A Class of Nonlinear Kalman Filters Under a Generalized Measurement Model With False Data Injection Attacks

Performance evaluation of Cubature Kalman filter in a GPS/IMU tightly-coupled navigation system

A new cyber-security approach for load frequency control of hybrid interconnected renewable power systems

Design of False Data Injection Attacks in Cyber-Physical Systems

The problem of tracking epidemic spreading on networks is relevant to the control of morbidity. The transmission dynamics of an epidemic can be described by a simple compartmental model. Specifically, the estimation of epidemic spreading on networks can be achieved by a nonlinear Kalman filter, which is a tool for state estimation of nonlinear systems. In this article, epidemic spreading on networks is described by compartmental models, such as susceptible-infected-susceptible, susceptible-infected-recovered, and susceptible-infected-recovered-susceptible models. The dynamics of epidemic spreading on homogeneous networks, including Erdös-Renyi network, Watts-Strogatz network, and Newman-Watts network, are estimated by several nonlinear Kalman filters, including extended Kalman filter, unscented Kalman filter, and third-degree and fifth-degree cubature Kalman filters. The performance comparison in terms of accuracy and stability forms a guideline of utilizing nonlinear Kalman filters for tracking epidemic spreading. The theoretical analysis has been validated through numerical experiments.

False data injection (FDI) attacks are malicious insertions of false data as sensor measurements in a cyber-physical system, in order to lead the system to take a wrong action. False data injection attacks do not attack the computational or network components of cyber-physical systems but the interface between the physical and the cyber part. Such attacks are powerful and can have catastrophic results. Defense against them can be achieved by limiting the attack surface through vulnerability analysis of the cyber-physical system design and by monitoring system operation in the field with monitors that observe system parameters and sensor measurements and detect abnormal operation early. In this chapter, we describe promising techniques for vulnerability analysis and dynamic monitoring, based on efficient SMT solvers and Kalman filter techniques, respectively.

Object-Oriented Environment for Assessing Tracking Algorithms

The cybersecurity of the smart grid is becoming a critical issue to the power systems. Mitigating potential cyberattacks on the control of the power electronic devices is an important concern in the controller design to enhance the resilience of the overall power grid. In this paper, a novel model predictive control (MPC) is proposed for the multilevel cascaded H-bridge inverters considering the false data injection (FDI) attacks. The FDI attack is a vicious attack scenario when the attack signals are injected into the sensors in the cyberphysical systems (CPS). It is shown that FDI signals can effectively penetrate the commonly used Kalman Filter (KF) based state estimation and jeopardize the control of the inverters. The k-Nearest Neighbors (KNN) algorithm is employed in the proposed scheme to mitigate the FDI attacks. The proposed KNN-based MPC scheme was tested with various types of attack signals. The results show that the proposed scheme exhibits a robust performance in the face of the malicious FDI attacks.

In networked control systems (NCS), agents participating in a network share their data with others to work together. When agents share their data, they can naturally expose the NCS to layers of faults and cyber-attacks, which can contribute to the propagation of error from one agent/area to another within the system. One common type of attack in which adversaries corrupt information within a NCS is called a false data injection (FDI) attack. This article proposes a control scheme, which enables a NCS to detect and mitigate FDI attacks and, at the same time, compensate for measurement noise and process noise. Furthermore, the developed controller is designed to be robust to unknown inputs. The algorithm incorporates a Kalman filter as an observer to estimate agents' states. We also develop a neural network (NN) architecture to detect and respond to any anomalies caused by FDI attacks. The weights of the NN are updated using an extended Kalman filter, which significantly improves the accuracy of FDI detection. A simulation of the results is provided, which illustrates satisfactory performance of the developed method to accurately detect and respond to FDI attacks.

