We study how to secure distributed filters for linear time-invariant systems with bounded noise under false-data injection attacks. A malicious attacker is able to arbitrarily manipulate the observations for a time-varying and unknown subset of the sensors. We first propose a recursive distributed filter consisting of two steps at each update. The first step employs a saturation-like scheme, which gives a small gain if the innovation is large corresponding to a potential attack. The second step is a consensus operation of state estimates among neighboring sensors. We prove the estimation error is upper bounded if the filter parameters satisfy a condition. We further analyze the feasibility of the condition and connect it to sparse observability in the centralized case. When the attacked sensor set is known to be time-invariant, the secured filter is modified by adding an online local attack detector. The detector is able to identify the attacked sensors whose observation innovations are larger than the detection thresholds. Also, with more attacked sensors being detected, the thresholds will adaptively adjust to reduce the space of the stealthy attack signals. The resilience of the secured filter with detection is verified by an explicit relationship between the upper bound of the estimation error and the number of detected attacked sensors. Moreover, for the noise-free case, we prove that the state estimate of each sensor asymptotically converges to the system state under certain conditions. Numerical simulations are provided to illustrate the developed results.
This paper is concerned with the problem of secure multi-sensors fusion estimation for cyber-physical systems, where sensor measurements may be tampered with by false data injection (FDI) attacks. In this work, it is considered that the adversary may not be able to attack all sensors. That is, several sensors remain not being attacked. In this case, new local reorganized subsystems including the FDI attack signals and un-attacked sensor measurements are constructed by the augmentation method. Then, a joint Kalman fusion estimator is designed under linear minimum variance sense to estimate the …
By using various sensors to measure the surroundings and sharing local sensor information with the surrounding vehicles through wireless networks, connected and automated vehicles (CAVs) are expected to increase safety, efficiency, and capacity of our transportation systems. However, the increasing usage of sensors has also increased the vulnerability of CAVs to sensor faults and adversarial attacks. Anomalous sensor values resulting from malicious cyberattacks or faulty sensors may cause severe consequences or even fatalities. In this paper, we increase the resilience of CAVs to faults and at…
Secure Safety Filter: Towards Safe Flight Control under Sensor Attacks
Department of Mechanical and Civil Engineering, California Institute of Technology（加州理工学院机械与土木工程系）；Secure Systems Research Center at Technology Innovation Institute（技术创新研究所安全系统研究中心）
This paper proposes a secure state estimation scheme with non-periodic asynchronous measurements for linear continuous-time systems under false data attacks on the measurement transmit channel. After sampling the output of the system, a sensor transmits the measurement information in a triple composed of sensor index, time-stamp, and measurement value to the fusion center via vulnerable communication channels. The malicious attacker can corrupt a subset of the sensors through (i) manipulating the time-stamp and measurement value; (ii) blocking transmitted measurement triples; or (iii) injectin…
University of Guelph（圭尔夫大学）；Chongqing University（重庆大学）
Trustworthy and reliable data delivery is a challenging task in Wireless Sensor Networks (WSNs) due to unique characteristics and constraints. To acquire secured data delivery and address the conflict between security and energy, in this paper we present an evolutionary game based secure clustering protocol with fuzzy trust evaluation and outlier detection for WSNs. Firstly, a fuzzy trust evaluation method is presented to transform the transmission evidences into trust values while effectively alleviating the trust uncertainty. And then, a K-Means based outlier detection scheme is proposed to …
Security is one of the major concerns in Industrial Wireless Sensor Networks (IWSNs). To assure the security in clustered IWSNs, this paper presents a secure clustering protocol with fuzzy trust evaluation and outlier detection (SCFTO). Firstly, to deal with the transmission uncertainty in an open wireless medium, an interval type-2 fuzzy logic controller is adopted to estimate the trusts. And then a density based outlier detection mechanism is introduced to acquire an adaptive trust threshold used to isolate the malicious nodes from being cluster heads. Finally, a fuzzy based cluster heads el…
A cyber-physical system (CPS) is a tight coupling of computational resources, network communication, and physical processes. They are composed of a set of networked components, including sensors, actuators, control processing units, and communication agents that instrument the physical world to make smarter. However, cyber components are also the source of new, unprecedented vulnerabilities to malicious attacks. In order to protect a CPS from attacks, three security levels of protection, detection, and identification are considered. In this chapter, we will discuss the identification level, i.…
This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter (KLF), a novel uncertain measurement model is proposed such that the innovation generated from binary sensor can be captured. When considering linear dynamic systems, a conservative estimation error covariance with adjustable parameters is constructed by matrix inequality, and then an optimal filter gain is derived by minimizing its trace. Meanwhile, the optimal…
