Local State Estimates Research Articles

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.

A distributed Kalman filter with symbolic zonotopes and unique symbols provider for robust state estimation in CPS

Robust state estimation is addressed in a noisy environment and within a distributed and networked architecture. Both bounded disturbances and random noises are considered. A Distributed Zonotopic and Gaussian Kalman Filter (DZG-KF) is proposed where each network node implements a local state estimator using symbolic Zonotopes and Gaussian noise Mergers (s-ZGM), a class of Set-membership and Probabilistic Mergers (SPM). Each network node communicates its own state information only to its neighbours. The proposed system includes a dedicated service called Unique Symbols Provider (USP) giving unique identifiers. It also includes Matrices with Labelled Columns (MLC) featuring column-wise sparsity, and symbolic zonotopes (s-zonotopes). This significantly enhances the propagation of uncertainties and preserves global dependencies that would otherwise be lost (or impeded) by the peer-to-peer communication through the network. A number of other network-related constraints can be managed within this framework. Numerical simulations show significant improvements compared to a non-symbolic approach.

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.

Fusion-Based FDI Attack Detection in Cyber-Physical Systems

This brief studies the alarm response problem of attack detection for cyber-physical systems under false data injection attacks. Notice that the faster the alarm response of the attack detection is, the less the system performance loss is. In this case, the distributed fusion strategy, which can potentially provide higher accuracy and reliability, is introduced, for the first time, to improve the speed of alarm response. Meanwhile, to ensure real-time anomaly detection online, a group of sensors deployed by different positions send their messages to a monitoring center through communication networks. Due to the limited bandwidth, multiple finite-level logarithmic quantizers are used to reduce the size of data packages containing residual messages (generated by local state estimators). Then, an optimal weighting fusion criterion is designed by establishing convex optimization problems such that the residual evaluation threshold is more accurate in the presence of quantization errors. Finally, an F-404 aircraft example is used to illustrate that the response speed of attack detection becomes faster as compared with the case of single sensor.

An Adaptive Distributed Quasi-Newton Method for Power System State Estimation

Multi-area state estimation (MASE) is indispensable for coordination among independent system operators in interconnected systems. In this paper, we propose an adaptive distributed quasi-Newton (A-DQN) algorithm with an optimal step length tuning strategy for MASE in electric power systems. To address the nonlinearity of the measurement model, nonlinear MASE is factorized into two linear estimation stages with a nonlinear transformation in between. A-DQN is then applied to solve the two linear estimation stages in which the decomposed solution for optimal step length is derived in closed form by exploiting the problem structure. With this method, each area performs a local state estimation with limited information exchange with its neighbors; thus, no central coordinator is needed. Based on a peer-to-peer communication paradigm, this method provides accurate estimation results and considers coupling among areas while the privacy and independence of each area remain well-preserved. Numerical tests demonstrated that the proposed algorithm outperforms MASE methods based on state-of-the-art algorithms such as the alternating direction method of multipliers, the matrix-splitting-based distributed Newton method, and the existing distributed Broyden–Fletcher–Goldfarb–Shanno algorithm.

Reliable fusion estimation over sensor networks with outliers and energy constraints

SummaryThis paper provides a reliable fusion scheme over sensor networks subject to abnormal measurements and energy constraints. Two kinds of channels are employed to implement the information transmission in order to extend the lifetime. Specifically, the one has the merit of high reliability by sacrificing energy cost and the other reduces the energy cost but could result in packet loss. For the addressed problem, a χ2 detection in local state estimator is first designed to remove abnormal measurements, which could come from outliers or a malicious modification by attackers. Then, a new strategy is developed to compensate the lost local estimation transmitted by low‐reliable channels. Furthermore, by view of matrix operation and probability theory, a set of recursive formulas are developed to calculate desired error covariance matrices of local state estimation, compensated state estimation as well as fusion estimation. The optimal fusion weights are obtained analytically and the advantage of fusion estimation is disclosed by resorting to these covariance matrices. Finally, a numerical example is used to illustrate the effectiveness of the proposed method.

