Distributed State Estimation Research Articles

Distributed robust filtering with hybrid consensus strategy for sensor networks

The problem of distributed state estimation for time-varying uncertain systems over a sensor network within the robust Kalman filtering framework is studied. It is assumed that the parameters of the underlying model are subjected to stochastic uncertainties. At the first step, the authors present a particular form of the Kalman filter named information form of a robust Kalman filter. Then, using a consensus scheme that guarantees an agreement in estimation among nodes, they propose a new consensus-based robust filtering approach. The consensus methodology is a hybrid method that is a combination of consensus on information (CI) and consensus on measurement (CM). To this end, before proposing the hybrid consensus filtering algorithm, distributed robust filtering based on CI and CM have been presented. Next, they show that the estimation error in the proposed consensus algorithm is exponentially mean square bounded using a Lyapunov function. Finally, they provide two illustrative examples to show the robust performance and effectiveness of the proposed consensus filtering algorithms.

Robust distributed state estimation for Markov coupled neural networks under imperfect measurements

In this paper, the issue of robust distributed state estimation is investigated for Markov coupled neural networks in the discrete-time domain. Fully considering network-induced phenomena, the signal quantization and sensor saturation existed in actual measurement are investigated in a unified framework through the Kronecker delta function. Moreover, a Markov chain is used to describe the structural variations in the addressed systems. The main attention of this paper is devoted to designing a mode-dependent estimator to estimate the system states through available output measurements, which ensures that the resulting system is stochastically stable and satisfies strictly dissipative property concurrently. By applying Lyapunov stability theory and a modified matrix decoupling method, some sufficient criteria are derived to obtain an explicit expression of the mode-dependent estimator. Finally, an example is presented to elucidate the validity of the proposed method.

Secure Information Fusion using Local Posterior for Distributed Cyber-Physical Systems

In modern distributed cyber-physical systems (CPS), information fusion often plays a key role in automate and self-adaptive decision making process. However, given the heterogeneous and distributed nature of modern CPSs, it is a great challenge to operate CPSs with the compromised data integrity and unreliable communication links. In this paper, we study the distributed state estimation problem under the false data injection attack (FDIA) with probabilistic communication networks. We propose an integrated ”detection + fusion” solution, which is based on the Kullback-Leibler divergences (KLD) between local posteriors and therefore does not require the exchange of raw sensor data. For the FDIA detection step, the KLDs are used to cluster nodes in the probability space and to partition the space into secure and insecure subspaces. By approximating the distribution of the KLDs with a general <inline-formula><tex-math notation="LaTeX">$\chi ^2$</tex-math></inline-formula> distribution and calculating its tail probability, we provide an analysis of the detection error rate. For the information fusion step, we discuss the potential risk of double counting the shared prior information in the KLD-based consensus formulation method. We show that if the local posteriors are updated from the shared prior, the increased number of neighbouring nodes will lead to the diminished information gain. To overcome this problem, we propose a near-optimal distributed information fusion solution with properly weighted prior and data likelihood. Finally, we present simulation results for the integrated solution. We discuss the impact of network connectivity on the empirical detection error rate and the accuracy of state estimation.

Distributed State Estimation for Linear Systems With Application to Full-Car Active Suspension Systems

In this article, we treat the problem of distributed state estimation for medium- to large-scale linear systems. We consider a system, which consists of several subsystems, and assume that there already exist linear local estimators for the individual subsystems. These existing local estimators could be designed using algorithms of different types. We propose a systematic approach to connect the local estimators through information flows, such that a distributed state estimation scheme is formed for the linear system. The convergence and boundedness of the estimation error for the developed distributed scheme are proven. The proposed method is applied to a full-car active suspension system. The entire system is decomposed into five subsystems interacting with each other. A distributed estimation architecture is established based on the proposed method. The effectiveness of the proposed approach for the full-car suspension system is illustrated using simulation results, which confirm good estimation performance.

