Abstract
This paper considers localization of a source or a sensor from distance measurements. We argue that linear algorithms proposed for this purpose are susceptible to poor noise performance. Instead given a set of sensors/anchors of known positions and measured distances of the source/sensor to be localized from them we propose a potentially non-convex weighted cost function whose global minimum estimates the location of the source/sensor one seeks. The contribution of this paper is to provide nontrivial ellipsoidal and polytopic regions surrounding these sensors/anchors of known positions, such that if the object to be localized is in this region, localization occurs by globally exponentially convergent gradient descent in the noise free case. Exponential convergence in the noise free case represents practical convergence as it ensures graceful performance degradation in the presence of noise. These results guide the deployment of sensors/anchors so that small subsets can be made responsible for practical localization in geographical areas determined by our approach.
This work is supported by National ICT Australia, which is funded by the Australian Government’s Department of Communications, Information Technology and the Arts and the Australian Research Council through the Backing Australia’s Ability Initiative and NSF grants CCF-0729025 and ECS-0622017.
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Fidan, B., Dasgupta, S., Anderson, B.D.O. (2008). Realistic Anchor Positioning for Sensor Localization. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_6
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DOI: https://doi.org/10.1007/978-1-84800-155-8_6
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