State Estimation Of Stochastic Systems Research Articles

Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

Fault-tolerant state estimation for stochastic systems over sensor networks with intermittent sensor faults

In this paper, the problem of distributed fault-tolerant state estimation is studied for stochastic systems over sensor networks with intermittent sensor faults. Compared with the traditional state estimation algorithms, the distinct advantage of fault-tolerant state estimation is that the estimator can keep good performance whether sensor faults occur or not. Different from the previous literature concerning with distributed fault diagnosis, the distributed fault diagnosis problem is investigated in this paper for intermittent faults, whose appearing time, disappearing time and magnitude are all nondeterministic. The distributed fault-tolerant state estimation scheme is constructed, in which the appearing time and disappearing time of intermittent faults are detected, intermittent faults are estimated and compensated. By means of the matrix inequality technique, the H∞ performance of state estimation errors is guaranteed by properly choosing the estimator parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed algorithm.

Event-based finite horizon state estimation for stochastic systems with network-induced phenomena

This paper investigates a finite horizon state estimation problem for a class of discrete-time stochastic systems with random transmission delays and out-of-order packets of data. Employing an event-driven signal-choosing scheme of logic zero-order-holder (LZOH), a system model is established synthetically in a unified form considering the network-induced phenomena, to drop out-of-order packets and improve system performance. By virtue of the established system model, a novel minimum error covariance matrix for the augmented state-space is obtained from the estimated variance constraint. With the aid of a finite horizon, the upper boundary of estimation error covariance is introduced during the information transmission from sensor to estimator, and the appropriate filter parameters are probed. To improve the estimation performance and alleviate the computation burden, an estimation-based compensation approach for random transmission delays is proposed using the received valid signals. Finally, the effectiveness and applicability of the proposed state estimation method are illustrated by a numerical simulation.

Stability analysis of Extended, Cubature and Unscented Kalman Filters for estimating stiff continuous–discrete stochastic systems

This paper studies stiffness and stability properties of Extended Cubature and Unscented Kalman Filters applied to continuous–discrete stochastic systems with stiff dynamic behavior. The main part of these methods relies on numerical integration of Moment Differential Equations (MDEs). Our focus is to understand how the stiffness of MDEs influences performance of the filters. The proposed linear stability analysis shows that the MDEs that havearisen within these methods can enlarge the stiffness of continuous-time stochastic model and, hence, require solvers with advanced stability properties for their effective and accurate treatment. Besides, the proposed nonlinear stability analysis proves that such MDEs may become extremely unstable in simulation intervals. The latter raises the uncertainty of state estimation and results in two interesting implications: (i) the lower-order Extended Kalman Filter outperforms the higher-order Cubature and Unscented Kalman Filters in the accuracy of state estimation of stochastic systems with unstable MDE behavior; (ii) the methods under exploration fail when the stiffness is large enough. Our theoretical consideration is supported by numerical tests with filters based on the MATLAB code ode15s, which is a benchmark solver for stiff ODEs. These are examined on linear and nonlinear stiff continuous-time stochastic models.

Event‐triggered state estimator for stochastic systems with unknown inputs

This article studies the problem of state estimation for stochastic systems with unknown inputs. To reduce the communication cost from the sensor to the remote processor, an event-triggered communication mechanism is proposed in terms of an event generator function for the innovation vectors. The event-triggered estimator is developed by introducing an input term in the steady-state Kalman filter for the corresponding nominal system. The input gain matrix is determined by treating the nominal estimator error dynamics as the desired performance. It is shown that the estimation error is bounded in mean square under certain conditions. A numerical example is provided to verify the effectiveness of the proposed estimator.

Approximation of optimal filter for Ornstein–Uhlenbeck process with quantised discrete-time observation

ABSTRACTQuantisation of signals is a ubiquitous property of digital processing. In many cases, it introduces significant difficulties in state estimation and in consequence control. Popular approaches either do not address properly the problem of system disturbances or lead to biased estimates. Our intention was to find a method for state estimation for stochastic systems with quantised and discrete observation, that is free of the mentioned drawbacks. We have formulated a general form of the optimal filter derived by a solution of Fokker–Planck equation. We then propose the approximation method based on Galerkin projections. We illustrate the approach for the Ornstein–Uhlenbeck process, and derive analytic formulae for the approximated optimal filter, also extending the results for the variant with control. Operation is illustrated with numerical experiments and compared with classical discrete-continuous Kalman filter. Results of comparison are substantially in favour of our approach, with over 20 times lower mean squared error. The proposed filter is especially effective for signal amplitudes comparable to the quantisation thresholds. Additionally, it was observed that for high order of approximation, state estimate is very close to the true process value. The results open the possibilities of further analysis, especially for more complex processes.

