Cramer-Rao Lower Bounds for Hybrid Distance Estimation Schemes

Abstract

This paper presents Cramer-Rao Lower Bounds (CRLBs) for hybrid distance estimation algorithms, i.e., for received signal strength (RSS) and time of arrival (TOA) as well as for RSS and time difference of arrival (TDOA) measurements. The CRLBs are first evaluated with a simple channel model that consists of additive white Gaussian noise (AWGN), path loss (PL) model, and shadow fading (SF) model in contrast to previous works. Several different CRLBs are developed as the SF can be treated as nuisance parameter. Further, we apply the CRLBs to the WINNER II channel model and to current communication systems. As expected, results show that the hybrid schemes always perform equal or better than RSS, TOA or TDOA only schemes, that the fourth type CRLB is the tightest bound, and that the distance when RSS performs better than TOA or TDOA increases with decreasing bandwidth.