Distributed Estimation Scheme Research Articles

A distributed state and fault estimation scheme for state-saturated systems with quantized measurements over sensor networks

This article explores a new framework of distributed state and fault estimation (DSFE) for the state-saturated systems over sensor networks. To this aim, the upper bound on estimation error covariance (EEC) is ensured and the explicit expression of the corresponding estimator gains is given with both quantization effects and state saturations. Further, a feasible upper bound is located on EEC and minimized by parameterizing the estimator gain. The matrix simplification technique is adopted to deal with the sensor network topology’s sparseness problem. Additionally, the estimation performance is first analyzed and then ensured by conducting a sufficient condition. At last, experiments are carried out to verify the feasibility of the developed DSFE method.

Distributed joint parameter and state estimation algorithm for large‐scale interconnected systems

SummaryThis paper proposes a distributed joint parameter and state variables estimation algorithm for large‐scale state‐space interconnected systems. In this distributed estimation scheme, each interconnected sub‐system is described by a linear discrete‐time state space mathematical model. Each sub‐system is supposed to be controlled by an intelligent controller that can communicate with its interconnected neighbors and exchange information, such as state variables. The proposed approach comprises two recursive estimation algorithms, a parameter estimation algorithm considering the state space model and a distributed Kalman filter for state variables estimation. It is a fully distributed cooperative approach that allows to reduce complexity and saves computational and communication resources. Theoretical analysis and numerical examples are provided to prove the feasibility and effectiveness of this joint estimation algorithm.

Distributed Phase Estimation at the Heisenberg Limit with Classical Light

Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future.

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.

Neural network based adaptive finite-time distributed estimation for an uncertain leader

This paper investigates a two-step finite-time distributed estimation scheme for an uncertain leader. Unlike the previous achievements, the leader with unknown nonlinearity and uncertain input is considered, and the whole scheme is fully distributed and output-based. Firstly, a local neural network (NN) finite-time observer is proposed to estimate the unavailable states / uncertain dynamics of the leader, where the NN is used to approximate the uncertain dynamics. Then, based on the local interaction among agents, an NN finite-time distributed observer is devised for all the followers to reconstruct the system states / NN weights broadcasted by the local observer. By utilizing a combination of the local and the distributed observer, the unavailable states and the uncertain dynamics of the leader can be reconstructed by each follower in a finite time. Finally, simulation examples are presented to demonstrate the validity of our scheme.

Distributed $H_{\infty }$-Consensus Estimation for Random Parameter Systems Over Binary Sensor Networks: A Local Performance Analysis Method

This paper deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus estimation problem for a class of discrete time-varying random parameter systems over binary sensor networks, where the statistical information of the random parameter matrix is characterized by a generalized covariance matrix known a priori. As a binary sensor can only provide one bit of information according to a given threshold, an indicator variable is introduced so as to extract functional information (from the sensor output) that can be employed to estimate the system state. With the introduced indicator variable, a distributed estimator is constructed for each binary sensor with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus performance constraint on the estimation error dynamics over a finite horizon. By means of a local performance analysis method, indicator-variable-dependent conditions are established for the existence of the desired distributed estimators whose gains are calculated by solving a set of recursive linear matrix inequalities. Finally, the applicability and effectiveness of the developed distributed estimation scheme are demonstrated through a numerical example.

Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions

AbstractThis study investigated the observer design schemes for interconnected nonlinear systems with actuator faults, sensor faults, external disturbances, and limited measured resources. A novel effective distributed estimation scheme is presented for the interconnected nonlinear system to estimate the states, faults, and lumped disturbances, simultaneously. To save communication resources and to improve information utilization, an adaptive event condition is designed in the sensor channel, and the triggered values are utilized to design the observer. Especially, to handle the sensor fault, the output is separated into two parts, and the estimation is realized with the help of a normal one. In the first part of this study, a class of interconnected nonlinear systems with partial loss of effectiveness of sensor fault is considered, and an event‐based distributed estimation scheme is established. In the second part, a class of more universal feedback interconnected nonlinear with both partial loss sensor fault and bias sensor fault is investigated. An augment system is formulated by an augmented vector composed of state and sensor faults. And then the estimation scheme is realized by utilizing the presented event‐based distributed observer. The convergence abilities of both the two conditions are proved and, finally, the estimation performances of the presented observer are verified by a numerical simulation system and an inverted pendulum system.

Plug-and-Play Design for Linear Distributed Observers

The distributed state estimation problem on linear time-invariant systems is addressed in this paper. We consider a scenario where the system outputs are measured via a group of sensors distributed over multiple nodes, where the joint measurements guarantee the detectability of the system. Each node is equipped with an observer exchanging its own state estimates with the neighboring nodes over a communication network, and the objective is to estimate the entire state of the system by each observer. Compared to existing designs requiring information on global graph topology or sensor placement at other nodes, our design is based only on local information. Hence, the proposed scheme is plug-and-play and scalable so that adding and removing nodes to the network or changing sensors at some existing nodes does not require observer redesign at any other node. Simulation results demonstrate the effectiveness of the proposed distributed estimation scheme.

