GOF analysis for Gaussianity assumption of range errors in WSN

Gaussianity assumption is prevalent and fundamental to many statistical theories and engineering applications. Range measurement errors are generally assumed to reveal Gaussian distribution. We wish to analyze the hypothesis that X_i ~ N(μ, σ²) for i = 0, 1, ..., n - 1 where n is total number of range measurements X. To scrutinize this hypothesis, instead of relying on artificially generated random variables, real time ranging data is obtained from experiments using IEEE 802.15.4 compliant devices, covering outdoor/indoor environment with both Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) conditions. Distribution of range measurements are analyzed using four goodness-of-fit (GOF) tests i.e. Graphical technique, Linear correlation coefficient (γ), Anderson-Darling (A²), and Chi-squared (χ²). It is observed that majority of the outcomes are same in all the tests with a high percentage disagreement with the assumption.