A Unified Bayesian Framework for Joint Estimation and Anomaly Detection in Environmental Sensor Networks

Abstract

Advanced large-scale environmental monitoring systems relying on the emerging aerial/terrestrial technologies of wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs), and mobile crowdsensing, impose strong requirements on the reliability of the collected data. Unfortunately, sensing units can suddenly suffer unexpected anomalies due to accidental faults or malicious causes. Outlier detection methods have been widely employed to identify and discard unreliable measurements from large data sets, but further improvements in the sensing processes can be obtained by adopting advanced signal processing algorithms that take full advantage of all the collected information without rejecting the measurements. In this paper, we propose a novel unified Bayesian framework that enable simultaneous estimation of a common parameter of interest and identification of multiple and possibly different types of anomalies that can affect sensors in environmental sensor networks. Specifically, we consider two rather general error models based on Gaussian mixtures able to capture different variations affecting the quality of the collected measurements. For each model, we illustrate the optimal joint maximum-likelihood and maximum a-posteriori (ML-MAP) estimation method, which represents the benchmark for the problem at hand, and propose novel reduced-complexity two-step algorithms able to achieve almost the same performance of the joint ML-MAP, but at a fraction of its computational cost. The derivations of all the algorithms are also extended to handle the more general case in which the probability of occurrence of anomalies is unknown and should be inferred from the data using an Empirical Bayes approach. Extensive performance analyses using both synthetic and real experimental data acquired in a network of environmental monitoring stations deployed in the Apulia region, south of Italy, demonstrate the effectiveness of the proposed framework.

Keywords

• Anomaly detection
• Gaussian mixture models
• maximum-likelihood and Bayesian estimation
• outlier detection
• sensor networks