Distributed State Estimation Algorithm Research Articles

Distributed cooperative tracking and cooperative guidance against maneuvering aerial target

This paper designs finite-time distributed state estimation algorithm and cooperative guidance law for high-maneuvering target salvo attack. Considering the maneuvering property of the target, a novel maneuvering model is proposed, which can adjust the maneuvering parameter adaptively. Based on the maneuvering target model, the interactive multiple models (IMM)-based distributed cubature information filtering (DCIF) algorithm is designed by two phases, named local filtering phase and consensus fusion phase. The final estimate results can be obtained by fusing the parallel local estimate results effectively with finite consensus fusion steps, which are used to design the cooperative guidance law for maneuvering target salvo attack. Besides, with necessary mild conditions, the lower bound and upper bound of the information matrix are proved to exist, and the stability of the proposed distributed algorithm is analyzed by Lyapunov stability theory and stochastic stability theory. Besides, the cooperative attack simulation example is given to validate the effectiveness of the proposed algorithm.

Covariance intersection based event-triggered distributed state estimation under channel independent DoS attacks

This paper investigates the event-triggered distributed state estimation problem for a class of discrete time-varying systems in the presence of denial-of-service (DoS) attacks, where each sensor node selectively shares its local information with neighbors. In contrast to the previous studies where the DoS attacks are considered on sensor-to-filter channels, we deal with the situation that DoS attacks jam each filter-to-filter communication channel independently. To reduce the communication rate and save network resources, a novel event-triggered communication strategy is presented that takes into account the impact of DoS attacks and is specialized for each communication channel. Based on the covariance intersection fusion rule and weight rearrangement method, a distributed state estimation algorithm is proposed. Further, the consistency of estimates and mean-square boundedness of estimation errors are proved under system collective observability and some other mild assumptions. Lastly, a numerical simulation is conducted to demonstrate the developed results and the effectiveness of the proposed algorithm.

Robust information filtering for distributed networks using mixed Gaussian distribution

This paper proposes a robust distributed state estimation algorithm for sensor networks. In a distributed sensor network, sensor nodes may be affected by outliers and thus influence the information fusion results. In this respect, the measurement likelihood and one-step state prediction are modeled by a mixture of Gaussian distributions. In this Gaussian mixture, one Gaussian uses nominal covariance, while the other uses adaptive covariance with larger values and lower probabilities. We build a centralized multi-sensor fusion model in the variational Bayesian framework based on the aforementioned mixture of Gaussian distributions. Then, a consensus strategy is employed to convert the centralized method into a distributed one. Each node completes estimation tasks separately based on the information from itself and nearby nodes. In addition, the weight of sensor information will adaptively update according to the Gaussian distribution that mainly affects the current sensor measurement noise. Finally, simulation experiments demonstrate the effectiveness of the proposed method in handling outlier effects.

Diffusion Nonlinear Estimation and Distributed UAV Path Optimization for Target Tracking with Intermittent Measurements and Unknown Cross-Correlations

This paper focuses on distributed state estimation (DSE) and unmanned aerial vehicle (UAV) path optimization for target tracking. First, a diffusion cubature Kalman filter with intermittent measurements based on covariance intersection (DCKFI-CI) is proposed, to address state estimation with the existence of detection failure and unknown cross-correlations in the network. Furthermore, an alternative transformation of DCKFI-CI based on the information form is developed utilizing a pseudo measurement matrix. The performance of the proposed DSE algorithm is analyzed using the consistency and the bounded error covariance of the estimate. Additionally, the condition of the bounded error covariance is derived. In order to further improve the tracking performance, a UAV path optimization algorithm is developed by minimizing the sum of the trace of fused error covariance, based on the distributed optimization method. Finally, simulations were conducted to verify the effectiveness of the proposed algorithm.

Distributed Maximum Correntropy Cubature Information Filtering for Tracking Unmanned Aerial Vehicle

Aiming at improving the performance of tracking unmanned aerial vehicle in the battlefield, this paper focuses on the algorithm involving tracking the maneuvering target with a distributed sensor network under non-Gaussian measurement noise. A novel distributed maximum correntropy cubature information filtering based on interactive multiple model is proposed. Taking advantage of the correntropy, we design a maximum correntropy cubature information filtering for each node to estimate the target state under non-Gaussian measurement noise. Then, distributed information fusion based on weighted average consensus is conducted to improve the stability of the sensor network. After that, the information pair is changed, so that a distributed state estimation algorithm based on interactive multiple model is developed to increase the accuracy of maneuvering target tracking. Simulation results and comparison with other algorithms in three typical non-Gaussian measurement noise scenarios are given to evaluate the effectiveness of the proposed algorithm.

