\documentclass[review=true, screen]{ocsmnar} % Only used to typeset XeLaTeX-Logo below. \usepackage{metalogo} % Adjust this to the language used. \usepackage[british]{babel} % use nice mathematical symbols \usepackage{amsfonts} \usepackage{adjustbox} \newcommand{\R}{\mathbb{R}} \newcommand{\Oc}{\mathcal{O}} \begin{document} \title{Anomaly Detection in Wireless Sensor Networks: A Survey} \seminar{SVS} % Selbstorganisation in verteilten Systemen \semester{Sommersemester 2020} \author{Anton Lydike} \affiliation{\institution{Universität Augsburg}} \begin{abstract} Anomaly detection is an important problem in data science, which is encountered often when data is collected and analyzed. An anomaly is often defined as a measurement that is inconsistent with the expected results. Since anomaly detection can be applied to many different environments, a multitude of different research contexts and application domains exist in which anomaly detection is researched. Anomaly detection in wireless sensor networks (WSN) is a relatively new addition to the field. The context of WSN introduces a lot of interesting new challenges, as nodes are often small devices running on battery power and cannot do complex computation on their own. Furthermore, in WSNs communication is often not perfect and messages get lost during operation. Any protocols that incur additional communication must have a good justification, as communication is expensive. All these factors create a unique environment, in which not many existing solutions to the problem are applicable. This paper will focus solely on anomaly detection in sensor data collected by the WSN. \end{abstract} \keywords{Wireless Sensor Networks, Anomaly detection, Outlier detection, Sensor calibration, Drift detection} \maketitle \section{Overview} There are many different approaches to anomaly detection, a common way to classify these is by their place of computation. An approach is considered centralized, when a large chunk of the computation is done at a single point, or at a later stage during analysis. A decentralized approach implies that a considerable amount of processing is done on the individual nodes, doing analysis while being deployed. It is also important to differentiate between online and offline detection. Online detection can run while the WSN is operating, while offline detection is done after the data is collected or during pauses of operation. Online detection often reduces mission duration due to increased power consumption, but can also have the opposite effect, if the analysis done can be used to reduce the amount of communication required for the WSN to function. \subsection{Anomaly Types} We need to clarify the different kinds of anomalies that can occur in WSN data sets. Commonly, four different kinds of anomalies that occur in WSN are considered (c.f. Figure~\ref{fig:noisetypes}): \begin{itemize} \item \emph{Spikes} are short changes with a large amplitude \item \emph{Noise} is (an increase of) variance over a given time \item \emph{Constant} is a the sudden absence of noise \item \emph{Drift} is an offset which increases over time \end{itemize} \begin{figure} \includegraphics[width=8.5cm]{img/anomaly_types.png} \caption{Spike, noise, constant and drift type anomalies in noisy linear data, image from Bosmal et al. \cite{bosman2013}} \label{fig:noisetypes} \end{figure} We will first look into sensor self-calibration, which often removes or reduces drift and constant offsets. Then we will look into model based techniques for outlier detection, and then into machine learning based approaches. Outlier detection is able to detect spikes, noise and drift type anomalies, while it has difficulties detecting constant type anomalies. A Noise anomaly is not the same as a noisy sensor, working with noisy data is a problem in WSN, but we will not focus on methods of cleaning noisy data, as it is not in the scope of this survey. Elnahrawy et al. \cite{elnahrawy2003} and Barcelo et al. \cite{barcelo2019} are a great places to start a survey in this direction. A fifth anomaly type, \emph{sensor failure}, is commonly added to anomaly detection \cite{rajasegarar2008,chandola2009}. Since sensor failure often manifests in these four different ways mentioned above, and we are not interested in sensor fault prediction, detection and management here, faulty sensors will not be discussed further. \section{Sensor Drift and Self-Calibration} Advancements in energy storage density, processing power and sensor availability have increased the possible length of deployment of many WSN. This increase in sensor lifetime, together with an increase in node count due to reduced part cost \cite{wang2016}, as well as the introduction of the Internet of Things (IoT) have brought forth new problems in sensor calibration and drift detection \cite{dehkordi2020}. Increasing the amount of collected data and the length of time over which it is collected introduces a need for