Topology Assessment Provided by Weighted Barycentric Parameters in Harsh Environment Wireless Location Systems

In wireless location systems deployed in open areas, the statistical distributions of the range estimates are very tractable. However, due to the nature of the wireless propagation in urban and indoor environments, the behavior of the range estimates in such environments is very different. Therefore, the performance assessment results obtained for the systems operating in open areas cannot be transferred to the ones deployed in realistic urban and indoor environments. In this paper, the systematic and random errors (accuracy and precision) and the dilution-of-precision (DOP) in harsh environments are derived for the two most common multilateration algorithms, as well as the performance theoretical benchmark. We show that these quantities are determined by geometric parameters that we call topology-assessment-weighted-barycentric-parameters (TAWBAP), which are the norm of weighted barycenters obtained from the positions of anchors and target. These parameters manage the performance of the multilateration process showing the influence of the geometric configuration in connection with the specific characteristics of each range estimate. The improvement in performance obtained by using the TAWBAP parameters as a network design rule is demonstrated by means of simulations as well as by measurements taken in a real indoor environment. This improvement outperforms at least 25% the one achieved by topology deployments that have been considered as optimal in the literature.