Abstract:
This report presents a detailed theoretical approach in developing the es- timator equations and its probability density functions (pdfs) in estimating distance and position of an unknown node in an indoor environment via the received signal strength (RSS) method. The channel parameter equations derived via the maximum likelihood estimation method are presented, in which the information is later used to derive the distance estimator equation and its pdf. It is shown in the report that the pdf of the distance estimator follows a lognormal distribution. The estimator equations for the Cartesian position of the unknown node are also derived and it is shown that both of the position estimator equations are a summation of 3 lognormal terms. Using the Cen- tral Limit Theorem, we have approximated the pdf of the position estimator as Gaussian. Finally, it can be shown in the report that the pdf of radius of positioning error can be approximated as having either Rayleigh distribution or Nakagami-m distribution. However, an empirical investigation must be carried out to determine which distribution provides the best t of the pdf of positioning error.
