A Theoretical Analysis on Sampling Size in WiFi Fingerprint-Based Localization

Abstract

This paper deals with a key problem in WiFi fingerprint-based localization, namely how to sample a sufficient number of received signal strength (RSS) measurements during an offline site survey. To this end, a probabilistic framework is firstly presented to characterize the ability of distinguishing two fingerprints, and is then applied in both the ideally infinite sampling case and the realistically finite sampling case with correlated samples. On these grounds, it is shown that the Euclidean distance between the vectors of mean RSS measurements at any two positions is the key factor of determining localization performance, and how several other factors affect localization performance. More importantly, based on the central limit theory, a quantitative analysis is conducted to describe the degradation in localization performance introduced by finite and correlated samples. In addition, provided that correlated samples satisfy the first order autoregressive model, an explicit formula is derived to describe the relationship between the correlation coefficient and the sampling sizes, which can be employed to guide the offline site survey. Extensive simulations are conducted to confirm the effectiveness of the probabilistic framework as well as the correctness of different analytical results, and an experiment is also carried out for validation. This paper not only helps to understand the basic mechanism of WiFi fingerprint-based localization, but also provides insightful guidelines for efficiently building a fingerprint database.