State Estimation Problem Research Articles

Innovation Sharing Distributed Kalman Filter with Packet Loss

This study investigates the problem of distributed state estimation. A distributed Kalman filter algorithm is proposed, in which sensors exchange their innovations. A detailed analysis is conducted for the case of two sensor networks, demonstrating that the proposed algorithm outperforms the case where each sensor runs a conventional Kalman filter without communication. The upper bounds of error covariance matrices are also derived in the case of packet loss. Numerical examples verify the effectiveness of the proposed algorithm.

Adaptive observer design for coupled ODE–hyperbolic PDE systems with application to traffic flow estimation

This paper studies the state estimation problem for a class of coupled linear ODE–hyperbolic PDE systems with unknown in-domain parameters. Based on the swapping transformation and the least squares parameter estimation method, a Luenberger-type adaptive boundary observer is designed to estimate the ODE–PDE states under the unknown parameters. The exponential convergence conditions w.r.t. the observer feedback gains are given by employing the Lyapunov technique. Finally, an application to traffic state estimation of the Aw–Rascle–Zhang (ARZ) model involving the unknown relaxation time and the boundary input speed deviation is provided to validate the theoretical result.

Recursive state estimation for two-dimensional systems over decode-and-forward relay channels: A local minimum-variance approach

The paper is concerned with the recursive state estimation problem for a class of two-dimensional systems over decode-and-forward relay channels subject to packet dropouts. Taking into account the sensor's limited transmission ability, a decode-and-forward relay is deployed between the sensor and the remote estimator to enlarge the propagation distance and improve the communication quality. The packet dropout phenomenon is described by two sequences of mutually uncorrelated random variables that obey Bernoulli distributions. The main objective of this paper is to design a recursive state estimator for the underlying system with guaranteed estimation performance. An upper bound on the estimation error variance is firstly derived by resorting to some coupled difference equations, and then such an upper bound is locally optimized at each iteration through proper design of the estimator gain. Furthermore, the impacts of the packet dropouts and the decode-and-forward relay on the estimation performance are evaluated with rigorously theoretical analysis. Finally, an illustrative example is presented to validate the effectiveness of the proposed estimation scheme.

ℓ1${\ell }_1$ norm‐based recursive estimation for non‐linear systems with non‐Gaussian noises

AbstractThis study addresses the state estimation problem of discrete‐time non‐linear stochastic systems with non‐Gaussian noises, particularly impulsive noises. Instead of minimizing the mean square error of the state estimate, which tends to excessively focus on outliers caused by non‐Gaussian noises, the norm‐based non‐linear recursive filter (L1KF) is put forward in this paper. Here, minimizing the norm of model errors is actually to pursue the minimum sum of absolute values of all errors, which is equitable to all model errors rather than paying much attention on outliers. To further improve estimation accuracy, a recursive nonlinear smoother (L1KS) is proposed, based on minimizing the norm of model errors. The proposed norm‐based filter and smoother are implemented using unscented transformation for statistical linear regression applied to nonlinear models. Additionally, the computational complexity of the proposed method is analysed. Simulation results of tracking a radar target with impulsive noises demonstrate the effectiveness and robustness of the proposed estimator.

Maximum correntropy unscented filter based on unbiased minimum-variance estimation for a class of nonlinear systems

Introduction: The unscented Kalman filter based on unbiased minimum-variance (UKF-UMV) estimation is usually used to handle the state estimation problem of nonlinear systems with an unknown input. When the nonlinear system is disturbed by non-Gaussian noise, the performance of UKF-UMV will seriously deteriorate.Methods: A maximum correntropy unscented filter based on the unbiased minimum variance (MCUF-UMV) estimation method is proposed on the basis of the UKF-UMV without the need for estimation of an unknown input and uses the maximum correntropy criterion (MCC) and fixed-point iterative algorithm for state estimation.Results: When the measurement noise of the nonlinear system is non-Gaussian noise, the algorithm performs well.Discussion: Our proposed algorithm also does not require estimation of an unknown input, and there is no prior knowledge available about the unknown input or any prior assumptions. The unknown input can be any signal. Finally, a simulation example is used to demonstrate the effectiveness and reliability of the algorithm.