The Optimal Distributed Weighted Least-Squares Estimation in Finite Steps for Networked Systems

This brief investigates the distributed state estimation problem for networked systems. Based on the coupled measurements and information exchanged with neighboring nodes, we propose a distributed estimation algorithm for each node to obtain the state estimate, which is equivalent to the centralized weighted least-squares (WLS) one. When the communication network of the system consists of an acyclic graph, the distributed state estimation algorithm converges in finite iterations. Then we demonstrate that the size of the abstract graph determines the number of iterations. Furthermore, we propose an algorithm for detecting false data attacks by distributed calculation. Finally, the numerical results verify the effectiveness of developed algorithms.

Information-weighted Consensus Filtering under Limited Communication

A distributed sensor network refers to a set of stationary or mobile agents equipped with sensors, each of which observes and estimates the state of some system, while utilizing the communication channels of the sensor network to improve the overall state estimation performance of the network. In particular, consensus-based distributed state estimation algorithms can compute accurate state estimates of the system at each agent under relaxed observability conditions, using a low communication bandwidth. A drawback of many existing consensus-based approaches is that they are developed under the presumption that a large number of consensus subiterations are used, which may not be possible in large-scale sensor networks, in the presence of communication delays and/or energy constraints. In this paper, we develop an extension of the Information-weighted Consensus Filter (ICF) for the case where only a limited number of consensus subiterations are possible. Through mathematical analysis and numerical simulations, it is shown that the proposed algorithm improves upon the existing algorithms under identical computation and communication requirements.

Distributed state estimation method based on WLS-AKF hybrid algorithm for active distribution networks

Given the difficulty of traditional state estimation methods in meeting the computational efficiency and accuracy requirements of active distribution networks, we propose a distributed state estimation (DSE) method for active distribution networks based on the weighted least squares-adaptive Kalman filter (WLS-AKF) hybrid algorithm. A multi-criteria partition model of an active distribution network that is suitable for DSE has been established. The model comprehensively considers the impact of partitioning results on DSE calculation accuracy and efficiency from the three perspectives of structure, measurement, and performance and solves the model using an improved genetic algorithm. A partition decoupling method is proposed herein, which completely decouples the sub-regions without requiring the measurement configuration of the sub-region boundary nodes and effectively reduces the DSE calculation scale. Furthermore, the paper proposes a DSE algorithm based on WLS-AKF that uses AKF to provide accurate pseudo-measurement of boundary nodes for WLS, which improves the calculation efficiency while ensuring the DSE calculation accuracy. The proposed method is analyzed and verified using the improved IEEE118 node system. The results show that the proposed method has high computational accuracy and efficiency, and can obtain high-precision estimation results in the case of missing data.

Novel event‐triggered distributed state estimation algorithm for nonlinear systems over wireless sensor networks

AbstractThis article focuses on the event‐triggered distributed state estimation for nonlinear dynamic systems over wireless sensor networks, where whether measurement should be transmitted from the sensor to the corresponding local estimator depends on a predesigned event‐triggered mechanism. To obtain a better estimation performance while saving the communication energy consumption, a novel event‐triggered nonlinear state estimator is designed by approximating the true posterior probability density function with minimum Kullback–Leibler divergence when the measurement is not transmitted. After local estimation results are produced in every local estimator through applying the cubature rule, according to a communication protocol and covariance intersection fusion strategy, an event‐triggered distributed cubature Kalman filtering (EDCKF) algorithm is developed. Compared with algorithms based on weighted average consensus, the proposed algorithm eliminates the disagreement between local estimators and obtains its best performance within a limited time. Moreover, sufficient conditions are obtained to prove the stability of the EDCKF algorithm. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed estimator and algorithm.

