30cm for a clock-drift xi < 3ppm and
atreply <650µs. We take the distance data from multiple
DWM1000 modules configured as an anchor. We also assume
the position of each anchor is fixed and known. An additional
DWM1000 module configured as a tag is attached to the
TWOR. The figure 4 shows the test environment used in the
experimental evaluation. We can write the distance between
k-anchor and tag as:
rk=p(xk−x1n)2+ (yk−x2n)2(12)
Where xk, ykare the position of the k-anchor. We assume there
is no z-level changes and the transceiver modules (anchors-tag)
are z-aligned. The radiation pattern (Fig. 4) in the horizontal
plane is omnidirectional [10] if the transceivers are vertically
oriented.
1) Sources of error: The ideal case appears when the
transceivers are in line of sight (LOS), here the only source of
error is systematic. Several factors as reflection and diffraction,
will affect the measurements [24]. When the robot navigates
in complex environments, it can be under a non-line of
sight (NLOS) conditions or multi-path phenomena, which
can affect the accuracy of the measurements. A deterministic
model for UWB channel mode must be capable of describing
LOS or NLOS conditions at the same time without a priori
information. Due to the difficulties presented in real scenarios,
Fig. 4. Deploy of tag and anchors in the system
we propose a previous experimental test to find a model for
signal attenuation in LOS conditions.
dk=q(ak−¯xn)T(ak−¯xn) + bias(rk) + vk(13)
Where akis the X-Y coordinates vector of the tag, and ¯xn
is the first two elements of the xnposition vector. The vector
vnis the observation noise modelled as a random variable
with white-Gaussian distribution, zero-mean and covariance
Qn. We can write the nonlinear observation model as:
dn=gn(xn,vn)(14)
In this section, we are going to compare classical position
estimators, such as Least Squares, Extended Kalman against
FIR Estimators, using a simple observation model and the bias-
corrected model. We propose a covariance model to mitigate
the error due to NLOS using a binary discrimination.
Our characterization environment was an ideal scenario,
with LOS connection between tag and anchor. In this condi-
tion, the measured signal corresponds to the distances between
transceivers with some additive noise. The measurements
succeed in an area of 5m x 8m with no obstacles between the
transceivers. The walls can’t induce multipath error, because
the distance between the transceivers is small, compared with
the distance of the multipath trajectory. With the DWM1000
modules vertically aligned and separated from the floor, at a
distance of 1.5m, we are making ranging measurements. When
the distance between transceivers is increasing, we get a bigger
bias, as shown in figure 5 .
2.3. Observation Model
3. Tracking Twor in Sensor Grid
3.1. Caracterization of Single Uwb Sensor in Los
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
136
Volume 21, 2022
0.5 1 1.5 2 2.5 3 3.5 4
distance [m]
0.15
0.2
0.25
0.3
0.35
bias [m]
bias
Excluded data
-0.2705x-0.2908+0.5113
Bounds (90%)
Fig. 5. Increase of the bias as a function of the distance
In LOS conditions, the destructive interference with ground
reflected signal can cause attenuation, leading to the bias
phenomena. To get an approximated model, we fit the bias
to a polynomial function, the equation 13 is now:
rk=q(ak−¯xn)T(ak−¯xn)(15)
dk=rk−0.2705r−0.2908
k+ 0.5113 + vk
We set the covariance of vkas the mean of the experimental
values, then σ2
v= 0.0105
0 0.5 1 1.5 2 2.5 3 3.5 4
distance [m]
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
0.014
0.015
0.016
v
2
Fig. 6. Covariance of the measurements
Finally, the observation model must be capable of minimiz-
ing the influence of NLOS measurements in the estimation,
thus we define a binary rule:
σ2
v,k =0.0105 |rk−Hnˆxn|<
100 otherwise (16)
With the restriction in Eq.16 the value of act as a threshold,
when the k-measurement is far from the predicted distance,
we must suppose an outlier. And then, we set his covariance
as a ’big’ value. This will cause that the estimator has less
confidence in the measurement. And then minimize their
impact on the state estimation.
When the robot navigates into a real scenario, without prior
knowledge of the space configuration, it will require many
static anchor nodes with a known position. We are going to
compare to different approaches, non-probabilistic approach
and stochastic algorithms.
