Robust minimum variance linear state estimators for multiple sensors with different failure rates

Hounkpevi, Franck O.; Yaz, E.

doi:10.1016/j.automatica.2006.12.025

Cited by 160 publications

(101 citation statements)

References 20 publications

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“…Therefore, the addressed filter design problem can be solved by means of the proposed filter structure (7)- (8 k and x 2 k , which confirm that the MSE stay below their upper bounds. Moreover, the trajectories of the actual states x i k and their estimateŝ x i k (i = 1, 2) are plotted in Figs.…”

Section: A Numerical Examplementioning

confidence: 88%

“…For more details we refer the reader to Appendix C of [6]. According to (8) and (19), the filtering error can be written as:…”

Section: Resultsmentioning

confidence: 99%

“…[3, 8-10, 22, 34]. To be more specific, the optimal estimation problems have been investigated in [8,22] for linear systems with multiple packet dropouts and the random sensor delays have been taken into account in [9,34]. It is worth mentioning that, in most reported results, the measurement signal has been assumed to be either completely lost or successfully transferred, and a typical way is to model the missing measurements by the Bernoulli distribution.…”

Section: Introductionmentioning

confidence: 99%

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Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

et al. 2012

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In this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0, 1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.

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Section: A Numerical Examplementioning

confidence: 88%

“…For more details we refer the reader to Appendix C of [6]. According to (8) and (19), the filtering error can be written as:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

et al. 2012

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“…However, due to the complexity of large-scale networks, the measurement signals may be missing/fading during the network transmission resulting from various causes such as sensors aging, intermittent sensor failures, limited bandwidth, network congestion or accidental loss of some collected data [6,8,16,18,19]. As such, in order to improve the estimation performance, it is vitally important to take the phenomenon of the missing measurements into account when designing the state estimator especially in the network settings [11,13,24]. In the past decade, the state estimation problems with missing measurements have drawn considerable research interest and a huge amount of results have been reported.…”

Section: Introductionmentioning

confidence: 99%

A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements

et al. 2016

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In this paper, the recursive state estimation problem is investigated for an array of discrete time-varying coupled stochastic complex networks with missing measurements. A set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements, where each sensor can have individual missing probability. The Taylor series expansion is employed to deal with the nonlinearities and the high-order terms of the linearization errors are estimated. The purpose of the addressed state estimation problem is to design a time-varying state estimator such that, in the presence of the missing measurements and the random disturbances, an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given. By using the Riccatilike difference equations approach, the estimator parameter is characterized by the solutions to two Riccati-like difference equations. It is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme.

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“…A common way for handling the missing measurement is to utilize the Bernoulli distributed (binary switching) white sequence specified by a conditional probability distribution in the output equation. Such kind of "binary" description has been employed in many papers such as [7,12,19,25] for filtering problems of linear/nonlinear systems with probabilistic measurement losses. It is worth mentioning that, comparing to large amount of results for missing measurements, the corresponding filter design problem for signals with limited amplitudes or saturation has received much less focus of research despite the fact that sensor saturations occur very often in practical engineering.…”

Section: Introductionmentioning

confidence: 99%

H∞ filtering with randomly occurring sensor saturations and missing measurements

2012

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In this paper, the H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

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Robust minimum variance linear state estimators for multiple sensors with different failure rates

Cited by 160 publications

References 20 publications

Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements

H∞ filtering with randomly occurring sensor saturations and missing measurements

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