State estimation and structure identification of complex networks with time‐varying delays and model uncertainty based on probabilistic graph neural network

SummaryIn this paper, the state estimation problem and structure identification problem are investigated for an array of complex networks with time‐varying delays and model uncertainty. Model uncertainty is generated by uncertain connections between nodes in complex networks. Combining probabilistic graph model and graph neural network, a probabilistic graph neural network is proposed to deal with the uncertainty, and the multiple linear terms of the errors between nodes are estimated. The purpose of the addressed state estimation problem is to design a state estimator such that, in the presence of the model uncertainty, the estimation error to converge to zero can be guaranteed and the explicit expression of the estimator parameters is given. Based on a Lyapunov function, the parameters of the estimator and the updating laws of the weights of probabilistic graph neural network can be obtained by the solutions to linear matrix inequalities. The purpose of the addressed structure identification problem is to infer a definite graph structure model based on Bayes' theorem in the presence of a stable probabilistic graph neural network and state estimator. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation and structure identification scheme.

Three‐phase state estimation in transmission networks with unbalanced loading utilising SCADA measurements

AbstractState estimation stands as one of the most crucial applications in energy management systems of control centres, ensuring the secure operation of the power system. The real‐time availability of accurate system variables, including voltages, currents, and power flows, presents an excellent opportunity to consider the actual network characteristics, including imbalances. This paper presents a linear and non‐iterative method to solve the three‐phase state estimation problem in transmission systems with unbalanced loading. The method utilises supervisory control and data acquisition measurements obtained from remote terminal units. The formulation is based on complex variables derived from traditional supervisory control and data acquisition measurements, with assumptions made regarding the availability of certain three‐phase bus voltages, as well as a number of three‐phase currents and active and reactive power flows. The proposed algorithm employs the classical weighted least squares technique for solving the three‐phase state estimation problem. Due to its straightforward and linear nature, the method ensures no convergence issues. To validate its effectiveness, the proposed method is validated on a three‐bus network and the IEEE 39‐bus network simulated using the three‐phase model within the DIgSILENT Power Factory environment.

Secure state estimation of networked switched systems under denial-of-service attacks

This paper studies the problem of secure state estimation of networked switched systems in the presence of denial-of-service (DoS) attacks, as well as disturbances and measurement noise. Firstly, a state transformation rule is designed to partition the original system into two subsystems, facilitating the design of discrete and continuous state observers. Secondly, by modifying the traditional super-twisting sliding-mode method and taking into account the frequency and duration characteristics of DoS attacks, we employ dynamic differential properties between different modes to design a switching law identification strategy. We show that this strategy can accurately estimate the switching state without imposing any requirement on the switching times and sequences. Thirdly, based on the identified activated mode, a set of mode-dependent continuous state sliding-mode observers is designed, that achieves continuous state estimation in finite time. The practicality and applicability of the developed results are validated through numerical simulations.

Optimal Estimation of a Signal Generated Using a Dynamical System Modeled with McKean-Vlasov Stochastic Differential Equations.

We consider, in this paper, the problem of state estimation for a class of dynamical systems governed via continuous-time McKean-Vlasov stochastic differential equations. The estimation problem is stated and solved under an H2 norm setting. We adopt a Riccati-based approach in order to solve the optimal estimation problem.

Variational robust filter for a class of stochastic systems with false and missing measurements

This paper investigates the state estimation problem for a class of stochastic system under randomly occurring measurement anomalies, and the Kalman filter is combined with variational Bayesian (VB) method to cope with the simultaneous occurrence of false and missing measurements. First, to unify the false and missing measurements into a modified measurement model, a categorical distributed vector is employed to establish a new measurement model including randomly occurring measurement anomalies. Next, the conjugate prior distributions for the unknown measurement anomaly parameters are determined, in which the probabilities of the measurement anomalies are modeled as Dirichlet distribution and the false measurement is described by Gaussian-inverse-Wishart distribution. Then, based on the constructed measurement model and VB inference, a variational robust KF is designed to simultaneously estimate the state and measurement anomaly parameters. Finally, the estimation performance of the proposed filter is illustrated through a simulation example.

