Estimation Problem For Systems Research Articles

Interval estimation of sensor fault in rotary steerable drilling tools based on set-membership approach

The rotary steerable drilling tools (RSDTs) are invented for high-precision wellpath control. Fault diagnosis is essential for the RSDT as it can improve the reliability of the drilling processes. To estimate the sensor fault of the RSDT, this paper investigates the interval estimation problem for Lipschitz nonlinear systems with sensor fault via the set-membership approach. Firstly, the RSDT is modeled by a discrete-time Lipschitz nonlinear system with unknown inputs, noises, and parameter uncertainties. Next, based on the ellipsoid bundles, a set-membership fault estimator is presented, where the unknown inputs are decoupled. Additionally, a sufficient condition, which is derived based on the P-radius of the ellipsoid bundles, is put forward to design the parameters of the estimator with Lipschitz nonlinear terms. Then, the interval estimations of the states and fault are obtained via ellipsoid bundles. Finally, the efficiency of the proposed approach is evaluated through numerical simulations and experiments.

Novel reachable set estimation results for delayed linear systems with bounded disturbance

Reachable set estimation is a prominent research topic in control theory and systems science. Reachable set estimation for time-delay systems has drawn a lot of interest. Until now, most approaches to the reachable set estimation problem of time-delay systems have involved building intricate Lyapunov functionals and utilizing LMI techniques. This has resulted in complicated LMI conditions and a proof procedure. The reachable set estimation issue for delayed linear systems with bounded disturbance will be reviewed in this paper. A novel reachable set estimation lemma with a time-delay term is proposed, and based on the acquired lemma, a sufficient condition is given to bound the reachable set estimation of the systems under discussion. In addition, an event-based sufficient criterion for reachable set estimation is also provided. The theoretical analysis in this paper is succinct when compared to previous findings, and the obtained conditions are simple to validate. Lastly, two examples are presented to confirm that the theoretical results hold true.

Identification of fractional Hammerstein systems with the conformable fractional derivative

SummaryIn this article, we study parameter estimation problems for fractional commensurate Hammerstein systems utilizing the conformable fractional derivative. Two algorithms are investigated: first, the Poisson moment functions (PMF) method, aiming to transfer the fractional derivative of the measurement signal into PMF using the fractional Laplace transform and convolution; second, a proposed new instrumental variable algorithm, which is based on the conformable fractional derivative. Both algorithms have been analyzed and shown to be consistent. A comprehensive complexity analysis is provided for each algorithm. Furthermore, a kind of special time‐varying systems are discussed under the conformable fractional derivative. Finally, an example is given to illustrate the effectiveness of the proposed algorithms.

Unscented Schmidt-Kalman filter on Lie groups with application to spacecraft attitude estimation

This paper addresses the estimation problem of nonlinear systems evolving on Lie groups with unknown parameters. More precisely, some parameters in the equations of motion or sensor measurements are unknown, such as gravitational anomalies and measurement biases, and are infeasible to estimate with available observations. The unscented Schmidt-Kalman filter (USKF) approach in Euclidean space is incorporated with exponential maps from Lie algebra to Lie groups, to develop USKF algorithms on Lie groups. Two types of USKFs are derived, respectively, from left-invariant and right-invariant state estimation errors. The two USKFs, not only account for the effect of unknown parameters but also provide estimates preserving the geometry of state manifold. They are advantageous over the extended Schmidt-Kalman filter for nonlinear systems in the sense of avoiding the computation of Jacobian and achieving higher or comparable estimation accuracy depending on the magnitude of parameters uncertainties. The proposed method is then applied to a spacecraft attitude estimation problem based on quaternion representation, where the magnitude of the gyroscope bias noise is unknown. Simulations are conducted to illustrate the effectiveness of the proposed algorithms in comparison with other methods.

A variational Bayesian based robust filter for unknown measurement bias and inaccurate noise statistics

In many practical fields, the unknown time-varying measurement biases (additive and multiplicative bias) and heavy-tailed measurement noise caused by some unpredictable anomalous behaviors may degrade the performance of conventional Kalman filter seriously. To solve the state estimation problem of systems with time-varying measurement biases and heavy-tailed measurement noise, this paper proposes a new variational Bayesian (VB) based robust filter. Firstly, the non-Gaussian measurement likelihood probability density function (ML-PDF) with multiplicative and additive measurement bias is built. Then, the conjugate prior distributions for unknown bias and noise scale parameters are selected, and the VB method is utilized to jointly infer the system state, unknown measurement biases and inaccurate measurement noise covariance matrix. Finally, a VB based robust filter is derived and its effectiveness is verified by the numerical simulations.