better quality control of the sensors that data came from. Ni et al. \cite{ni2009} noticed drift as high as 200\% in soil CO$_2$ sensors, while Buonadonna et al. \cite{buonadonna2005} noticed that his light sensors (which were calibrated to the manufacturer's specification) were performing very poorly when measured against laboratory equipment. It is out of these circumstances, that the need arises for better and more frequent sensor calibration. \begin{figure*}[ht] \includegraphics[width=\textwidth]{img/calibration_attributes.png} \caption{Categories of calibration approaches, from Barcelo-Ordinas et al. \cite{barcelo2019}} \label{fig:calcats} \end{figure*} The field of self-calibration in WSN quite broad, in order to get an overview over all approaches Barcelo-Ordinas et al. \cite{barcelo2019} categorized each approach by seven different attributes (Figure~\ref{fig:calcats}): \begin{itemize} \item \emph{Area of interest} distinguishes between \emph{micro} (calibrating sensors to minimize error to a single data point), and \emph{macro} (calibrating nodes to minimize error over a given area of nodes). \item \emph{Number of sensors} determines if data from other sensors is used, so called \emph{sensor fusion}, or if is done with just a \emph{single sensor}. \item \emph{Ground truth} specifies, if the calibration is done in relation to a known good sensor \emph{non-blind}, or without one \emph{blind}. If both calibrated and uncalibrated sensors are used, the approach is considered \emph{semi-blind}. \item \emph{Position from reference} is the distance between the calibration target and the point where the reference data is collected. If data from the close neighborhood is used, the approach is considered \emph{collocated}. If instead nodes are calibrated hop-by-hop in an iterative fashion, it is called \emph{multi-hop}. In \emph{model-based} calibration, fixed ground truth sensors are used in combination with a model to predict sensor error. \item \emph{Calibration time} distinguishes between \emph{pre/post-\break deployment calibration}, \emph{periodic} (calibration at given intervals) and \emph{opportunistic} (when nodes in a mobile network come into range of a calibration source). \item \emph{Operation mode} is either \emph{offline} (calibration when the node is not used) and \emph{online} (calibration during normal operation). \item \emph{Processing mode} divides the approaches into \emph{centralized} processing, meaining calibration parameters are calculated by a central node and then distributed over the network, and \emph{decentralized}, where a single node, or collection of nodes collaborate to calculate their calibration parameters. \end{itemize} This level of specialization requires its own survey, which most recently was Barcelo-Ordinas et al. \cite{barcelo2019}. They categorize 39 approaches into these attributes and discuss them in-depth. We will instead just look at some central problems and ideas to these approaches, focusing especially on the aspects around ground truth: \subsection{Problems in Blind Self-Calibration Approaches} The central problem in self-calibration is predicting the error of a given sensor. Since this is such a broad problem, many different solutions exist. Kumar et al. \cite{kumar2013} proposes a solution that uses no ground-truth sensors and can be used online in a distributed fashion. It uses spatial Kriging (gaussian interpolation) and Kalman filtering (a linear approximation model accounting for noise, explained in detail in \ref{sec:kalman}) on neighborhood data in order to reduce noise and remove drift. This solution suffers from accumulative error due to a missing ground truth, as the system has no point of reference or general model to rely on. The uncertainty of the model, and thereby the accumulative error can be reduced by increasing the number of sensors which are used. A common method for gaining more measurements is increasing network density \cite{wang2016}, or switching from a single-sensor approach to sensor fusion. Barcelo-Ordinas et al. \cite{barcelo2018} explores the possibility of adding multiple copies of the same kind of sensor to each node. All of these approaches are shown to reduce the accumulative error inherent in blind self-calibration approaches but cannot completely negate it. This is a problem for networks who are planned to operate over large time span (e.g. multiple years). In those cases, non-blind calibration might be a better suited solution. \subsection{Non-Blind Self-Calibration Techniques} Non-blind, also known as reference-based calibration approached rely on known-good reference information. This data is often gathered from much more expensive sensors, which often come with restrictions on their use, e.g. local weather stations not reporting continuos data, and not at the exact location of the WSN. Another method is simply calibrating the sensors in a laboratory setting (e.g. \cite{ramanathan2006}). A known-good