Bayesian Signal Processing for Robust IoT: Classical vs. Graph Based Methods for Joint Estimation and Anomaly Detection

Internet of Things (IoT) is recognized as a key enabler of an increasing number of applications, including monitoring of parameters such as temperature, pH, particulate matter, etc. Unfortunately, IoT devices are vulnerable to sudden anomalies caused by accidental faults or malicious behaviors (e.g., byzantine attacks), underscoring the need for robust methods. While anomaly detection has been widely employed to identify and discard unreliable measurements or outliers, further improvements in the sensing processes can be obtained by adopting signal processing algorithms that take full advantage of all the collected information without rejecting any of the measurements. In this contribution, we focus on Bayesian approaches that perform joint estimation of a parameter of interest and anomaly detection, i.e., classification of each IoT node as regular or anomalous. More specifically, we illustrate the joint maximum-likelihood and maximum a posteriori (ML-MAP) approach for both the classical paradigm, where a common (average) parameter is estimated, and the graph signal processing (GSP) paradigm that leverages the graph structure to capture data correlations. We present results on synthetic and experimental data, highlighting the strengths and limitations of the two paradigms.