Measurement Sensitivity and Estimation Error in Distribution System State Estimation using Augmented Complex Kalman Filter

Distribution state estimation (DSE) is an essential part of an active distribution network with high level of distributed energy resources. The challenges of accurate DSE with limited measurement data is a well-known problem. In practice, the operation and usability of DSE depend on not only the estimation accuracy but also the ability to predict error variance. This paper investigates the application of error covariance in DSE by using the augmented complex Kalman filter (ACKF). The Kalman filter method inherently provides state error covariance prediction. It can be utilized to accurately infer the error covariance of other parameters and provide a method to determine optimal measurement locations based on the sensitivity of error covariance to measurement noise covariance. This paper also proposes a generalized formulation of ACKF to allow scalar measurements to be incorporated into the complex-valued estimator. The proposed method is simulated by using modified IEEE 34-bus and IEEE 123-bus test feeders, and randomly generates the load data of complex-valued Wiener process. The ACKF method is compared with an equivalent formulation using the traditional weighted least squares (WLS) method and iterated extended Kalman filter (IEKF) method, which shows improved accuracy and computation performance.

Distributed State Estimation for a Class of Jointly Observable Nonlinear Systems

State estimation for a class of nonlinear systems using a network of distributed observers is dealt with in this paper. We propose a network of observers, each of which has its own local measurements which may not be sufficient for observability of the system, while the joint measurements of the sensors in the network guarantees the observability. We derive sufficient conditions on the proposed observers such that the estimated states of each observer asymptotically converge to the states of the system using local measurements and the estimates of a subset of observers in its neighborhood. Accordingly, it is assumed that each observer has access to the estimates of its neighbors via a communication network. The main problem of existing distributed state estimation strategies in the literature is their limitation to linear systems or to nonlinear systems with observable nonlinearities (by considering nonlinearities as states to be estimated). However, based on the proposed strategy, distributed state estimation of a more general class of nonlinear systems can be devised. A numerical example is provided to evaluate the accuracy of the obtained results.

Distributed State Estimation Under Random Parameters and Dynamic Quantizations Over Sensor Networks: A Dynamic Event-Based Approach

This paper deals with the distributed state estimation problem for an array of discrete time-varying systems over sensor networks under dynamic event-based transmission scheme (DETS), random parameter matrices (RPMs) and dynamic measurement quantization (DMQ). Different from the existing static event-based transmission scheme with fixed threshold, the employed DETS introduces an auxiliary offset variable in the triggering condition to dynamically regulate the inter-event time. The RPMs are considered in both state and observation equations so as to better reflect the engineering reality. A dynamic quantizer is utilized to account for the phenomenon of incomplete measurements during the data transmission. The aim of the addressed problem is to design a distributed state estimator such that, in the simultaneous presence of the DETS, RPMs and DMQ, an upper bound is guaranteed on the estimation error covariance, and such an upper bound is minimized at each time-step by choosing proper gain matrices. To overcome the difficulties induced by the sparseness of the network topology, a matrix simplification technique is proposed. Moreover, a sufficient condition is provided to ensure that the estimation error is bounded in the mean-square sense. Finally, an illustrative example is presented to demonstrate the theoretical results.

ADMM-based Distributed State Estimation for Power Systems: Evaluation of Performance

Abstract Recently, distributed algorithms for power system state estimation have attracted significant attention. Along with such advantages as decomposition, parallelization of the original problem and absence of a central computation unit, distributed state estimation may also serve for local information privacy reasons since the only information to be transferred is the boundary states of neighboring areas. In this paper, we propose some novel approaches for speeding up the ADMM-based distributed state estimation algorithms by utilizing some recent results in optimization theory. We also thoroughly analyze the theoretical and practical performance, concluding that accelerated approach outperforms the existing ones. The theoretical considerations are verified through the experiments on a scalable example.

Fully Distributed State Estimation for Power System with Information Propagation Algorithm

In this paper, a new fully distributed state estimation (DSE) based on weighted least square (WLS) method and graph theory is proposed for power system. The proposed method is fully distributed so that the centralized facilities, e.g., supervisory control and data acquisition (SCADA) and centralized estimators, are not required. Also, different from the existing DSE methods, the proposed method is a bus-level DSE method, in which the power system is not required to be partitioned into several areas. In order to realize the proposed fully distributed DSE method, a novel information propagation algorithm is developed in this paper. This algorithm has great potential in future applications since it is useful to broadcast the local information of the nodes to the entire system in a fully distributed network. The proposed DSE method is compared with the conventional centralized state estimation method and existing multi-area DSE method in different models in this paper. The results show that the proposed method has better performance than the traditional methods.

Distributed $\mathcal{H}_\infty$ Gaussian Consensus Filtering for Discrete-Time Systems over Lossy Sensor Networks

This paper studies the problem of distributed state estimation for discrete-time systems over a sensor network through unreliable transmission channels subject to diverse packet dropout probabiliti...

