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Here we devise an approach to model error and its propagation. Without approximations, we define the uncertainty of a measurement as its maximum possible error ( maper ). Thus, we propose and solve analytically two optimization problems. The one designed to determine the uncertainty of a measurement, the other specifically designed to optimize the accuracy of a RFID location system. The usefulness of this general approach is shown by applying it to the particular instance of estimating the coordinates of a person in real-time using RFID devices. This way, exact formulae to evaluate the quality of this measurement are mathematically deduced, which is useful, for example, to predict whether an inexpensive RFID location technology can meet a desired quality standard or not. The second optimization problem proposed here defines an optimal range ( orange ) for the RFID devices employed. Again, analytically, its exact formulae were derived. We propose an approach to distribute RFID tags for a positioning system based solely on RFID technology. In the light of the formulae, its quality is good enough as to locate emergency phone calls in real time. We found that key to an optimal performance is the range used and the distance between consecutive tags.   Electronic supplementary material  The online version of this article (doi:10.1186/s40064-015-1084-6) contains supplementary material, which is available to authorized users.

An expression of uncertainty and its application to positioning: a quality-metric and optimal ranges for the identification of cells with RFID