Positioning is a task of increasing importance in today’s life, with applications in many different contexts. The fact that people spend most of their time inside buildings makes indoor positioning a fundamental research topic. A variety of approaches to indoor positioning have been proposed over the years; however, most often it is carried out through WiFi fingerprinting, by reason of its ease of deployment. WiFi fingerprints are (arrays of) signal strengths of access points observed at given locations. A fingerprint can thus be viewed both as a point in the real-world 2D/3D (geometrical) space and as a point in the high dimensional (fingerprint) space determined by access points. In this paper, we explore the relationships between these two spaces. To the best of our knowledge, such an investigation has never been systematically carried out in the literature, that mainly focuses on position estimation. We first highlight some connections between the geometrical and the fingerprint space. Then, we show that, by making use of conventional approaches, it is unfeasible to reconstruct real-world spatial knowledge on the basis of fingerprint data only. All findings are supported by a thorough analysis that takes into consideration various metrics, fingerprint representations (i.e., normalization functions), and granularity levels (e.g., a single building rather than a single floor), and makes use of 15 public well-recognized indoor datasets. Some general considerations on the outcomes of the analysis conclude the paper.
