Remote State Estimation Research Articles

Event-triggered remote state estimation over a collision channel with incomplete information

This paper investigates the stochastic event-triggered remote state estimation problem over a collision channel. The remote estimator does not have the knowledge of the measurement in the case of collision and the origin of the data packet in the case of successful transmission, resulting in the non-Gaussianity of the estimation process in the two cases. By using a commonly used Gaussian approximation method, the posterior distribution of the system state is proved to be a mixture of two Gaussians and a mixture of three Gaussians in the cases of collision and successful transmission, respectively. Then an approximate minimum mean squared error estimator with adaptive weights is proposed, and the weights convexly combine the estimates for the possible transmission situations. Moreover, the proposed estimator is also shown to be conventional forms under three extreme situations. Finally, numerical results illustrate the effectiveness of the proposed estimator based on the incomplete information.

An efficient encoding mechanism against eavesdropper with side channel information

In this paper, we investigate the privacy-preserving problem in remote state estimation by extending the lightweight encoding mechanism (Yang et al., 2020) to a more competitive scenario, where the adversary can intercept the system data more effectively, i.e., it is considered to be able to gather data from both the channel and the side channel. A transferable framework based on side channel information is established for analyzing the validity of encoding mechanisms. By resorting to padding and random injecting, a lightweight encoding mechanism is proposed to resist eavesdropping attacks. Furthermore, a sufficient condition to ensure the privacy of information is derived by transforming the communication data. Finally, numerical examples are given to verify the results.

A class of stealthy attacks on remote state estimation with intermittent observation

Network attacks always threaten economic operations and personal privacy, which have resulted in severe and irreparable damage. Therefore, the investigation of network attacks is essential for network security. This paper concentrates on designing two stealthy attack strategies for remote state estimation with intermittent observations, where the attackers can select one of the designed stealthy attack strategies depending on their capabilities, available resources, and information. Furthermore, for real-time communication rates, a novel detector is introduced to determine if the system is compromised by attackers at each moment. Then, an algorithm for state estimation is derived under the proposed stealthy attack strategies. Furthermore, the attack parameters in the proposed attack strategies are discussed by applying linear matrix inequalities. Finally, a numerical example illustrates the effects of the detector and attack strategies.

On Two Sensors Scheduling for Remote State Estimation With a Shared Memory Channel in a Cyber-Physical System Environment.

This article studies two sensors scheduling with a shared memory channel for remote state estimation in cyber-physical systems (CPSs). We consider that each sensor monitors a plant and sends its local estimate to the remote estimator over a shared memory communication channel, of which the packet reception results between two successive time instants are correlated. This article focuses on how the two sensors are scheduled to minimize the total estimation errors at the remote side. The problem is formulated as the Markov decision process (MDP) and the optimal policy is derived. Moreover, the threshold structure of the optimal policy is given to reduce computation overhead. After proving the Whittle indexability of the overall system under a given condition, the Whittle index policy is adopted to further reduce the computation overhead. Numerical simulations are given to illustrate the theoretical results.

Two‐channel false data injection attacks on multi‐sensor remote state estimation

AbstractThis paper investigates a security problem in cyber‐physical systems (CPSs) under multisensory framework. In the considered system, the feedback and feed‐forward channels may suffer from false data injection (FDI) attacks. The attacker aims at disturbing the systems by modifying the sensors' measurements and injecting external control inputs while keep ( )‐stealthiness. Two types of multi‐sensor fusion Kalman filters, which are equivalent in the absence of attacks, are adopted by the remote state estimator. When the system is maliciously attacked, the necessary and sufficient condition is obtained to guarantee the equivalence of the sequential Kalman filter and data compression Kalman filter under two‐channel attacks. Moreover, suboptimal ( )‐stealthiness attack strategies for these Kalman filters are obtained by applying two‐stage optimization method, convex analysis and monotonic optimization techniques. Finally, simulations on a numerical example of a quadrotor are carried out to validate the feasibility of theoretical results.

