On the usage of Homogeneous Transformation Matrices for Visible Light Position Estimation Systems

This paper discusses a visible light positioning sys- tem based on a non-imaging sensor, comprised of a regular arrangement of photo-detectors with applications to mobile robotics. In order to easily accommodate the requirements to deal with both position and displacement, homogeneous transforma- tion matrices are used, as these are often used in robotics, namely for navigation purposes. In this representation, the updated robot position is efficiently computed from its previous position by an ingenious matrix decomposition methodology. This work considered the usage of visible light position methods applied to position estimation of an autonomous agent inside a room. Position estimation is based on angle of arrival and trilateration methods, using least squares approach. The achieved results show that the proposed methodology performs comparably to other methods reported in the literature, achieving a maximum error under 1 cm in a room of 3 m by 3 m with 16 light beacons.