Receiver sites for accurate indoor position location systems

Hyperbolic radio-location systems possess intrinsic uncertainty that depends on the sensor's geometry and the modulation's time resolution. In this paper the best locations for the receivers to minimize the uncertainty in 2-dimensional (2-D) and 3-dimensional (3-D) models for indoor systems are found. For this purpose the minimum number of receivers with clear line-of-sight (LOS) to the emitter, required for locating a source, are three and four in 2-D and 3-D respectively. For 2-D, a triangular area and for 3-D a tetrahedron volume are considered the building blocks that are used to extend results to more arbitrarily shaped areas. The criteria for minimization of location uncertainty is uncertainty area or the largest diagonal in 2-D and the multiplication of line-of-position (LOP) errors in 3-D. Finally a theorem is given for the number of sensors that is sufficient to cover the entire area in 2-D and 3-D cases.