Statistical analysis of wireless sensor network Gaussian range estimation errors

Wireless sensor network (WSN) localisation has attracted significant research interest. The quality of time-of-flight ranging when used as the basis of localisation, has a direct impact on precision and accuracy. Recently significant attention has been devoted to modelling and analysis of range estimation error (REE) in indoor and cluttered environments. A Gaussianity assumption for the distribution of REE is a common practice in the literature. The motivation of this study is to analyse this assumption. To scrutinise this, rather than relying on computer generated data, a real IEEE 802.15.4 compliant WSN test-bed is used for collecting ranging data, covering outdoor and indoor environments for both line-of-sight and non-line-of-sight propagation conditions. The distribution of REE is analysed using both graphical and numerical goodness-of-fit (GOF) techniques, that is, quantile-quantile plotting, empirical cumulative distribution function plotting, probability density function plotting, linear correlation coefficient (γ) test, kurtosis (K) test, skewness (S) test, Anderson-Darling (A²) test and chi-squared (χ²) test. The GOF statistical analysis of the experimental results suggest that REE is not Gaussian distributed. A novel means of enhancement called the range filtration algorithm (RFA) is proposed. The RFA is based on the A² test, it filters out the range estimates with high errors.