Non-parametric estimation of error bounds in LOS and NLOS environments

In this paper we propose an efficient and accurate method to evaluate on-site the fundamental error bounds for wireless sensor network (WSN) localization. While there exist efficient tools like Cramèr-Rao lower bound (CRLB) and position error bound (PEB) to estimate error limits, in their standard formulation they all need an accurate knowledge of the statistic of the ranging error. This requirement, especially under non line-of-sight (NLOS) environments, is impossible to be met a-priori. We show therefore that collecting a number of samples from each link and applying them to a non-parametric estimator, like the Gaussian kernel (GK) and Edgeworth expansion (EE), could lead to a quite accurate reconstruction of the error distribution and then, in turn, of the error bounds. The EE method is then for the first time employed to reconstruct the error statistic in a much more efficient way - less number of samples required - with respect to the GK. We finally show that with our EE method it is possible to get fundamental error bounds almost as accurate as the theoretical case, i.e. when perfect a priori knowledge of the error distribution is available.