New signal location method based on signal-range data for proximity tracing tools

Several technological solutions have emerged over the last several months to support proximity contact tracing to fight the COVID-19 pandemic. For this reason, today more than ever, accurate signal location is needed, even in indoor public areas (supermarkets, public transport, etc.). In a previous work, we proposed five methods to solve the problem of signal localization using elements of pole-polar geometry. The proposals were innovative, since they solved a geometric problem (locating a point in a coordinate system) only by applying concepts of geometry. Among these developed methods, the PPC (Pole-Polar Centroid model) was also presented. Although the PPC solves the problem of locating a device with better precision than conventional methods (based on numerical or optimization methods), its accuracy was found to be the worst among the five proposed geometric methods. In this context, this work proposes an extension to our PPC method, called the weighted Pole-Polar Centroid method (wPPC), which improves the accuracy of the previous PPC results. Such an extension does not change the complexity O(m ²) or the minimum dimensionality (m = 2) of nodes, which integrate a location network to perform the triangulation of such signals. Moreover, this extension estimates a device's location coordinates by means of the interaction, via signals, of this device with the network nodes distributed in any coordinate system. An IEEE 802.11 network infrastructure is used to accomplish the experiments. Errors in signal data are common, and our new proposed method, the wPPC, can mitigate the influence of these errors, produce more accurate results than the PPC, and outperform some of the other four proposed geometric methods and current numeric methods. Despite the use of an IEEE 802.11 network infrastructure for testing here, this range-based method for signal triangulation can be applied to any signal type (such as Wi-Fi, Bluetooth, and light and sound propagation).