Range based sensor node localization in the presence of unknown clock skews

Abstract

We deal with the positioning problem based on two-way time-ofarrival (TW-TOA) measurements in asynchronous wireless sensor networks. The optimal estimator for this problem poses a difficult global optimization problem. To avoid the drawbacks in solving the optimal estimator, we use approximations and derive linear models, which facilitate efficient solutions. In particular, we employ the least squares method and solve a general trust region subproblem to find a coarse estimate. To further refine the estimate, we linearize the measurements and obtain a linear model which can be solved using regularized least squares. Simulation results illustrate that the proposed approaches asymptotically attain the Cramér-Rao lower bound.

Robust Second-Order Cone Relaxation for TW-TOA-Based Localization With Clock Imperfection

“…Due to the non-convex nature of the RLS problem, we apply the second-order cone relaxation technique to relax it as an SOCP, which can be efficiently solved using available solvers. Comparing with [8], our method does not estimate the turn-around times. Instead, it only requires to know the estimated ranges of the turn-around times and the upper bound of the clock skews, which are generally easier to acquire than their variances.…”

“…The processing time taken at the anchor is called the turn-around time, which is typically unknown. By denoting T i as the turn-around time at the ith anchor, the TW-TOA measurements can be expressed as [8]:…”

“…In this letter, we also address the TW-TOA based localization problem using the measurement model in [8]. Different from [8], we take the clock skews and the turn-around times as nuisance parameters and formulate a worst-case robust least squares (RLS) problem that is not sensitive to the nuisance parameters.…”

“…Wang et al proposed to localize a target using the two-way TOA (TW-TOA) measurements [7], in which both the anchors and the target record the time stamps to compute the TW-TOA measurements, and their clock skews are also included in the TW-TOA measurements. Different from [7], the work [8] addressed the TW-TOA based localization problem based on a new measurement model, in which only the target node is required to record the time stamps and the clock offset is eliminated. However, this model introduces some unknown auxiliary variables, i.e., the turn-around times.…”

“…Different from [8], we take the clock skews and the turn-around times as nuisance parameters and formulate a worst-case robust least squares (RLS) problem that is not sensitive to the nuisance parameters. Due to the non-convex nature of the RLS problem, we apply the second-order cone relaxation technique to relax it as an SOCP, which can be efficiently solved using available solvers.…”