Robust Centralized Fusion Research Articles

Fusion steady‐state robust filtering for uncertain multisensor networked systems with application to autoregressive moving average signal estimates

AbstractThis article is concerned with the centralized fusion (CF) robust steady‐state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including state‐dependent and noise‐dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances. By using a model transformation approach, the initial multisensor system under study is transformed into a multi‐model multisensor system only with uncertain noise variances. By introducing an augmented state vector, the CF system is obtained. In the light of the minimax robust estimation method, and based on the worst‐case fusion system with conservative upper bounds of uncertain noise variances, the CF robust steady‐state Kalman estimators (predictor, filter, and smoother) are proposed in a unified form. By means of the permutation matrices and Lyapunov equation method, the robustness of CF estimators is proved. The accuracy relations among the robust local and fusion steady‐state estimators are proved. An example applied to autoregressive moving average signal estimation is put forward, and the robust CF steady‐state signal estimators are proposed. Simulation experiment shows the correctness of the proposed approach.

Centralized fusion robust filtering for networked uncertain systems with colored noises, one-step random delay, and packet dropouts

This paper studies the estimation problem for multisensor networked systems with mixed uncertainties, which include colored noises, same multiplicative noises in system parameter matrices, uncertain noise variances, as well as the one-step random delay (OSRD) and packet dropouts (PDs). This study utilizes the centralized fusion (CF) algorithm to combing all information received by each sensor, which improve the accuracy of the estimation. By using the augmentation method, de-randomization method and fictitious noise techniques, the original uncertain system is transformed into an augment model with only uncertain noise variances. Then, for all uncertainties within the allowable range, the robust CF steady-state Kalman estimators (predictor, filter, and smoother) are presented based on the worst-case CF system, in light of the minimax robust estimation principle. To demonstrate the robustness of the proposed CF estimators, the non-negative definite matrix decomposition method and Lyapunov equation approach are employed. It is proved that the robust accuracy of CF estimator is higher than that of each local estimator. Finally, the simulation example applied to the uninterruptible power system (UPS) with colored noises and multiple uncertainties illustrates the effectiveness of the proposed CF robust estimation algorithm.

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

SummaryThe 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.

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

SummaryThis 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.

Robust centralized and weighted measurement fusion white noise deconvolution estimators for multisensor systems with mixed uncertainties

SummaryEstimating the input signal of a system is called deconvolution or input estimation. The white noise deconvolution has important applications in oil seismic exploration, communications, and signal processing. This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) white noise deconvolution estimators for a class of uncertain multisensor systems with mixed uncertainties, including uncertain‐variance multiplicative noises in measurement matrix, missing measurements, and uncertain‐variance linearly correlated measurement and process white noises. By introducing the fictitious noise, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time‐varying white noise deconvolution estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities are analyzed and compared. Compared with the CF algorithm, the WMF algorithms can significantly reduce the computational burden when the number of sensors is larger. The corresponding robust fused steady‐state white noise deconvolution estimators are also presented. A simulation example with respect to the multisensor IS‐136 communication systems shows the effectiveness and correctness of the proposed results.

Robust Centralized and Weighted Measurement Fusion Kalman Predictors with Multiplicative Noises, Uncertain Noise Variances, and Missing Measurements

For multisensor uncertain systems with mixed uncertainties, including multiplicative noises in state and process noise transition matrices, uncertain-variance multiplicative and additive white noises, and missing measurements, this paper addresses the problem of designing robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman predictors. By introducing fictitious noises, the system under study is converted into a system with only uncertain noise variances. According to the minimax robust estimation principle, which is based on the worst-case system with conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman predictors are presented in a unified framework. Using the Lyapunov equation, the robustness of these predictors is proven in the sense that the actual prediction error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using an information filter, they are proven to have the same robust and actual accuracies. The complexity analysis shows that when the number of sensors is larger, the WMF algorithm more significantly reduces the computational burden than the CF algorithm. The corresponding robust fused steady-state Kalman predictors are also presented. The three modes of convergence in a realization among the time-varying and steady-state robust fused Kalman predictors are proposed and proven using the dynamic error system analysis method. Two simulation examples, autoregressive moving average signal processing and an uninterruptible power system, demonstrate the effectiveness of the proposed methods.

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.

Robust Centralized Fusion Kalman Filters with Uncertain Noise Variances

This paper studies the problem of the designing the robust local and centralized fusion Kalman filters for multisensor system with uncertain noise variances. Using the minimax robust estimation principle, the centralized fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bound of noise variances. A Lyapunov approach is proposed for the robustness analysis and their robust accuracy relations are proved. It is proved that the robust accuracy of robust centralized fuser is higher than those of robust local Kalman filters. Specially, the corresponding steady-state robust local and centralized fusion Kalman filters are also proposed and the convergence in a realization between time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A Monte-Carlo simulation example shows the robustness and accuracy relations. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5490 Full Text: PDF