The introduction of information and communication technologies makes network environments increasingly open, leaving smart-grid control systems incredibly vulnerable to malicious attacks. False data injection (FDI) attacks stealthily tamper with measurement data, resulting in erroneous decisions made by the control center that greatly influence the normal operation of the power system. By taking advantage of real-time data acquisition with edge computing, in this article, we propose a scheme based on classification of predicted residuals (CPRs) for the FDI attack detection. The CPR scheme first predicts the acquired measurement data at the edge of the sensing network via developing an accurate prediction model. Followed the novel real-time classification method under the edge devices supporting, it classifies the predicted residuals independent of the false data to enhance the detection accuracy. Through these two steps, the detection rate of FDI attacks is greatly improved. The proposed scheme is validated in a real microgrid testbed. Experimental results show that the CPR scheme performs well in detecting FDI attacks and remains sensitive in injection attack probability and magnitude. The detection scheme even has effectiveness at low injection attack probability and magnitude (5% and 0.018 per thousand, respectively). Furthermore, it also proves that the proposed scheme has applicability in high real-time requirements at the edge of smart grids.

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate.

In the recent years, cyberattacks to smart grids are becoming more frequent. Among the many malicious activities that can be launched against smart grids, the False Data Injection (FDI) attacks have raised significant concerns from both academia and industry. FDI attacks can affect the (internal) state estimation process—critical for smart grid monitoring and control—thus being able to bypass conventional Bad Data Detection (BDD) methods. Hence, prompt detection and precise localisation of FDI attacks are becoming of paramount importance to ensure smart grids security and safety. Several papers recently started to study and analyse this topic from different perspectives and address existing challenges. Data‐driven techniques and mathematical modelling are the major ingredients of the proposed approaches. The primary objective is to provide a systematic review and insights into FDI attacks joint detection and localisation approaches considering that other surveys mainly concentrated on the detection aspects without detailed coverage of localisation aspects. For this purpose, more than 40 major research contributions were selected and inspected, while conducting a detailed analysis of the methodology and objectives in relation to the FDI attacks detection and localisation. Key findings of the identified papers were provided according to different criteria, such as employed FDI attacks localisation techniques, utilised evaluation scenarios, investigated FDI attack types, application scenarios, adopted methodologies and the use of additional data. Finally, open issues and future research directions were discussed.

Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

Kalman filters are very popular in turbofan engine community for health monitoring purposes. In this study, in order to get better performance in terms of filtering accuracy and noise adaptability, an Adaptive Square Root Cubature Kalman Filter (ASRCKF) was proposed to estimate health parameters of the turbofan engine gas path components. In the ASRCKF algorithm, the mean value and covariance of the engine nonlinear function were calculated by cubature rule-based numerical integration method and used as a substitute for nonlinear model in nonlinear Kalman filter. The latest information of measurement parameters in the recursion and filtering process was used to estimate and self-adjust the noises cross-covariance by removable window method to get higher filtering accuracy. Compared with the Extended Kalman Filter (EKF) and Square Root Cubature Kalman Filter (SRCKF), the simulation results in the gradual and rapid deterioration process of turbofan engine gas path components indicate that the higher accuracy and faster convergence can be obtained through ASRUKF, which can be used in health parameters estimation and condition monitoring of turbofan engine gas path.1

In this study, to enhance the system reliability under false data injection (FDI) attacks and DC-link voltage (DCLV) sensor failures, a hybrid control strategy for a DC microgrid (DCMG) based on the Lagrange extrapolation and voltage observer is proposed. Under normal conditions without FDI attacks or DCLV sensor failures, the DCMG system works in a distributed control scheme. To enhance the reliability of the system under the DCLV sensor failure or FDI attack, the DCMG system utilizes a hybrid control strategy that combines distributed control with decentralized control. The hybrid control strategy is achieved by the proposed detection algorithms for FDI attacks and DCLV sensor failures. The detection of FDI attacks is accomplished by comparing the predicted secondary controller output based on the Lagrange extrapolation with the actual one. When a power agent detects an FDI attack, its control mode is switched to decentralized control by using the proposed hybrid control strategy. The DCLV sensor failure detection algorithm to enhance system reliability against DCLV sensor failures is achieved by comparing the estimated DCLV with the measured one from the voltage observer. Upon detecting a DCLV sensor failure, the operation of the power agent is switched to the current control mode to sustain the system operation even under DCLV sensor failures. The proposed detection algorithms are simple, effective, and precise, operating without mutual interference that deteriorates the detection accuracy. Simulation and experiments are carried out under various uncertain test conditions to validate the reliability and effectiveness of the proposed control strategy.