Optimal Fuser Research Articles

Minimax Robust Optimal Estimation Fusion for Distributed Multisensor Systems with a Relative Entropy Uncertainty

This paper considers the robust estimation fusion problem for distributed multisensor systems with uncertain correlations of local estimation errors. For an uncertain class characterized by the Kullback-Leibler (KL) divergence from the actual model to nominal model of local estimation error covariance, the robust estimation fusion problem is formulated to find a linear minimum variance unbiased estimator for the least favorable model. It is proved that the optimal fuser under nominal correlation model is robust while the estimation error has a relative entropy uncertainty.

Covariance Intersection Fusion Kalman Estimator for Multi-Sensor System with Measurements Delays

To handle the state estimation fusion problem between local estimation errors for the system with unknown cross-covariances and to avoid a large computation complexity of cross-covariances, for a multi-sensor linear discrete time-invariant stochastic system with time-delayed measurements, by the measurement transformation method, an equivalent system without measurement delays is obtained, and then using the covariance intersection (CI) fusion method, the covariance intersection fusion steady-state Kalman estimator is presented. It is proved that its accuracy is higher than that of each local estimator, and is lower than that of optimal Kalman fuser weighted by matrices with known cross-covariances. A Monte-Carlo simulation example shows the above accuracy relations, hence it has good performances.

Multisensor Covariance Intersection Fusion Kalman Filters

For multisensor system with colored measurement noises, the common disturbance noises and measurement biases, the batch covariance intersection fusion (BCI) Kalman filter and the sequential covariance intersection fusion (SCI) Kalman filter are presented, which can avoid the computation of the local filtering errors and reduce the computational burden significantly. Under the linear unbiased minimum variance (ULMV) criterion, the three weighted fusion Kalman filters (weighted by matrices, scalars or diagonal matrices) are also presented. Their accuracy relations are analyzed and compared. Specially, the accuracy of the proposed covariance intersection fusion Kalman filters are higher than that of each local Kalman filters, and is lower than that of optimal fuser weighted by matrices. The geometric interpretation of the accuracy relations is given by the covariance ellipses. A Monte-Carlo simulation example for a tracking system verifies the correctness of the theoretical accuracy relations.

Covariance Intersection Fusion Smoothers for Multichannel ARMA Signal with Colored Measurement Noises

For multichannel autoregressive moving average (ARMA) signal with colored measurement noises, based on classical Kalman filtering theory, a covariance intersection (CI) fusion smoother without cross-covariances is presented by the augmented state space model. It has the advantage that the computation of cross-covariances is avoid, so it can significantly reduce the computational burden, and it can solve the fusion problem for multi-sensor systems with unknown cross-covariances. Under the unbiased linear minimum variance (ULMV) criterion, three optimal weighted fusion smoothers with matrix weights, scalar weights and diagonal weights are also presented respectively. The accuracy comparison of the CI fuser with the other three weighted fusers is given. It is shown that its accuracy is higher than that of each local smoother, and is lower than or close to that of the optimal fuser weighted by matrices. So the presented fusion smoother is better in performance.

Covariance Intersection Fusion Kalman Estimators for Multi-Sensor System with Colored Measurement Noises

For multi-sensor system with colored measurement noises, using the observation transformation, the system can be converted into an equivalent system with correlated measurement noises. Based on this method, using the classical Kalman filtering, this study proposed a Covariance Intersection (CI) fusion Kalman estimator, which can handle the fused filtering, prediction and smoothing problems. The advantage of the proposed method is that it can avoid the computation of the cross-covariances among the local filtering errors and can reduce the computational burden significantly, as well as the CI fusion algorithm can be used in the uncertain system with unknown cross-covariances. Based on classical Kalman filtering theory, the centralized fusion and three weighted fusion (weighted by matrices, scalars and diagonal) estimators are also presented respectively. Their accuracy comparisons are given. The geometric interpretations based on covariance ellipses are also given. The experiment results show that the accuracy of the CI fuser is higher than that of the each local smoothers and is lower that that of the centralized fusion Kalman smoother or the optimal fuser weighted by matrix. The MSE curves show that the accuracy of the CI fuser is close to the optimal fuser weighted by matrix in most instances, which means that our proposed method has higher accuracy and good performance.

Multi-Channel ARMA Signal Covariance Intersection Fusion Kalman Smoother

For the multi-channel ARMA signal with two sensors, by the classical Kalman filtering method and the covariance intersection (CI) fusion method, a covariance intersection fusion steady-state Kalman signal smoother is presented, which is independent of the unknown cross-covariance. It is proved that its accuracy is higher than that of each local Kalman signal smoother, and is lower than that of the optimal signal fuser weighted by matrices. The geometric interpretation of the above accuracy relations are presented based on the covariance ellipses. A simulation example result shows its effectiveness and correctness.

