Local State Estimates Research Articles

Identification and distributed fusion filter for multi-sensor networked systems with stochastic deception attacks

In the multi-sensor networked systems, each sensor produces its local state estimate based on its own observations, and then sends it to a fusion center (FC) for fusion estimation. During transmitting local state estimates to the fusion center, the data may suffer from stochastic deception attacks from malicious attackers, where the probabilities of attacks and the variances of attack noises are unknown. Using a correlation function method (CFM), the probabilities of attacks and the variances of attack noises in individual channels are identified in parallel. The possibly attacked local state estimate is filtered to reproduce local state estimate in the FC. Using the matrix-weighted fusion algorithm in the linear unbiased minimum variance (LUMV) criterion, a distributed fusion filter is performed based on the reproduced local state estimates. A simulation example illustrates the validity of the algorithms.

Contribution of PRIDE VLBI products to the joint JUICE-Europa Clipper moons’ ephemerides solution

In the coming decade, JUICE and Europa Clipper radio-science will yield the most accurate estimation to date of the Galilean moons’ physical parameters and ephemerides. JUICE’s PRIDE (Planetary Radio Interferometry and Doppler Experiment) will help achieve such a solution by providing VLBI (Very Long Baseline Interferometry) observations of the spacecraft’s lateral position, complementing nominal radio-science measurements. In this paper, we quantify how PRIDE VLBI can contribute to the moons’ ephemerides determination, in terms of attainable solution improvement and validation opportunities. To this end, we simulated VLBI data for JUICE, but also investigated the possibility to perform simultaneous tracking of JUICE and Europa Clipper, thus ultimately generating both single- and dual-spacecraft VLBI. We considered various tracking and data quality scenarios for both VLBI types, and compared the formal uncertainties provided by covariance analyses with and without VLBI. These analyses were performed for both global and local (i.e. per-flyby) estimations of the moons’ states, as eventually achieving a global solution first requires proceeding arc-per-arc. We showed that both single- and multi-spacecraft VLBI measurements only bring limited improvement to the global state estimation, but significantly contribute to the moons’ normal points (i.e. local states at flyby times), most notably in the out-of-plane direction. Additionally, we designed a validation plan exploiting PRIDE VLBI to progressively validate the classical radio-science solution, whose robustness and statistical realism is sensitive to modelling inconsistencies. By improving the local state estimations and offering various validation opportunities, PRIDE will be invaluable in overcoming possible dynamical challenges. It can therefore play a key role in reconstructing a global solution for the Galilean moons’ dynamics with the uncertainty levels promised by JUICE-Europa Clipper analyses. This, in turn, is critical to the accurate characterisation of tidal dissipation in the Jovian system, holding the key to the long-term evolution of the Galilean moons.

Stealthy attacks against distributed state estimation of stochastic multi-agent systems under composite attack detection mechanisms

This paper is concerned with the security problem of distributed state estimation for stochastic multi-agent systems (MASs) under directed topology. First, in the absence of attacks, an optimal distributed filter is proposed to reconstruct the states of MASs by minimizing the mean square error, which makes full use of the measurable local output information and relative state estimates of agents. Moreover, instead of using a single detection mechanism to measure the stealthiness of attacks, based on the structure of the derived filter, a composite attack detection mechanism capable of simultaneously detecting anomalies in the sensor channels of the agents themselves and the network topologies between different agents is utilized in this paper. Then, from the perspective of potential adversaries, two stealthy attack strategies are established through a joint design of sensor and topology attacks, enabling attackers to fulfill diverse attack objectives while evading the given composite detection mechanisms. Finally, simulation results are provided to verify the availability of the designed filter and attack generation schemes.

Distributed moving horizon fusion estimation for linear constrained uncertain systems

AbstractIn this paper, the distributed moving horizon fusion estimation of uncertain systems with constraints of system noise and state variables is studied. Firstly, relying on the basic idea of consensus algorithm, the cost function in the performance index is reconstructed by weighted fusion of the state prediction values. Secondly, considering the performance index with uncertain parameters, the min‐max optimization problem of the algorithm is transformed into the least squares optimization problem based on 2‐norm regularization method. Thirdly, the scalar‐weighted linear minimum variance fusion estimation strategy is used to realize the weighted fusion of local state estimation values. Then, on the premise of minimum network connectivity and collective observability, the stability of the proposed algorithm is studied, and the sufficient conditions for the expected convergence of the fused estimation error norm square are given. Finally, the effectiveness of the algorithm is verified by numerical simulation.

