Fusion Steady-state Kalman Filter Research Articles

Multi-Sensor Information Fusion Predictive Control Algorithm for System with Random Time-Delay Observations

The multi-sensor information fusion predictive control algorithm for discrete-time linear time-invariant stochastic control system with random time-delay observations is presented in this paper. The algorithm applies the fusion steady-state Kalman filter to the predictive control. It avoids the complex Diophantine equation and it can obviously reduce the computational burden. The algorithm can deal with the multi-sensor discretetime linear time-invariant stochastic controllable system based on the linear minimum variance optimal information fusion criterion. The fusion method includes the centralized fusion, global optimality weighted measurement fusion. And the two fusion method is completely functionally equivalence. Compared with the single sensor case, the accuracy of the fused filter is greatly improved. A simulation example of the target tracking controllable system with two sensors shows its effectiveness and correctness.

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.

The accuracy comparison of multisensor covariance intersection fuser and three weighting fusers

For multisensor systems with exactly known local filtering error variances and cross-covariances, a covariance intersection (CI) fusion steady-state Kalman filter without cross-covariances is presented. It is rigorously proved that it has consistency, and its accuracy is higher than that of each local Kalman filter and is lower than that of the optimal Kalman fuser with matrix weights. Under the unbiased linear minimum variance (ULMV) criterion, it is proved that the accuracy of the fuser with matrix weights is higher than that of the fuser with scalar weights, and the accuracy of the fuser with diagonal matrix weights is in between both of them, and the accuracies of all three weighting fusers and the CI fuser are lower than that of centralized Kalman fuser, and are higher than that of each local Kalman filter. The geometric interpretations of the above accuracy relations are given based on the covariance ellipsoids. A Monte-Carlo simulation example for tracking system verifies correctiveness of the proposed theoretical accuracy relations, and shows that the actual accuracy of the CI Kalman fuser is close to that of the optimal Kalman fuser, so that it has higher accuracy and good performance. When the actual local filtering error variances and cross-covariances are unknown, if the local filtering estimates are consistent, then the corresponding robust CI fuser is also consistent, and its robust accuracy is higher than that of each local filter.

Information Fusion Kalman Filter for Two-Sensor System with Time-Delayed Measurements

For the two-sensor linear discrete stochastic system with time-delayed measurements, an equivalent system without time-delayed measurements is obtained by introducing a new measurement process. Then a covariance intersection (CI) fusion steady-state Kalman filter is presented based on the modern time series analysis method. Compared with the optimal Kalman fusers weighted by matrices, diagonal matrices and scalars, this CI Kalman fuser avoids computing the cross-covariances among the local filtering errors. It is proved that its accuracy is higher than that of each local filter, and is lower than that of the Kalman fuser weighted by matrices. The geometric interpretations of these fusers’ accuracy relations are given based on the covariance ellipses. A Monte-Carlo simulation example for target tracking system verifies the correctness of the proposed accuracy relations, i.e. the actual accuracy of the CI Kalman fuser is close to that of the fuser weighted by matrices, and is higher than that of each local filter, so it has higher accuracy and good performances.

Self-tuning measurement fusion Kalman filter with correlated measurement noises

For the multisensor system with correlated measurement noises and unknown noise statistics, based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances and cross-covariances is obtained. Further, a self-tuning weighted measurement fusion Kalman filter is presented, based on the Riccati equation. By the Dynamic Error System Analysis (DESA) method, it rigorously proved that the presented self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion steady-state Kalman filter in a realization or with probability one, so that it has asymptotic global optimality. A simulation example for a target tracking system with 3-sensor shows that the presented self-tuning measurement fusion Kalman fuser converges to the optimal steady-state measurement fusion Kalman fuser.

Distributed optimal fusion steady-state Kalman filter for systems with coloured measurement noises

Based on the optimal fusion criterion weighted by matrices in the linear minimum variance sense, an optimal information fusion steady-state Kalman filter is given for the discrete time-invariant linear stochastic control system measured by multiple sensors with coloured measurement noises, which is equivalent to an optimal information fusion steady-state Kalman predictor with a two-layer fusion structure for system with correlated noises. Furthermore, the steady-state optimal fusion predictor can be obtained only by fusing once after all local subsystems enter the steady-state predictions. The solution of steady-state prediction error cross-covariance matrix between any two subsystems can be obtained by iteration with an arbitratry initial value, whose convergence is proved. Applying it to a tracking system with three sensors shows its effectiveness.