Remote State Estimation Research Articles

Optimal stealthy deception attack strategy under energy constraints

This article explores the issue of devising optimal stealthy deception attack strategy based on remote state estimation in cyber-phsical systens (CPSs) under energy constraints. Taking the energy limitations into consideration, the attacker needs to launch signals under stealth conditions and alters the transmitted data in a limited time span with a limited number of changes. The stealth attack model is proposed, which enables the attack signal to evade the detector without being detected. By analyzing various forms of continuous attacks and discrete attacks, we study five different attack sequences and find the optimal attack sequence by evaluating the long-range remote estimation error. Using the Lagrange multiplier means, the optimal parameters are obtained to maximize the long-range estimation error while guaranteeing the integral stealth of the detector. The calculation process is summarized in Algorithm 1. Simulation instances are given to demonstrate the authenticity of this paper’s work.

Unscented-Kalman-Filter-Based Remote State Estimation for Complex Networks With Quantized Measurements and Amplify-and-Forward Relays.

In this article, the remote estimation problem is addressed for a class of discrete-time complex networks under the influence of probabilistic quantization and amplify-and-forward (AF) relays. The underlying complex network model, which is inherently nonlinear and stochastic, is affected by additive process and measurement noises. Owing to the limited bandwidth of the transmission channel, the measurement outputs are quantized by a probabilistic quantizer prior to transmission. To enhance the signal quality over long-distance transmissions, the quantized measurements are sent to AF relays and subsequently forwarded to the estimator. Utilizing the unscented Kalman filter approach, a novel state estimator is designed to minimize an upper bound on the estimation error covariance. Moreover, sufficient conditions are derived to ensure that the estimation error is exponentially bounded in the mean-square sense. Lastly, the efficacy of the proposed scheme is illustrated through numerical simulations.

Optimal innovation-based attacks against remote state estimation with side information and historical data

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.

Importance-driven denial of service attack strategy design against remote state estimation in multi-agent intelligent power systems

This paper introduces a novel importance-driven denial of service (IDoS) attack strategy aimed at impairing the quality of remote estimators for target agents within multi-agent intelligent power systems. The strategy features two key aspects. Firstly, the IDoS attack strategy concentrates on target agents, enabling attackers to determine the voltage sensitivity of each agent based on limited information. By utilizing these sensitivities, the proposed strategy selectively targets agents with high sensitivity to amplify disruption on the target agent. Secondly, unlike most existing denial of service attack strategies that adhere to predefined attack sequences, IDoS attacks can selectively target important packets on highly sensitive agents, causing further disruption to the target agent. Simulation results on the IEEE 39-Bus system demonstrate that, compared to existing denial of service attack strategies, the proposed IDoS attack strategy significantly diminishes the estimation quality of the target agent, confirming its effectiveness from an attacker's perspective.

Optimal Stealthy Attacks With Energy Constraint Against Remote State Estimation.

This article investigates the problem of energy-constrained stealthy attack strategy against remote state estimation for cyber-physical systems. Taking into account the energy constraint, the malicious attacker is required to schedule the off-line generated signals to modify the transmitted data with limited times over a finite-time horizon under the stealthiness condition, which makes the design of attack strategy more complex. Different from the attack schedules which are studied on the basis of prescribed attack signals in the existing results, the attack strategy is presented under the framework of collaborative design to deteriorate the estimation performance to the largest extent, which yet leads to the coupling between the attack schedules and attack signals. To overcome the difficulty without sacrificing the optimality, the attack design problem is solved in two steps. First, analyze the problem with the given attack schedule to derive the optimal attack signals. Then, the optimal schedule is obtained by efficiently solving the nonlinear 0-1 programming problem based on the algorithm of reducing the search space which is designed to eliminate a part of the nonoptimal solutions. To demonstrate the theoretical results, a simulation example is provided.

