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Error Distribution of Range Measurements in

Wireless Sensor Networks (WSNs)

In this paper the main objective is to scrutinize this assumption for different environments.

Experiments are performed in both outdoor and indoor environments with Line-of-Sight (LOS)

and Non-Line-of-Sight (NLOS) conditions using IEEE 802.15.4 compliant devices. These

devices consist of a low-cost 2.45 GHz chipset and use Time-of-Flight (TOF) measurement

technique for range estimation. Our results and analysis are based on four different statistical

Goodness-of-Fit (GOF) tests i.e., a graphical technique, Linear correlation coefficient, Anderson-

Darling, and Chisquared for investigating the Gaussianity of range measurements.

In several sensor networks mainly for environmental applications such as water quality

monitoring, precision agriculture, and indoor air quality monitoring, the on hand sensing data

may be rendered useless by a lack of accurate sensor location estimation. The availability of

accurate sensor location estimates can help reduce configuration requirements and device cost.

Further, accurate sensor location estimates enable applications such as inventory management

,intrusion detection, detecting and monitoring car thefts, and vehicle tracking and detection .The

assumption of Gaussianity is prevalent and fundamental to many statistical theories and

engineering applications. In recent years a lot of research has been done in the field oflocalization in WSNs and all the existing localization methods are based on the Gaussianity

assumption such that either the range estimates r or the noise/error distorting the range

estimates are assumed to be Gaussian distributed.

GOODNESS OF FIT (GOF) TESTS-

A. Graphical TechniqueB. Linear Correlation Coefficient ()C. Anderson-Darling Test (A2)D. Chi-Squared Test (_2)The experiments have been performed in an indoor and an outdoor environment with both LOSand NLOS conditions. For each condition three different sets of experiments have been

performed and for each set of experiments the transmitter and receiver nodes are mounted on a

tripod at a specific height. The three different heights used are 0.5 m, 1.0 m and 1.5 m. At each

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height five experiments were performed with different ranges of 10 m, 20 m, 30 m, 40 m and 50

m. For each range 500 iterations are executed giving 500 range estimates.

GRAPHICAL AND NUMERICAL RESULTS-

It is observable from the results that each method is powerful in scrutinizing the hypothesis of

Gaussianity however the graphical and techniques are less consistent but simpler to use in

comparison with the A2 and _2 tests. The end results acquired from A2 and _2 appears more

valid and authentic as they can be compared with standard critical values for these tests whereas

in the case of graphical technique the outcomes are to be visually examined and for linear

correlation coefficient, , technique some generalization has to be made for validating the

hypothesis. The results encourage further investigation into the topic. The central limit theorem

(CLT) states that the sum of large numbers of independent, statistically more or less identical,

random variables has an approximately Gaussian distribution, so in future the effect of the

number of range estimates n on Gaussianity will be examined and the outdoor NLOS condition

will be studied in more detail. It will also be investigated why 75% of the result negates the

hypothesis of Gaussianity. If Gaussian distribution is not the perfect model for the error

distribution in range estimates, then which statistical model can best describe the observational

error distribution in ranging.

Submitted byPriti Singh Tanwar

(1125938)