دانلود رایگان مقاله محلی سازی راست نمایی حداکثر

Abstract

Maximum likelihood is a criterion often used to derive localization algorithms. In particular, in this paper we focus on a distance-based algorithm for the localization of nodes in static wireless networks. Assuming that Ultra Wide Band (UWB) signals are used for inter-node communications, we investigate the ill-conditioning of the Two-Stage Maximum-Likelihood (TSML) Time of Arrival (ToA) localization algorithm as the Anchor Nodes (ANs) positions change. We analytically derive novel lower and upper bounds for the localization error and we evaluate them in some localization scenarios as functions of the ANs’ positions. We show that particular ANs’ configurations intrinsically lead to ill-conditioning of the localization problem, making the TSML-ToA inapplicable. For comparison purposes, we also show, through some examples, that a Particle Swarm Optimization (PSO)-based algorithm guarantees accurate positioning also when the localization problem embedded in the TSML-ToA algorithm is ill-conditioned.

4. Conclusion

In this paper, we have studied the conditioning of the TSMLToA localization algorithm. Using norm inequalities, we have derived novel lower and upper bounds for the positioning error. Then, we have considered scenarios with different ANs’ positions and we have shown how the lower and upper bounds behave as functions of the ANs’ positions. Moreover, for each ANs’ configuration, we have solved the localization problem by means of the TSML-ToA algorithm, showing that the obtained position estimates can be far inaccurate. Finally, we have shown that the localization errors obtained with the TSML-ToA algorithm can be avoided using a localization approach based on the PSO algorithm.