Stochastic event-triggered remote state estimation over Gaussian channels without knowing triggering decisions: A Bayesian inference approach

This paper investigates the stochastic event-triggered remote state estimation problem over a Gaussian communication channel. The triggering decisions of the sensor determine the transmissions of measurements, and are unknown to the remote estimator due to the interference of channel noises. Based on a commonly-accepted Gaussian assumption, an approximate minimum mean squared error estimator with adaptive weights is derived by a Bayesian inference approach. The approximate estimator convexly combines the estimates for both transmission and no transmission cases, and the weights are adaptively updated according to the received data. Further, the proposed estimator behaves like the Kalman filtering with intermittent observations under two extreme situations. Finally, the a posteriori distribution of the estimation process is analyzed when the remote estimator knows the triggering decisions. Numerical results demonstrate that the performance of our estimator is comparable to those that know the triggering decisions, and also better than the detection-based estimator.

Optimal transmission scheduling for remote state estimation in CPSs with energy harvesting two-hop relay networks

This paper considers the optimal transmission power scheduling for accurate remote state estimation in cyber–physical systems (CPSs). The plant is modeled as a discrete-time stochastic linear system with sensor measurements transmitted to the remote estimator over an intelligent relay. A dynamic cooperative team is formulated in which the sensor and the relay sharing the same cost function are equipped with corresponding energy harvesters, and need to decide on the transmission power levels to minimize the average error covariance at the remote estimator. Since the nodes make simultaneous decisions to achieve a common goal, the sensor and the relay do not have access to the transmission power that will be selected by another node in advance, and hence they cannot build a value estimation of the cost function directly at each time point, which poses a challenge to determine the optimal transmission policies of both sides. To overcome this challenge, we provide a local-action value function and prove that both nodes select the transmission power with respect to the local-action value function without any loss of performance. In addition, a Markov decision process (MDP) and a multi-agent reinforcement learning algorithm are presented to obtain the optimal transmission power schedule over an infinite time horizon. Finally, simulation examples are provided to corroborate and illustrate the theoretical results.

On the Semidecidability of the Remote State Estimation Problem

In this article, we consider the decision problem associated with the task of remotely estimating the state of a dynamic plant via a noisy communication channel. Given a machine-readable description of the plant’s and channel’s characteristics, does there exist an algorithm that decides whether remote state estimation is possible? From an analytic point of view, this problem has been shown to involve the zero-error capacity of the communication channel. By applying results from Turing machine theory and zero-error coding, we analyze several related variants of the decision problem mentioned above. Our analysis also incorporates a weakened form of the state estimation objective, which has been shown to depend on the classical Shannon Capacity instead. In the broadest sense, our results yield a fundamental limit to the capabilities of computer-aided design tools and adaptive autonomous systems, assuming they are based on digital hardware.

Stochastic Data-Based Denial-of-Service Attack Strategy Design Against Remote State Estimation in Interval Type-2 T–S Fuzzy Systems

This article focuses on designing a novel stochastic data-based denial-of-service (DoS) attack strategy that can intercept measurements and reduce the quality of remote state estimation in interval type-2 (IT2) T–S fuzzy systems. The new proposed DoS attack strategy has two main characteristics. First different from most of the existing DoS models, it is data-based, which mainly attacks the packets playing important roles in the system performance. Therefore, compared with the existing indiscriminate DoS attack approaches, the data-based DoS attack is more intelligent and can cause larger disruptions. Second, the proposed attack strategy is random, which has better concealment than the periodic or consecutive DoS attack models. Then, by using a stochastic method, the relationship among attack effect, attack probability, and attack parameter are analyzed and shown in Theorem <xref ref-type="theorem" rid="theorem9" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</xref> . Furthermore, if the attacks are energy-constrained, the relation between the attack rate threshold and the upper bound of the attack parameter is expressed analytically, which is shown in Theorem <xref ref-type="theorem" rid="theorem12" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</xref> . Simulation results demonstrate that, compared with some existing DoS models, the proposed stochastic data-based DoS attack strategy brings about greater destructiveness to the estimation quality of the systems, which demonstrates the effectiveness of the proposed attack strategy from the attacker’s perspective.

Zonotopic resilient state estimation for unmanned surface vehicles subject to integrity attacks

This work concerns the problem of resilient state estimation for unmanned surface vehicle systems subject to integrity attacks under peak-bounded perturbations. A novel resilient remote state estimation method is proposed based on zonotopic reachability analysis. The compromised sensors are identified based on the so-called predicted output set and zonotope support strip. Then, a resilient state reachable set is obtained by using the sensor data from the remaining benign measurements. For enhancing the performance of estimation, segment minimization is introduced to optimize the obtained state reachable set. Simulation results are provided to testify the effectiveness of the proposed method.

