Zi Li Deng

Two-level robust sequential covariance intersection fusion Kalman predictors over clustering sensor networks with uncertain noise variances

This paper studies the problem of designing two-level robust sequential covariance intersection SCI fusion Kalman predictors for the clustering sensor networks with noise variances uncertainties. The sensor networks consist of many clusters, which are partitioned by the nearest neighbour rule. According to the minimax robust estimation principle, based on the worst-case conservative clustering sensor network with the conservative upper bound of noise variances, the two-level SCI fusion Kalman predictors are presented where the first level is the local SCI fusion predictors and the second level is the global SCI fusion predictor. This two-level fused structure can significantly reduce the communicational burden and save the energy sources. The robustness of the local and fused Kalman predictors is proved based on the Lyapunov equation method, and the robust accuracy relations are proved. A simulation example verifies the correctness and effectiveness of the proposed robust SCI predictor.

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.

Parallel Covariance Intersection Fusion Optimal Kalman Filter

For multisensor network systems with unknown cross-covariances, a novel multi-level parallel covariance intersection (PCI) fusion Kalman filter is presented in this paper, which is realized by the multi-level parallel two-sensor covariance intersection (CI) fusers, so it only requires to solve the optimization problems of several one-dimensional nonlinear cost functions in parallel with loss computation burden. It can significantly reduce the computation time and increase data processing rate when the number of sensors is very large. It is proved that the PCI fuser is consistent, and its accuracy is higher than that of each local filter and is lower than that of the optimal Kalman fuser weighted by matrices. The geometric interpretation of accuracy relations based on the covariance ellipses is given. A simulation example for tracking systems verifies the accuracy relations.

Covariance Intersection Fusion Kalman Estimators

By the CI (Covariance Intersection) fusion algorithm, based on the ARMA innovation model, the two-sensor CI fusion Kalman estimators are presented for the systems with unknown cross-covariance. It is proved that their estimation accuracies are higher than those of the local Kalman estimators, and are lower than those of the optimal fused Kalman estimators. A Monte-Carlo simulation result shows that the actual accuracy of the presented CI fusion Kalman estimator are close to those of the optimal fused Kalman estimators with known cross-covariance.

Robust Weighted Measurement Fusion Kalman Predictor with Uncertain Parameters and Noise Variances

For the multisensor time-invariant system with uncertainties of both the noise variances and parameters, by introducing a fictitious white noise to compensate the uncertain parameters, the uncertain system can be converted into the conservative system with known parameters and uncertain noise variances. Using the minimax robust estimation principle, and the Lyapunov equation approach, a robust weighted measurement fusion Kalman predictor is presented based on the worst-case conservative system with the conservative upper bounds of noise variances. A Monte-Carlo simulation example shows its effectiveness.

The Design of a Robust Weighted Measurement Fusion Steady-State Kalman Filter

For the linear discrete-time multisensor time-invariant system with uncertain model parameters and measurement noise variances, by introducing fictitious noise to compensate the parameter uncertainties, using the minimax robust estimation principle, based on the worst-case conservative multisensor system with conservative upper bounds of measurement and fictitious noises variances, a robust weighted measurement fusion steady-state Kalman filter is presented. By the Lyapunov equation approach, it is proved that when the region of the parameter uncertainties is sufficient small, the corresponding actual fused filtering error variances are guaranteed to have a less-conservative upper bound. Simulation results show the effectiveness and correctness of the proposed results.

Robust Centralized Fusion Steady-State Kalman Filter with Uncertain Parameters and Measurement Noise Variances

For the linear discrete time multisensor system with uncertain model parameters and measurement noise variances, the centralized fusion robust steady-state Kalman filter is presented by a new approach of compensating the parameter uncertainties by a fictitious noise. Based on the Lyapunov equation, it is proved that for given fictitious noise variance, the variances of the actual filtering errors have a less-conservative upper bound when the uncertainty of parameters is limited in a sufficiently small region which is called as robust region of the parameter uncertainties. Further, a simulation example demonstrates how to search the robust region. It is also proved that the robust accuracy of the centralized fusion robust steady-state Kalman filter is higher than that of each local robust Kalman filter. A simulation example shows its effectiveness.

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 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.

Covariance Intersection Fusion Robust Time-Varying Kalman Filter for Two-Sensor System with Uncertain Noise Variances

This paper investigates the problem of designing covariance intersection fusion robust time-varying Kalman filter for two-sensor time-varying system with uncertain noise variances. Using the minimax robust estimation principle, the local and covariance intersection (CI) fusion robust time-varying Kalman filters are presented based on the worst-case conservative system with the conservative upper bounds of noise variances. Their robustness is proved based on the proposed Lyapunov equation, and the robust accuracy of time-varying CI fuser is higher than that of each local robust time-varying Kalman filter. A two-sensor tracking system simulation verifies the robustness and robust accuracy relations.