Data‐driven parallel Koopman subsystem modeling and distributed moving horizon state estimation for large‐scale nonlinear processes

AbstractIn this article, we consider a state estimation problem for large‐scale nonlinear processes in the absence of first‐principles process models. By exploiting process operation data, both process modeling and state estimation design are addressed within a distributed framework. By leveraging the Koopman operator concept, a parallel subsystem modeling approach is proposed to establish interactive linear subsystem process models in higher‐dimensional subspaces, each of which correlates with the original nonlinear subspace of the corresponding process subsystem via a nonlinear mapping. The data‐driven linear subsystem models can be used to collaboratively characterize and predict the dynamical behaviors of the entire nonlinear process. Based on the established subsystem models, local state estimators that can explicitly handle process operation constraints are designed using moving horizon estimation. The local estimators are integrated via information exchange to form a distributed estimation scheme, which provides estimates of the unmeasured/unmeasurable state variables of the original nonlinear process in a linear manner. The proposed framework is applied to a chemical process and an agro‐hydrological process to illustrate its effectiveness and applicability. Good open‐loop predictability of the linear subsystem models is confirmed, and accurate estimates of the process states are obtained without requiring a first‐principles process model.

Optimal energy allocation based on SINR under DoS attack

According to signal to interference plus noise ratio (SINR) of channel, we consider optimal attack schedule against remote state estimation in cyber–physical systems (CPSs) under denial of service (DoS) attack. Each physical process has a smart sensor that acquires the measurement of the system and transmits its local state estimation to the remote estimation terminal through a wireless channel. At each time step, a DoS attacker can send a jamming attack to one of the two channels. On the side of the attacker, this paper aims to search an optimal strategy, which maximizes the estimation error of the remote estimator. We propose an algorithm to obtain the optimal attack schedule policy by using of Markov decision process (MDP). A numerical example is provided to demonstrate the effectiveness of the proposed methods.

Distributed Moving-Horizon Estimation With Event-Triggered Communication Over Sensor Networks

This paper is concerned with the distributed moving-horizon estimation problem for linear discrete-time systems over wireless sensor networks. To reduce the communication burden, an event-triggered communication mechanism is proposed to govern the transmission of one-step predictions and measurements in each node. Under such a mechanism, a novel event-triggered distributed moving-horizon estimator is designed to deal with the state estimation problem subject to noise and state constraints. Each node computes its local state estimate by minimizing a cost function, which includes the event-triggered one-step predictions and measurements from the neighbors. It is proved that the developed distributed estimator is stable with the uniformly bounded estimation error in each node, provided by network connectivity, regional observability and small enough triggering parameters. A numerical simulation is given to verify the effectiveness of the proposed estimation algorithm.

Adaptive Fuzzy Decentralized Output-Feedback Control of Large-Scale Systems With Sensor Faults: A Multichannel Asynchronous Triggering Approach

This paper proposes an adaptive fuzzy decentralized output feedback control scheme for large-scale systems with multichannel asynchronous event-triggering. Uncertain system dynamics, unknown interconnections and time-varying sensor faults are handled simultaneously, even though only the corrupted measured local output is available for the design procedure. First, local state estimation filters are designed to estimate the unmeasured states. Then, considering that the resource-limited communication and computation may exist in all three types of channels including state estimation filter-to-controller channel, parameter estimator-to-controller channel and controller-to-actuator channel, an asynchronous event-triggering framework with time-varying triggering threshold is developed for multiple channels to release the communication and computation burden. Compared with the existing synchronous triggering mechanism, the proposed asynchronous one has several advantages: 1) the redundant signal transmission is reduced, 2) the triggering conditions for different channels are uncorrelated, which enables the designer to adjust the signal transmission frequency of each channel independently, and 3) the robustness could be improved in the face of noise as ideal synchronous triggering is not easy to be achieved in practice. In addition, both gain and bias faults, which are allowed to be unknown and time-varying, are covered in a unified sensor fault model. It is proved that, with the proposed control scheme, all the closed-loop signals are semi-globally uniformly ultimately bounded and the output tracking error converges into an adjustable residual set without Zeno behavior. Finally, simulation and comparison results illustrate the effectiveness and advantages of the proposed control scheme.