1) Least Squares Estimator: A set of discrete measure-
ments ynare assumed to be a linear function of unknown
parameters and some additive noise. Then, for the linear model
yn= Hnxn+ vnthe solution ˆxnthat minimize the squared-
error is given by:
ˆxn= (HT
nHn)−1HT
nyn(17)
To get a linear model from the measurement, we rewrite the
euclidian distance between node and anchor, then we get:
R=x2+y2
ˆxn= [x y R]T
Hn=
−2x1−2y11
−2x1−2y11
.
.
..
.
..
.
.
−2xn−2yn1
yn=
d2
1−x2
1−y2
1
d2
2−x2
2−y2
2
.
.
.
d2
n−x2
n−y2
n
2) Extended Kalman Filter: Consider the nonlinear system
defined by equations 11,14. Assume we have an initial state
x0with known mean and covariance. The noises wnand vn
are temporally uncorrelated. In the initial step, we made a
prediction of state using:
ˆx−
n=fn(ˆxn−1,un,0)
P−
n= FnPn−1FT
n+ WnQnWT
n
The correction step is given by
Kn= P−
nHT
n(HnP−
nHT
n+ VnRnVT
n)−1
ˆxn= ˆx−
n+ Kn(yn−h(ˆx−
n,0))
Pn= (I −KnHn)P−
n
Where Fnis the Jacobian of the system model evaluated in the
previous estimation point ˆxn−1and Hnis the Jacobian of the
observation model evaluated in the predicted state ˆx−
n.Qnis
the noise model covariance, and Rnis the measurement noise
covariance. In our case, Wnand Vnare the identity matrix I.
3.2. Tag Localization
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
137
Volume 21, 2022
3) Extended Optimal Finite Impulse Response Filter:
The EOFIR filter is the most general optimal FIR estimator
(Algorithm 1). We compute optimal estimates using Kalman
recursions. The estimation will be bounded and the EOFIR
Filter is BIBO stable for stable systems. The EOFIR filter has
better response in the presence of disturbance due to the length
of the horizon [m, k].
Algorithm 1: EOFIR Filtering Algorithm
Input: yk,ˆxm,Pm,Qk,Rk,N
Output: ˆxk
1for k= 1,2··· do
2if k > N −1then
3m=k−N+ 1
4else
5m= 0
6end
7for l=m+ 1 : kdo
8¯x−
l=fl(¯xl−1)
9P−
l=FlPl−1FT
l+Ql
10 Sl=HlP−
lHT
l+Rl
11 Kl=P−
lHT
lS−1
l
12 ¯xl= ¯x−
l+Kl(yl−hl(¯x−
l))
13 Pl= (I−KlHl)P−
l
14 end
15 ˆxk= ¯xk
16 end
The EOFIR filter requires a horizon length of N, this can
be determined experimentally. The greater the value of N,
the slow the estimate computation. The EOFIR Filter has a
batch form [26], which is more quickly running on parallel
computing. The value of Nwhich minimizes the RMSE is
known as Nopt.
For the test environment, we deploy 7 anchors in fixed
positions in a room of 6x5m approximately. We don’t use
any particular arrangement for the tags. They were positioned
arbitrarily. The robot has an I2C digital compass S320160 to
get its orientation. In our experiment, the robot always follows
a tangent orientation to the trajectory. The precision of the
compass is ±4deg. The path described by the TWOR is
circular. The localization estimation is in figure 7. And the
errors can be viewed in figure 8.
•In red, we can observe the result for the non-probabilistic
method. Even without knowledge of the model, the LS
estimator can recover the trajectory but with a large bias.
The RMSE for this estimator was 0.1572 m.
•In magenta, the classical EKF algorithm was used assum-
ing no errors due to fading. The estimation was better
than in LS estimator. The RMSE was 0.0124
•In blue, the EKF filter with bias correction, the improve-
ments over the previous localization algorithms are clear,
the RMSE is 0.0091.
•Finally, in orange, the EOFIR algorithm with Nopt = 8,
this is the best result with an RMSE of 0.0065.
Fig. 7. Estimated position of TWOR
0 100 200 300 400 500 600 700
-0.4
-0.2
0
0.2
0.4
xerror
LS
EKF
EKF-bias
EOFIR-bias
0 100 200 300 400 500 600 700
-0.4
-0.2
0
0.2
0.4
yerror
Fig. 8. Error obtained with the localization algorithms
In this paper, we develop an environment test for tracking a
TWOR in UWB sensor network. Then, through a simple ex-
periment, we determine the effects of fading in LOS conditions
and propose a bias correction to the observation model. Finally,
we perform a comparison between positioning algorithms
considering unbiased/biased measurements. It should be noted
that the EOFIR filter has better results than the EKF Filter, but
in theory, both filters are equivalent. In a real scenario, each
anchor is in different conditions (LOS, NLOS, and multipath),
and the EOFIR filter has more robustness against disturbance
than the EKF Filter. The first was always bounded and hence it
is inherently stable. The second one was derived in IIR form,
so it has a slow disturbance rejection.
