Robust State Estimation Problem Research Articles

STATE ESTIMATION FOR A CLASS OF FRACTIONAL-ORDER UNCERTAIN NONLINEAR SYSTEMS

The robust state estimation problem for a class of fractional-order uncertain non- linear systems is investigated in this paper. The class of fractional-order uncertain nonlinear systems is more general than the existing one in the literature. For the first time, a method based on a new fractional-order state observer is proposed to give robust state estimation of the fractional-order uncertain nonlinear systems. A new condition for the existence of the fractional-order observer in terms of an optimization problem is proposed. The effectiveness of the proposed method is demonstrated through two examples.

Event-triggered state and fault simultaneous estimation for nonlinear systems with time delays

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method.

Robust State Estimation for T–S Fuzzy Markov Jump Systems

The problem of robust state estimation for a class of uncertain nonlinear systems with Markov jump is investigated. The uncertain nonlinear system under consideration is represented by the Takagi–Sugeno (T–S) fuzzy model because it is difficult to describe. Firstly, different from the traditional T–S fuzzy modeling method, the deviation of the linear system approaching a nonlinear system is considered, which is represented as a model error in system modeling. Secondly, through a robust state estimation method based on the sensitivity penalty, we develop a robust state estimator for linear subsystems, and the fuzzy robust state estimator is obtained by fuzzy rules. Thirdly, the stability and boundedness of the fuzzy robust state estimator are proved under the assumption conditions to ensure the reliability of the obtained estimator. Finally, some numerical examples are given to verify the effectiveness of the fuzzy robust state estimator.

Robust Linearly Constrained Square-Root Cubature Kalman Filter for Mismatched Nonlinear Dynamic Systems

This letter addresses the robust state estimation problem for mismatched nonlinear dynamic systems. In this context, we are interested in nonlinear filters able to provide consistent estimates while mitigating the impact of possible modeling errors. We focus on the cubature Kalman filter (CKF) and its square-root form (SCKF), being the most promising nonlinear Gaussian filters, the latter providing improved numerical stability. We leverage on the recently introduced linearly constraint Kalman filter, and derive its sigma-point-based counterparts, the linearly constrained CKF (LC-CKF) and SCKF (LC-SCKF). Such formulation can be exploited, using the correct constraints, to mitigate a large number of model misspecifications. To assess the validity of this approach, we consider an illustrative vehicle navigation problem. Results are provided to support the discussion and show the good performance of the new filters with respect to the state-of-the-art, which are robust to different types of mismatches between the assumed dynamic system model and the true one.

Distributionally Robust State Estimation for Linear Systems Subject to Uncertainty and Outlier

Parameter uncertainties and measurement outliers unavoidably exist in a real linear system. Such uncertainties and outliers make the true joint state-measurement distributions (induced by the true system model) deviate from the nominal ones (induced by the nominal system model) so that the performance of the optimal state estimator designed for the nominal model becomes unsatisfactory or even unacceptable in practice. The challenges are to quantitatively describe the uncertainties in the model and the outliers in the measurements, and then robustify the estimator in a right way. This article studies a distributionally robust state estimation framework for linear systems subject to parameter uncertainties and measurement outliers. It utilizes a family of distributions near the nominal one to implicitly describe the uncertainties and outliers, and the robust state estimation in the worst case is made over the least-favorable distribution. The advantages of the presented framework include: 1) it only uses a few scalars to parameterize the method and does not require the structural information of uncertainties; 2) it generalizes several classical filters (e.g., the fading Kalman filter, risk-sensitive Kalman filter, relative-entropy Kalman filter, outlier-insensitive Kalman filters) into a unified framework. We show that the distributionally robust state estimation problem can be reformulated into a linear semi-definite program and in some special cases it can be analytically solved. Comprehensive comparisons with existing state estimation frameworks that are insensitive to parameter uncertainties and measurement outliers are also conducted.

A robust distributed secure interval observation approach for uncertain discrete-time positive systems under deception attacks

This paper deals with the network-based robust distributed state estimation problem of a class of discrete-time positive systems with bounded parameter perturbation and bounded disturbance. The system outputs are measured by multiple groups of sensors and transmitted to observers through communication networks suffering from deception attacks. To attain real-time monitoring and interval estimation of the system state and achieve a satisfactory estimation accuracy, a distributed secure interval observation approach is presented, where the interval observer is composed of an upper-bounding observer and a lower-bounding observer. The construction of each interval observer is based on the system positivity and the bounds of parameter perturbation, disturbance input and attack signals. Using the stochastic finite-time boundedness and l1-gain analysis method together with the linear programming technique, some sufficient conditions on analysis, design and optimization of the distributed interval observers for the uncertain positive system against deception attacks are established. The practicability and advantage of the proposed approach is checked by a numerical example, which comes from the remote monitoring of power distribution in smart grid.

