Figure 2.

The proposed indoor positioning system. $i$: index of the repeaters ($i$ = 1, 2, 3); $j$: index of the satellites ($j$ = 1, 2, …, $n$ ); $Ri$: $i$th repeater; $Sj$: $j$th satellite; $d_i$: indoor distance from repeater $Ri$ to the receiver (with a clock bias of $t_{bias}^{receiver}$ ); $D_{Ri}^{Sj}$: distance from ith repeater ($Ri$:) to the $j$th satellite ($Sj$ ); ${\tau }_i$: propagation delay of the ith repeater; $t_{bias}^{Sj}$: satellite clock bias of the $j$th satellite.