3.3. Results
4. Conclusions
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
138
Volume 21, 2022
[1] A. S. Kundua, O. Mazumdera, P. K. Lenkab, S. Bhaumik, ”Om-
nidirectional assistive wheelchair: Design and control with isometric
myoelectric based intention classification,” Procedia Computer Science,
2017, 105, 6874.
[2] J. Moreno, E. Clotet, R. Lupiaez, M. Tresanchez, D. Martnez, T.
Palleja, et al., ”Design, implementation and validation of the three-
wheel holonomic motion system of the assistant personal robot (APR)”.
Sensors, 2016, 16(10), 1658.
[3] J. Qian, B. Zi, D. Wang, Y. Ma, D. Zhang, ”The design and devel-
opment of an omni-directional mobile robot oriented to an intelligent
manufacturing system,” Sensors, 2017,17(9), 2073.
[4] Anand Singh Rajawat, Pradeep Bedi, S. B. Goyal, Piyush Kumar Shukla,
Atef Zaguia, Aakriti Jain, Mohammad Monirujjaman Khan, ”Reformist
Framework for Improving Human Security for Mobile Robots in Indus-
try 4.0”, Mobile Information Systems, vol. 2021, Article ID 4744220,
10 pages, 2021. https://doi.org/10.1155/2021/4744220
[5] G. I. R. K. Galgamuwa, L. K. G. Liyanage, M. P. B. Ekanayake and B.
G. L. T. Samaranayake, ”Simplified controller for three wheeled omni
directional mobile robot,” 2015 IEEE 10th International Conference on
Industrial and Information Systems (ICIIS), 2015, pp. 314-319, doi:
10.1109/ICIINFS.2015.7399030.
[6] T. Terakawa, M. Komori, K. Matsuda, ”Motion Analysis of an Omni-
directional Mobile Robot with Wheels Connected by Passive Sliding
Joints,” In: Uhl, T. (eds) Advances in Mechanism and Machine Science.
IFToMM WC 2019. Mechanisms and Machine Science, 2019, vol 73.
Springer, Cham.
[7] Luis Gracia, Josep Tornero,”A Practical Approach for Motion Planning
of Wheeled Mobile Robots,” In (Ed.), Motion Planning. IntechOpen,
2008, https://doi.org/10.5772/6017
[8] S. Kallweit, R. Walenta, M. Gottschalk,”ROS Based Safety Concept
for Collaborative Robots in Industrial Applications,” In: Borangiu, T.
(eds) Advances in Robot Design and Intelligent Control. Advances in
Intelligent Systems and Computing, 2016, vol 371. Springer, Cham.
https://doi.org/10.1007/978-3-319-21290-6 3
[9] M. von Tschirschnitz, M. Wagner, M. O. Pahl and G. Carle, ”Clock Error
Analysis of Common Time of Flight based Positioning Methods,” 2019
International Conference on Indoor Positioning and Indoor Navigation
(IPIN), 2019, pp. 1-8, doi: 10.1109/IPIN.2019.8911772.
[10] F.B. Sorbelli, C.M. Pinotti, G. Rigoni, ”Range-free Localization Al-
gorithms with Mobile Anchors at Different Altitudes: A Comparative
Study,” ACM International Conference Proceeding Series, 2020; Vol-
F1656, pp. 883894.
[11] N. Ayoobi, M. Ghavami, A. Rabiei, ”A novel motion-model-free UWB
short-range positioning method,” Signal, Image and Video Processing,
2020, doi:14. 10.1007/s11760-019-01613-2.
[12] Anton Ledergerber, Rafaello DAndrea, ”Ultra-wideband range
measurement model with Gaussian processes,”IEEE Conference
on Control Technology and Applications (CCTA),2017,
doi:10.1109/ccta.2017.8062738
[13] J. Youssef, B. Denis, C. Godin and S. Lesecq, ”Enhanced UWB Indoor
Tracking through NLOS TOA Biases Estimation,” IEEE GLOBECOM
2008 - 2008 IEEE Global Telecommunications Conference, 2008, pp.