Fuzzy EKF-Based Intrusion Detection and Accurate State Estimation of Interconnected DC MGs With CPLs

With the advancement of digital technologies in complex and large-scale power systems, the issue of cyber-attack detection has become of paramount importance to maintain system reliability and performance. In this regard, accurate state estimation plays a key role and leads to proper supervisory decision-making. To detect cyber-attacks in direct current microgrids (DC MGs), a new centralized attack detection system based on the Kalman filter and clustering approach is proposed. On the other hand, appearing nonlinear loads such as constant power loads (CPLs) make the overall system behavior nonlinear and conventional linear Kalman filters ineffective. So, in this paper, an extended Kalman filter (EKF) is utilized. By constructing several output vectors and parallel EKFs, local state estimations are achieved. They are then used to detect attacks based on the residuals and localize them based on the fuzzy clustering approach. The local healthy estimations are aggregated to compute global estimations with low noise. The simulation results on a five-area interconnected DC MG subjected to data integrity and denial-of-service (DoS) attacks show that the proposed approach can detect attacks, evaluate how many attacks occur in the case of multiple attacks, localize the attacks, and obtain accurate state estimations.

Sensor Scheduling for Remote State Estimation with Limited Communication Resources: A Time- and Event-Triggered Hybrid Approach.

This paper proposes a time- and event-triggered hybrid scheduling for remote state estimation with limited communication resources. A smart sensor observes a physical process and decides whether to send the local state estimate to a remote estimator via a wireless communication channel; the estimator computes the state estimate of the process according to the received data packets and the known scheduling mechanism. Based on the existing optimal time-triggered scheduling, we employ a stochastic event trigger to save precious communication chances and further improve the estimation performance. The minimum mean-squared error (MMSE) state estimate is derived since the Gaussian property is preserved. The estimation performance upper bound and communication rate are analyzed. The main results are illustrated by numerical examples.

A protocol for Decentralized Synchronous Diagnosis with Coordination

Recently, a new architecture for decentralized diagnosis of Discrete Event Systems, called Decentralized Synchronous Diagnosis, has been proposed in the literature. In this scheme, local diagnosers are computed based on the fault-free behavior of the system components, which, in comparison with the classical diagnosis approach, reduces the size of local diagnosers for implementation. Although this method has been successfully implemented, its main drawback is the emergence of an exceeding fault-free language of the system for diagnosis, which reduces the diagnosis efficiency. To circumvent this problem, in this paper, a protocol for Decentralized Synchronous Diagnosis with Coordination (DSDC), which refines the diagnosis status using cluster automata of the local component models, is proposed. The protocol is based on the implementation of local state estimators of the fault-free component models of the system which communicate cluster automata to a coordinator. The indication of the fault occurrence is carried out by the coordinator according to the observed behavior of the system. To do so, communication rules between local state estimators and the coordinator are proposed. The protocol prevents the emergence of an exceeding fault-free language for diagnosis, which guarantees the same diagnosis performance as the traditional monolithic approach. In addition, the implementation of the DSDC in a didactic manufacturing system is presented to illustrate the results.

Optimal transmission strategy for multiple Markovian fading channels: Existence, structure, and approximation

This paper investigates the optimal transmission strategy for remote state estimation over multiple Markovian fading channels. A smart sensor is used to obtain a local state estimate of a system, and transmits it to a remote estimator. A new transmission strategy is proposed by co-designing the channel allocation and the transmission power control. The co-designing problem is modeled as a constrained Markov decision process (CMDP) to minimize the expected average estimation error covariance subject to the energy constraint over an infinite horizon. The CMDP is then relaxed as an unconstrained Markov decision process (UMDP) using the Lagrange multiplier method. Sufficient conditions for the existence of the optimal stationary policy for the UMDP are established to obtain the optimal transmission strategy. The structure of the optimal transmission power control policy for the UMDP with discounted cost is also elucidated. Taking account of the discrete-continuous hybrid action space, a parameterized deep Q-network (P-DQN) algorithm is employed to obtain an approximate optimal policy for the UMDP. Finally, a moving vehicle example is introduced to illustrate the effectiveness of the developed methods.

