A study of uncertain state estimation

2006

Physical Review E, 2014

Observability of state variables and parameters of a dynamical system from an observed time series is analyzed and quantified by means of the Jacobian matrix of the delay coordinates map. For each state variable and each parameter to be estimated a measure of uncertainty is introduced depending on the current state and parameter values, which allows us to identify regions in state and parameter space where the specific unknown quantity can (not) be estimated from a given time series. The method is demonstrated using the Ikeda map and the Hindmarsh-Rose model.

2008

The use of Kalman filtering is very common in state estimation problems. The problem with Kalman filters is that they require full prior knowledge about the system modeling. It is also assumed that all the observations are fully received. In real applications, the previous assumptions are not true all the time. It is hard to obtain the exact system model and the observations may be lost due to communication problems. In this paper, we consider the design of a robust Kalman filter for systems subject to uncertainties in the state and white noise covariances. The systems under consideration suffer from random interruptions in the measurements process. An upper bound for the estimation error covariance is proposed. The proposed upper bound is further minimized by selection of optimal filter parameters. Simulation example shows the effectiveness of the proposed filter.

Conference on Decision and Control, 2004

The aim of this paper is to investigate the problem of the joint estimation of both the state and parameters for a class of discrete-time linear systems driven by additive noise, not necessarily Gaussian. A recursive quadratic filter with respect to the observations is here proposed and implemented, by opportunely extending the state space also with the inclusion of the

2009

Abstract In this paper, we consider the robust Kalman filtering for uncertain discrete time-varying systems, to solve the problem of simultaneously state and fault estimation. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and measurement matrices. The approach suggested rests on the use of the Augmented State Robust Kalman Filter (ASRKF) based on the optimization of an upper bound on the variance error of the state estimation.

Applied Mathematics Letters, 2001

A general clsss of dwxete-time uncertam nonlinear stochastic systems corrupted by finite energy dssturbances and estimation performance crlterla are considered These performance criteria include guaranteed-cost suboptimal versions of estimation obJectives hke HZ, H,, stochsstlc passwlty, etc Smear state estimators that sat&y these crlterla are presented A common matrix mequality formulation 1s used m charactenzatlon of estimator design equations

2007 European Control Conference, 2007

This paper presents a state estimator for systems linear in an unknown parameter. The estimate is given via a weighted mean of both an under-and an over-estimate provided by an interval observer. The weighting factor is computed in real-time from the difference between the output measurements and the interval bounds. The convergence of the estimate is first shown for a class of LTI systems. The generalization to a class of nonlinear systems is then presented. Both cases are illustrated with numerical simulations.

IEEE Transactions on Automatic Control, 1971

Ahtract-This paper is concerned with the problem of estimating the state of a linear dynamic system using noise-corrupted observations, when input disturbances and observation errors are onknown except for the fact that they belong to given bounded sets. The cases of both energy constraints and individual instantaneous constraints for the uncertain quantities are considered. In the former case, the set of possible system states compatible with the observations received is shown to be an ellipsoid, and equations for its center and weighting matrix are given, while in the latter case, equations describing a boonding ellipsoid to the set of possible states are derived. All three problems of filtering, prediction, and smoothing are examined by relating them to standard tracking problems of optimal control theory. The resulting estimators are similar in strnctnre and comparable in simplicity to the corresponding stochastic linear minimum-variance estimators, and it is shown that they provide distinct advantages over existing schemes for recursive estimation with a set-membership description of uncertainty.

IFAC Proceedings Volumes, 2004

Set-membership approaches generally deal with bounded uncertainties. In this context, an observer aims at computing at each sample time a domain that is guaranteed to include the set of states which are consistent both with the uncertain model and with the uncertain measurements. Given an algorithm implementing the observation of uncertain linear systems, an extended observer can be used to deal with non-linear systems and/or to adapt some parameters. This paper focuses on such an extension. An application to a generic bioreactor illustrates the proposed approach and outlines some perspectives for future work.

arXiv (Cornell University), 2019

In the present work, an optimization-based algorithm for state estimation under model uncertainty and bounded disturbances is presented. In order to avoid to solve a non-convex optimization problem, model and state estimation problems are divided into two convex formulations which are solved within a fixed-point iteration scheme with standard available solvers. Guaranty of robust global stability are given for the case of bounded disturbances and uncertainty, and convergence to the true system and vector state are given for the case of vanishing disturbances.