Graph-Oriented Generalization of Range Positioning: Identification of Critical Cases and Performance of Gauss-Newton Methods

Abstract:
The concept of range-positioning was generalized using description on a graph. Ranges from static to mobile nodes and between mobile nodes can flexibly be included into the position calculation. The classical concept of a graph was extended by using appropriate edge- and node-attributes to describe a range positioning problem within a unified model. Based on graph-theoretic considerations different types of range positioning problems were identified with respect to existence and uniqueness of solutions and performance of solution methods. Within a generalized model, generally applicable solution methods gain special importance. Newton- and Gauss-Newton methods were implemented and evaluated with respect to problem-type. Accuracy and convergence were investigated by simulation.