In wireless sensor networks, the problem of anchor (whose locations are a priori known) placement plays a vital role in improving the estimation accuracy of sensor (whose locations are unknown and need to be determined) locations. This paper deals with single-hop sensor localization from a novel perspective. On the one hand, unlike existing studies relying on ideal independent identically distributed (i.i.d.) noises in distance measurements, namely distance-independent noises, this paper defines a more realistic noise model in the sense that the noise variance is a function of sensor-to-anchor distances, namely distance-dependent noises. On the other hand, other than evaluating the localization performance for sensors at deterministic locations, a statistical approach is adopted by assuming a uniform and random distribution within a unit disk for the sensor location and evaluating the mean value of the associated Fisher information matrix determinant as the optimality metric for anchor placement. Through this metric, the optimal anchor placement is investigated from both theoretical and simulative perspectives. In the literature of optimal anchor placement with distance-independent noises, it has been addressed or conjectured to be true that it is optimal to have anchors equally spaced on the boundary. However, after a thorough analysis, it is shown that this conclusion is generally incorrect, but approaches to be true provided that the number of anchors goes to infinity. This study not only provides useful guidance for optimally deploying anchors in practice, but also yields valuable insights for future research on optimal anchor placement.
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Having only two anchors in a plane, though results in flip ambiguities, is indicative of understanding the characteristics of localization performance.
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This work is supported by the National Natural Science Foundation of China under Grant 41401519, the “Grassland Elite” Project of the Inner Mongolia Autonomous Region under Grant CYYC5016, and the Postgraduate Scientific Research Innovation Foundation of Inner Mongolia under Grant 11200-12110201.
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Miao, Q., Huang, B. On the optimal anchor placement in single-hop sensor localization. Wireless Netw 24, 1609–1620 (2018). https://doi.org/10.1007/s11276-016-1424-7
- Sensor localization
- Optimal anchor placement
- Heteroscedastic noises
- Fisher information matrix (FIM)