Using Kullback-Leibler Divergence to Analyze the Performance of Collaborative Positioning
Nounagnon, Jeannette Donan
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Geolocation accuracy is a very crucial and a life-or-death factor for rescue teams. Natural disasters or man-made disasters are just a few convincing reasons why fast and accurate position location is necessary. One way to unleash the potential of positioning systems is through the use of collaborative positioning. It consists of simultaneously solving for the position of two nodes that need to locate themselves. Although the literature has addressed the benefits of collaborative positioning in terms of accuracy, a theoretical foundation on the performance of collaborative positioning has been disproportionally lacking. This dissertation uses information theory to perform a theoretical analysis of the value of collaborative positioning.The main research problem addressed states: 'Is collaboration always beneficial? If not, can we determine theoretically when it is and when it is not?' We show that the immediate advantage of collaborative estimation is in the acquisition of another set of information between the collaborating nodes. This acquisition of new information reduces the uncertainty on the localization of both nodes. Under certain conditions, this reduction in uncertainty occurs for both nodes by the same amount. Hence collaboration is beneficial in terms of uncertainty. However, reduced uncertainty does not necessarily imply improved accuracy. So, we define a novel theoretical model to analyze the improvement in accuracy due to collaboration. Using this model, we introduce a variational analysis of collaborative positioning to deter- mine factors that affect the improvement in accuracy due to collaboration. We derive range conditions when collaborative positioning starts to degrade the performance of standalone positioning. We derive and test criteria to determine on-the-fly (ahead of time) whether it is worth collaborating or not in order to improve accuracy. The potential applications of this research include, but are not limited to: intelligent positioning systems, collaborating manned and unmanned vehicles, and improvement of GPS applications.
- Doctoral Dissertations