Sensor Fault-Tolerant State Estimation by Networks of Distributed Observers

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme.

Adaptive neural-network-based distributed fault estimation for heterogeneous multi-agent systems

This contribution addresses the issue of distributed fault estimation for heterogeneous multi-agent systems which are composed of unmanned ground vehicles and unmanned aerial vehicles in the presence of actuator faults, completely unknown nonlinearities and external disturbances. Given that these two types of agents have different state dimensions and the motion of unmanned aerial vehicles in the XOY plane and Z-axis is relatively independent, the heterogeneous multi-agent systems can be divided into the XOY plane of all agents’ position subsystem and the Z-axis of unmanned aerial vehicles’ position subsystem. Then, combining the influences of completely unknown nonlinearities and external disturbances, an adaptive neural-network-based distributed fault estimation scheme is proposed to effectively estimate unknown actuation effectiveness parameters and can be applied to XOY plane and Z-axis of heterogeneous multi-agent systems separately. During the design of the observer, the neural network methodology is adopted to approximate completely unknown nonlinearities and a proper adaptive update law to estimate the 2-norm upper bound of disturbances and compensate for the influences of disturbances is designed. With output from a local agent and its neighbors, the proposed observer can be built on this agent, realizing simultaneous estimation of possible faults occurring in both the selected agent and its neighbor agents, which presents a new distributed framework. At last, simulation results are shown to illustrate the feasibility and effectiveness of the presented fault estimation algorithm.

Cooperative pointing control of collinear double-integrators without angular velocity

We deal with the cooperative pointing control problem of collinear double-integrators with unknown rotational inertia in this paper. In particular, we consider the case that the rotational angular velocity information is not available for this coordination task. First, we propose a cooperative pointing control protocol without using the rotational angular velocity measurements. By means of the passivity tool, a distributed estimation scheme is devised to access the relative rotational angular velocity information at each agent via the relative rotational angle information of the agent and its left and respectively right neighbors. Subsequently, we redesign the cooperative pointing control protocol as well as the distributed estimation scheme in the presence of saturated relative rotational angle information. It turns out that, here the unknown rotational inertia does not prevent the coordination task because of the bidirectional interactions. Meanwhile, two local estimation schemes are also presented respectively for the above two control protocols. Besides the rigorous convergence analysis, the effectiveness of our obtained theoretical results is illustrated through numerical simulations.

Resilient Event-Triggered Distributed State Estimation for Nonlinear Systems Against DoS Attacks.

This article investigates the resilient event-triggered (ET) distributed state estimation problem for nonlinear systems under denial-of-service (DoS) attacks. Different from the existing results mainly considering linear or specified nonlinear systems, more general nonlinear systems are considered in this study. Moreover, the considered DoS attacks are able to compromise different communication links among estimators independently. In this context, by resorting to the techniques of incremental homogeneity, a nonlinear ET distributed estimation scheme is designed to estimate the states and regulate the data transmission. Under this scheme, the resilient state estimation is achieved by employing a multimode switching estimator, and the problem of efficiency loss of the ET mechanism caused by DoS attacks is solved by designing a dynamic trigger threshold with switched update laws. Then, based on the decay rates of the Lyapunov function corresponding to different communication modes, sufficient conditions are given to guarantee the stability of the estimation error system under DoS attacks. Finally, simulation results are provided to verify the effectiveness of the proposed method.

PeerProbe: Estimating Vehicular Neighbor Distribution With Adaptive Compressive Sensing

Acquiring the geographical distribution of neighbors can support more adaptive media access control (MAC) protocols and other safety applications in Vehicular ad hoc network (VANETs). However, it is very challenging for each vehicle to estimate its own neighbor distribution in a fully distributed setting. In this paper, we propose an online distributed neighbor distribution estimation scheme, called PeerProbe, in which vehicles collaborate with each other to probe their own neighborhood via simultaneous symbol-level wireless communication. An adaptive compressive sensing algorithm is developed to recover a neighbor distribution based on a small number of random probes with non-negligible noise. Moreover, the needed number of probes adapts to the sparseness of the distribution. We implement a prototype system to verify the feasibility of PeerProbe in various typical vehicular channel conditions. We further conduct extensive simulations and the results demonstrate that PeerProbe is lightweight and can accurately recover highly dynamic neighbor distributions in critical channel conditions.

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time‐scale multiplicity

AbstractIn this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two‐time‐scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time‐scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one‐directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.

Communication-Efficient Coordinated RSS-Based Distributed Passive Localization via Drone Cluster

Multi-UAV passive localization via received signal strength (RSS) is extremely important for wide applications such as rescue and battlefield combat. However, the energy consumption of UAVs is a key issue in this UAVs-enabled application. Usually, the communication overhead plays an important role in the energy consumption. To address this problem, we design two distributed methods for this multi-UAV system with considerable performance under low communication overhead. Firstly, a distributed majorize-minimization (DMM) method is proposed. To accelerate its convergence, a tight upper bound of the objective function from the primary one is derived. Furthermore, a distributed estimation scheme using the Fisher information matrix (DEF) is presented, only requiring one round of communication between edge UAVs and central UAV. Simulation results show that the proposed DMM outperforms the existing distributed iterative methods in terms of root of mean square error (RMSE) under low communication overhead. Moreover, the most communication-effective DEF with local search estimation performs much better than the proposed DMM in terms of RMSE, but has a higher computational complexity.