State estimation of stochastic systems with switching measurements: A polynomial approach

AbstractThe state estimation problem is here investigated for a class of stochastic linear switching‐output systems, in which the output matrix switches in a finite set of possible values according to a not directly measured discrete Markov sequence. This note presents a real‐time algorithm, based on the optimal polynomial filtering approach, which achieves the simultaneous estimation of both the continuous system state and the switching parameter. The state and observation noises do not need to be Gaussian. It is shown that the optimal filter of degree one (best affine filter) does not solve the parameter estimation problem, due to a structural first‐order unobservability property, and therefore the use of higher‐order filters becomes necessary. As an application of the proposed filter, the problem of the online simultaneous estimation of the transmitted signal and of the impulse response samples of a multipath fast‐fading digital communication channel is considered in this paper. Differently from other approaches, the polynomial filter solves the problem without the use of training sequences (preambles) in the transmitted data, so that the information flow through the channel is not interrupted. Copyright © 2009 John Wiley & Sons, Ltd.

State Estimation for Stochastic System with Power Measurement

State Estimation for Stochastic System with Power Measurement

Effective state estimation of stochastic systems

In the present paper, for constructing the minimum risk estimators of state of stochastic systems, a new technique of invariant embedding of sample statistics in a loss function is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant estimator, which has smaller risk than any of the well‐known estimators. There exists a class of control systems where observations are not available at every time due to either physical impossibility and/or the costs involved in taking a measurement. In this paper, the problem of how to select the total number of the observations optimally when a constant cost is incurred for each observation taken is discussed. To illustrate the proposed technique, an example is given and comparison between the maximum likelihood estimator (MLE), minimum variance unbiased estimator (MVUE), minimum mean square error estimator (MMSEE), median unbiased estimator (MUE), and the best invariant estimator (BIE) is discussed.

Optimal state estimation for stochastic systems: an information theoretic approach

In this paper, we examine the problem of optimal state estimation or filtering in stochastic systems using an approach based on information theoretic measures. In this setting, the traditional minimum mean-square measure is compared with information theoretic measures, Kalman filtering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman filter is the optimal filter not only for the mean-square error measure, but for several information theoretic measures which are introduced in this work. For nonlinear systems, these same measures generally are in conflict with each other, and the feedback control policy has a dual role with regard to regulation and estimation. For linear stochastic systems with general noise processes, a lower bound on the achievable mutual information between the estimation error and the observation are derived. The properties of an optimal (probing) control law and the associated optimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system with an affine linear filter for the homogeneous system, under some reachability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian.

Stochastic Signal Detection From A Saturated Noisy Observation And Its Application To Room Acoustics

In the measurement of actual phenomena, the observed data often suffer from loss or distortion due to the limited dynamic range of the measurement instruments. This paper describes a new method of dynamical state estimation for stochastic systems, in a practical case in which the observed data fluctuates within a finite amplitude domain owing to the dynamic range of the measurement instrument. The state estimation method proposed for use with such incomplete observation data (with information loss or distortion) is a theoretically based improvement of the wide sense digital filter, for situations in which the data is contaminated by an external noise of arbitrary distribution type. A recurrence type estimation algorithm is explicitly derived in series expansion form from the Bayesian viewpoint, with the aim of utilizing hierarchically the linear and non-linear correlation information between the observed value and the unknown state variable. The proposed estimation theory is experimentally confirmed by applying it to a problem of background noise correction in room acoustics.

State estimation of stochastic system with power measurement devices

Electrical Engineering in JapanVolume 97, Issue 4 p. 115-122 Article State estimation of stochastic system with power measurement devices Mitsuo Ohta, Mitsuo Ohta Hiroshima UniversitySearch for more papers by this authorTsuyoshi Okita, Tsuyoshi Okita Hiroshima UniversitySearch for more papers by this authorShizuma Tamaguchi, Shizuma Tamaguchi Hiroshima UniversitySearch for more papers by this author Mitsuo Ohta, Mitsuo Ohta Hiroshima UniversitySearch for more papers by this authorTsuyoshi Okita, Tsuyoshi Okita Hiroshima UniversitySearch for more papers by this authorShizuma Tamaguchi, Shizuma Tamaguchi Hiroshima UniversitySearch for more papers by this author First published: 1977 https://doi.org/10.1002/eej.4390970417Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume97, Issue41977Pages 115-122 RelatedInformation