Unambiguous Association of Crowd-Sourced Radio Maps to Floor Plans for Indoor Localization

In many survey-free Wi-Fi indoor localization systems, including the Adaptive indoor Wi-Fi Positioning System (AWPS) we proposed earlier, there is a need to associate unlabeled measurements to a floor plan. In this paper, we address the problem of how to associate a topological radio graph generated by crowd-sourced RSS measurements to an isomorphic Euclidean graph representing the physical space which may come from a geographic information system (GIS) or through automatic image analysis of a paper floor plan. We introduce the concept of Minimum Symmetric Structures (MSS) and Co-rooted Congruent Structures (COCS) as new ways of characterizing automorphism which prevent unambiguous association, and present a structure analysis algorithm for detecting these structures. Then, we derive rules on the number and locations of markers, or RSS measurements with location labels, needed for resolving the automorphism. Applying the analysis proposed in this paper to hypothetical floor plans as well as floor plans used in AWPS and other existing systems, we will demonstrate that often very few location labels are needed in a SLAM system.