Fully Distributed Filtering With a Stochastic Event-Triggered Mechanism

This article focuses on distributed filtering for a discrete time-varying system observed by multiple smart sensors, where every sensor only measures partial state information of the target system and then sends it to a corresponding remote estimator. Subsequently, the estimator performs the local Kalman filter and shares its estimates with the estimators in its neighborhood in a distributed way. This article aims to reduce the communication rate between sensors and estimators, and guarantee the estimation performance, simultaneously. To achieve this goal, a novel distributed information fusion algorithm is designed by embedding a stochastic event-triggered communication mechanism. Based on a new developed mathematics technique, the consistency and stability of the proposed distributed state estimation algorithms are both ensured. Furthermore, compared with the literature, the stability can be guaranteed with a milder collectively uniformly observable condition. Moreover, the tradeoff between the communication rate and estimation performance is analyzed in a closed-form expression. Finally, the effectiveness of the theoretical results is demonstrated by several comparative numerical examples.

Sensor network based distributed state estimation for maneuvering target with guaranteed performances

This paper proposes a sensor network information fusion based distributed state estimation algorithm for tracking non-cooperative maneuvering target. In order to lower the communication burden and energy consumption, an event-triggered mechanism is introduced. The distributed state estimation algorithm for maneuvering target tracking is designed by two stages, namely, local filtering stage and consensus fusion stage. The algorithm proposed in this paper can be used to obtain the high accurate state estimation of the target by introducing a multiple suboptimal fading factor even when the target makes big maneuvering. Moreover, a contribution factor is designed in the information fusion stage to improve the accuracy of maneuvering target state estimation and reduce the consensus iteration times. Besides, the stochastic boundedness of the event-triggered distributed estimation algorithm is proved by introducing a stochastic process. Finally, Monte Carlo numerical simulation example is designed to illustrate the effectiveness of the algorithm.

Distributed Data-Driven Intrusion Detection for Sparse Stealthy FDI Attacks in Smart Grids

The stealthy false data injection (FDI) attacks in smart grids can bypass the bad data detection, and thus make an incorrect state estimate in the control center. In this brief, a distributed data-driven intrusion detection approach is proposed to reveal the existence of the sparse stealthy FDI attack in a multi-area interconnected power system. The proposed distributed intrusion detection approach avoids the over-fitting issue that is extensively seen when implementing machine learning algorithms for large-scale systems. Firstly, each area estimates the entire system state based on a distributed state estimation algorithm. Then, the state of each local area is used as trained neural network input to detect the stealthy FDI attacks. Simulation results on the IEEE 118-bus system verify that the proposed method not only reduces the risk of over-fitting, but also can locate the areas which have been attacked.

Distributed secure estimation for cyber-physical systems with fading measurements and false data injection attacks

This paper is concerned with the distributed secure estimation problem for a cyber-physical system (CPS) with fading measurements and false data injection (FDI) attacks, where the fading probability of measurements is assumed to be individual for each sensor, and the FDI attacks occur at the physical system layer to intensively modify the system's state. For improving security of the system, an attack detection mechanism is proposed based on an FDI attack observer constructed by minimising the upper bound of observation error covariance. Then a complete distributed state estimation algorithm is given to provide locally reliable estimation. A sufficient condition is provided to guarantee boundedness of the estimation error covariance. Finally, the effectiveness of the proposed method is illustrated by numerical simulation and practical example simulation.

Event-triggered distributed state estimation over wireless sensor networks

This paper focuses on the event-triggered distributed state estimation over sensor networks, in which each sensor node selectively transmits the local information to its neighbors for the reduced communication bandwidth and the prolonged network lifetime. Based on an individual stochastic triggering condition, an event-triggered minimum mean square error (MMSE) estimator is proposed in a recursive form, and then an event-triggered distributed state estimation algorithm is developed by repeatedly fusing the local information and the event-triggered information. It is shown that, under network connectivity, collective observability and large enough triggering parameters, the distributed estimator in each sensor node is stable with the uniformly bounded estimation error in mean square. Finally, a target tracking example is provided to illustrate the practical effectiveness of the proposed technique.

