On the Positioning of Sensors with Simultaneous Bearing and Range Measurement in Wireless Sensor Networks

Hybrid range and bearing based approach towards active localization of beacons will be widely celebrated in the near future, due to the protocols used for data transmission through targeted beam of radiation in 5G networks. This technique, which is one of the building blocks of 5G infrastructure does not only allow extremely high data rates but will also allow the estimation of direction of arrival/departure of the signal. Thus, in this paper a hybrid angle/range based approach towards positioning is under focus. A linear least squares approach will be applied to the unbiased version of hybrid direction of arrival-time of flight (DoA-ToF) measurement model. Thus, the unbiasing constant is first calculated followed by the theoretical mean squares expression calculation, to be utilized for selecting only those reference beacons that guarantee an improvement in the accuracy of the least squares approach. A critical distance expression is also derived that determines the relationship between the noise variance of angle and range estimates in terms of the distance between nodes. Furthermore, a weighted least squares solution is presented which exploits the noise covariance matrix of the hybrid measurement model. Finally, the weighted solution is bounded by the linear Cramér-Rao bound (LCRB) for the hybrid signal model.