| Popis: |
In this thesis we examine localization in wireless sensor networks starting with a brief overview of the basics of radiolocation techniques and then look at some of the most well-known commercial positioning techniques and localization algorithms. We then concentrate on the application of the Fastmap (FM) algorithm in the field of wireless sensor localization. Our first contribution in this thesis is the mathematical analysis of the FM algorithm in terms of the mean squared error (MSE) of the coordinate estimate under a multiplicative noise model followed by the optimum placement of anchor nodes. The algorithm is compared to Linear Least Squares (LLS) algorithm, which is well known and has a similar complexity to that of FM. Another contribution is proposing the angle-projected FM algorithm for wireless sensor nodes localization in order to enhance the connectivity of the network and the overall performance. A comprehensive study and mathematical analysis in terms of the MSE for this algorithm is presented and it is also compared with the original FM algorithm. We also propose a weighted Fastmap (WFM) algorithm in which more than one pair of anchor nodes is used to evaluate the first coordinate (i.e., x-coordinate) of the unknown nodes in order to reduce the effect of error dependency in the y-coordinate estimation. (In the original FM algorithm only one pair of anchor nodes was employed.) The optimal WFM weights are determined via (constrained) minimization of the MSE of the estimated node coordinates. A simplification of the WFM is also introduced, called the averaged FM (AFM), where complexity is reduced at the expense of degradation in the overall WFM performance. Both the WFM and AFM exhibit improved performance over the original FM algorithm. Finally, an unbiased version of the WFM, AFM and FM is presented in which an estimate of the bias term is removed to improve the overall MSE performance. The effect of this modification on the algorithms' performance is then analysed and discussed. |
