Design of Grouped Sensor Geometry in Sky-wave Time-difference-of-arrival Localization Systems*

This paper studies the design problem of grouped sensor geometry for sky-wave time-difference-of-arrival (TDOA) localization systems. The sky-wave TDOA localization system is based on a non-line-of-sight (NLOS) scenario, where signals are reflected by ionosphere-layer before arriving at sensors. In the literature, the grouped sensor scheme has been proposed to alleviate the impact of ionosphere-layer height (IH) errors, but the geometry design of grouped sensor is still an unsolved problem. In fact, the traditional design methodology is proposed for line-of-sight (LOS) scenarios and relies on special structures of cost function. However, these structures do not exist necessarily in our background. For this reason, we replace the cost function by a simpler version and introduce an additional sensor placement constraint to provide the required structures, which make traditional design methodology applicable. Due to the approximations made during this process, the designed geometries are suboptimal. But it is shown that optimizing over the proposed simpler cost function guarantees that the cramer-rao bound (CRB) will not attain its largest value. Performance comparison validates the novelty of design results.