Optimal design and allocation of stealthy attacks against remote state estimation for cyber-physical systems

This paper studies the design and allocation problem for stealthy attacks against remote state estimation for cyber-physical systems, where the data are transmitted through multiple wireless communication channels. With limited budget for the available energy at each step and total energy over the finite-time horizon, the aim of the stealthy attacker is to maximize the estimation error based on the collaboration between the attack matrices and schedule, which is formulated as the optimization problem with multi-variable coupling. Under the presented framework of stepwise optimization, the optimization problem is separated into two subproblems with the guarantee of optimality. First, for the optimal design of attack matrices, the analytical expression is derived by employing the proposed data isolation technique instead of the assumption utilized in the existing results that the output matrix is of full row rank. And then, for the optimal allocation of energy constrained attacks, the scheduling sequence is obtained by solving the transformed linear 0-1 programming. Finally, simulation results sustain the performance of the presented attack strategy.

Event-Based Remote State Estimation for Nonlinear Systems: A Box Particle Filtering Method.

This article is concerned with the problem of event-based remote state estimation for nonlinear/non-Gaussian systems on a wireless network with limited bandwidth. To reduce unnecessary data transmissions, a novel event-triggering mechanism is developed by using the least-square technique. Based on this, an event-triggered box particle filtering scheme is designed to realize the minimum mean-squared error estimation at the remote estimator end, in which the posterior probability density functions are calculated separately according to the information of the event-triggered indicator to avoid the problem of excessive estimation error. Different from the existing approaches, the proposed algorithm does not depend on any Gaussian assumptions and reduces the computational complexity under the premise of ensuring the estimation performance. Finally, two simulation examples are performed to demonstrate the validity of the proposed algorithm.

Subsystem-importance-aware DoS attacks and countermeasures

This paper is concerned with the security issue of remote state estimation in multi-systems. Note that different subsystems or local state information possess varying levels of importance. A novel denial-of-service (DoS) attack type, referred to as a subsystem-importance-aware DoS attack, is proposed. The importance of a subsystem refers to the quantitative impact of its information on the correctness or accuracy of decision-making for the entire system. Here, the importance of a subsystem is positively correlated with the power allocated to transmit local information. Additionally, it is assumed that the attacker has access to the transmission power of all subsystems. The optimal attack strategies are then investigated under different subsystem-importance weight functions and the error functions that are related to the packet arrival rate, and the closed-form solutions under some special cases are provided. Furthermore, potential defense strategies are investigated, leveraging the gap in the interpretation of the subsystem importance between the attacker and the defender, formulated as a Stackelberg game. Finally, numerical examples are provided to illustrate the theoretical results and provide insights into possible countermeasures against our proposed attack.

A Privacy-Preserving Approach Against Eavesdropping Attacks on Remote State Estimation for Cyber–Physical Systems

A Privacy-Preserving Approach Against Eavesdropping Attacks on Remote State Estimation for Cyber–Physical Systems

A Lightweight Sensor Scheduler Based on AoI Function for Remote State Estimation Over Lossy Wireless Channels

A Lightweight Sensor Scheduler Based on AoI Function for Remote State Estimation Over Lossy Wireless Channels

Remote State Estimation With Posterior-Based Stochastic Event-Triggered Schedule

This paper aims to study the state estimation problem under the stochastic event-triggered (SET) schedule. A posterior-based SET mechanism is proposed, which determines whether to transmit data by the effect of the measurement on the posterior estimate. Since this SET mechanism considers the whole posterior probability density function, it has better information screening capability and utilization than the existing SET mechanisms that only consider the first-order moment information of measurement and prior estimate. Then, based on the proposed SET mechanism, the corresponding exact minimum mean square error estimator is derived by Bayes rule. Moreover, the prediction error covariance of the estimator is proved to be bounded under moderate conditions. Meanwhile, the upper and lower bounds on the average communication rate are also analyzed. Finally, two different systems are employed to show the effectiveness and advantages of the proposed methods.