State estimation for semi-Markovian switching CVNNs with quantization effects and linear fractional uncertainties

This paper is concerned with the robust state estimation problem for semi-Markovian switching complex-valued neural networks with quantization effects (QEs). The uncertain parameters are described by the linear fractional uncertainties (LFUs). To enhance the channel utilization and save the communication resources, the measured output is quantized before transmission by a logarithmic quantizer. The purpose of the problem under consideration is to design a full-order state estimator to estimate the complex-valued neuron states. Based on the Lyapunov stability theory, stochastic analysis method, and some improved integral inequalities, sufficient conditions are first derived to guarantee the estimation error system to be globally asymptotically stable in the mean square. Then, the desired state estimator can be directly designed after solving a set of matrix inequalities, which is robust against the LFUs and the QEs. In the end of the paper, one numerical example is provided to illustrate the feasibility and effectiveness of the proposed estimation design scheme.

Robust State Estimation for Time-Delay Linear Systems With External Inputs

Robust state estimation problem is investigated for discrete-time linear state space models with uncertain parameters, deterministic control input and d-step state delay. Firstly, the original system is transformed into a non-time-delay system based on the method of state augmentation. Then a robust state estimation algorithm is proposed based on the sensitivity penalty method and the derivation is given. Moreover, compared with the standard Kalman filter, this algorithm has similar iterative form and considerable computational complexity. Finally, numerical simulations are utilized to show the effectiveness of this algorithm.

A Partial-Node-Based Approach to State Estimation for Complex Networks With Sensor Saturations Under Random Access Protocol.

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed H∞ performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based H∞ state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

Event-triggered robust state estimation for systems with unknown exogenous inputs

An event-triggered robust state estimation problem for linear time-varying systems subject to Gaussian noises and non-stochastic unknown exogenous inputs is investigated in this work. To design the estimator, the state estimation problem is formulated as an optimization problem with a risk-sensitive cost function. This problem is solved by constructing a reference probability measure, under which the cost function has a simpler form and an information state can be developed. The obtained robust state estimator is shown to have a recursive form parameterized by a Riccati-type time-varying matrix equation. The effectiveness of the proposed event-based robust state estimator is illustrated with numerical examples.

Distributed Grid State Estimation Under Cyber Attacks Using Optimal Filter and Bayesian Approach

Smart grid is built by combination of electric and information technologies and achieves the two-way interaction between power utilization and power generation. Unfortunately, new security threats appears together with cyber-physical communication systems. In order to properly monitor power network, an effective cyber attack detection and state estimation method are required to know attack and system states. This article considers the problem of robust grid state estimation and suggests a technique for distributed state estimation in power networks. First, the distribution power system incorporating multiple synchronous generators is modeled as a state-space framework, where attack occurs in measurements. Basically, the false data injection attacks can interfere with state estimation process by tampering with sensor measurements. Using mean squared error principle, the distributed dynamic state estimation algorithm is designed where local and neighboring gains are obtained using optimal filter and graph theory. For local gain computation, the attack parameter is obtained using the Bayesian learning process. The convergence condition of the proposed approach is derived. Extensive simulation results show that the proposed approach is able to estimate the system state within a short period of time. Hopefully, the proposed methodology can be used to tolerate the cyber attacks for improving the confidence of the grid state estimation process.

Robust state estimation for fractional-order delayed BAM neural networks via LMI approach

This paper is concerned with the robust state estimation problem for a class of delayed fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with norm-bounded uncertainties. The objective of the study is to construct an efficient estimator in such a way that the behavior of the corresponding error state is stable in the Mittag-Leffler sense. Distinct to the previous studies, the state estimation problem of FOBAM NNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global Mittag-Leffler stability of the error system are derived as a set of solvable linear matrix inequalities (LMIs) without uncertainties. The proposed stability conditions are further extended to the FOBAM NNs by considering the effect of uncertainties. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.

Robust event-triggered state estimation: A risk-sensitive approach

In this work, we investigate a robust event-triggered remote state estimation problem for linear Gaussian systems with a stochastic event-triggering condition. The reference measure approach is used to obtain a robust event-triggered estimate that minimizes the so-called risk-sensitive criterion, which refers to the expectation of the exponential of the sum of the squared estimation error. We introduce the reference measure, under which, the measurements are identically independently distributed (i.i.d.) and independent of the states, and propose a map to link the “real-world” measure to the reference measure so that the recursions of the information states under the reference measure can be obtained. Based on these results, the risk-sensitive criteria are reformulated under the reference measure and closed-form expressions of the risk-sensitive event-triggered posterior and prior estimates are presented, which are shown to evolve in simple recursive Kalman-like structures. Moreover, two sufficient stability conditions for the proposed estimators are given, where the first requires the solution of a time-varying Riccati equation to be positive-definite and satisfy a specific inequality, which can be further extended to the scenario when the weighting matrix in the risk-sensitive criterion is time-variant; the second gives the range of values of the risk-sensitive parameter and covariance of the initial state for which the proposed estimators are stable. Comparative simulation results demonstrate that the proposed risk-sensitive event-triggered estimator is more robust to model uncertainties compared with a typical minimum mean squared error (MMSE) estimator with stochastic event-triggered sensor scheduling.