Optimal Design of Islanded Microgrids Considering Distributed Dynamic State Estimation

This article proposes an optimal zone clustering algorithm of islanded microgrids (IMG) based on supply adequacy taking into account the dynamic performance of distributed state estimation units. The IMG is partitioned into several localized, yet coupled zones, where each zone is responsible for its local state estimate and performs data fusion to reach consensus for shared state variables between zones. The technique proposes a novel algorithm to optimally define the placement of the virtual boundaries of the zones by minimizing the potential power transfer between adjacent zones. The proposed algorithm adopts the distributed particle filter (DPF) technique for the state estimation process. The proposed algorithm also has the ability to come up with one optimal configuration considering different events and scenarios that might occur in the IMG. Monte Carlo simulations demonstrate the efficacy of the proposed technique in the presence of severely corrupted measurements and state values as well as displaying tolerance to major load changes within the IMG. The DPF shows similar performance when compared to its centralized implementation while also providing computational savings by a factor of the number of zones.

Results on distributed state estimation for LTI systems facing communication failures

We address distributed estimation of the state of a linear plant by a set of agents. The problem is cast in a setting where the communication capabilities of an agent might be deactivated from time to time, due to failures in the communication devices or malicious attacks. An observer architecture is proposed to achieve our estimation goal, based on a multi-hop subspace decomposition. Uniform exponential convergence to zero of the estimation errors is proven in the presence of communication failures, under a persistence of excitation assumption. Finally, the observer performance is evaluated in simulation, showing the merits of the proposed method and suggesting directions for future developments.

Resilient Consensus-Based Distributed Filtering: Convergence Analysis Under Stealthy Attacks

In this article, we consider the security problem for the consensus-based distributed state estimation. To resist the malicious attacker who can falsify the data transmitted through the wireless channel, each node equips with an attack defender, which is based on the measurement of its built-in sensor. Under the stealthy attack, which can deceive the defender, we investigate the resilience and convergence of the distributed estimation in two different attack scenarios. For the attack with enough communication resources, we provide a sufficient condition of the optimal attack to quantify the maximum estimation performance degradation. We also analyze the resilience of the worst case distributed estimation caused by the attacker. For the attack with limited resources, the optimal Kalman gain for each node is derived to maximize its estimation performance under the attack. We also give a sufficient condition to guarantee the convergence of the distributed estimation in this case. Finally, numerical simulations are provided to illustrate the effect of the defender on guaranteeing the resilience of sensor networks against attacks.

Robust distributed state estimation of active distribution networks considering communication failures

Due to the large scale and three-phase unbalance problem of active distribution networks (ADNs), traditional centralized state estimation (CSE) cannot meet the requirements on estimation accuracy and efficiency for real-time analysis and control of distribution systems. This paper presents a novel consensus-based coordination distributed state estimation (CC-DSE) approach considering communication failures in ADNs. A network partition approach coupled with placement of phasor measurement units (PMUs), which is based on topology analysis, is firstly executed to divide the large-scale distribution network into several sub-regions. Then, the local state estimation (SE) of each sub-region is executed in parallel by improved weighted least squares (WLS) method with revising weights adaptive to residuals without changing the initial objective function, which can mitigate the negative effect of inner-region communication failures. The data coordination is embedded in the iteration of improved WLS of each sub-region estimation by consensus algorithm, which is robust to data missing and bad data caused by inter-region communication failures. The CC-DSE has better performance in accuracy, efficiency and robustness compared with CSE and distributed state estimation (DSE), which is demonstrated by the simulation results of the unbalanced IEEE 123 bus distribution network.

Security distributed state estimation for nonlinear networked systems against DoS attacks

SummaryThis paper is concerned with security distributed state estimation for nonlinear networked systems against denial‐of‐service attacks. By taking the effects of resource constraints into consideration, an event‐triggered scheme and a quantization mechanism are employed to alleviate the burden of network. A mathematical model of distributed state estimation is constructed for nonlinear networked systems against denial‐of‐service attacks. Sufficient conditions ensuring the exponential stability of the estimation error systems are obtained by utilizing the Lyapunov stability theory. The explicit expressions of the designed state estimators are acquired in terms of the linear matrix inequalities. Finally, a numerical example is used to testify the feasibility of the proposed method.