Set-membership-based distributed moving horizon estimation of large-scale systems

This work is concerned with the design of a two-step distributed state estimation scheme for large-scale systems in the presence of unknown-but-bounded disturbances and noise. The set-membership approach is employed to construct a compact set containing the states consistent with system measurements and bounded noise and disturbances. The tightened feasible region is then provided to a moving horizon estimator that determines the optimal state estimates. Partitioning of the overall problem and coordination of the resulting subproblems are achieved using decomposition of the optimality conditions and community detection. The proposed strategy is tested on a case study based on a reactor–separator system widely used in the literature. Its performance is compared to those of centralized and distributed (without set-membership) implementations, allowing to highlight its effectiveness.

Credibility-based distributed frequency estimation for plug-in electric vehicles participating in load frequency control

The accurate, robust and economic acquisition of frequency signals of plug-in electric vehicles (PEVs) is a vital prerequisite to regulate the frequency of power systems with the participation of a large number of PEVs. While the communication links among PEVs are vulnerable to cyber attacks, we propose a credibility-based distributed frequency estimation scheme to detect and isolate compromised PEVs participating in the frequency regulation. In this scheme, each PEV can distinguish its neighbors’ misbehavior based on the distributed frequency estimation and/or frequency measurements taken only at distribution substations. Then, a distributed load frequency control (DLFC) strategy is designed to integrate the credibility-based resilient distributed frequency estimation scheme. Tests under a variety of communication topologies are conducted to verify the proposed credibility-based distributed frequency estimation scheme. Simulation results of a four-area power system validate the proposed DLFC strategy after detecting and isolating the compromised PEVs can regulate the frequency quickly when suffering load variations.

Approaches to Chernoff fusion with applications to distributed estimation

In large scale information fusion networks the statistical dependencies between nodes are rarely known. Failing to account for this detail in the design of distributed estimation schemes may lead to statistical inconsistencies and may even cause some estimators to diverge at various nodes within the network. Among the approaches that have been proposed to address this problem, covariance intersection and its generalization are perhaps the most well-known. Owing to its relationship with the statistical divergence known as Chernoff information the latter approach is referred to here as Chernoff fusion. Using Chernoff fusion requires tuneup for the fusion parameters, where in some applications, the Chernoff fusion may cause overhead. This work is concerned with the practical application of Chernoff fusion for distributed estimation. We provide a technique for fast particle filters fusion based on a linear variant of Chernoff fusion as well as a recursive tuning technique of the underlying mixing weights. The viability of the proposed schemes are demonstrated in such applications as distributed object tracking, cooperative robots localization, and image classification with ensembles of convolutional neural networks.

Distributed State Estimation of a Non-linear process system with interconnected subsystems

In this paper authors propose a distributed state estimation scheme for the hybrid system with interconnected subsystems to estimate the states. The system considered in this work has different subsystems which can interact with each other via their states over a communication network. The objective is to implement the distributed state estimation scheme for interconnected subsystems in which each subsystem sensors are connected to the communication network, the estimator has been used for each subsystem to estimate the current states by utilizing the states of the neighboring subsystems over the communication network. The proposed state estimation framework utilizes unscented Kalman filter algorithm. Unscented Kalman filter has been designed for each subsystem to estimate the current state estimates which corrupted by state and measurement noise. The benchmark system taken to implement distributed state estimation is continuous stirred tank reactor units which are strongly interconnected via their neighboring states. The reactors temperature is maintained at unstable operating point by a decentralized proportional integral controller for each subsystem by utilizing the measurements of the sensors from the network. The estimation framework has been verified in the absence of the network failure to stabilize the plant at unstable operating point. The estimate of the corresponding subsystems is used to compute the controller output in the absence of the network failure with minimal sharing over the network.

Exploiting classification for fountain data estimation in wireless sensor networks

SummaryIn order to correct and avoid channel error, fountain codes were the best solution by limiting feedback channels and reducing energy consumption. Multi‐hops transmission is the principal limitation of the deployment and the use of these codes. Indeed, relayed transmission conducts to the generation of useless data, named overflow leading to a waste of energy, the most critical issue, and the big challenge in WSN. In this paper, based on a clustered architecture and estimation, we consider a distributed estimation scheme composing of sensor members and the cluster head. In order to reduce the number of a useless encoded packet generated as well as the impact of the overflow, we determine the optimal minimal number of encoded packets needed for data decoding. Sensor observations are encoded using fountain codes, and then messages are collected at the cluster head where a final estimation is provided within learning method. Then messages are collected at the cluster head where a final estimation is provided with a classification based on Bayes rule. The main goal of this paper is to determine the number of encoded packets by exploiting the classification model for fountain data estimation to minimize the overflow and extend the network lifetime.