Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

Yang, Chunshan; Yang, Zhibo; Deng, Zili

doi:10.1016/j.inffus.2018.01.014

Cited by 60 publications

(79 citation statements)

References 47 publications

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“…The optimal (minimum variance) filtering for worst‐case system is called minimax robust filtering. Designing the minimum variance estimator for the worst‐case system will yield the minimax robust estimator . The problem is to design the local and fusion robust steady‐state Kalman estimators (predictor, filter, and smoother)

{\overset{true^}{x}}_{θ} (() t | t + N) ((), N = - 1, N = 0, N > 0)

for uncertain multisensor networked system to , such that their actual steady‐state estimation error variances

{\overset{true‾}{P}}_{θ} ((), N)

, yielded by all admissible uncertainties, have the corresponding minimal upper bounds P θ ( N ), ie,

{\overset{true‾}{P}}_{θ} ((), N) \leq P_{θ} ((), N),

where θ = i , m ,CI denote the i th local robust estimator, the fusers weighted by matrices, and the CI fusers, respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

“…For multisensor systems with multiplicative noises, uncertain noise variances, and correlated measurement and process noises, applying the minimax robust estimation principle and fictitious noise technique, the robust local and information fusion Kalman estimators have been proposed in other works . More concretely, for linear discrete‐time systems with same multiplicative noises in the state and measurement matrices, as well as the process and measurement noise transition matrices, and with the uncertain‐variance linearly correlated white noises, the robust time‐varying and steady‐state Kalman estimators were presented in the work of Liu et al However, it is limited to the single‐sensor systems.…”

Section: Introductionmentioning

confidence: 99%

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Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

Liu

Deng

2019

Adaptive Control & Signal

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Summary In this paper, the weighted fusion robust steady‐state Kalman filtering problem is studied for a class of multisensor networked systems with mixed uncertainties. The uncertainties include same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one‐step random delay and inconsecutive packet dropouts, which modeled by sequences of Bernoulli variables with different probabilities. By defining a new observation vector and applying the augmented method, the system under study is converted into one with only uncertain noise variances. The sufficient conditions for the existence of steady‐state estimators are given. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are proposed. Applying the optimal fusion algorithm weighted by matrices and the covariance intersection fusion algorithm, the two kinds of robust fusion steady‐state Kalman estimators are derived in a unified framework. The robustness of the proposed fusion estimators is proved by applying the permutation matrices and the global Lyapunov equations method, such that, for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fusion steady‐state Kalman estimators are proved. An example with application to autoregressive moving average signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

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{\overset{true^}{x}}_{θ} (() t | t + N) ((), N = - 1, N = 0, N > 0)

for uncertain multisensor networked system to , such that their actual steady‐state estimation error variances

{\overset{true‾}{P}}_{θ} ((), N)

, yielded by all admissible uncertainties, have the corresponding minimal upper bounds P θ ( N ), ie,

{\overset{true‾}{P}}_{θ} ((), N) \leq P_{θ} ((), N),

where θ = i , m ,CI denote the i th local robust estimator, the fusers weighted by matrices, and the CI fusers, respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

Liu

Deng

2019

Adaptive Control & Signal

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show abstract

Section: Introductionmentioning

confidence: 99%

“…In the past few years, some important results have been reported concerned with robust filtering for systems with uncertain noise variances. 9,[21][22][23][24][25] For the linear discrete time-varying multisensor stochastic systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust information fusion Kalman filters have been presented in the work of Qi et al 9 The actual estimation error variances or their traces of each estimator are guaranteed to have a minimal upper bound for all the admissible uncertainties of noise variances. However, the limitation of the aforementioned work 9 is that only the noise variance uncertainties are considered, whereas multiplicative noises, missing measurements, and packet dropouts are not considered, and it cannot handle the systems with correlated noises.…”

