A Distributed State Estimation Algorithm for Linear Dynamic Systems with Cross-Correlated Noises

The AC-DC hybrid microgrid is a credible evolution path for the microgrid. State estimation in complex distribution network is a significant foundation for the safe operation. In AC-DC hybrid microgrid, centralised state estimation algorithms have quite a few deficiencies such as large communication capacity and privacy protection. In response to these obstacles, this paper proposed a novel distributed state estimation algorithm. First, a three-stage state estimation model was established for AC-DC hybrid microgrid, in which the second stage is a nonlinear transform for the linearisation of the nonlinear state estimation progress so that the first and third stage can solve the linear state estimation problem. Furthermore, the Lagrangian relaxation method was ultilised for the distributed problem solution. In the proposed algorithm, AC subsystems and DC subsystems respectively execute state estimation through local information, and the overall consistency of the system state estimation can be eventually achieved according to the transfer iteration of the boundary information. The computational efficiency and convergence of the proposed method was ensured owing to the combination of bilinear theory and Lagrangian relaxation. Simulation results indicate that the proposed method can achieve its goal and be superior to existing method in efficiency.

This paper presents a novel coordinated algorithm, Fast Distributed State Estimation with Linear Coordination (FDSELC), considering Phasor Measurement Units (PMUs) measurements at both subsystem and coordination levels. At the subsystem level, the estimators apply augmented Fast Decoupled State Estimation algorithm to reduce the computational time at the first step. At the coordination level, linear estimators based on PMUs measurements are able to coordinate the voltage states of boundary buses, which lead to the further improvement of computational performance. Tests on the IEEE 118-bus system demonstrate the performance of the novel FDSELC algorithms. The results are compared with centralized and other distributed state estimation algorithms in terms of both the estimation quality and computational cost. In addition, the proposed FDSELC algorithm with the distributed control architecture is suitable for future smart grids. In this situation, a large power grid can be decomposed into subsystems, and those subsystems can be estimated, monitored and controlled separately.

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori (MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems.

In this paper, a distributed control scheme is proposed to mitigate the challenges of voltage regulation in DC distribution systems and facilitate high penetration of distributed and renewable energy resources. The proposed control scheme consists of two main stages. In the first stage, a distributed state estimation algorithm is implemented to estimate the voltage profile in a DC distribution system and enhance the AC/DC converter operation in order to keep the system voltage within its specified limits. Further, in case of occurrence of voltage violation that cannot be handled by the AC/DC interfacing converter a reconsideration of power management would take place. Thus, in the second stage, a distributed power management optimization problem is formulated to maximize the total DGs' revenue; while keeping the voltages of all system buses within limits. The formulated problem is classified as a convex optimization problem under global constraints. A distributed Lagrangian Primal-Dual Subgradient (DLPDS) algorithm that is superior in solving such optimization problems is proposed in this work.

This 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.

State estimation plays a vital role in UAV navigation and control. With the continuous decrease in sensor cost and size, UAVs equipped with multiple LiDARs, Inertial Measurement Units (IMUs), and cameras have attracted increasing attention. Such systems can acquire rich environmental and motion information from multiple perspectives, thereby enabling more precise navigation and mapping in complex environments. However, efficiently utilizing multi-sensor data for state estimation remains challenging. There is a complex coupling relationship between IMUs’ bias and UAV state. To address these challenges, this paper proposes an efficient and accurate UAV state estimation method tailored for multi-LiDAR–IMU–camera systems. Specifically, we first construct an efficient distributed state estimation model. It decomposes the multi-LiDAR–IMU–camera system into a series of single LiDAR–IMU–camera subsystems, reformulating the complex coupling problem as an efficient distributed state estimation problem. Then, we derive an accurate feedback function to constrain and optimize the UAV state using estimated subsystem states, thus enhancing overall estimation accuracy. Based on this model, we design an efficient distributed state estimation algorithm with multi-LiDAR-IMU-Camerafusion, termed DLIC. DLIC achieves robust multi-sensor data fusion via shared feature maps, effectively improving both estimation robustness and accuracy. In addition, we design an accelerated image-to-point cloud registration module (A-I2P) to provide reliable visual measurements, further boosting state estimation efficiency. Extensive experiments are conducted on 18 real-world indoor and outdoor scenarios from the public NTU VIRAL dataset. The results demonstrate that DLIC consistently outperforms existing multi-sensor methods across key evaluation metrics, including RMSE, MAE, SD, and SSE. More importantly, our method runs in real time on a resource-constrained embedded device equipped with only an 8-core CPU, while maintaining low memory consumption.

ABSTRACTAs a result of the rapid growth of distributed state estimation in modern power systems, power networks are facing increasingly serious security problems, thus requiring the advancement of defense techniques against cyber attacks. This paper is devoted to investigating distributed consensus state estimation with a defense mechanism against false data injection (FDI) attacks for power systems. By introducing a transformation matrix, the local subsystem model associated with the mixed remote terminal unit and phasor measurement unit measurements is constructed. Taking into account historical estimation information on state variables without being attacked, a defense mechanism constructed by secure historical estimation value is presented to protect the estimator against FDI attacks while maintaining accuracy in estimation. Then a distributed Kalman consensus filter (DKCF) is hosted to estimate the dynamic states of power systems under FDI attack protector. Considering scalability in large‐scale power systems, a suboptimal DKCF with the designed protector is developed. By means of the Lyapunov‐based approach, a sufficient condition is provided to ensure that the proposed estimator equipped with the defense mechanism is stable. Finally, the proposed distributed state estimation algorithms are validated on an IEEE benchmark 14‐bus power system.