Distributed Moving-Horizon Estimation With Arrival-Cost Consensus

The paper deals with the problem of estimating the state of a linear system over a peer-to-peer network of linear sensors. The proposed approach is fully distributed, scalable, and allows for taking into account constraints on noise and state variables by resorting to the moving-horizon estimation paradigm. Each network node computes its local state estimate by minimizing a cost function defined over a sliding window of fixed size. The cost function includes a fused arrival cost, which is computed in a distributed way by performing a consensus on the local arrival costs. The proposed estimator guarantees stability of the estimation error dynamics in all network nodes, under the minimal requirements of network connectivity and collective observability, and for any number of consensus steps. Numerical simulations are provided to demonstrate the practical effectiveness of the approach.

Information Bounds for State Estimation in the Presence of an Eavesdropper

Remote state estimation problems in the presence of eavesdroppers have recently been investigated in the literature. For unstable systems, it has been shown that it is possible to keep the expected estimation error covariance bounded, while the expected eavesdropper error covariance becomes unbounded in the infinite horizon. In this note, we consider an alternative notion of security based on the amount of information revealed to the eavesdropper. Upper and lower bounds on the information revealed are derived. In particular, in the infinite horizon, it is shown that with unstable systems, any transmission policy (within the class of stationary deterministic policies where the sensor at each time step can either transmit its local state estimate or not) which keeps the expected estimation error covariance bounded must always reveal a non-zero expected amount of information to the eavesdropper.

Reliable Data Fusion of Hierarchical Wireless Sensor Networks With Asynchronous Measurement for Greenhouse Monitoring

This paper investigates the data fusion problem of wireless sensor networks (WSNs) for the greenhouse monitoring system. Considering the characteristics of local consistency and slow change of the greenhouse environmental information, the hierarchical structure of WSNs is proposed for the greenhouse monitoring system, and the two-stage data fusion scheme is presented for the hierarchical network. In the first stage, the weighted data fusion algorithm of WSNs on local state estimation is designed for the cluster, which would improve the fusion accuracy and the ability of anti-interference of the system. Moreover, the multirate measurement mode is proposed to reduce the energy consumption of WSNs under the premise of satisfying the information sensing performance of the system. In the second stage, the data fusion at the sink node is conducted on the support function with the consistency analysis of data from different clusters. The simulation analysis on the greenhouse temperature information is provided to show the effectiveness of the proposed data fusion scheme.

Distributed output-feedback model predictive control for multi-agent consensus

We propose a distributed output-feedback model predictive control approach for achieving consensus among multiple agents. Each agent computes a distributed control action based on an output-feedback measurement of a local neighborhood tracking error and communicates information only to its neighbors, according to a communication network modeled as a directed graph. Each agent computes its distributed control action by solving a local min–max optimization problem that simultaneously computes a local state estimate and control input under worst-case assumptions on unmeasured input disturbances and measurement noise. Under easily verified controllability and observability assumptions, this distributed output-feedback model predictive control approach provides an upper bound on the group consensus error, thereby ensuring practical consensus in the presence of unmeasured disturbances and noise. A numerical example with four agents connected in a directed graph is given to illustrate the results.

Localised sequential state estimation for advection dominated flows with non-Gaussian uncertainty description

This paper presents a new iterative state estimation algorithm for advection dominated flows with non-Gaussian uncertainty description of L∞-type: uncertain initial condition and model error are assumed to be pointwise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this L∞-type bounding set by a union of possibly overlapping ellipsoids, which are localised (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard L2-type filter (e.g. Kalman minimax filter) which uses Gaussian/ellipsoidal uncertainty description and observations (if any) which correspond to this sub-domain. The resulting local state estimates are stitched together by the iterative d-ADN Schwarz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples.

