Minimising the number of ranging sensors verifying target positioning uncertainty

Indoor positioning applications are increasingly popular due to the availability of effective and low cost ranging sensors. Many solutions have been proposed recently using these type of sensors to estimate the coordinates (position) of a target within a given target uncertainty. In this paper, we consider the problem of deploying a large scale infrastructure that solves the positioning task with guaranteed estimation uncertainty while minimising the number of ranging sensors. To this end, we adopt a two steps procedure. In the first step, we identify a basic cell structure compounded of a small number of sensors deployed in symmetric configurations. We study the problem in general terms and we specifically focus on how to maximise the area covered by this basic structure using the smallest possible number of three ranging sensors. In the second step, we use this basic cell as an elementary tile structure to be used in standard coverage algorithm minimising the portion of space left uncovered. The approach is validated through a large number of simulations and experimental results.