On the CRLB scaling law for Received Signal Strength (RSS) geolocation

Cramer-Rao bounds for geolocation based on Received Signal Strength (RSS) have previously been studied under a Log Normal (LN) fading model. We compare this with a new bound under purely Gaussian (G) conditions, and find that location error is dramatically reduced. The focus of this paper is on the “scaling law” that underlies the bounds for LN and G conditions, that is, the relation between the increase in the number of sources and the resultant accuracy improvement. With a large enough number of sources, even the LN performance should eventually become quite good. We determine the scaling law in closed form for sources on a circle, and on a 1-D grid. The case of the 2-D grid is examined numerically. When SoO are on a circle, location error decreases with the square-root of the number of sources. This result also seems to hold approximately for a finite 2-D grid with the LN model.