On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method

The robust Kalman filter design problem for two-dimensional uncertain linear discrete time-varying systems with stochastic noises is investigated in this study. First, we prove that the solution to a certain deterministic regularized least squares problem constrained by the nominal two-dimensional system model is equivalent to the generalized two-dimensional Kalman filter. Then, based on this relationship, the robust state estimation problem for two-dimensional uncertain systems with stochastic noises is interpreted as a deterministic robust regularized least squares problem subject to two-dimensional dynamic constraint. Finally, by solving the robust regularized least squares problem and using a simple approximation, a recursive robust two-dimensional Kalman filter is determined. A heat transfer process serves as an example to show the properties and efficacy of the proposed filter.

Robust interval observer for switched systems with unknown inputs: Application to vehicle dynamics estimation

This paper investigates the problem of robust state estimation and unknown input interval reconstruction for uncertain switched linear systems. Parameters uncertainty are supposed to be provided with known bounded compact set. A design method for obtaining interval observers that provide guaranteed lower and upper bounds of the state and unknown inputs is proposed. By adopting multiple quadratic ISS-Lyapunov function and average dwell time concept, new and less conservative stability conditions are derived, and a set of numerical feasible linear matrix inequalities (LMIs) are given. An application to vehicle lateral dynamics estimation is considered to show the effectiveness of the algorithms. Experimental data obtained with a prototype vehicle are used to confirm the performance of the proposed approach.

Robust Fuzzy Filter Design for Nonlinear Parabolic Partial Differential Systems with Continuous Wiener Noise and Discontinuous Poisson Noise

This paper addresses a robust \(H_{\infty }\) fuzzy filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with continuous random fluctuation, discontinuous Poisson jumping noise, random external disturbance and measurement noise in the spatiotemporal domain. For NSPDSs, the robust \(H_{\infty }\) filter design problem through a measurement output needs to solve a complex second-order Hamilton Jacobi integral inequality. In order to simplify the design procedure, a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, the robust \(H_{\infty }\) fuzzy filter design problem can be reformulated as a diffusion matrix inequality (DMI) problem. Since the DMI problem is difficult to be solved via traditional algebraic techniques, we utilize the divergence theorem and Poincare inequality to transform the DMIs to a set of linear matrix inequalities (LMIs) which could be easily solved with the help of MATLAB LMI Toolbox. Finally, a robust state estimation problem of an ecology system with intrinsic spatiotemporal continuous Wiener noise and discontinuous Poisson jump fluctuation is provided as an example to illustrate the design procedure and to confirm the \(H_{\infty }\) filtering performance of the proposed \(H_{\infty }\) fuzzy filter design method.

Robust finite-time state estimation for uncertain discrete-time Markovian jump neural networks with two delay components

Abstract This paper considers the problem of robust finite-time state estimation for a class of discrete-time neural networks with two delay components and Markovian jump parameters. A new discrete-time Lyapunov–Krasovskii functional containing two independent delay components is constructed. Some well-known inequalities are introduced to reduce the conservatism. To ensure the existence of the state estimator, sufficient conditions are derived in the form of linear matrix inequalities, which can be checked easily by the MATLAB LMI toolbox. Finally, an example is given to show the effectiveness of the designed estimator.

State estimation for stochastic discrete-time systems with multiplicative noises and unknown inputs over fading channels

This paper deals with robust state estimation problem for a class of stochastic discrete-time systems with multiplicative noises and unknown inputs over fading channels. An unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so-called P-estimation. The filter gain matrix is derived through solving a recursive Riccati equation and a generalized Lyapunov equation. A necessary and sufficient condition that guarantees the existence of the filter is given, which establishes a fundamental limit on the mean square capacity of each fading channel. Unknown input estimation and finite horizon stability of the proposed filter are also discussed. To illustrate the effectiveness of the proposed approach, the proposed algorithm is applied to a faulty remote controlled uninterruptible power system, where both the state and the fault are estimated.

An event-triggered approach to robust state estimation for wireless sensor networks

Robust state estimation problem for wireless sensor networks consisting of multiple remote units and a fusion unit is investigated subject to a limitation on the communication rate. An analytical robust fusion estimator based on an event-triggered transmission approach is derived to reduce the network traffic congestion and save the energy consumption of the sensor units. Some conditions guaranteeing the uniformly bounded estimation errors of the robust fusion estimator are investigated. Numerical simulations are provided to show the effectiveness of the proposed approach.

TDOA/FDOA based target tracking with imperfect position and velocity data of distributed moving sensors

This paper addresses the target tracking problem using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measured by moving sensor network whose position and velocity are noise contaminated. It is a known fact that the existing approaches to this problem still have two unsolved technical issues; the unsatisfactory convergence behavior of the tracking filter mainly caused by severe nonlinearity of the problem itself and the tracking performance degradation due to the sensor position and velocity errors. In order to resolve these matters radically, the given target tracking problem is formulated as the robust state estimation problem of the linear system with stochastic uncertainties in its measurement matrix and solved by using the robust Kalman filter theory. The proposed scheme enables us to overcome the inherent limitations of the conventional nonlinear filters for its linear filter structure. It can also prevent the performance degradation due to imperfect sensor position and velocity information. Through the simulations, the effectiveness and reliable target tracking performance of the proposed method are demonstrated.