CRLBs for WSNs localization in NLOS environment

Determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of localization in wireless sensor networks (WSNs) is a very important issue. Currently, CRLBs have been derived for line-of-sight (LOS) situation in WSNs. However, one of major problems for accurate localization in WSNs is non-line-of-sight (NLOS) propagation. This article proposes two CRLBs for WSNs localization in NLOS environment. The proposed CRLBs consider both the cases that positions of reference devices (RDs) are perfectly or imperfectly known. Since non-parametric kernel method is used to build probability density function of NLOS errors, the proposed CRLBs are suitable for various distributions of NLOS errors. Moreover, the proposed CRLBs provide a unified presentation for both LOS and NLOS environments. Theoretical analysis also proves that the proposed CRLB for NLOS situation becomes the CRLB for LOS situation when NLOS errors go to 0, which gives a robust check for the proposed CRLB.