sensor is used for calibration within a controlled environment pre and/or post deployment as per the manufacturers specifications and the calibration parameters are applied to the collected data. While this improves the accuracy of the measured data, this is of limited usefulness if live readings from the network need to be accurate. An approach by Hasenfratz et al. \cite{hasenfratz2012} can calibrate low-cost gas sensors instantly with a calibrated sensor nearby, enabling calibration in the field without the need of an controlled environment or laboratory setting. This of course comes with a tradeoff in accuracy, but they show that the calibration is as good or better than the manufacturers. An ozone sensor calibrated using this scheme is only off by $\pm 2$ppb (parts per billion) when compared to a calibrated ozone sensor, despite the manufacturers claimed accuracy of $\pm 20$ppb. While these results are remarkable, it is not always feasible to visit every sensor in a WSN. Maag et al. \cite{maag2017} propose a solution to this problem. They formulate a hybrid solution, where calibrated sensor arrays can be used to calibrate other non-calibrated arrays in a local network of air pollution sensors over multiple hops with minimal accumulative errors. They show 16-60\% lower error rates than other iterative approaches currently in use. \subsection{An Example for Blind Calibration} \label{sec:kalman} Sirisanwannakul et al \cite{Sirisanwannakul2021} uses a blind centralized approach, where humidity sensors are calibrated using Kalman filtering in combination with a neural network to detect and counteract sensor drift. Kalman filtering consists of two phases, prediction and update. A Kalman filter can, given the previous state of knowledge at step $k-1$ consisting of an estimated system state and uncertainty, calculate a prediction for the next system state and its uncertainty. This is called the prediction phase. Then, a new (possibly skewed) measurement is observed and used to compute a prediction of the actual current state and uncertainty. This is called the update phase. The filter is recursive in nature and can be calculated with limited hardware in real-time, making it useful for many different anomaly detection applications. Kalman filters are based on a linear dynamical system on a discrete time domain. It represents the system state as vectors and matrices of real numbers. In order to use Kalman filters, the observed process must be modeled in a specific structure: \begin{itemize} \item $F_k$, the state transition model for the $k$-th step \item $H_k$, the observation model for the $k$-th step \item $Q_k$, the covariance of the process noise \item $R_k$, the covariance of the observation noise \item Sometimes a control input model $B_k$ \end{itemize} These models must predict the true state $x$ and an observation $z$ in the $k$-th step according to: \begin{align*} x_k &= F_kx_{k-1} + B_ku_k + w_k \\ z_k &= H_kx_k+v_k \end{align*} Where $w_k$ and $v_k$ is noise conforming to a zero mean multivariate normal distribution $\mathcal{N}$ with covariance $Q_k$ and $R_k$ respectively ($w_k \sim \mathcal{N}(0,Q_k)$ and $z_k \sim \mathcal{N}(0,R_k) $). The Kalman filter state is represented by two variables $\hat{x}_{k|j}$ and $P_{k|j}$ which are the state estimate and covariance at step $k$ given observations up to and including $j$. When entering step $k$, we can now define the two phases. \textbf{Prediction phase:} \begin{align*} \hat{x}_{k|k-1} &= F_k \hat{x}_{k-1|k-1}+B_ku_k \\ P_{k|k-1} &= F_kP_{k-1|k-1} F_k^\intercal+Q_k \end{align*} Where we predict the next state and calculate our confidence in that prediction. If we are now given our measurement $z_k$, we enter the next phase. \\ \textbf{Update phase:} \begin{align*} \tilde{y}_k &= z_k - H_k\hat{x}_{k|k-1} & \text{Innovation (forecast residual)} \\ S_k &= H_kP_{k|k-1} H_k^\intercal+R_k & \text{Innovation variance} \\ K_k &= P_{k|k-1}H_k^\intercal S_k^{-1} & \text{Optimal Kalman gain} \\ \hat{x}_{k|k} &= \hat{x}_{k|k-1} + K_k\tilde{y}_k & \text{State estimate} \\ P_{k|k} &= (I-K_kH_k)P_{k|k-1} & \text{Covariance estimate} \end{align*} After the update phase, we obtain $\hat{x}_{k|k}$, which is our best approximation of our real state. Sirisanwannakul et al. takes the computed Kalman gain and compares its bias. In normal operation, the gain is biased towards the measurement. If the sensor malfunctions, the bias is towards the prediction. But if the gains bias is between prediction and measurement, the system assumes sensor drift and corrects automatically. Since this approach lacks a ground truth measurement it cannot recalibrate the sensor, but the paper shows that accumulative error can be reduced by more than 50\%. \section{Outlier detection - model-based approaches} A centralized WSN is defined by the existence of a central entity, called the \emph{base station} or \emph{fusion centre}, where all data is delivered to and