Minimizing Uncertainty through Sensor Placement with Angle Constraints

摘要: We study the problem of sensor placement in environments which localization is a necessity, such as ad-hoc wireless networks that allow few anchors know their location or arrays are tracking target. In most these situations, quality depends on relative angle between target and pair sensors observing it. this paper, we consider placing small number ensure good angular $\alpha$-coverage: given $\alpha$ $[0,\pi/2]$, for each $t$, there must be at least two $s_1$ $s_2$ $\angle(s_1 t s_2)$ interval $[\alpha, \pi-\alpha]$. One main difficulties encountered problems since constraints depend sensors, building solution account inherent dependency selected feature generic Set Cover techniques do not for. introduce general framework guarantees an coverage arbitrarily close to any $\alpha <= \pi/3$ apply it variety get bi-criteria approximations. When required constant fraction $\alpha$, obtain results strictly better than what standard geometric methods give. $(1-1/\delta)\cdot\alpha$, $\mathcal{O}(\log \delta)$- approximation with $\alpha$-coverage plane. presence additional distance visibility constraints, gives $\mathcal{O}(\log\delta\cdot\log k_{OPT})$-approximation, where $k_{OPT}$ size optimal solution. also use our give \delta)$-approximation ensures $(1-1/\delta)\cdot \alpha$-coverage covers every within $3R$.