Event-Triggered Reverse Attacks on Remote State Estimation

Security issues in cyber-physical systems have attracted increasing attention in recent years. In this paper, a security problem in a remote estimation application is considered, where an attacker tries to degrade estimation performance via malicious attacks. In our scenario, a smart sensor transmits its innovation to a remote estimator with a residue-based false data detector. Instead of assuming that the attacker launches a consecutive man-in-the-middle attack, we consider the case with intermittent attacks. Reverse attack is a simple attack strategy, which enables an attacker to change signs of the innovation sequences. Therefore, owing to the above reasons, an event-triggered reverse attack strategy is proposed to degrade system performance. First, the stealthiness of the event-triggered linear deception attack strategy is studied. Then, the evolution of the estimation error covariance is computed and the reverse attack is proven to be the optimal linear deception attack. We demonstrate that our event-triggered reverse attack is more destructive than a random reverse attack. Furthermore, a convex optimization problem is established to design event-triggered parameters. Comparisons of attack strategies are provided in a numerical example to validate the superiority of the reverse attack.

Hybrid Adjusting Variables-Dependent Event-Based Finite-Time State Estimation for Two-Time-Scale Markov Jump Complex Networks.

This article investigates the problem of dynamic event-triggered finite-time H∞ state estimation for a class of discrete-time nonlinear two-time-scale Markov jump complex networks. A hybrid adjusting variables-dependent dynamic event-triggered mechanism (DETM) is proposed to regulate the releases of measurement outputs of a node to a remote state estimator. Such a DETM contains both an additive dynamically adjusting variable (DAV) and a multiplicative adaptively adjusting variable. The aim is to design a DETM-based mode-dependent state estimator, which guarantees that the resultant error dynamics is stochastically finite-time bounded with H∞ performance. By constructing a mode-dependent Lyapunov function with multiple DAVs and a singular perturbation parameter associated with time scales, a matrix-inequalities-based sufficient condition is derived, the feasible solutions of which facilitate the design of the parameters of the state estimator. The validity of the designed state estimator and the superiority of the devised DETM are verified by two examples. It is verified that the devised DETM is capable of saving network resources and simultaneously improving the estimation performance.

Allocation of Eavesdropping Attacks for Multi-System Remote State Estimation

In recent years, the problem of cyber–physical systems’ remote state estimations under eavesdropping attacks have been a source of concern. Aiming at the existence of eavesdroppers in multi-system CPSs, the optimal attack energy allocation problem based on a SINR (signal-to-noise ratio) remote state estimation is studied. Assume that there are N sensors, and these sensors use a shared wireless communication channel to send their state measurements to the remote estimator. Due to the limited power, eavesdroppers can only attack M channels out of N channels at most. Our goal is to use the Markov decision processes (MDP) method to maximize the eavesdropper’s state estimation error, so as to determine the eavesdropper’s optimal attack allocation. We propose a backward induction algorithm which uses MDP to obtain the optimal attack energy allocation strategy. Compared with the traditional induction algorithm, this algorithm has lower computational cost. Finally, the numerical simulation results verify the correctness of the theoretical analysis.

Optimal redundant transmission scheduling for remote state estimation via reinforcement learning approach

This paper studies the optimal redundant transmission scheduling for remote state estimation. Multiple smart sensors observe some systems, and transmit the local state estimates via independent channels to a remote estimator (RE), where packet losses may occur with some particular probabilities. To improve the estimation performance, some redundant channels are adopted for the data transmission. Since the number of redundant channels is fixed, the optimal redundant scheduling for multiple sensors is worth investigating to determine how to allocate the redundant channels. To address this problem, the redundant transmission scheduling is modeled as a Markov decision process (MDP) to minimize the estimation error for all systems. By constructing a sufficient condition, one ensures that the MDP has an optimal deterministic and stationary policy. Meanwhile, the threshold structure of the redundant transmission scheduling policy is verified to further decrease the complexity of the calculation. Reinforcement learning (RL) is used for this problem, and a near-optimal policy is obtained by dueling double-deep Q-networks (D3QN) algorithm. Finally, an illustrative simulation is presented to demonstrate its effectiveness.

