Grid Arrangement Constraints-Based Localization for Location-Unknown Anchors Using AOA and TOA Measurements

The widespread use and development of location-based services have led to extensive research on wireless sensor network (WSN) positioning schemes. Positioning requires a wireless terminal, that is, an anchor that can provide a reference for positioning. If there is an error in the relative position of the anchor, the positioning accuracy of the target will be decreased. For this reason, it is critical to know the precise relative position of the anchors to obtain the accurate positioning of the target. In this study, assuming the relative positions of
$N$
anchors are unknown, we formulate the problem of estimating the positions of
$N-1$
anchors relative to the reference anchor, which is done by using the angle of arrival and time of arrival measurements as a least-squares problem. Moreover, we propose a grid arrangement constraints-based two-step weighted least squares, which is a method to achieve highly accurate positioning by taking advantage of the regularity in the placement of anchors. Numerical simulation results show that for the case of an infinitely measurable range, the root mean square error of the proposed method is the smallest of the methods addressed in this study and smaller than that of the Cramer–Rao lower bound, regardless of the measurement noise, anchor interval, and number of anchors. In addition, numerical simulation results show that the proposed method is also effective in the case of a finitely measurable range. Although the proposed method is limited by a grid-like arrangement, it is an excellent positioning method.