Assessment of optimum geometric distribution of anchors in non-GNSS wireless location systems

The final precision achieved by a wireless location system depends basically on the accuracy of the range estimates and on the geometric distribution between anchors and target, being the second issue easier to manage in the design of a wireless location system. The results related to the impact of the geometric distribution, addressed for GNSS location systems, cannot be used directly to other wireless location systems, since the trilateration algorithms used and the characteristics of range estimates can be rather different. In this paper we develop an exhaustive study on the impact of the geometric distribution of anchors for the two most usual algorithms used in non-GNSS wireless location systems, taking into account the non ideal characteristics of the range noises in those location systems. From this study we present two parameters, particular to these two algorithms, which quantify the suitability of the geometric distribution taking values between 0 and 1, depending only on the geometric distributions. We show that armed with these new parameters, it is possible to design the wireless location system in an optimum way. Moreover, we present more optimum geometric distributions than the ones known in the literature.