Abstract
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.
Highlights
Wireless sensor networks (WSNs) have been widely used for monitoring and control in military, environmental, health, and commercial systems [1,2,3,4]
Since global positioning system (GPS) is currently a costly solution, only a small percentage of sensors are equipped with GPS receivers called reference devices (RDs), whereas the other sensors are blindfolded devices (BDs)
These classic Multi-dimensional scaling (MDS) approaches based on principal component analysis may not scale well with network size as its complexity is cubic in the number of sensors
Summary
Wireless sensor networks (WSNs) have been widely used for monitoring and control in military, environmental, health, and commercial systems [1,2,3,4]. 2. The proposed CRLBs based on non-parametric kernel method can be applicable for different cases including various distributions of NLOS errors, single or multi-reflections model. CRLBs in NLOS environment Modeling range measurements The derivation of CRLB is based on the PDF of NLOS errors. The proposed CRLBs based on survey measurements and non-parametric method are necessary since they are applicable for all distributions of NLOS errors. For the case with insufficient samples, the problem of the determination of the CRLB for WSNs location system in NLOS environments will become unsolvable This experiment is to evaluate the non-parametric kernel method for estimating the PDF of NLOS errors from survey data. The number of samples can be determined by substituting the survey data of NLOS errors into the derived CRLB and using the method in the above section. It can be seen that the case without uncertainty has the lower CRLB than the case with uncertainty
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