Sensor node localization based on two-way time-of-arrival ranging with imperfect clocks
In this talk, we will discuss the positioning of sensors nodes based on two-way time-of-arrival (TW-TOA) measurements when the nodes have imperfect clocks. More precisely, the problem is to localize a single target node using distance measurements to a number of nodes at a priori known positions (anchor nodes). The target node clock is assumed to follow an affine relationship with the anchor node clocks. That is, the target node clock will, in general, run too quick or too slow and will be offset compared with the anchor node clocks. The clock rate is sometimes called clock skew and is ideally equal to one, indicating that the clock runs at the same rate as the global reference time. The anchor nodes are assumed to have perfect clock skews, but unknown and different offsets. The TW-TOA measurement process will remove the clock offsets, but the clock skew difference will affect the distance measurements and, therefore, also the position estimate, if not properly accounted for. We model the target node clock skew as a nuisance parameter and show that the resulting maximum likelihood (ML) estimator is difficult to compute. To find more tractable estimators, we apply a nonlinear pre-processing step to convert the ML problem into a linear least squares problem under a quadratic constraint. The latter problem is shown to be a special case of the so-called generalized trust region problem, which we can solve exactly under mild conditions. We develop two suboptimal positioning methods and compare the performance and complexity with the ML estimator and the Cramér-Rao bound. The developed methods are numerically shown to offer good performance, but with less complexity (and accuracy) compared with the ML estimator.
This presented research is joint work with Mohammad Gholami, Chalmers University, and Sinan Gezici, Bilkent University.
Erik G. Ström (https://sites.google.com/site/erikgstrom/) received the M.S. degree from the Royal Institute of Technology (KTH), Stockholm, Sweden, in 1990, and the Ph.D. degree from the University of Florida, Gainesville, in 1994, both in electrical engineering. He accepted a postdoctoral position at the Department of Signals, Sensors, and Systems at KTH in 1995. In February 1996, he was appointed Assistant Professor at KTH, and in June 1996 he joined Chalmers University of Technology, Gothenburg, Sweden, where he is now a Professor in Communication Systems since June 2003. Dr. Ström currently heads the Division for Communications Systems, Information Theory, and Antennas at the Department of Signals and Systems at Chalmers and leads the competence area Sensors and Communications at the traffic safety center SAFER, which is hosted by Chalmers. His research interests include signal processing and communication theory in general, and constellation labelings, channel estimation, synchronization, multiple access, medium acccess, multiuser detection, wireless positioning, and vehicular communications in particular. Since 1990, he has acted as a consultant for the Educational Group for Individual Development, Stockholm, Sweden. He is a contributing author and associate editor for Roy. Admiralty Publishers FesGas-series, and was a co-guest editor for the Proceedings of the IEEE special issue on Vehicular Communications (2011) and the IEEE Journal on Selected Areas in Communications special issues on Signal Synchronization in Digital Transmission Systems (2001) and on Multiuser Detection for Advanced Communication Systems and Networks (2008). Dr. Ström was a member of the board of the IEEE VT/COM Swedish Chapter 2000–2006. He received the Chalmers Pedagogical Prize in 1998 and the Chalmers Ph.D. Supervisor of the Year award in 2009.