Covariance Intersection Fusion Kalman Smoother for Systems with Colored Measurement Noises

For the two-sensor system with unknown cross-covariances, and with colored measurement noises, by the classical Kalman filtering method and the covariance intersection (CI) fusion method, a covariance intersection fusion steadystate Kalman smoother is presented, which avoids the computation of cross-covariances. The accuracy relations of the CI Kalman smoother, the local and optimal fused Kalman smoother are proved, i.e., the accuracy of CI fuser is higher than that of each local Kalman smoother, and lower than that of optimal fuser weighted by matrices with known cross-covariance. The formula of the actual smoothing error variance of the CI fuser is given and the geometric interpretation of the above accuracy relations is presented based on the covariance ellipses. A Monte-Carlo simulation results show its effectiveness and correctness.

Multi-channel ARMA Signal Covariance Intersection Fusion Kalman Predictor

For multi-channel ARMA signal with two sensors and unknown cross-covariances between the local Kalman predicting errors, based on the transformation of ARMA signal model to the state space model, a covariance intersection (CI) fusion steady-state Kalman signal predictor is presented. The accuracy comparison of CI Kalman signal fuser with the Kalman fuser weighted by matrices, diagonal matrices, and scalars is given. The geometric interpretation of accuracy relations is given by the covariance ellipses. Its accuracy is higher than that of each local Kalman predictor, and lower than that of optimal Kalman predictor weighted by matrices. A Monte-Carlo simulation results show its effectiveness and its actual accuracy is close to that of the optimal fuser weighted by matrices.

Self-Tuning Weighted Measurement Fusion Kalman Filter for Multi-Channel AR Signals and Its Convergence

For the multisensor multi-channel autoregressive (AR) signals with colored measurement noises, when the model parameters and noise variances are partially unknown, the consistent estimators of unknown AR model parameters and noise variance are obtained by the bias compensated recursive least-squares (BCRLS) algorithm. Then, substituting these estimators into the optimal weighted measurement fusion signal Kalman filter, a self-tuning weighted measurement fusion signal Kalman filter is presented. Further, applying the dynamic error system analysis (DESA) method, it is rigorously proved that the proposed self-tuning fusion signal Kalman filter converges to the optimal fuser in a realization, so that it has asymptotic global optimality. A simulation example shows their effectiveness.

Optimal and self-tuning weighted measurement fusion Wiener filter for the multisensor multichannel ARMA signals

For the multisensor multichannel autoregressive moving average (ARMA) signals with white measurement noises, using the modern time series analysis method, based on the ARMA innovation models, white noise estimators, and measurement predictors, an optimal weighted measurement fusion Wiener filter is presented by the weighted least squares (WLS) method. It can handle the fused filtering, smoothing and prediction problems in a unified framework. When the noise variances and model parameters are unknown, based on the on-line identification of the local and fused ARMA innovation models, a self-tuning weighted measurement fusion Wiener filter is presented. By the dynamic error system analysis (DESA) method, it is rigorously proved that the self-tuning fuser converges to the optimal fuser in a realization, so that it has the asymptotic optimality. Compared with the globally optimal centralized fusion time-varying Kalman filter, the proposed optimal and self-tuning Wiener fusers have the asymptotic global optimality, whose accuracies are higher than these of the optimal and self-tuning distributed Wiener fusers and local Wiener filters, respectively. A simulation example shows their effectiveness.

Self-tuning decoupled information fusion Wiener state component filters and their convergence

For the multisensor systems with unknown noise variances, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances are obtained, and under linear minimum variance optimal information fusion criterion weighted by scalars for state components, a class of self-tuning decoupled fusion Wiener filters is presented. It realizes the self-tuning decoupled local Wiener filters and self-tuning decoupled fused Wiener filters for the state components. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. The dynamic error system analysis (DESA) method is presented, by which the problem of convergence in a realization for self-tuning fusers is transformed into the stability problems of non-homogeneous difference equations, and the decision criterions of the stability are also presented. It is strictly proved that if the parameter estimation of the MA innovation models is consistent and if the measurement process is bounded in a realization or with probability one, then the self-tuning fusers will converge to the optimal fusers in a realization or with probability one, so that they have the asymptotic optimality. They can deal with the systems with the non-stationary or Gaussian measurement processes. They can reduce the computational burden, and are suitable for real time applications. A simulation example for a target tracking system with 3-sensor shows their effectiveness.