Local State Estimates Research Articles

Optimal scheduling of multiple sensors over shared channels with packet transmission constraint

Abstract In this work, we consider the optimal sensory data scheduling of multiple process. A remote estimator is deployed to monitor S independent linear time-invariant processes. Each process is measured by a sensor, which is capable of computing a local estimate and sending its local state estimate wrapped up in packets to the remote estimator. The lengths of the packets are different due to different dynamics of each process. Consequently, it takes different time durations for the sensors to send the local estimates. In addition, only a portion of all the sensors are allowed to transmit at each time due to bandwidth limitation. We are interested in minimizing the sum of the average estimation error covariance of each process at the remote estimator under such packet transmission and bandwidth constraints. We formulate the problem as an average cost Markov decision process (MDP) over an infinite horizon. We first study the special case when S = 1 and find that the optimal scheduling policy always aims to complete transmitting the current estimate. We also derive a sufficient condition for boundedness of the average remote estimation error. We then study the case for general S . We establish the existence of a deterministic and stationary policy for the optimal scheduling problem. We find that the optimal policy has a consistent property among the sensors and a switching type structure. A stochastic algorithm is designed to utilize the structure of the policy to reduce computation complexity. Numerical examples are provided to illustrate the theoretical results.

Optimal distributed Kalman filtering fusion for multirate multisensor dynamic systems with correlated noise and unreliable measurements

An optimal distributed fusion estimation problem is concerned in this study for a kind of linear dynamic multirate sensors systems with correlated noise and stochastic unreliable measurements. The system is formulated at the finest scale with multiple sensors at different scales observing a common target independently with different sampling rates. The noise between different sensors is relevant, moreover, is also correlated with the system noise. The authors derive the local state estimation algorithms under the circumstance of total reliable measurements and stochastic unreliable measurements occur occasions, and the optimal distributed Kalman filter fusion algorithm, respectively. The authors provide a simulation example to illustrate the effectiveness and feasibility of the proposed algorithm.

Gas turbine performance monitoring based on extended information fusion filter

Performance monitoring is a critical issue for gas turbine engine for improving the operation safety and reducing the maintenance cost. With regard to this, variants of Kalman-filters-based state estimation have been employed to detect gas turbine performance, but the classical centralized Kalman filters are subject to heavy computational effort and poor fault tolerance. A novel nonlinear fusion filter algorithm using information description with distributed architecture is proposed and applied to gas turbine performance monitoring. This methodology is developed from federated Kalman filter, and a bank of local extended information filters and one information mixer are combined with extended information fusion filter. The local state estimates and covariance calculated in parallel by the local extended information filters are integrated in the information mixer to yield a global state estimate. The global state estimate of nonlinear system is fed back to the local filters with weighted factor for next iteration. The aim of the proposed methodology is to reduce the computational efforts of state estimation and improve robustness to sensor faults in cases of gas turbine performance monitoring. The simulation results on a turbofan engine confirm the extended information fusion filter's effective capabilities in comparison to the general central ones.

Transmission scheduling for remote state estimation and control with an energy harvesting sensor

This paper studies a remote state estimation problem where a sensor, equipped with energy harvesting capabilities, observes a dynamical process and transmits local state estimates over a packet dropping channel to a remote estimator. The objective is to decide, at every discrete time instant, whether the sensor should transmit or not, in order to minimize the expected estimation error covariance at the remote estimator over a finite horizon, subject to constraints on the sensor’s battery energy governed by an energy harvesting process. We establish structural results on the optimal scheduling which show that, for a given battery energy level and a given harvested energy, the optimal policy is a threshold policy on the error covariance. Similarly, for a given error covariance and a given harvested energy, the optimal policy is a threshold policy on the current battery level. An extension to the problem of transmission scheduling and control with an energy harvesting sensor is also considered.

Robust Distributed Fault Estimation for a Network of Dynamical Systems

In this paper, the robust distributed fault estimation problem is considered for a network of dynamical systems with external disturbances. Based on local output measurements and state estimates from neighbors, a distributed intermediate estimator is constructed for each node. By spectral decomposition of the Laplacian and proper scalings of the faults and the disturbances, a specially structured global error system can be created. It is proved that the states of the global error system are uniformly ultimately bounded with an explicit error bound. Compared with the existing results, the proposed fault estimation strategy has no requirements of the observer-matching condition and the preliminary knowledge of the upper bounds of the faults; moreover, the robustness of the global error system can be ensured by directly adjusting the design parameters of the intermediate estimators, without introducing any performance specifications. Simulation examples verify the effectiveness of the proposed method.

Multi-Sensor Optimal Data Fusion Based on the Adaptive Fading Unscented Kalman Filter.