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we parameterize the dynamical system state path using a linear basis. Then, we construct a physics-informed prior probability measure for the coefficients of the linear basis such that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Outlier‐resistant state estimation for complex networks with random false data injection attacks under encoding–decoding mechanism

SummaryThis article focuses on the outlier‐resistant state estimation problem for discrete time‐varying complex networks (TVCNs) affected by random false data injection attacks (FDIAs) under an encoding–decoding mechanism (EDM). From the perspective of information security, a uniform‐quantization‐based EDM is employed to encrypt the transmitted data. During the data transmission process, a set of independent random variables governed by Bernoulli distribution is introduced to characterize the occurrence of random FDIAs. For the purpose of alleviating the passive impact of potential measurement outliers, a saturation structure is adopted during the estimator design. The gain matrix is given by minimizing the upper bound of estimation error covariance. According to the stochastic analysis method, it is shown that the state estimation error is bounded exponentially in mean‐square sense by providing new sufficient condition. It should be noted that we make the first attempt to develop new outlier‐resistant state estimation method with performance evolution criterion in the time‐varying perspective for TVCNs with random FDIAs under EDM. Finally, a simulation example with comparative experiment is presented to illustrate the effectiveness of the newly presented outlier‐resistant estimation algorithm.

Contingency detection in modern power systems: A stochastic hybrid system method

This paper introduces a new stochastic hybrid system (SHS) framework for contingency detection in modern power systems (MPS). The framework uses stochastic hybrid system representations in state space models to expand and facilitate capability of contingency detection. In typical microgrids (MGs), buses may contain various synchronous generators, renewable generators, controllable loads, battery systems, regular loads, etc. For development of SHS models in power systems, this paper introduces the concept of dynamic and non-dynamic buses. By converting a physical power grid into a virtual linearized state space model and representing contingencies as random switching of system structures and parameters, this paper formulates the contingency detection problem as a joint estimation problem of discrete events and continuous states in stochastic hybrid systems. This method offers unique advantages, including using common measurement signals on voltage and current synchrophasors to detect different types and locations of contingencies, avoiding expensive local direct fault measurements and detecting certain contingencies that cannot be directly measured. The method employs a small and suitably-designed probing signal to sustain the ability of persistent contingency detection. Joint estimation algorithms are presented with their proven convergence and reliability properties. Examples that use an IEEE 5-Bus system demonstrate the main ideas and derivation steps. Simulation case studies on an IEEE 33-Bus system are used for detecting transmission line faults and sensor interruptions.

Probability‐guaranteed encoding–decoding‐based state estimation for delayed memristive neutral networks with event‐triggered mechanism

SummaryThis article handles the probability‐guaranteed state estimation problem for a class of nonlinear memristive neural networks (MNNs) by using an event‐triggered mechanism. Both time‐varying delays and incomplete measurements are considered in the MNNs dynamics. To mitigate the impact of limited communication bandwidth, a communication protocol is proposed that incorporates an encoding–decoding technique in addition to an event‐triggered scheme. The aim is to devise a state estimator that can estimate the states of MNNs, ensuring that the state estimation error falls within the required ellipsoidal area with a desired chance. We obtain sufficient conditions for the feasibility of the addressed problem, where the requested gains can be found iteratively by solving certain convex optimization problems. On the basis of the proposed framework, some issues are further presented to determine locally optimal estimator parameters according to different specifications. Finally, we utilize an illustrative numerical example to show the validity of our provided theoretical results.

Set-valued state estimators for a class of uncertain discrete-time nonlinear systems

Set-membership state estimation problem for a certain class of discrete-time nonlinear systems is tackled in this work. First, this problem is formulated as a reachability analysis problem. Then, to avoid the wrapping effect, explicit expression of the general solution of this class of systems is used to design new set-valued state estimation schemes. Moreover, for practical considerations, two periodically re-initialized algorithms based on both interval analysis and zonotope computation are introduced. The merit of the proposed approach is illustrated on a numerical example and its performance is compared to that of other methods borrowed from the literature.

