WSN06-2: Sensor Localization from WLS Optimization with Closed-form Gradient and Hessian

A non-parametric, low-complexity algorithm for accurate and simultaneous localization of multiple sensors from scarce and imperfect ranging information is proposed. The technique is based on a weighted least-squares (WLS) optimization, where the gradient and Hessian of the quadratic objective are given in closed-form. The performance of the proposed technique is studied through extensive computer simulations, with the intra-node distances randomly generated in accordance to a statistical model constructed from the results of a measurement campaign conducted with a pair of impulsive ultra-wideband (UWB) radios in an indoor scenario. The simulation results reveal that the proposed algorithm, despite its low complexity, is nearly as accurate as the known alternative of best performance, which is based on semi-definite programming and demands significantly more computational power.