Guaranteeing Differential Privacy in Distributed Fusion Estimation

With the increasing openness of networked sensor systems, information leakage has become an ever-critical issue due to the malicious eavesdropping attacks on privately available data. The distributed fusion estimates (DFEs), which perform well by combining local state estimates (LSEs) supplied by multiple sensors, imperatively require privacy-preserving. Notice that the eavesdropper can acquire DFEs by wiretapping fusion information from FC and weighting LSEs from sensors. For countering such dual eavesdropping, we introduce the idea called differential privacy from database literature. Basically, the publicly released estimates (PREs), which gather statistical information about DFEs, are considered to be disturbed with stochastic noises. The lower bounds of noise covariances can be designed with the privacy parameters and estimation systems. Furthermore, we disperse the location of noise insertion from PREs to LSEs. In this case, the eavesdropper cannot obtain optimal estimate even if it fuses local data by using original criterion, while the differential privacy is still satisfied. Finally, a target tracking system with multi-sensor observation is given to verify the effectiveness of the proposed methods.

Distributed fusion filtering for cyber-physical systems under Round-Robin protocol: a mixed H 2/H ∞ framework

ABSTRACT In this paper, the distributed mixed fusion filter design problem is investigated for a class of cyber-physical systems subject to non-ideal measurements under Round-Robin protocol. To save the limited communication resources, the Round-Robin protocol is employed to schedule the data transmissions from the sensors to the remote filters. The measurement is imperfect by taking into account the noises, the random saturations, nonlinearity perturbations and packet dropouts. The objective of this study is to propose a desired fusion filtering method that ensures the prescribed performance constraints on both the local and fusion filtering error dynamics. With the aid of Lyapunov function and stochastic analysis technique, a sufficient condition is established to guarantee the mixed / performance index for the local filtering error systems, and then the filter parameter matrices are derived by resorting to the solutions to some matrix inequalities. Subsequently, on the basis of the obtained local state estimates, the proper fusion parameters are acquired by solving a convex optimisation problem. Finally, a numerical example is provided to demonstrate the effectiveness of the designed fusion filter.

Decentralized State Estimation-Based Optimal Integral Model Predictive Control of Voltage and Frequency in the Distribution System Microgrids

The power distribution system is undergoing a shift from centralized to decentralized operation due to the large-scale integration of distributed energy resources (DER). To increase the scalability and reduce the dependency on communication networks, there is a strong need for a decentralized control framework that can maintain the nominal voltage and frequency in a microgrid. In this article, a novel decentralized state estimation-based optimal voltage and frequency restoration strategy is proposed. The framework computes the optimal integral model predicted control reference signal to the primary controller, that is unaffected by the local measurement noise, hence, ensuring stable power-sharing among the DERs. The proposed framework is built on a first-order DER model and a local/global measurements-based local state estimation technique, facilitating deployability to the grid edge devices. The capabilities of the proposed framework are tested and validated on a real-time simulator with a full system dynamic model considering an islanded section of the IEEE 123 node distribution network for the various grid events. It is observed that the framework offers significant transient performance improvement in comparison to the Linear Quadratic Regulator method, with around 70% faster voltage restoration when the communication latency is considered.

Distributed encryption fusion estimation against full eavesdropping

This paper is concerned with the privacy-preserving distributed fusion estimation problem against full eavesdropping, where the eavesdropper can completely and precisely obtain the information transmitted from local sensors to legitimate user. To depict the privacy-preservation level, we propose novel confidentiality index and rank based on the estimation performances of both eavesdropper and legitimate user. Then, a new encryption approach, which is composed of two-step sequential noise injections, is developed such that the highest confidentiality rank can be achieved. It is rather remarkable that the weighting fusion matrix, which is unique in the distributed fusion estimation field, is utilized to design perturbation noises. In this case, the compensating fusion estimator of legitimate user can effectively reduce the adverse impact of disturbance with null space design in the proposed approach. Moreover, the probability distribution of inserted noises simultaneously satisfies the differential privacy, which strongly enhances the confidentiality level of local state estimates. Finally, an illustrative example is provided to verify the effectiveness and advantages of the proposed methods.

