Correlation analysis and statistical characterization of heterogeneous sensor data in environmental sensor networks

Abstract

Abstract In wireless sensor networks, missing data is an inevitable phenomenon due to the inherent limitations of the sensor nodes, such as battery power constraints of nodes, missing communication links, bandwidth limitation, etc. Missing data adversely affects the quality of data received by the sink node. Since the data acquired by the sensor nodes in a multimodal environmental sensor network are spatially and temporally correlated, these correlations play a pivotal role in missing data recovery and data prediction. This paper proposes an analytical framework to characterize the correlation between two different pairs of modalities in an environmental sensor network using a set of classical and robust measures of correlation coefficient estimates. Monte Carlo simulation is performed to approximately model sensed environmental data characteristics. Three classical estimates (Pearson’s correlation coefficient, Spearman’s rank correlation coefficient, and Kendall’s-tau rank correlation coefficient), and four robust estimates of correlation coefficients are used to establish the correlation between different pairs of sensed modalities in the data characteristics. The efficacy of these estimates is obtained using the two performance metrics, mean-squared error (MSE) and relative estimation efficiency (RE). Stationarity analysis among the acquired environmental variables shed light upon the best estimates of the correlation coefficient, which could be used for prediction of temperature modality in a known region of slope/stationarity in the data characteristics. The robustness of the correlation coefficient estimates in the presence of outliers present in the data due to noise, errors, low residual battery power of sensor nodes, etc. is also investigated.