Finite-time cooperative tracking for high-maneuvering aerial target with sensor network

The finite-time distributed state estimation (DSE) problems based on sensor network for discrete-time nonlinear systems are considered in this paper. Considering the uncertainty of the target maneuvers, the interactive multiple models (IMM) based distributed estimation framework is established by local filter and consensus fusion. In the proposed distributed algorithm, partial of the output of the system can be collected by some sensors and the sensor network is supposed to be collectively observable. According to the consensus protocol, the final estimate results are obtained by fusing local estimate results of each sensor after the consensus fusion stage. The distributed estimate results can be obtained with finite-time when the consensus fusion step is larger than the diameter of the network, and the convergence rate of estimate error of the proposed distributed estimate algorithm can be guaranteed. Besides, the existence of the lower and upper bounds of the error covariance matrix are proved with some necessary assumptions. Finally, numerical simulation example is given for tracking the target with different maneuvers.

State Estimation for Recurrent Neural Networks With Intermittent Transmission.

This work addresses the state estimation problem for recurrent neural networks over capacity-constrained communication channels. The intermittent transmission protocol is used to reduce the communication load, where a stochastic variable with a given distribution is used to describe the transmission interval. A corresponding transmission interval-dependent estimator is designed, and an estimation error system based on it is also derived, whose mean-square stability is proved by constructing an interval-dependent function. By analyzing the performance in each transmission interval, sufficient conditions of the mean-square stability and the strict (Q,S,R) - γ -dissipativity are established for the estimation error system. Finally, the correctness and the superiority of the developed result are illustrated by a numerical example.

Stealthy attacks against distributed state estimation of stochastic multi-agent systems under composite attack detection mechanisms

This paper is concerned with the security problem of distributed state estimation for stochastic multi-agent systems (MASs) under directed topology. First, in the absence of attacks, an optimal distributed filter is proposed to reconstruct the states of MASs by minimizing the mean square error, which makes full use of the measurable local output information and relative state estimates of agents. Moreover, instead of using a single detection mechanism to measure the stealthiness of attacks, based on the structure of the derived filter, a composite attack detection mechanism capable of simultaneously detecting anomalies in the sensor channels of the agents themselves and the network topologies between different agents is utilized in this paper. Then, from the perspective of potential adversaries, two stealthy attack strategies are established through a joint design of sensor and topology attacks, enabling attackers to fulfill diverse attack objectives while evading the given composite detection mechanisms. Finally, simulation results are provided to verify the availability of the designed filter and attack generation schemes.

Distributed consensus filtering in sensor networks considering correlated estimation errors

This paper focuses on the distributed state estimation (DSE) problem in sensor networks through the application of a consensus-based methodology. In practical scenarios, the estimation errors within the sensor network exhibit inherent correlation, primarily arising from the consideration of same prior estimate and process noise in a distributed estimation system. However, prevailing distributed approaches, particularly those embedded within consensus-based DSE frameworks, simply assume independence among estimation errors or utilize a suboptimal strategy that neglect cross-covariance matrix, which may lead to a degraded estimation results. To address this limitation, we propose the fusion algorithm Weighted Average Consensus considering Correlated Estimates Errors, abbreviated as WACCEE. The algorithm improves DSE performance by integrating the correlation among local estimation errors as indicated by the cross-covariance matrix into the fusion process. Furthermore, we prove that the proposed WACCEE fusion algorithm exhibits consensus. Additionally, the stability of the WACCEE filters is guaranteed through an analysis of mean-square exponential boundedness of the estimation error using stochastic stability theory. Finally, the effectiveness of the proposed algorithm substantiated by its application to a target tracking case study and a connected undirected sensor network.

Finite‐horizon estimation for 2‐D systems with time‐correlated multiplicative noises: A recursive iterative coupled estimator design

AbstractThis paper addresses the state estimation problem for a class of two‐dimensional shift‐varying systems with time‐correlated multiplicative measurement noises and additive noises. The time‐correlated multiplicative noises can be described as a linear system model corrupted by white noise. The main objective of this paper is to propose a recursive iterative coupled new‐type estimators and design the estimated gain reasonably to guarantee the minimum error covariance at each step. First, two new‐type coupling estimators are designed by introducing a new term. The unbiasedness of the two estimators are guaranteed by resorting to the mathematical inductive approach. Subsequently, an effective estimation is proposed given initial conditions. Moreover, the boundedness performance is investigated of the error covariance, and an upper bound is given based on the spectral norm. Finally, two numerical example are presented as an example to show the effectiveness of the estimation algorithm.