Energy scheduling for DoS attack over multi-hop networks: Deep reinforcement learning approach

This paper studies the energy scheduling for Denial-of-Service (DoS) attack against remote state estimation over multi-hop networks. A smart sensor observes a dynamic system, and transmits its local state estimate to a remote estimator. Due to the limited communication range of the sensor, some relay nodes are employed to deliver data packets from the sensor to the remote estimator, which constitutes a multi-hop network. To maximize the estimation error covariance with energy constraint, a DoS attacker needs to determine the energy level implemented on each channel. This problem is formulated as an associated Markov decision process (MDP), and the existence of an optimal deterministic and stationary policy (DSP) is proved for the attacker. Besides, a simple threshold structure of the optimal policy is obtained, which significantly reduces the computational complexity. Furthermore, an up-to-date deep reinforcement learning (DRL) algorithm, dueling double Q-network (D3QN), is introduced to approximate the optimal policy. Finally, a simulation example illustrates the developed results and verifies the effectiveness of D3QN for optimal DoS attack energy scheduling.

Detection-estimation strategies for delayed systems with unavailable packet sequence

In this paper, we study the problem of remote state estimation on networks with random delays and unavailable packet sequence due to malicious attacks. Two maximum a posteriori (MAP) schemes are proposed to detect the unavailable packet sequence. The first MAP strategy detects the packet sequence using data within a finite time horizon; the second MAP strategy detects the packet sequence by a recursive structure, which effectively reduces the computation time. With the detected packet sequence, we further design a linear minimum mean-squared error (LMMSE) estimation algorithm based on smoothing techniques, rather than using the classic prediction and update structure. A wealth of information contained in the combined measurements is utilized to improve the estimation performance. Finally, the effectiveness of the proposed algorithms is demonstrated by simulation experiments.

Multi-channel transmission scheduling with hopping scheme under uncertain channel states

This paper investigates the multi-channel transmission scheduling problem for remote state estimation based on a hopping scheme in cyber-physical systems. The smart sensor sends multiple subpackets over different orthogonal channels to the remote end simultaneously. Owing to the randomness and vulnerability of transmission environments, the uncertain multi-channel states are considered in this paper, which relaxes the assumption of existing deterministic models. The objective is to find an appropriate hopping scheme that minimizes the remote estimation error covariance. First, the multi-channel selection problem is modeled as a multi-arm bandits (MAB) matrix via taking the packet receiving probability as the gain. From the perspective of strategy and channel, two exponential-weight online learning algorithms are designed with the assistance of transmission energy switching policy. Then, based on Bernstein’s inequality for martingales and mini-batching loop, the upper bounds of algorithms’ regret values are analyzed under stochastic and adversarial channel states, respectively. Further, the estimator expression in iterative form and a sufficient condition for the error covariance to be bounded are derived. Finally, an example of unmanned vehicle moving demonstrates all the theoretical results.

Remote State Estimation in Networked Systems: Data Pre-Processing or Not?

Remote State Estimation in Networked Systems: Data Pre-Processing or Not?

Event-Triggered Sensor Scheduling for Remote State Estimation With Error-Detecting Code

This letter addresses the problem of remote state estimation subject to packet dropouts, focusing on the use of an event-triggered sensor scheduler to conserve communication resources. However, packet dropouts introduce significant challenges, as the remote estimator cannot distinguish between packet loss caused by poor channel conditions and the event trigger. To overcome this issue, we propose a novel formulation that incorporates error-detecting codes. We prove that the Gaussian property of the system state, commonly utilized in the literature, does not hold in this scenario. Instead, the system state follows an extended Gaussian mixture model (GMM). We present an exact minimum mean-squared error (MMSE) estimator and an approximate estimator, which significantly reduces algorithm complexity without sacrificing performance. Our simulation results show that the approximate estimator achieves nearly the same performance as the exact estimator while requiring much less computation time. Moreover, the proposed event trigger outperforms existing schedulers in terms of estimation accuracy.