A Distributed Robust Power System State Estimation Approach Using $t$-Distribution Noise Model

In practical power system applications, the distribution of the measurement noise is sometimes unknown and deviates from the assumed Gaussian noise model due to measurement outliers. In such cases, the performances of the state estimators based on Gaussian noise assumption may deteriorate significantly. In this article, we propose a fully distributed and robust power system state estimation approach based on the $t$ -distribution noise model and the maximum likelihood criterion. The $t$ -distribution is used to model Gaussian and non-Gaussian statistics in the field of robust statistics. The matrix-splitting techniques are employed to carry out the extensive matrix inversion of the gain matrix in a distributed way to achieve efficient computation. In the proposed distributed estimation framework, each local control area only requires limited data exchange with its neighboring areas. Simulations on the IEEE 14-bus, 118-bus and 300-bus systems are used to verify the effectiveness and robustness of the proposed distributed state estimation algorithm.

Globally optimal distributed time-varying weight information filter of mobile sensor network

The networked state estimation for a linear dynamic system is studied in this paper. Firstly, a time-varying distributed communication protocol governed by the network topology is introduced for delivering information among the neighboring sensors. Secondly, based on this protocol, a two stage distributed state estimation algorithm is presented to achieve the global optimal results in a least square sense. In the first stage of the proposed algorithm, distributed computation on the sum of global information vector contributions is conducted, and the second stage is to derive the state estimations via utilizing the interaction results offered by the first stage. Thirdly, it is shown that the proposed algorithm only demands finite neighbor interaction times to obtain global optimal estimations. The optimality and stability properties of the proposed algorithm are also proved by using the Riccati equation. Finally, through numerical simulations, it is further illustrated that the proposed algorithm could outperform the previous distributed estimators.

Distributed state estimation for uncertain linear systems: A regularized least-squares approach

This paper addresses the state estimation problem for a discrete-time uncertain system with a network of sensors, where the system is not necessarily observable by each sensor and deterministic uncertainties exist in the system matrices. A new robust estimator is designed for each sensor, using only its own and neighbor’s information, which is fully distributed. Moreover, a novel information fusion strategy is developed to guarantee the estimation performance, based on the collective observability of the sensor network, which greatly relaxes the technical assumption of the proposed estimator. Theoretically, it can be ensured that if the observed system is time-varying, the gains of the estimator will be bounded. Furthermore, if the system is time-invariant, these gains will be convergent. Subsequently, the estimation error covariance will be ultimately bounded if the observed system is quadratically bounded. In the end, the superiority of the proposed robust distributed state estimation algorithm is illustrated by several numerical simulation examples.

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.

Complex system decomposition for distributed state estimation based on weighted graph

In this work, a systematic subsystem decomposition procedure for complex process systems is proposed for distributed state estimation. In the proposed procedure, both the connectivity within a system and the strength of connections are taken into account. A nonlinear process is first presented by a directed graph in which a node denotes either a state or a measured output of the nonlinear process. In the directed graph, nodes are connected via weighted edges and the weights reflect the strength of connection between two nodes. Based on the weighted directed graph, community structure detection is used to divide all the variables into smaller groups, such that the intra-connection within each group is made much stronger than the interaction among different groups. Subsystem models that are appropriate for distributed state estimation are configured based on the variables assigned to the groups. A comparative study between the proposed procedure with a procedure based on unweighted directed graph is conducted through extensive simulations. In the simulations, a numerical example and a chemical process example are considered. Three commonly used distributed state estimation algorithms designed based on the two decomposition procedures are applied to the two examples. A few guidelines on when to use weighted graphs for decomposition for distributed state estimation are concluded.

ADMM-Based Distributed State Estimation of Smart Grid Under Data Deception and Denial of Service Attacks

Smart grid (SG) represents a large-scale network system with the tight integration of a physical power network and an information network, which makes it more vulnerable to hybrid cyber attacks against different regional subsystems. First, an alternating direction method of multipliers-based distributed state estimation method is developed to overcome the limitation of conventional state estimation and performance analysis of SG against a single type of cyber attacks. Regional subsystems are partitioned via the ${K}$ -means method. Second, a novel distributed state estimation method integrated with the characteristics of data deception attacks and denial of service (DoS) attacks is proposed to account for the simultaneous presence of different cyber attacks on individual regional subsystems. Third, the convergence of a distributed state estimation algorithm under hybrid cyber attacks is proved theoretically. Furthermore, the relationships between the convergence and algorithm parameters as well as the occurring probability of DoS attacks are established. Finally, the simulations on a modified IEEE 118-bus system are given to demonstrate the feasibility and effectiveness of the proposed method.