Secure Estimation for Attitude and Heading Reference Systems Under Sparse Attacks

This paper focuses on the problem of secure attitude estimation for autonomous vehicles. Based on the established AHRS measuring model and the attack model, we have decomposed the optimal Kalman estimate into a linear combination of local state estimates. We then propose a convex optimization-based approach, instead of the weighted sum approach, to combine the local estimate into a more secure estimate. It is shown that the proposed secure estimator coincides with the Kalman estimator with certain probability when there is no attack, and can be stable when $p$ elements of the model state are compromised. Simulations have been conducted to validate the proposed secure filter under single and multiple measurement attacks.

Consensus Based Strong Tracking Adaptive Cubature Kalman Filtering for Nonlinear System Distributed Estimation

The distributed cubature Kalman filter is widely used in the field of target tracking, however, the presence of model uncertainties will undermine its tracking stability and effectiveness for tracking maneuvering target. In order to eliminate this effect on maneuvering target tracking, this paper develops a distributed consensus based strong tracking cubature Kalman filter scheme. First, each node obtains its local estimation with the usage of local observations via strong tracking cubature Kalman filter, where the suboptimal fading factor and adaptive factor are introduced for adaptively modifying the filter gain. Then, the designed filter gain is used for updating the local state estimation. Second, after all, nodes have achieved its local estimation, each node exchanges its local estimation to its neighbors and updates its local estimation according to the consensus communication protocol. It can be further proved that the distributed interaction between neighbors will contribute to enhancing the tracking stability. The detailed proof for stochastic boundedness of the estimation error is analyzed by introducing a stochastic process. Simulation results demonstrate that the proposed algorithm can achieve higher tracking accuracy than the existing methods for tracking a maneuvering target.

Secure State Estimation Against Integrity Attacks: A Gaussian Mixture Model Approach

We consider the problem of estimating the state of a linear time-invariant Gaussian system using $N$ sensors, where a subset of the sensors can potentially be compromised by an adversary. In this case, locating the compromised sensors is of crucial importance for obtaining an accurate state estimate. Inspired by the clustering algorithm in machine learning, we propose a Gaussian-mixture-model-based (GMM-based) detection mechanism. It clusters the local state estimate autonomously and provides a belief for each sensor, based on which measurements from different sensors can be fused accordingly. When a subset of the sensors are under the optimal innovation-based deception attacks, we derive the remote estimation error covariance recursions under different detection mechanisms, e.g., distributed $\chi ^2$ false-data detector, centralized $\chi ^2$ false-data detector, and GMM-based detection algorithm. The performance of the proposed GMM-based detection algorithm is further evaluated through average belief in the same attack scenario. Moreover, we discuss applications of GMM-based detection algorithm on other attack scenarios, e.g., false-data injection attack, replay attack, and $\epsilon$ -stealthy attack. Simulation examples are provided to demonstrate the developed results.

Observer Design for Triangular Systems Under Weak Observability Assumptions

This paper presents results on the solvability of the observer design problem for general nonlinear triangular systems with inputs, under weak observability assumptions. The local state estimation is exhibited by means of a delayed time-varying Luenberger-type system. In order to achieve the global estimation, a switching sequence of observers is designed.

Distributed adaptive output consensus tracking of nonlinear multi-agent systems via state observer and command filtered backstepping

This paper investigates the adaptive fuzzy output consensus tracking control for nonlinear multi-agent systems in the presence of input saturation. The interaction among the agents is described by a directed graph. Firstly, a local fuzzy state estimator is proposed to reconstruct the unmeasured state of each agent. Then, a novel command filtered backstepping based distributed adaptive control law is designed, where theunknown nonlinear dynamics are approximated by using the fuzzy logic system. The proposed control law can guarantee that the output consensus tracking errors converge into a sufficiently small neighborhood of the origin and all signals in the closed-loop system are bounded although the input saturation exists. Simulation results show the effectiveness of the proposed design.

