Robust Least-SquareLocalization Based on Relative Angular Matrix in Wireless Sensor Networks

Abstract

Accurate position information plays an important role in wireless sensor networks (WSN), and cooperative positioning based on cooperation among agents is a promising methodology of providing such information. Conventional cooperative positioning algorithms, such as least squares (LS), rely on approximate position estimates obtained from prior measurements. This paper explores the fundamental mechanism underlying the least squares algorithm’s sensitivity to the initial position selection and approaches to dealing with such sensitivity. This topic plays an essential role in cooperative positioning, as it determines whether a cooperative positioning algorithm can be implemented ubiquitously. In particular, a sufficient and unnecessary condition for the least squares cost function to be convex is found and proven. We then propose a robust algorithm for wireless sensor network positioning that transforms the cost function into a globally convex function by detecting the null space of the relative angle matrix when all the targets are located inside the convex polygon formed by its neighboring nodes. Furthermore, we advance one step further and improve the algorithm to apply it in both the time of arrival (TOA) and angle of arrival/time of arrival (AOA/TOA) scenarios. Finally, the performance of the proposed approach is quantified via simulations, and the results show that the proposed method has a high positioning accuracy and is robust in both line-of-sight (LOS) and non-line-of-sight (NLOS) positioning environments.

TDoA Localization in Wireless Sensor Networks Using Constrained Total Least Squares and Newton’s Methods

“…and D(•) is the diagonal matrix whose diagonal is taken from the vector •. In [48], the approximation in (18) is not taken into account. However, the quadratic term of the additive noise brings about more complexity.…”

“…However, the quadratic term of the additive noise brings about more complexity. From ( 16) and (18), one can see that there are errors at both sides of (12). The TDoA localization can be considered as a structured TLS problem, when the perturbations have a special structure as shown in ( 16) and (18).…”

“…The limitation of the TDoA localization in this model is that the approximation in (18) causes the loss of the accuracy for all methods designed to handle the TDoA localization problem. To overcome this issue, one should avoid the approximation in (18) and has to deal with the second-order term of the noise. We shall leave this idea for a future work.…”

Refinement of TOA Localization with Sensor Position Uncertainty in Closed-Form

“…With the rise of the fifth-generation communication system (5G), Internet of things, automatic pilot and unmanned aerial vehicle, localization continues to receive great attention [1][2][3][4]. Based on different type of measurements, the common localization methods estimate the source position using time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), Doppler frequency, Fingerprint and received signal strength (RSS) [5][6][7][8][9][10][11][12][13]. To improving the accuracy further, a series of hybrid method is developed by combining several kinds of measurements [14][15][16].…”