Error bounds for wireless localization in NLOS environments

Abstract

An efficient and accurate method to evaluate the fundamental error bounds for wireless sen-sor localization is proposed. While there already exist efficient tools like Cram`er-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, under Non-Line-of-Sight (NLOS) environments, is impossible to be met a priori. Therefore, it is shown that collecting a small number of samples from each link and applying them to a non-parametric estimator, like the Gaussian kernel (GK), could lead to a quite accurate reconstruction of the error distribution. A proposed Edgeworth Expansion method is employed to reconstruct the error statistic in a much more efficient way with respect to the GK. It is shown that with this method, it is possible to get fundamental error bounds almost as accurate as the theoretical case, i.e. when a priori knowledge of the error distribution is available. Therein, a technique to determine fundamental error limits – CRLB and PEB – onsite without knowledge of the statistics of the ranging errors is proposed.