This paper presents a new optimal data fusion methodology based on the adaptive fading unscented Kalman filter for multi-sensor nonlinear stochastic systems. This methodology has a two-level fusion structure: at the bottom level, an adaptive fading unscented Kalman filter based on the Mahalanobis distance is developed and serves as local filters to improve the adaptability and robustness of local state estimations against process-modeling error; at the top level, an unscented transformation-based multi-sensor optimal data fusion for the case of N local filters is established according to the principle of linear minimum variance to calculate globally optimal state estimation by fusion of local estimations. The proposed methodology effectively refrains from the influence of process-modeling error on the fusion solution, leading to improved adaptability and robustness of data fusion for multi-sensor nonlinear stochastic systems. It also achieves globally optimal fusion results based on the principle of linear minimum variance. Simulation and experimental results demonstrate the efficacy of the proposed methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integrated navigation.

Multi-sensor Optimal Data Fusion for INS/GNSS/CNS Integration Based on Unscented Kalman Filter

This paper presents an unscented Kalman filter (UKF) based multi-sensor optimal data fusion methodology for INS/GNSS/CNS (inertial navigation system/global navigation satellite system/celestial navigation system) integration based on nonlinear system model. This methodology is of two-level structure: at the bottom level, the UKF is served as local filters to integrate GNSS and CNS with INS respectively for generating the local optimal state estimates; and at the top level, a novel optimal data fusion approach is derived based on the principle of linear minimum variance for the fusion of local state estimates to obtain the global optimal state estimation. The proposed methodology refrains from the use of covariance upper bound to eliminate the correlation between local states. Its efficacy is verified through simulations, practical experiments and comparison analysis with the existing methods for INS/GNSS/CNS integration.

A Hybrid Kalman Filtering Approach Based on Federated Framework for Gas Turbine Engine Health Monitoring

The Kalman filter (KF) is the most common state estimation method for gas turbine health monitoring, and it runs in the centralized architecture. However, health estimation cannot be achieved by the KF-based method as sensor fault occurs, and malfunction of the central monitoring unit will unavoidably result to the termination of the diagnosis task. For these purposes, this paper develops a novel hybrid federated KF approach from the previous achievements. The hybrid KF consists of a bank of local filters and one master filter, and the federated filtering structure and asynchronous fusion mechanism are designed. Both the linearized KF and extended KF are employed as the local filters based on the linear correlation of thermodynamic parameters. The local state estimates and covariance are yielded in parallel, and then integrated in a master filter to produce global state estimate. The proposed methodology is evaluated and compared with the general federated KFs in terms of estimation accuracy, computational efforts, and robustness to sensor fault in the application of gas turbine health monitoring. The result shows that the hybrid KF is the best balance off the involved performance, and confirms our viewpoints in this paper.

Distributed Fault-Tolerant Control of High-Order Input-Output Multi-Agent Systems

In this paper, a distributed adaptive fault-tolerant control (FTC) scheme for a class of nonlinear uncertain input-output multi-agent systems is developed. A decentralized local nonlinear observer is employed for estimating the state variables of each agent, and a distributed local FTC component is designed for each agent in the distributed system by utilizing local output measurements and state estimation information exchanged between neighboring agents. The time-varying leader’s command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges measurement information only with its neighbors through a bidirectional but asymmetric topology. Under certain assumptions, the closed-loop stability and leader-follower consensus properties of the distributed system are rigorously established.

Transmission Scheduling for Remote State Estimation Over Packet Dropping Links in the Presence of an Eavesdropper

This paper studies transmission scheduling for remote state estimation in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, while an eavesdropper can successfully overhear each sensor transmission with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behavior in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded, for all eavesdropping probabilities strictly less than one.

DoS Attacks on Remote State Estimation With Asymmetric Information

In this paper, we consider remote state estimation in an adversarial environment. A sensor forwards local state estimates to a remote estimator over a vulnerable network, which may be congested by an intelligent denial-of-service attacker. It is assumed that the acknowledgment information from the remote estimator to the sensor is hidden from the attacker, which, thus, leads to asymmetric information between the sensor and attacker. Considering the infinite-time goals of the two agents and their asymmetric information structure, we model the conflicting nature between the sensor and the attacker by a stochastic Bayesian game. Solutions for this game under two different structures of public information history are investigated, that is, the open-loop structure (in which players cannot observe their opponents’ play) and the closed-loop one (in which players can observe the play causally). For the open-loop history case, the original game problem is transformed into a static Bayesian game. We provide the unique mixed-strategy equilibrium explicitly for this game, and analyze the sensor's advantages brought by the extra information. When it comes to the closed-loop case, the dynamic nature of history structure introduces additional difficulties solving the original problem. Thus, to derive stationary optimal power schemes for each agent, we convert the original game into a continuous-state stochastic game and discuss the existence of optimal transmission/jamming power strategies. Furthermore, an algorithm based on multiagent reinforcement learning is proposed to find such strategies, and numerical examples are provided to illustrate the developed results.