Distributed Moving Horizon Fusion Estimation for Nonlinear Constrained Uncertain Systems

This paper studies the state estimation of a class of distributed nonlinear systems. A new robust distributed moving horizon fusion estimation (DMHFE) method is proposed to deal with the norm-bounded uncertainties and guarantee the estimation performance. Based on the given relationship between a state covariance matrix and an error covariance matrix, estimated values of the unknown parameters in the system model can be obtained. Then, a local moving horizon estimation optimization algorithm is constructed by using the measured values of sensor nodes themselves, the measured information of adjacent nodes and the prior state estimates. By solving the above nonlinear optimization problem, a local optimal state estimation is obtained. Next, based on covariance intersection (CI) fusion strategy, the local optimal state estimates sent to the fusion center are fused to derive optimal state estimates. Furthermore, the sufficient conditions for the square convergence of the fusion estimation error norm are given. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed algorithm.

Bias Accuracy Maintenance Under Unknown Disturbances by Multiple Homogeneous MEMS Gyroscopes Fusion

Bias accuracy of micromachined gyroscope is deteriorated severely when suffering from unknown environmental disturbances (UD), such as temperature, vibration, and shock. In this article, gyros array using a two-stages UD-decoupled fusion strategy is for the first time proposed to maintain high-accuracy bias under unknown disturbances. In detail, the evolvement model of the individual gyroscope among four-gyros array is first deduced to decouple UD. Then, local estimator is devised to simultaneously derive the estimates of the state, the bias, and the UD of each gyro among the array in the first stage, respectively. Further, due to the nonoptimal local state estimates caused by the inherent response difference between each gyro, the global state fusion estimator weighted by dynamic coefficients is devised to achieve the uniformly optimal state estimate of gyros array in the second stage. The experimental test shows that RMSE of the estimate based on the proposed method is evaluated as 0.13°/s, which is reduced by 92.4%, 87%, 82.4%, and 51.9% compared with kalman filter (KF), internal model approach (IMA), distributed optimal linear fusion estimator (DOLFE), and minimal learning parameter-neural network (MLP-NN), respectively. The tested scale factor of the array is calibrated as 5.9 mv/°/s and the corresponding bias stability is calculated as 0.019°/s, which is improved by 68.8%, 54.8%, 34.5%, and 17.4% compared with KF, IMA, DOLFE, and MLP-NN, respectively. Not only is bias accuracy under UD not deteriorated, on the contrary, the accuracy is improved significantly by 3.7 times compared with that without UD. The proposed array-based UD-decoupled method paves an effective path to apply microgyro in actual environment engineering.

A Novel Global Set-Membership Filtering Approach for Localization of Automatic Guided Vehicles

This article investigates the localization problem of the automatic guided vehicle (AGV) system. In order to improve the reliability and flexibility of the localization process, a distributed sensor network structure is introduced to realize the localization of the AGV. Moreover, considering the influence of unknown-but-bounded noise and the accuracy requirements of the localization, a novel global set-membership filtering approach is proposed to obtain accurate localization results including a distributed set-membership filtering (DSMF) strategy and a circumscribed rectangle method. First, a DSMF strategy is designed to obtain local state estimation ellipsoids. Sufficient conditions for the existence of the state estimation ellipsoids are derived and a convex optimization process is developed to obtain the optimal local estimation ellipsoids. Then, a circumscribed rectangle method is proposed to fuse all local state estimation ellipsoids and obtain global set-membership filtering results. The proposed fusion method does not have a complicated optimization process, and can obtain more accurate estimation ellipsoids than local estimation results. Performance analysis verifies the effectiveness of the proposed global set-membership filtering approach.

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.