Formula and performance simulation of a signal strength based position estimation in lognormal channels

Derivation of a formula to estimate the location of a receiver by using the received signal strengths is presented. The formula is derived for a one-dimensional system in which the receiver is placed between two transmitters. Lognormal channel with a known path loss exponent is assumed. The derivation is based on the maximum likelihood estimation. The performance of this technique is evaluated by simulation. The simulation results show that the performance of this estimation depends on the location of the receiver. The accuracy of this estimation is worst when the receiver is placed exactly halfway between the two transmitters. Moreover, the performance of this estimation degrades as the separation distance of the transmitters increases. As a consequence, the signal strength can be used for location positioning with the limitation on the distance.