A Game Approach to Distributed Robust Optimal Filtering With Consensus Through Multiple Sensors: Theory and Application

This article addresses the problem of distributed state estimation on the infinite-time horizon for discrete-time systems with multiple sensors. The desired filter, referred to as distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> Gaussian filter, reaching a tradeoff between optimality and robustness, constructs a local estimate based on its own observation and on those collected from its neighbors. A Nash game approach is used to deal with such a multiobjective distributed filtering problem, and causal bounded Nash equilibrium strategies, consisting of the optimal filter gains and the corresponding worst-case disturbance signals, are analytically conducted based on solutions to a set of cross-coupled algebraic Riccati equations. Moreover, to further improve the cohesiveness among local estimates, additional consensus objective is taken into consideration by exchanging prior estimates among neighboring nodes. A choice of the consensus term, with which the error dynamics are shown to be internally stable, is derived via a numerically tractable and efficient method. Finally, an application to speed monitoring through wireless sensor network is included to show the validity of the presented results.

Multiagent approach for consensus control in the energy internet network

Energy internet network is an energy supply and demand system which based on the power grid, that can make a variety of energy interoperability, allowing all constituent elements to exchange information and interaction. However, any anomaly/failure in a part of the network can quickly spread over the network and lead to new unpredicted failures. Hence, timely cyber-attacks detection and mitigation is crucial. In this study, for timely detection, firstly propose a distributed state estimator assuming regular system operation, that achieves near-optimal performance based on the local Kalman filters and with the exchange of necessary information between local nodes over EI network. To enhance the security, consensus control approach can provide fault tolerance and timely attack mitigation and further recovery, thereby providing the EI with strong security in distributed. In this paper, therefore, a distributed Kalman filter with consensus control approach for multiagent systems (MAS) was proposed to investigate the energy internet recovered with links failure by cyber-attacks. The proposed algorithm is verified in the energy internet through a MAS model using MATLAB software.

Event-based distributed state estimation for linear systems under unknown input and false data injection attack

This paper investigates an event-based distributed state estimation problem for a linear system subject to unknown input and false data injection attack. The unknown input is treated as a process with a non-informative prior. An event-triggered transmission scheme is designed to reduce exchange of unreliable state estimate information between sensor nodes. In order to defend against false data injection attack, a novel event-based distributed state estimator is proposed by using state estimate information that comes from individual node and neighboring nodes, where filter gains are derived by minimizing an upper bound of estimation error covariance. Then sufficient conditions are established to ensure asymptotic boundedness of the designed estimation error covariance. Finally, effectiveness of the proposed technique is demonstrated by a numerical example.

Forming Distributed State Estimation Network From Decentralized Estimators

In this paper, we focus on the distributed state estimation of nonlinear systems comprised of several subsystems. We assume that a decentralized state estimation system already exists for the nonlinear system, where the local estimators can be of different types. In order to achieve improved estimation performance, the existing decentralized estimators may be connected together via a communication network to form a distributed state estimation network. We propose a systematic approach to take advantage of the existing decentralized estimators potentially of different types to form a distributed state estimation network without performing a complete redesign of the estimation system. Specifically, a compensator is designed for each subsystem, and is connected to the corresponding decentralized estimator to obtain an augmented estimator (AE). The AEs for the subsystems communicate with each other to exchange subsystem state estimates and measurements via a communication network every sampling time. We derive sufficient conditions on the convergence and boundedness of the estimation error of the proposed distributed estimation network. The proposed approach is demonstrated via the application to two chemical process examples and one hybrid tank plant.

Sequential Monte Carlo Filter for State-of-Charge Estimation of Lithium-Ion Batteries Based on Auto Regressive Exogenous Model

The state of charge (SOC) of lithium-ion batteries (LIBs) is an important evaluation index in battery management system of energy storage systems. However, it is always a challenging task to accurately estimate SOC of LIBs, because of the existence of nonlinear characteristics and significant temperature effects. To improve the SOC estimation accuracy and robustness, a model-based estimation approach for SOC and impedance of LIBs is proposed against uncertain loading profiles and ambient temperatures. First an auto regressive exogenous model for online model order determining and parameters identification is established to monitor parameters variations based on numerical subspace state space system identification method. Second, a sequential Monte Carlo filter is employed to overcome the nonlinear and non-Gaussian error distribution state estimation problems caused by complicated open-circuit voltage characteristics. Finally, evaluation of the adaptability and generality of the proposed method are verified by different LIBs under different operating conditions. Experimental results indicate that the proposed method shows great performance, whose estimation value converges to real SOC within an error of $\pm \text{3}\%$ , and the battery model can simulate battery dynamics robustly with high accuracy.