Ultrasound TDoA Positioning Using the Best Linear Unbiased Estimator and Efficient Anchor Placement

In this article, positioning based on ultrasound time-difference-of-arrival (TDoA) measurements is investigated. The best linear unbiased estimator (BLUE) algorithm is proposed, compared to a least-squares estimator (LSE), and validated using numerical simulations. Optimal placement of anchor nodes is also investigated by evaluating and minimizing the geometrical dilution of precision (GDOP) with some geometrical constraints. The comparison was carried out by assuming the multipath channel affecting line-of-sight (LoS) propagation. It is shown that the accuracy and the processing time of the proposed BLUE approach are similar to that of the LSE while providing a simpler implementation. It is also shown that anchors' constellations that minimize the GDOP can lead to increased robustness to multipath and that the BLUE provides a more robust performance than LSE when multipath is introduced in a LoS environment.