Mathematics-based localizaion framework
Szakács Tamás
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Eszterházy Károly Főiskola
Ruzsa Zoltán
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Bay Zoltán Alkalmazott Kutatási Közhasznú Nonprofi
Király Roland
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Eszterházy Károly Főiskola
Parisek Zsolt
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Bay Zoltán Alkalmazott Kutatási Közhasznú Nonprofi
The problem, hereby, ([1, 2, 3, 4]) is how to provide information related
to a precept object’s position and movement on the basis of the information
given by the presence sensor. By presence sensor we mean a sensor which
detects the presence of a certain object and transmit it binary (presented, or
not).
We consider the position of the sensors and the likelihood-function of
perception and non perception (i.e. that in case of a possible position of the
given object what is the probability of the presence sensor to sign positively,
negatively) as known and try to use these to locate.
We examine two different methods. First is the maximum likelihood es-
timation concerning the position of the object ([1, 2]) secondly we use the
Bayesian probability to calculate the probability of the object being in a given
set. ([5]).
In general we introduce the use of the two methods with the likelihood
function of only one perception given by a single sensor. Then, we inves-
tigate the joint likelihood function of independent observations carried out
simultaneously. Furthermore we examine the likelihood function of multiple
sensors’ observations which are time dependant and have been carried out in
different time. It can be used to locate moving objects. Finally we examine
how we can use the sequence of observations made by a sensor within short
time limits.
Besides introducing this mathematical problem we also present possible
fields of applying these theses. We review the mathematically based frame-
work which can be used to prove if the solution to the problem is correct with
the help of actual devices like RFID-antennas and RFID-tools.
References
[1] Qiang Le and Lance M Kaplan. Design of operation parameters to resolve two targets
using proximity sensors. In Information Fusion (FUSION), 2010 13th Conference on,
pages 1–8. IEEE, 2010.
[2] Qiang Le and Lance M Kaplan. Target localization using proximity binary sensors.
In Aerospace Conference, 2010 IEEE, pages 1–8. IEEE, 2010.
[3] J Miguez and A Artes-Rodriguez. Monte carlo algorithms for tracking a maneuvering
target using a network of mobile sensors. In Computational Advances in Multi-Sensor
Adaptive Processing, 2005 1st IEEE International Workshop on, pages 89–92. IEEE,
2005.
[4] Ruixin Niu and P Varshney. Target location estimation in wireless sensor networks
using binary data. In Proceedings of the 38th Annual Conference on Information
Sciences and Systems, Princeton, NJ, 2004.
[5] Ruşen Öktem and Elif Aydin. An rfid based indoor tracking method for navigating
visually impaired people. Turk J Elec Eng & Comp Sci, 18(2), 2010.
This article was financed by the project TÁMOP-4.2.2.C-11/1/KONV-2012-0014
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