Section: Introductionmentioning

confidence: 99%

“…For multisensor systems with multiplicative noises, uncertain noise variances, and correlated measurement and process noises, applying the minimax robust estimation principle and fictitious noise technique, the robust local and information fusion Kalman estimators have been proposed in some works. [21][22][23][24][25] More concretely, for multisensor systems with same multiplicative noises in state and measurement matrices, and uncertain-variance linearly correlated additive white noises, the weighted state fusion robust Kalman estimators are presented. 21 However, the missing measurements and packet dropouts are not considered in the work of Liu et al 21 For multisensor systems with multiplicative noises in state matrix, missing measurements, and uncertain-variance linearly correlated additive white noises, the robust centralized and weighted measurement fusion Kalman estimators are presented.…”

Section: Introductionmentioning

confidence: 99%

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Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay, missing measurements, and uncertain‐variance multiplicative and additive white noises

Liu

Tao

Fan

et al. 2019

Intl J Robust & Nonlinear

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Summary The robust fusion steady‐state filtering problem is investigated for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, one‐step random delay, missing measurements, and uncertain noise variances, the phenomena of one‐step random delay and missing measurements occur in a random way, and are described by two Bernoulli distributed random variables with known conditional probabilities. Using a model transformation approach, which consists of augmented approach, derandomization approach, and fictitious noise approach, the original multisensor system under study is converted into a multimodel multisensor system with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case subsystems with conservative upper bounds of uncertain noise variances, the robust local steady‐state Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the optimal fusion algorithm weighted by matrices, the robust distributed weighted state fusion steady‐state Kalman estimators are derived for the considered system. In addition, by using the proposed model transformation approach, the centralized fusion system is obtained, furthermore the robust centralized fusion steady‐state Kalman estimators are proposed. The robustness of the proposed estimators is proved by using a combination method consisting of augmented noise approach, decomposition approach of nonnegative definite matrix, matrix representation approach of quadratic form, and Lyapunov equation approach, such that for all admissible uncertainties, the actual steady‐state estimation error variances of the estimators are guaranteed to have the corresponding minimal upper bounds. The accuracy relations among the robust local and fused steady‐state Kalman estimators are proved. An example with application to autoregressive signal processing is proposed, which shows that the robust local and fusion signal estimation problems can be solved by the state estimation problems. Simulation example verifies the effectiveness and correctness of the proposed results.

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Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays, multiplicative noises, and uncertain noise variances

RanChenjian

DENGZi-Li

2020

Adaptive Control & Signal

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In this article, the robust distributed fusion Kalman filtering problems are addressed for the networked mixed uncertain multisensor systems with random one-step measurement delays, multiplicative noises, and uncertain noise variances. A new augmented state approach with fictitious measurement noises modeled by the first-order moving average models is presented, by which the original system is transformed into a standard uncertain system only with uncertain-variance fictitious white noises. Based on the minimax robust estimation principle and Kalman filtering theory, a universal integrated covariance intersection (ICI) fusion approach is presented in the sense that first of all the robust local estimators and their conservative error variances and crosscovariances are presented, and then integrating the local estimation information yields ICI fusers. An extended Lyapunov equation approach with two kinds of Lyapunov equations is presented in order to prove the robustness and to compute fictitious noise statistics. Applying these approaches, the minimax robust local, ICI, and fast ICI fused Kalman estimators (predictor, filter, and smoother) are presented, such that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, accuracy relations, and convergence are also proved. The proposed ICI fusers improve the robust accuracies and overcome the drawbacks of the original covariance intersection fusers, such that the robust local estimators and their conservative variances are assumed to be known, and their conservative crosscovariances are ignored. Two simulation examples applied to the offshore platform system verify their correctness, effectiveness, and applicability. K E Y W O R D S integrated covariance intersection fusion approach, minimax robust Kalman estimators, mixed-uncertain networked systems, multiplicative noises, random measurement delays, uncertain noise variances

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Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

Cited by 60 publications

References 47 publications

Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

Weighted fusion robust steady‐state estimators for multisensor networked systems with one‐step random delay and inconsecutive packet dropouts

Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay, missing measurements, and uncertain‐variance multiplicative and additive white noises

Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays, multiplicative noises, and uncertain noise variances

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