A kernel-based approximate dynamic programming approach: Theory and application

This article proposes a novel kernel-based Dynamic Programming (DP) approximation method to tackle the typical curse of dimensionality of stochastic DP problems over the finite time horizon. Such a method utilizes kernel functions in combination with Support Vector Machine (SVM) regression to determine an approximate cost function for the entire state space of the underlying Markov Decision Process (MDP), by leveraging cost function computed for selected representative states. Kernel functions are used to define the so-called kernel matrix, while the parameter vector of the given kernel-based cost function approximation is computed by moving backwards in time from the terminal condition and by applying SVM regression. This way, the difficulty of selecting a proper set of features is also tackled. The proposed method is then extended to the infinite time horizon case. To show the effectiveness of the proposed approach, the resulting Recursive Residual Approximate Dynamic Programming (RR-ADP) algorithm is applied to the sensor scheduling design in multi-process remote state estimation problems.

Optimal denial‐of‐service attack scheduling for remote state estimation with time‐varying interference power

AbstractThis article examines resource scheduling optimization for cyber‐physical systems that include a smart sensor, a remote estimator, and an attacker. The attacker's objective is to use denial‐of‐service (DoS) attack to jam the wireless channel, causing packet loss and reducing system performance. We consider a more realistic scenario where other interfering sources exist and conduct research based on the signal‐to‐interference‐plus‐noise ratio (SINR) model. Through this model, we investigate two cases: constant high or low interference power and time‐varying interference power. Different levels of attack power lead to varying packet loss rates, and the same attack power may result in different packet loss rates in different interference environments. Therefore, the attacker needs to consider the impact of other interferences to find the optimal attack strategy that increases the estimation error of the information‐physical system while reducing energy consumption. We describe this optimization problem in a Markov decision process (MDP) framework and demonstrate the existence of an optimal deterministic Markovian strategy. We also establish the monotonicity of the optimal strategy in two different cases and investigate the extreme case. Simulation results support our theoretical results.

Inversion Attack and Countermeasure for Event-Based Sensor Schedule in Remote State Estimation

Inversion Attack and Countermeasure for Event-Based Sensor Schedule in Remote State Estimation

Structure-Enhanced DRL for Optimal Transmission Scheduling

Remote state estimation of large-scale distributed dynamic processes plays an important role in Industry 4.0 applications. In this paper, we focus on the transmission scheduling problem of a remote estimation system. First, we derive some structural properties of the optimal sensor scheduling policy over fading channels. Then, building on these theoretical guidelines, we develop a structure-enhanced deep reinforcement learning (DRL) framework for optimal scheduling of the system to achieve the minimum overall estimation mean-square error (MSE). In particular, we propose a structure-enhanced action selection method, which tends to select actions that obey the policy structure. This explores the action space more effectively and enhances the learning efficiency of DRL agents. Furthermore, we introduce a structure-enhanced loss function to add penalties to actions that do not follow the policy structure. The new loss function guides the DRL to converge to the optimal policy structure quickly. Our numerical experiments illustrate that the proposed structure-enhanced DRL algorithms can save the training time by 50% and reduce the remote estimation MSE by 10% to 25%, when compared to benchmark DRL algorithms. In addition, we show that the derived structural properties exist in a wide range of dynamic scheduling problems that go beyond remote state estimation.

Remote State Estimation Under DoS Attacks in CPSs With Arbitrary Tree Topology: A Bayesian Stackelberg Game Approach

Remote State Estimation Under DoS Attacks in CPSs With Arbitrary Tree Topology: A Bayesian Stackelberg Game Approach