Linear recursive state estimators under uncertain observations

Hadidi, Mohamed T.; Schwartz, S.C.

doi:10.1109/tac.1979.1102171

Cited by 177 publications

(100 citation statements)

References 7 publications

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“…In close relation to estimation in lossy sensor networks, there also has been a long history of research on filtering with missing signals at certain points of time, i.e., the output does not necessarily contain the signal in question and it may be only a noise component. Such models were referred to as systems with uncertain observations [15], [10], [7], [18], where a typical method for stability analysis is to construct a deterministic recursion utilizing the statistics of the uncertainty sequence indicating the availability of signals.…”

Section: A Background and Related Workmentioning

confidence: 99%

Stability of Kalman filtering with Markovian packet losses

2007

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Abstract-We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices {Pt, t ≥ 1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.

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Section: A Background and Related Workmentioning

confidence: 99%

Stability of Kalman filtering with Markovian packet losses

2007

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“…This challenging parametrization is chosen in order to illustrate the power of the proposed method, and in particular that the algorithm will accurately detect the information content of the available data at any time and adapt the weights accordingly when using R t defined by (15). Therefore, the proposed NMHE algorithm is applied to the combined state and parameter estimation problem by considering the parameters λ 1 , λ 2 as augmented states,λ 1 = 0, andλ 2 = 0.…”

Section: B Example 2 -Estimation Of Bottom Hole Pressure During Oil mentioning

confidence: 99%

Regularized Nonlinear Moving Horizon Observer for Detectable Systems

Sui

Johansen

2010

IFAC Proceedings Volumes

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Moving horizon estimation provides a general method for state estimation with strong theoretical convergence properties under the critical assumption that global solutions are found to the associated nonlinear programming problem at each sampling instant. A particular benefit of the approach is due to the use of a moving window of data that is used to update the estimate at each sampling instant. This provides robustness to temporary data deficiencies such as lack of excitation and measurement noise, and the inherent robustness can be further enhanced by introducing regularization mechanisms. In this paper we study moving horizon estimation in cases when output measurements are lost or delayed, which is a common situation when digitally coded data are received over low quality communication channels or random access networks. Modifications to a basic moving horizon state estimation algorithm and conditions for exponential convergence of the estimation errors are given, and the method is illustrated by using a simulation example and experimental data from an offshore oil drilling operation.

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“…For linear stochastic systems, the related work was started in [15,22] where the missing data was modeled as a binary switching sequence specified by a conditional probability distribution. Based on this model for observations missing, some results have recently been reported on the filtering problems for linear stochastic systems, see [12,13,[28][29][30] for some examples.…”

Section: Introductionmentioning

confidence: 99%

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

Wang

et al. 2010

Signal Processing

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This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

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Linear recursive state estimators under uncertain observations

Cited by 177 publications

References 7 publications

Stability of Kalman filtering with Markovian packet losses

Stability of Kalman filtering with Markovian packet losses

Regularized Nonlinear Moving Horizon Observer for Detectable Systems

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

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