Fundamental limits on localization in single input multiple output visible light systems
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Visible light systems have recently been considered as an e ective and promising solution for indoor positioning. In this thesis, a theoretical accuracy analysis is conducted for position estimation in visible light systems based on received signal strength (RSS) measurements. Considering a single light emitting diode (LED) at the transmitter and multiple photo-detectors (PDs) at the receiver, the Cram er-Rao lower bound (CRLB) is derived for both a generic three-dimensional scenario and speci c con gurations of the PDs at the receiver. For the special case in which the height of the receiver is known, a compact expression is derived for the CRLB, considering a uniform circular layout and the same elevation angle for all the PDs. Asymptotic analysis and accuracy of derived compact expression is investigated for this con guration of the system. In addition, the optimal placement of the PDs at the receiver is investigated by taking the e ects of the elevation angle parameter of the PDs into consideration. The optimal values are obtained theoretically and also veri ed by simulations. Numerical examples are presented to illustrate the impacts of system parameters on localization accuracy, namely radius of the uniform circular layout, elevation angle and number of PDs. Finally, theoretical limits are compared against the maximum likelihood estimator (MLE) as a benchmark to evaluate the performance of receiver position estimation.
KeywordsCramér-Rao lower bound
Single input multiple output (SIMO)
Received signal strength
Maximum likelihood estimator