Event-triggered distributed state estimation over wireless sensor networks

This paper investigates the distributed state estimation problem for spacecraft thermal experiments over sensor networks. The state estimators are designed in a distributed fashion to estimate the surplus temperature of the target node in the spacecraft. In particular, the randomly occurring time-varying sensor transmission delays are considered during the state estimation, which is more practical under networked environment. By employing the Lyapunov–Krasovskii functional approach, sufficient criteria are established and the desired distributed state estimator gains can be derived, such that the estimation error system can be asymptotically stable. Finally, the illustrative example is provided for demonstrating the effectiveness of the proposed method.

In this paper, the distributed state estimation problem is investigated for a class of uncertain sensor networks. The target plant is described by a set of uncertain difference equations with both discrete-time and infinite distributed delays, where two random variables are introduced to account for the randomly occurring nonlinearities. The sensor measurement outputs are subject to randomly occurring sensor saturations due to the physical limitations of the sensors. Through available output measurements from each individual sensor and its neighboring sensors, this paper aims to design distributed state estimators to approximate the states of the target plant in a distributed way. Sufficient conditions are presented which not only guarantee the estimation error systems to be globally asymptotically stable in the mean square sense but also ensure the existence of the desired estimator gains.

SUMMARYIn this paper, the distributed state estimation problem is investigated for a class of sensor networks described by uncertain discrete‐time dynamical systems with Markovian jumping parameters and distributed time‐delays. The sensor network consists of sensor nodes characterized by a directed graph with a nonnegative adjacency matrix that specifies the interconnection topology (or the distribution in the space) of the network. Both the parameters of the target plant and the sensor measurements are subject to the switches from one mode to another at different times according to a Markov chain. The parameter uncertainties are norm‐bounded that enter into both the plant system as well as the network outputs. Furthermore, the distributed time‐delays are considered, which are also dependent on the Markovian jumping mode. Through the measurements from a small fraction of the sensors, this paper aims to design state estimators that allow the nodes of the sensor network to track the states of the plant in a distributed way. It is verified that such state estimators do exist if a set of matrix inequalities is solvable. A numerical example is provided to demonstrate the effectiveness of the designed distributed state estimators. Copyright © 2011 John Wiley & Sons, Ltd.

Distributed state estimation system is beneficial in power grids with complex structures and large quantities of measurements because of its advantages, such as high computational efficiency and enhanced reliability. This study investigates a novel multi-area distributed state estimation algorithm for large-scale interconnected power systems. The state estimation model of the entire power grid is effectively decomposed into a group of estimation models that can be locally solved using an area estimator. The global information required by an estimator in solving its estimation model is effectively synthesized as two average values, and an average consensus-based algorithm is developed for an area estimator to access the required global information in a distributed fashion. Bad data are identified and eliminated after the convergence of the iterative estimation process. Simulation results of the IEEE 14-bus test system are provided to show the correctness and effectiveness of the proposed algorithm. Solution accuracy, computational efficiency and state estimation speed are compared with those of existing centralized, hierarchical and distributed methods by the numerical example in the IEEE 300-bus test system.

This article is concerned with the robust distributed state estimation problem for a class of uncertain sensor networks with multiple stochastic communication delays. A sequence of mutually independent random variables obeying the Bernoulli distribution is introduced to account for the randomly occurred communication delays. Both the discrete-time target plant and the sensor model are subject to parameter uncertainties as well as stochastic disturbance. The parameter uncertainties are norm-bounded and enter both the system and the measurement matrices. The external stochastic disturbance is given in the form of a scalar Wiener process. Through available output measurements from not only each individual sensor but also its neighbouring sensors, we aim to design distributed state estimators in order to approximate the state of the target plant. By using the Kronecker product, stochastic analysis is carried out to derive a sufficient criterion ensuring the estimation error systems to be convergent in the mean square sense for all randomly occurred delays, admissible stochastic disturbance and parameter uncertainties. Then, an explicit expression of the individual estimator is given in terms of the solution to a convex optimisation problem that can be easily solved by using the semi-definite programme method. A numerical example is given at the end of this article to demonstrate the usefulness of the developed theoretical results.

The paper illustrates the development and the implementation of a Distribution State Estimation (DSE) algorithm for the Low Voltage Test Facility with Distributed Energy Resources of the Italian Research center RSE. The algorithm is integrated into a Distribution Management System within the control system of the Test Site organized as a microgrid. The Test Facility is equipped with conventional and renewable generation plants, storage systems and programmable loads. Switching boxes allow to obtain a very high number of different topology configurations. The paper shows details of the methodologies and theoretical bases adopted for the algorithm design, implementation and testing of a two level state estimation procedure. Simulation and comparison with field results allow the evaluation of the power contributions to total nodal injections, in all the possible grid configurations.

In this paper, the distributed state estimation problem is investigated for a class of discrete time-varying nonlinear systems over sensor networks with sensor resolution, where a binary encoding scheme is employed to address bandwidth limitations. The measurement output is converted into a binary bit string, conveyed through a memoryless binary symmetric channel subject to a certain probability of bit flips, and then reconstructed by a decoder. The influence of both sensor resolution and binary encoding scheme on estimation accuracy is considered simultaneously, where a distributed recursive state estimation strategy over sensor networks is constructed. Subsequently, the estimator gain that minimizes the upper bound on the estimation error covariance is obtained by solving Riccati-like difference equations. Finally, the validity of the developed algorithm is displayed through a simulation example.