Q$1$ Routing Localization is one of the most important issues in wireless sensor networks.

$($a$)$ Describe the mechanism of Time of Arrival $($ToA$)$ to estimate the distance

between two nodes.

$(4$ marks$)$

$($b$)$ Consider three anchor nodes with known position, $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3).$

The unknown node is located at position $(x_u,y_u).$ Assume that the distance from

$(x_u,y_u)$ to all three nodes are perfect distances.$|$

$($i$)$ Formulate the necessary linear matrix equation to represent the

solution of $(x_u,y_u).$

$(10$ marks$)$

$($ii$)$ Figure $1$ shows three anchors of known position and a node of unknown

location. If the distances $r_1,r_2$ and $r_3$ are given as $3\mathrm{.}6,1\mathrm{.}41$ and $2\mathrm{.}24$

respectively, deduce the coordinate of the unknown node.help