1-5, doi: 10.1109/GLOCOM.2008.ECP.925.
[14] A. Ledergerber and R. Dandrea, ”Calibrating Away Inaccuracies in Ultra
Wideband Range Measurements: A Maximum Likelihood Approach,”
in IEEE Access, vol. 6, pp. 78719-78730, 2018, doi: 10.1109/AC-
CESS.2018.2885195.
[15] N. M. Senevirathna, O. De Silva, G. K. I. Mann and R. G. Gosine,
”Kalman Filter based Range Estimation and Clock Synchronization for
Ultra Wide Band Networks,” 2020 IEEE/RSJ International Conference
on Intelligent Robots and Systems (IROS), 2020, pp. 9027-9032, doi:
10.1109/IROS45743.2020.9340971.
[16] Bas van der Heijden, Anton Ledergerber,Rajan Gill, Rafaello DAn-
drea, ”Iterative Bias Estimation for an Ultra-Wideband Localiza-
tion System,” IFAC-PapersOnLine, 2020, Vol 53,pp. 1391-1396.
10.1016/j.ifacol.2020.12.1889.
[17] K. Yu, K. Wen, Y. Li, S. Zhang and K. Zhang, ”A Novel NLOS Mitiga-
tion Algorithm for UWB Localization in Harsh Indoor Environments,”
in IEEE Transactions on Vehicular Technology, vol. 68, no. 1, pp. 686-
699, Jan. 2019, doi: 10.1109/TVT.2018.2883810.
[18] T. Zhou, Y. Cheng, B. Lian and Y. Zhang, ”Research on UWB
Localization Based on TOA in Indoor NLOS Environment,” 2018 9th
International Conference on Information Technology in Medicine and
Education (ITME), 2018, pp. 983-988, doi: 10.1109/ITME.2018.00219.
[19] G. Campion, G.Bastin, B. DAndrea-Novel, ”Structural properties and
classification of kinematic and dynamic models of wheeled mobile
robots,” In Proceedings of the 1993 IEEE International Conference
onRobotics and Automation, Atlanta, GA, USA, 26 May 1993, pp.
462469
[20] A. Gfrerrer, ”Geometry and kinematics of the Mecanum
wheel,”Computer Aided Geometric Design, Volume 25, Issue 9,
2008,pp. 784-791
[21] Y. Jiang and V. C. M. Leung, ”An Asymmetric Double Sided
Two-Way Ranging for Crystal Offset,” 2007 International Sympo-
sium on Signals, Systems and Electronics, 2007, pp. 525-528, doi:
10.1109/ISSSE.2007.4294528.
[22] D. Neirynck, E. Luk and M. McLaughlin, ”An alternative double-
sided two-way ranging method,” 2016 13th Workshop on Position-
ing, Navigation and Communications (WPNC), 2016, pp. 1-4, doi:
10.1109/WPNC.2016.7822844.
[23] Lian Sang C, Adams M, Hrmann T, Hesse M, Porrmann M,
R¨
uckert U. ”Numerical and Experimental Evaluation of Error Esti-
mation for Two-Way Ranging Methods,” Sensors. 2019; 19(3):616.
https://doi.org/10.3390/s19030616
[24] R. Zetik, M. Eschrich, S. Jovanoska and R. S. Thoma, ”Looking behind
a corner using multipath-exploiting UWB radar,” in IEEE Transactions
on Aerospace and Electronic Systems, vol. 51, no. 3, pp. 1916-1926,
July 2015, doi: 10.1109/TAES.2015.140303.
[25] Sidorenko Juri, Schatz Volker, Scherer-Negenborn Norbert, Arens
Michael, Hugentobler Urs. ”Decawave UWB Clock Drift Cor-
rection and Power Self-Calibration,” Sensors, 2019, 19(13):2942,
doi:10.3390/s19132942.
[26] Shmaliy, Y., Zhao, S. (2022). Optimal and robust state estimation: Finite
Impulse Response (FIR) and Kalman approaches. Wiley-IEEE Press.
References
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
WSEAS TRANSACTIONS on SYSTEMS
DOI: 10.37394/23202.2022.21.14
Jorge A. Ortega-Contreras, Yuriy S. Shmaliy,
Jose A. Andrade-Lucio, Miguel Vazquez-Olguin,
Eli G. Pale-Ramon, Karen Uribe-Murcia
E-ISSN: 2224-2678
139
Volume 21, 2022