Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements

Wang, Shaoying; Fang, Huajing; Tian, Xin

doi:10.1016/j.dsp.2015.10.007

Cited by 33 publications

(40 citation statements)

References 28 publications

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“…Up to now, many important results have been reported concerned with robust or optimal state estimation for networked systems with multiplicative noises, missing measurements, random delays, and packet dropouts . For uncertain networked systems with multiplicative noises in state and measurement matrices, multistep random delays, packet dropouts, and one‐step auto‐correlated and cross‐correlated process noises and measurement noises, the optimal linear estimators in the minimum variance sense are designed via projection theory .…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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show abstract

“…However, the multiplicative noises are not considered in the work of the aforementioned authors . For uncertain networked systems with multiplicative noises, multistep random delays, packet dropouts, and one‐step auto‐correlated and cross‐correlated process noises and measurement noises, the optimal linear estimators in the minimum variance sense are designed via projection theory . However, the missing measurements are not considered in the work of Wang et al, and it is limited to the single‐sensor systems.…”

Section: Introductionmentioning

confidence: 99%

“…For uncertain networked systems with multiplicative noises, multistep random delays, packet dropouts, and one‐step auto‐correlated and cross‐correlated process noises and measurement noises, the optimal linear estimators in the minimum variance sense are designed via projection theory . However, the missing measurements are not considered in the work of Wang et al, and it is limited to the single‐sensor systems. For uncertain multisensor networked systems with multiplicative noises, one‐step random transmission delay, and packet dropouts, a distributed fusion filter was proposed based on the well‐known fusion algorithm weighted by matrices in the linear minimum variance sense .…”

Section: Introductionmentioning

confidence: 99%

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

Liu

Wang

Deng

2018

Intl J Robust & Nonlinear

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Summary This paper addresses the problem of designing robust fusion time‐varying Kalman estimators for a class of multisensor networked systems with mixed uncertainties including multiplicative noises, missing measurements, packet dropouts, and uncertain‐variance linearly correlated measurement and process white noises. By the augmented approach, the original system is converted into a stochastic parameter system with uncertain noise variances. Furthermore, applying the fictitious noise approach, the original system is converted into one with constant parameters and uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of the noise variances, the five robust fusion time‐varying Kalman estimators (predictor, filter, and smoother) are presented by using a unified design approach that the robust filter and smoother are designed based on the robust Kalman predictor, which include three robust weighted state fusion estimators with matrix weights, diagonal matrix weights, and scalar weights, a modified robust covariance intersection fusion estimator, and robust centralized fusion estimator. Their robustness is proved by using a combination method, which consists of Lyapunov equation approach, augmented noise approach, and decomposition approach of nonnegative definite matrix, such that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. The accuracy relations among the robust local and fused time‐varying Kalman estimators are proved. A simulation example is shown with application to the continuous stirred tank reactor system to show the effectiveness and correctness of the proposed results.

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“…Recently, in [14], the problem of state estimation was solved for a class of linear discrete-time stochastic systems subject to missing data and correlated noises, where the estimators were unbiased and the estimation error covariances were minimized. Based on the state augmentation approach and the projection theory, in [15], the optimal linear estimator was designed in the minimum variance sense for linear uncertain systems with correlated noises and incomplete measurements 2 Discrete Dynamics in Nature and Society and the sufficient condition on the existence of steady-state estimators was shown. In [16], the distributed and centralized fusion filtering problems were discussed for the sensor networked systems with stochastic uncertainties and correlated random transmission delays, where the recursive algorithms for the optimal linear distributed and centralized filters were derived by the innovation sequence analysis method.…”

Section: Introductionmentioning

confidence: 99%

Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements

You

Jiang

Huang

et al. 2018

Discrete Dynamics in Nature and Society

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The locally optimal filter is designed for a class of discrete-time systems subject to stochastic nonlinearity functions, finite-step correlated noises, and missing measurements. The multiplicative noises are employed to describe the random disturbances in the system model. The phenomena of missing measurements occur in a random way and the missing probability is characterized by Bernoulli distributed random variables with known conditional probabilities. Based on the projection theory, a class of Kalman-type locally optimal filter is constructed and the filtering error covariance matrix is minimized in the sense of minimum mean square error principle. Also, by solving the recursive matrix equation, we can obtain the filter gain. Finally, two examples are provided: one is a numerical example to illustrate the feasibility and effectiveness of the proposed filtering scheme; the other is to solve the problem of target estimation for a tracking system considering networked phenomena.

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Minimum variance estimation for linear uncertain systems with one-step correlated noises and incomplete measurements

Cited by 33 publications

References 28 publications

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

Robust fusion time‐varying Kalman estimators for multisensor networked systems with mixed uncertainties

Kalman Filtering Algorithm for Systems with Stochastic Nonlinearity Functions, Finite-Step Correlated Noises, and Missing Measurements

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