Tek girdili çok çıktılı görünür ışık sistemleri ile konumlandırmada temel limitler

Visible light systems have recently been considered as an effective 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 Cramer-Rao lower bound (CRLB) is derived for both a generic three-dimensional scenario and specific configurations 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 configuration of the system. In addition, the optimal placement of the PDs at the receiver is investigated by taking the effects of the elevation angle parameter of the PDs into consideration. The optimal values are obtained theoretically and also verified 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.