Signal Strength Localization Bounds in Ad Hoc and Sensor Networks when Transmit Powers are Random

Abstract

Sensor localization bounds have been derived assuming that received signal strength (RSS) measurements are performed with perfectly known sensor transmit powers. In this paper the Bayesian Cramer-Rao bound is derived assuming transmit powers are random with known prior distribution. Further, both directional measurements on each link, from i to j and from j to i, and their correlation, are explicitly considered. Results show that random transmit powers have a small (5-13%) impact on coordinate estimation bounds. However, using only the average of the directional measurements can significantly increase these bounds