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

Scalable Distributed State Estimation over Binary Sensor Networks with Energy Harvester

This paper deals with distributed state estimation problem for discrete time-varying systems over binary sensor networks, where every binary sensor is equipped with an energy harvester. The input of every binary sensor considers the randomly occurring missing measurements. The differences between the real and estimated inputs of binary sensor are employed to derive useful information in order to address the insufficient information for estimation purpose. The information from neighboring nodes is transmitted only if its energy level is positive, where a random variable is introduced to formulate the energy level. By means of the available information, distributed estimator is constructed for each binary sensor and the desirable performance constraints is given for the dynamic characteristics of estimation errors within a finite time horizon. Sufficient conditions are established for the existence of desired distribution estimation quantities through local performance analysis methods. Also, the desired distributed estimator gains are calculated recursively, which means the desirable scalability. Ultimately, the viability and efficiency of the distributed scheme are exhibited through a practical illustration.

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.

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.

Optimal parameter estimation for uncertain structural systems under unknown random excitations

An optimal parameter estimation method for uncertain structural systems under unknown random excitations is proposed, which combines the Bayesian inference and stochastic dynamics using geometrically averaged likelihood and optimal response estimation. The general description of optimal parameter estimation problems for uncertain dynamic systems under only stochastic responses measured is presented. The posterior probability density conditional on measured responses is expressed by the likelihood function conditional on system parameters based on Bayes’ theorem. For finite time processes, the parameter estimation problem as the probability integral of conditional means is converted into the optimization problem expressed as maximizing the posterior probability density. A geometrically averaged likelihood function is defined and used for calculating the logarithmic posterior probability density. This estimation can avoid the numerical singularity of the likelihood function and reduce the effects of incomplete posterior probability density and inaccurate prior statistics of unknown random excitations, and then it will be more reasonable and effective. Furthermore, the differential equations for system response means and covariances are derived and solved based on stochastic dynamics theory. The means and covariances conditional on responses at the present instant are expressed by the previous statistics based on optimal response estimation. By combining two results, the analytical expressions of the averaged likelihood function and logarithmic posterior probability density are obtained which will be more reliable and accurate. The proposed optimal estimation method is verified by numerical results for a five-storey frame structure under base random excitation. The estimated results are not affected by the prior statistics errors of random excitation as a factor. For noisy observation, the Kalman filtering is incorporated in the estimation method and hence the estimation is more accurate and robust even for low signal noise ratios. The optimal estimation method has the potential for application to general uncertain systems.

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.

Fusion estimation against mixed network attacks for systems with random parameter matrices, correlated noises, and quantized measurements

This paper is concerned with the information fusion estimation problems for stochastic uncertain systems with quantized measurements and mixed network attacks including random deception attack and denial-of-service (DoS) attack. The cross-correlated random parameter matrices and addictive noises simultaneously exist in the studied system. By resorting to the optimal prediction compensation mechanism for DoS attack, an optimal centralized fusion filter in the linear minimum variance sense is proposed using an innovation analysis approach. In addition, the Kalman-like recursive distributed optimal linear fusion predictor and filter without feedback are presented based on local estimators from single-sensor subsystems. The estimation error cross-covariance matrices between two arbitrary local estimators, and those between local and prior fusion estimators are derived. They have good flexibility due to the parallel structure. However, they have lower accuracy than the centralized fusion estimators. To further improve the estimation accuracy, the distributed optimal linear fusion predictor and filter with feedback are also presented. They avoid the calculation of cross-covariance matrices. Moreover, it has been mathematically proved that they have the same estimation accuracy as the centralized fusion estimators. A simulation example demonstrates the effectiveness of the proposed algorithms.

An improved Cauchy robust correction-sage Husa extended Kalman filtering algorithm for high-precision SOC estimation of Lithium-ion batteries in new energy vehicles

The accurate estimation of battery State of Charge (SOC) is a key technology in the research of electric vehicle battery management systems. In order to solve the problem of inaccurate noise estimation in nonlinear systems, an improved Cauchy robust correction-Sage Husa extended Kalman filtering (CRC-SHEKF) algorithm is proposed for high-precision SOC estimation of lithium-ion batteries in new energy vehicles. Considering the polarization effect of the battery, the FFRLS algorithm is used for online parameter identification of the Dual Polarization model. Using robust data correction methods, the Cauchy robust function is simplified for real-time correction of the covariance matrix Q of system state noise and the covariance matrix R of the observed noise in the filtering process and combined with SHEKF for SOC estimation. The experimental results show that under different temperature conditions and complex working conditions, the proposed CRC-SHEKF algorithm has the minimum mean absolute error (MAE), root mean square error (RMSE), and maximum error (MAX). Under the condition of the Beijing bus dynamic stress test (BBDST) at 15 °C, the MAE, RMSE, and MAX of the CRC-SHEKF algorithm are 0.392 %, 0.716 %, and 0.945 %, with the computing time of only 4.839 s. The algorithm proposed in this article has high accuracy and robustness, and has practical application value, providing a reference for the application of lithium battery condition monitoring.

Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term

A novel algorithm utilizing an extended zonotopic Kalman filter based on the orthotope search expansion method is introduced to solve the state estimation problem in discrete-time linear parameter-varying systems when the dual noise of the systems is assumed to be bounded but unknown. First, to identify unknown parameters, an orthotope search expansion method is proposed with a measurement strip constraint. Subsequently, based on the parameter identification orthotopic set, an extended zonotopic Kalman filter algorithm is proposed to derive an estimation interval that wraps the true state of the system. Next, by minimizing the size of the zonotope, the optimal gain matrix for the extended zonotopic Kalman filter algorithm is determined. Finally, the proposed methods are demonstrated for their effectiveness and accuracy through the presentation of two simulation examples.

Kalman filtering based on dynamic perception of measurement noise

In this work, we focus on the online state estimation problem for linear systems in non-Gaussian measurement noise. Specifically, the measurement noise is modeled as a Gaussian mixture model (GMM). Then, Kalman innovation is used to approximate the current measurement noise, and dynamically perceive its responsiveness to each sub-model of the GMM. The responsiveness from different Gaussian scales is mapped to a new cost function, while the corresponding Kalman filter algorithm is derived. The theoretical steady-state error and computational complexity analysis of the algorithm are also given. The simulation and real experimental results agree with the theoretical predictions and demonstrate the superior performance of the proposed algorithm.

Prescribed‐time sensor fault estimation for linear systems with unknown inputs by periodic delayed observers

SummaryThis paper studies the problem of sensor fault estimation for linear systems in the presence of unknown inputs in both input and output channels. Relying on matrix equation theory, the unknown inputs are first removed from the output channel. Second, an augmented descriptor system is constructed by treating both system state and sensor fault as (pseudo)‐state variables. Third, the augmented descriptor system is transformed into a regular one, followed by the elimination of the unknown input from the state equation. Finally, a reduced‐order prescribed‐time sensor fault estimator is obtained by using periodic delayed observers. This matrix equation based approach is then complemented by an alternative one, which relies on successive transformations of state, input and outputs. This approach sheds light on the adopted solvability conditions throughout the paper and on the role of different directions in the output space in handling unknown inputs, sensor faults and the core state estimation problem. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed methodologies.

Moving horizon estimation based on distributionally robust optimisation

This paper presents a novel moving horizon estimation approach based on distributionally robust optimisation to tackle the state estimation problem of non-linear systems with missing noise distribution information. The proposed method adopts a fuzzy set to mitigate the impact of uncertainties on state estimation. Specifically, the method derives an empirical distribution within the prediction window using a priori data and constructs a fuzzy sphere set using the Wasserstein metric with the empirical distribution as the sphere centre. This enables the estimation of the state sequence under the worst probability distribution of the fuzzy set. To demonstrate the effectiveness of the proposed method, a simple simulation example is conducted to compare its performance with that of traditional moving horizon estimation. The results provide evidence of the feasibility and superiority of the proposed approach.

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

SummaryThis paper proposes a set‐membership state estimation method for Switched Linear Parameter Varying (SLPV) systems subject to unknown but bounded parametric uncertainties, disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed at every time iteration. The size of this zonotope is designed to be convergent and bounded by satisfying ‐radius‐based and Average Dwell Time (ADT) conditions that are formulated in the Linear Matrix Inequality (LMI) framework. An extension of the state estimation method is presented to address the fault/disturbance estimation problem for SLPV systems. By using the state augmentation technique, the fault/disturbance estimation problem is transformed into a state estimation problem of the generated augmented descriptor switched LPV system. An application to vehicle lateral dynamics fault estimation is used for assessment purposes. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods.

Variable step‐size estimation over UDP‐based wireless networks with application to a hydrogen‐powered UAV

AbstractIn this paper, the problem of state estimation for systems over wireless networks using user datagram protocol is focused on. It is known that for such a system, the probability density function of the system state follows a Gaussian mixture model (GMM), and the number of components in this model grows exponentially over time, which makes the computation of optimal estimates infeasible. To compute optimal estimates, based on Kullback‐Leibler divergence, a strategy with variable step‐sizes to truncate and fuse the GMM is proposed. Based on the obtained GMM, a variable step‐size estimator is designed to compute optimal estimates during an estimation cycle. The advantages of the proposed estimator are twofold: (1) its estimation performance is superior to that of existing one‐step fast estimators; (2) its estimation efficiency is much higher than that of the optimal estimator. Finally, trajectory tracking has been proposed for a real‐world hydrogen‐powered unmanned aerial vehicle to show the effectiveness of our methods.

Distributed order estimation for continuous-time stochastic systems

In this paper, we investigate the distributed estimation problem of continuous-time stochastic dynamic systems over sensor networks when both the system order and parameters are unknown. We propose a local information criterion (LIC) based on the L0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_0$$\\end{document} penalty term. By minimizing LIC at the diffusion time instant and utilizing the continuous-time diffusion least squares algorithm, we obtain a distributed estimation algorithm to simultaneously estimate the unknown order and the parameters of the system. By dealing with the effect of the system noises and the coupling relationship between estimation of system orders and parameters, we establish the almost sure convergence results of the proposed distributed estimation algorithm. Furthermore, we give a simulation example to verify the effectiveness of the distributed algorithm in estimating the system order and parameters.