Event-triggered information fusion for networked systems with missing measurements and correlated noises

This paper is concerned with the state estimation fusion problem for networked systems subject to bandwidth constraints and network-induced measurement missing. The stochastic networked system with correlated noises is firstly transformed to an equivalent one, whose process noise is independent of sensor measurement noises. To increase the efficiency of limited communication resource, a closed-loop event-triggered mechanism is designed based on the measurement innovation and Mahalanobis transformation, where data transmission is triggered only when the predefined condition is satisfied. The phenomenon of measurement missing is characterized as a series of independent Bernoulli sequences. For every sensor subsystem, optimal local event-triggered state estimators including filter, predictor and smoother are given in terms of Minimum Mean Square Error (MMSE). The statistical knowledge of event-triggered sampling and missing measurements is utilized in the design of local estimators. Then, based on the linear minimum variance criterion, the corresponding globally optimal event-triggered fusion estimators are proposed by a matrix-weighted combination of all available local estimates from sensor subsystems. The proposed decentralized fusion estimators have good abilities in reliability, fault tolerance and computation efficiency due to the netted parallel structure. The effectiveness and feasibility of the proposed algorithms is demonstrated by a numerical example.

Spatio-Temporally Smooth Local Mapping and State Estimation Inside Generalized Cylinders With Micro Aerial Vehicles

In this letter, we consider state estimation and local mapping with a micro aerial vehicle inside a tunnel that can be modeled as a generalized cylinder, using a three-dimensional lidar and an inertial measurement unit. This axisymmetric environment poses unique challenges in terms of localization and mapping. The point cloud data returned by the sensor consists of indiscriminate partial cylindrical patches complicating data association. The proposed method reconstructs an egocentric local map through an optimization process on a nonlinear manifold, which is then fed into a constrained unscented Kalman filter. The proposed method easily adapts to different diameters, cross sections, and changes in center line curves. The proposed approach outperforms our previous contribution [T. Ozaslan, G. Loianno, J. Keller, C. J. Taylor, V. Kumar, J. M. Wozencraft, and T. Hood, “Autonomous navigation and mapping for inspection of penstocks and tunnels with MAVs,” IEEE Robotics Automation Letter , vol. 2, no. 3, pp. 1740–1747, Jul. 2017] in terms of mapping quality and robustness to noncylindrical cross sections. Our motivation is to automate the labor intensive, dangerous, and the expensive inspection of penstocks with the least operator intervention. We present experimental results obtained in Center Hill Dam, TN, USA, to validate the proposed approach.

A robust D–S fusion algorithm for multi-target multi-sensor with higher reliability

This paper addresses the problem of track fusion for unordered distributed sensors with unknown measurement noise. A robust Dempster–Shafer (D–S) fusion algorithm is proposed, which includes three parts, namely, the local track estimation, the track association, and the state fusion. First, a labeling VB-PHD filter is derived to present target states with track labels and the unknown measurement noises of local sensors. Next, a heuristic D–S method is proposed to determine the relationship of local tracks and fused tracks, where the accumulated information is taken into account. Finally, a fusion method is given to show the state fusion results, which can fully utilize local state estimates and measurement noise information. Simulation results are provided to illustrate the high precision of tracking and good robustness, comparing with the traditional methods.

Distributed state estimation for a stochastic linear hybrid system over a sensor network

In this study, the authors consider the distributed state estimation problem of a stochastic linear hybrid system (SLHS) observed over a sensor network. The SLHS is a dynamical system with interacting continuous state dynamics described by stochastic linear difference equations and discrete state (or mode) transitions governed by a Markovian process with a constant transition matrix. Most existing hybrid estimation algorithms are based on a centralised architecture which is not suitable for distributed sensor network applications. Further, the existing distributed hybrid estimation algorithms are restrictive in sensor network topology, or approximate the consensus process among connected sensor agents. This study proposes a distributed hybrid state estimation algorithm based on the multiple model based approach augmented with the optimal consensus estimation algorithm which can locally process the state estimation and share the estimation information with the neighbourhood of each sensor agent. This shared information comprises local mode-conditioned state estimates and edge-error covariances, and is used to bring about an agreement or a consensus across the network. The proposed distributed hybrid state estimation algorithm is demonstrated with an illustrative aircraft tracking example.