Connected and Automated Vehicles (CAVs) rely on the correctness of position and other vehicle kinematics information to fulfill various driving tasks such as vehicle following, lane change, and collision avoidance. However, a malicious vehicle may send false sensor information to the other vehicles intentionally or unintentionally, which may cause traffic inconvenience or loss of human lives. Here, we take the advantage of cloud-computing and increase the resilience of CAVs to malicious vehicles by assuming each vehicle shares its local sensor information with other vehicles to create informat…
Attitude estimation is the process of computing the orientation angles of an object with respect to a fixed frame of reference. Gyroscope, accelerometer, and magnetometer are some of the fundamental sensors used in attitude estimation. The orientation angles computed from these sensors are combined using the sensor fusion methodologies to obtain accurate estimates. The complementary filter is one of the widely adopted techniques whose performance is highly dependent on the appropriate selection of its gain parameters. This paper presents a novel cascaded architecture of the complementary filte…
Chongqing University of Posts and Telecommunications（重庆邮电大学）；University of Guelph（圭尔夫大学）
Traditional machine learning techniques have been widely used to establish the trust management systems. However, the scale of training dataset can significantly affect the security performances of the systems, while it is a great challenge to detect malicious nodes due to the absence of labeled data regarding novel attacks. To address this issue, this paper presents a generative adversarial network (GAN) based trust management mechanism for Industrial Wireless Sensor Networks (IWSNs). First, type-2 fuzzy logic is adopted to evaluate the reputation of sensor nodes while alleviating the uncerta…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and interval-quantized messages from neighboring sensors successively, an extended state based distributed Kalman filter (DKF) is proposed for simultaneously estimating both system state and uncertain dynamics. To alleviate the effect of observation biases, an event-triggered update based DKF is presented with a tighter mean square error bound than that of the time-driven one b…
Given a linear dynamical system affected by noise, we study the problem of optimally placing sensors (at design-time) subject to a sensor placement budget constraint in order to minimize the trace of the steady-state error covariance of the corresponding Kalman filter. While this problem is NP-hard in general, we consider the underlying graph associated with the system dynamics matrix, and focus on the case when there is a single input at one of the nodes in the graph. We provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. Next, we consider the prob…
Secure Set-based State Estimation for Safety-Critical Applications under Adversarial Attacks on Sensors
Digital Futures and Department of Decision and Control Systems, EECS, KTH Royal Institute of Technology（数字未来学院与控制系，电气电子计算机科学与工程学系，皇家理工学院）；Department of Mechanical Engineering, Eindhoven University of Technology（机械工程系，埃因霍温理工大学）；School of Computation, Information and Technology, Technical University of Munich（计算、信息与技术学院，慕尼黑工业大学）
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of a Kalman filter by its estimation error covariance. Using tools from random matrix theory, we derive probabilistic bounds on the estimation error covariance in the semi-definite sense. We indirectly improve the performance of our Kalman filter for the maximum eigenvalue metric and show that under certain conditions the optimal sampling distribution that min…
In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard. We then introduce the notion of eigenvalue observability and show that the state can be reconstructed in polynomial time when each eigenvalue is observable by at least $2s+1$ sensors and at most $s$ sensors are corrupted by an adversary. However, there is a gap between eigenvalue observability and the possibility of reconstructing the state despite attacks -…
Recent developments in communication technologies, such as 5G, together with innovative computing paradigms, such as edge computing, provide further possibilities for the implementation of real-time networked control systems. However, privacy and cyber-security concerns arise when sharing private data between sensors, agents and a third-party computing facility. In this paper, a secure version of the distributed formation control is presented, analyzed and simulated, where gradient-based formation control law is implemented in the edge, with sensor and actuator information being secured by ful…
This paper focuses on \textit{joint detection, tracking and classification} (JDTC) of a target via multi-sensor fusion. The target can be present or not, can belong to different classes, and depending on its class can behave according to different kinematic modes. Accordingly, it is modeled as a suitably extended Bernoulli \textit{random finite set} (RFS) uniquely characterized by existence, classification, class-conditioned mode and class\&mode-conditioned state probability distributions. By designing suitable centralized and distributed rules for fusing information on target existence, class…
Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design-time) to minimize the trace of the steady state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and s…
