Cramer-Rao Lower Bound Analysis of Data Fusion for Fingerprinting Localization in Non-Line-of-Sight Environments

Abstract

This paper proposes a novel framework for analyzing the localization accuracy of data fusion for fingerprinting approaches in non-line-of-sight (NLOS) environments. Using simulation data generated for two very different NLOS environments (a suburban area of <inline-formula> <tex-math notation= LaTeX >$3.3km\\times 3.3km$ </tex-math></inline-formula> in Santa Clara, California, and a mountainous area of <inline-formula> <tex-math notation= LaTeX >$11.4km\\times 11.4km$ </tex-math></inline-formula> in the Caspian region), we establish novel channel models for measurement differences of three data types (received signal strength indicator (RSS), time of arrival (TOA) and direction of arrival (DOA)) at <inline-formula> <tex-math notation= LaTeX >$K$ </tex-math></inline-formula> neighboring nodes of an arbitrary node. The crucial point is that the modeling errors for each of the three data types are shown to be jointly Gaussian distributed. Based on these measurement difference models, Cramer-Rao Lower Bound (CRLB) is used as a benchmark to evaluate <inline-formula> <tex-math notation= LaTeX >$K$ </tex-math></inline-formula>-nearest neighbor (KNN) and Weighted <inline-formula> <tex-math notation= LaTeX >$K$ </tex-math></inline-formula>-Nearest Neighbor (WKNN). It is shown that the proposed CRLB analyses can be employed to evaluate fingerprinting systems with various designs (such as different data types and fusion options) and different configurations (such as densities of reference nodes and numbers of anchor nodes) in diverse NLOS environments(such as suburban and mountainous regions).