Algebraic and statistical conditions for use of SLL

Common approaches for indoor positioning based on cellular communication systems use the received signal strength (RSS) as measurements. In order to work properly, such a system often requires many calibration points before its start. Applying Simultaneous Localization and Learning (SLL) a self-calibrating RSS-based positioning system can be realized. Clearly, SLL avoids the requirement for manually obtained reference measurements. This paper explores the algebraic and statistical conditions required to perform the SLL approach. Firstly, as basis of the analysis a closed form of SLL is introduced. As main result of this paper the algebraic and statistical conditions are revealed that need to be satisfied such that SLL can successfully be utilized, leading to a self-calibration of RSS-based positioning systems. While the analysis is restricted to the one-dimensional case and although the extension of the analysis to higher dimensions is more complex, the results can straightforwardly be extended to the more-dimensional cases.