Triggered Communication in Distributed Adaptive High-Gain EKF

This paper deals with the design of a distributed adaptive high-gain extended Kalman filtering (AHGEKF) approach based on triggering communication for nonlinear systems being composed of several interconnected subsystems. For each subsystem, a local AHGEKF is designed, which receives local measurements, communicates with other filters, and computes local state estimates. In order to reduce the information transmission frequency among the distributed estimators, a communication trigger is designed for each filter. Each filter transmits its current state estimate when its corresponding triggering criterion is satisfied. Sufficient conditions are provided under which the convergence and ultimate boundedness of the estimation error is guaranteed. A simulated chemical process is used to demonstrate the applicability and performance of the proposed approach.

Distributed networked set-membership filtering with ellipsoidal state estimations

This paper addresses the problem of distributed networked set-membership filtering with ellipsoidal state estimations for a class of discrete time-varying systems in the presence of unknown-but-bounded process and measurement noises. Both global and local ellipsoidal state estimations are provided to locate the true state (target) via a distributed filtering network. A new geometric method based on Minkowski sum is proposed to produce the global ellipsoidal estimation. A novel convex optimization approach is developed to derive some sufficient conditions on the existence of local networked set-membership filters and to obtain the local ellipsoidal estimations by exchanging information among neighboring filters via communication networks. An experiment is conducted based on a 2-kW single-phase grid-connected power generation system platform to demonstrate the feasibility and the effectiveness of the proposed method in the real application.

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 $L^\infty$-type: uncertain initial condition and model error are assumed to be pointvise bounded in space and time, and the observation noise has uncertain but bounded second moments. The algorithm approximates this $L^\infty$-type bounding set by a union of possibly overlapping ellipsoids, which are localized (in space) on a number of sub-domains. On each sub-domain the state of the original system is estimated by the standard $L^2$-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 Schwartz method to reconstruct the state of the original system. The efficacy of the proposed method is demonstrated with a set of numerical examples.

Secure Dynamic State Estimation by Decomposing Kalman Filter

We consider the problem of estimating the state of a linear time-invariant Gaussian system in the presence of sparse integrity attacks. The attacker can control p out of m sensors and arbitrarily change the measurements. Under mild assumptions, we can decompose the optimal Kalman estimate as a weighted sum of local state estimates, each of which is derived using only the measurements from a single sensor. Furthermore, we propose a convex optimization based approach, instead of the weighted sum approach, to combine the local estimate into a more secure state estimate. It is shown that our proposed estimator coincides with the Kalman estimator with certain probability when all sensors are benign, and we provide a sufficient condition under which the estimator is stable against the (p, m)-sparse attack when p sensors are compromised. A numerical example is provided to illustrate the performance of the proposed state estimation scheme.

On Remote State Estimation in the Presence of an Eavesdropper

This paper studies a remote state estimation problem in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, which at the same time can be overheard by an eavesdropper with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behaviour in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded.

Optimal Scheduling of Multiple Sensors with Packet Length Constraint

This paper considers the problem of sensory data scheduling of multiple processes. There are n independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit in each time step. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.

A Randomized Variance-based Sensor Scheduling for Remote State Estimation

In this paper, the problem of sensor transmission power schedule for remote state estimation is studied. A sensor sends its local state estimate to a remote estimator through an unreliable wireless channel where packet dropouts may occur. A transmission module at the sensor side needs to decide the transmission power levels that correspond to different packet arrival rates. By extracting the information of the acknowledgement (ACK) sequence from the remote estimator, we propose a randomized variance-based sensor transmission power schedule. A closed-form expression for its asymptotic estimation performance is obtained based on the Markov chain theory. Numerical examples are presented to illustrate the implementation and performance of the proposed method.

Distributed State Estimation of Smart Grids with Packet Losses

AbstractThis paper explores the problem of distributed state estimation including packet losses for the environment‐friendly renewable microgrid incorporating electricity generating circuits. The problem is becoming critical due to the global warming, increasing green house gas emissions, and practical infeasibility with computational burden of the large‐scale centralized power system monitoring. To address the impending problem, a novel distributed state estimation algorithm is derived in the context of smart grids. Specifically, after modelling the microgrid, this paper proposes a local state estimation algorithm considering packet losses. Then a novel optimal weighting factor calculation method for the global state estimation is proposed. Particularly, it can automatically adjust the optimal weighting factors for different sensor measurements based on the observation. Simulations results show that the desired state estimation accuracy is achieved.

State estimation in a decentralized discrete time LQG control for a multisensor system

Abstract In the paper a state filtration in a decentralized discrete time Linear Quadratic Gaussian problem formulated for a multisensor system is considered. Local optimal control laws depend on global state estimates and are calculated by each node. In a classical centralized information pattern the global state estimators use measurements data from all nodes. In a decentralized system the global state estimates are computed at each node using local state estimates based on local measurements and values of previous controls, from other nodes. In the paper, contrary to this, the controls are not transmitted between nodes. It leads to nonconventional filtration because the controls from other nodes are treated as random variables for each node. The cost for the additional reduced transmission is an increased filter computation at each node.