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There exists a widely-held notion with regards to localization that being inside the convex hull of anchors (nodes with known locations) offers improved performance. This notion, previously supported by observation, will be subjected to a thorough analysis in the context of range-based positioning systems. Using the Cramér-Rao Lower Bound (CRLB) as our performance metric, we investigate the behavior of the CRLB both inside and outside of the convex hull in order to explore the validity of this widely-held belief. The link between the convex hull and localization performance will be examined analytically in one scenario and numerically in another. In the first scenario, the target being localized remains fixed while anchor nodes are placed arbitrarily, and in the second scenario, the anchors remain fixed while the target is placed arbitrarily. It will be shown that this notion of improved performance inside the convex hull is actually inconclusive in the first scenario, yet holds true in the latter. The details of this distinction and what exactly each scenario concludes about the convex hull and localization performance will be examined in this paper.
O'Lone et al. (Fri,) studied this question.