analyzed. It is often assumed, that the base station does not have limits on its processing power or storage. Centralized approaches are not optimal in hostile environments, but that is not our focus here. Since central anomaly detection is closely related to the general field of anomaly detection, we will not go into much detail on these solution, instead focusing on covering solutions more specific to the field of WSN. \subsection{Statistical Analysis} Classical Statistical analysis is done by creating a model of the expected data and then finding the probability for each recorded data point. Improbable data points are then deemed outliers. The problem for many statistical approaches is finding this model of the expected data, as it is not always feasible to create it in advance. It also bears the problem of bad models or slow changes in the environment \cite{mcdonald2013}. Sheng et al. \cite{sheng2007} propose an approach to global outlier detection, meaning a data point is only regarded as an outlier, if their value differs significantly from all values collected over a given time, not just from local sensors near the measured one. They propose that the base station requests bucketed histograms of each nodes sensors data distribution to reduce the data transmitted. These histograms are polled, combined, and then used to analyze outliers by looking at the maximum distance a data point can be away from his nearest neighbors. This method bears some problems, as it fails to account for non gaussian distribution. Another problem is the use of fixed parameters for outlier detection, requiring prior knowledge of the data collected and anomaly density. These fixed parameters also require an update, whenever these parameters change. Due to the histograms used, this method cannot be used in a shifting network topology. Böhm et al. \cite{böhm2008} propose a solution not only to non gaussian distributions, but also to noisy data. They define a general probability distribution function (PDF) with an exponential distribution function (EDF) as a basis, which is better suited to fitting around non gaussian data as seen in Figure~\ref{fig:probdistböhm}. They then outline an algorithm where the data is split into clusters, for each cluster an EDF is fitted and outliers are discarded. This method does not require any prior parametrization and is therefore more robust to configuration error. Since this process not only detects outliers, but does a complete clustering of the given data, it is computationally much more expensive than other methods for detecting outliers. However, since this is a complete clustering algorithm, it can be used in offline analysis for clustering and will produce good results quicker than PCA or similar algorithms. Outlier detection is more a byproduct of clustering, than the end result. \begin{figure} \includegraphics[width=8.5cm]{img/probability-dist-böhm.png} \caption{Difference of fitting a gaussian PDF and a customized exponential PDF. Image from \cite{böhm2008}.} \label{fig:probdistböhm} \end{figure} \subsection{Density Based Analysis} Outliers can be selected by looking at the density of points as well. Breuning et al. \cite{breuning2000} propose a method of calculating a local outlier factor (LOF) of each point based on the local density of its $n$ nearest neighbors. The problem lies in selecting good values for $n$. If $n$ is too small, clusters of outliers might not be detected, while a large $n$ might mark points as outliers, even if they are in a large cluster of less than $n$ points. This problem is further exasperated when we try to use this in a WSN setting, for example by streaming through the last $k$ points, as cluster size will not stay constant as incoming data might be delayed or lost in transit. Papadimitriou et al. \cite{papadimitriou2003} introduces a parameterless approach. They formulate a method using a local correlation integral (LOCI), which does not require parametrization. It uses a multi-granularity deviation factor (MDEF), which is the relative deviation for a point $p$ in a radius $r$. The MDEF is simply the number of nodes in an $r$-neighborhood divided by the sum of all points in the same neighborhood. LOCI provides an automated way to select good parameters for the MDEF and can detect outliers and outlier-clusters with comparable performance to other statistical approaches. They also formulate aLOCI, a linear approximation of LOCI, which also gives accurate results while reducing runtime. This approach can be used centralized, decentralized or clustered, depending on the scale of the event of interest. aLOCI seems great for even running on the sensor nodes itself, as it has relatively low computational complexity. \subsection{Principal Component Analysis} Principal components of a point cloud in $\R^n$ are $n$ vectors $p_i$, where $p_i$ defines a line with minimal average square distance to the point cloud while lying orthogonal to all $p_j, j