Predictive Model-Based and Control-Aware Communication Strategies for Cooperative Adaptive Cruise Control

Utilizing Vehicle-to-everything (V2X) communication technologies, vehicle platooning systems are expected to realize a new paradigm of cooperative driving with higher levels of traffic safety and efficiency. Connected and Autonomous Vehicles (CAVs) need to have proper awareness of the traffic context. The cooperative platoon’s performance will be influenced by the communication strategy. In particular, time-triggered or event-triggered are of interest here. The expenses related to communication will increase significantly as the number of connected entities increases. Periodic communication can be relaxed to more flexible aperiodic or event-triggered implementations while maintaining desired levels of performance. This paper proposes a predictive model-based and control-aware communication solution for vehicle platoons. The method uses a fully distributed Event-Triggered Communication (ETC) strategy combined with Model-Based Communication (MBC) and aims to minimize communication resource usage while preserving desired closed-loop performance characteristics. In our method, each vehicle runs a remote vehicle state estimator based on the most recently communicated model and the event-driven communication scheme only updates the model when the performance metric error exceeds a certain threshold. Our approach achieves a significant reduction in the average communication rate (82%) while only slightly reducing control performance (e.g., less than 1% speed deviation).

The multi-action transmission scheduling problem for remote state estimation under global energy constraint

The multi-action transmission scheduling problem for remote state estimation under global energy constraint

Multisensor Scheduling for Remote State Estimation Over a Temporally Correlated Channel

This article studies multisensor scheduling for remote state estimation in cyber-physical systems. We consider that each sensor monitors a dynamic process and sends its data to the remote end. This article focuses on minimizing remote estimation errors over a temporally correlated communication channel. The problem is formulated as the Markov decision process (MDP) with finite-horizon cost criterion. The optimal structured policies are derived for both Markov packet dropout and finite-state Markov channel models, which can reduce computation overhead. For the infinite-horizon case, we design algorithms to address the issues of unknown channel statistics and the curse of dimensionality in the MDP, respectively. Particularly, a heuristic algorithm with linear complexity is proposed to schedule multisensor in a decentralized manner. Simulation examples are provided to verify the theoretical results.

Sensors Scheduling for Remote State Estimation Over an Unslotted CSMA/CA Channel

This article investigates the sensor selection problem for remote state estimation. A set of sensors measures a process's state and sends the measurements to a remote estimator over an unslotted carrier sense multiple access/collision avoidance (CSMA/CA) channel in IEEE 802.15.4-based wireless body area networks. This article aims to answer which sensors should be selected according to probability so that the state estimation error covariance and the energy consumption of sensors can be optimized. A common assumption in most existing methods about sensor scheduling is that the packet loss process is unrelated to the channel input. This article analyzes the relationship between channel input and packet loss rate by modeling the communication process. A scheduling scheme is proposed to increase channel utilization from the perspective of sensor information fusion. Then the constraint on the performance metrics is presented. By transforming the sensor selection problem into a constrained optimization problem, the solution to the optimization problem is obtained by a numerical algorithm. Finally, the validity of the model and the feasibility of the sensor scheduling are demonstrated by a numerical simulation.

Eavesdropping Strategies for Remote State Estimation Under Communication Constraints

This paper studies the confidentiality issue of wireless sensor networks under communication constraints from the perspective of an eavesdropper. The considered communication constraints include both medium access constraint and bandwidth limitation. Specifically, the former results in only one sink node gaining access to the shared network at each time step, while the latter requires data to be quantized by a probabilistic quantizer before being transmitted. The task of the eavesdropper is to develop eavesdropping strategies for the constrained network to infer the state of the system as accurately as possible. Since the data is generally unreadable to unauthorized third parties in terms of secure transmission, an eavesdropper with limited power must decide which sink nodes’ data needs to be decrypted. By analyzing the impact of different decryption strategies on the eavesdropping performance, a deciphering scheduling is proposed, which minimizes the expected estimation error without exceeding the energy budget. Besides, a recursive reset algorithm is put forward based on the properties of the probabilistic quantizer, which reflects that an eavesdropper can infer whether its own estimate is accurate enough from the decoded data. Moreover, a sufficient condition is established in which the eavesdropping performance is improved under the proposed algorithm. A numerical example is provided to demonstrate the validity of the developed approaches.