Fuentes Michel, J: Non-Linear Estimation, Filtering and Smoo

The current development of wireless networks has expanded its range of applications. One of the most important developments is the capacity of the nodes of wireless networks to estimate the range towards other nodes. Using this range information, many approaches have been proposed in order to transform the ranges from multiple nodes into position information, known as the positioning problem. This position information is used to give a position context to other information that is gathered by additional sensors mounted in the sensor nodes. However, many of these solutions to the positioning problem fail to deliver the position information in a robust manner, due to geometrical limitations, the characteristics of the ranging process itself and the environment where the wireless network is deployed, commonly known as multipath reflections. Additionally, traditional solutions lack of scalability to an arbitrary number of nodes.The present work proposes a set of solutions to the positioning problem in a robust manner. These solutions are scalable to an arbitrary number of nodes and dimensions and are able to deal with problems caused by multipath reflections and the uncertainty of the range measurements themselves. One characteristic that separates the proposed solutions from the others available is the separation of the positioning process and the filtering process. In this way, problems caused by linear assumptions are suppressed without introducing biases in the final position estimation. Additionally, with the proposed solutions filters can be fine tuned to specific applications without influencing the positioning solution. These solutions are based on heuristic processes that require less computational power than other complicated analytic solutions, thus making the solutions proposed attractive for its implementation in embedded systems or networks with limited resources.In order to prove the advantages of the solutions proposed, different industrial environments