Delay Systems Distributed Fusion Filtering

Because of the aging of the components, lack of sensitivity and delay in information transmission, there is time-delay phenomenon. State estimation for time-delay systems is widely applied in signal processing, controlling and network systems. The study of state estimation for time-delay systems is of great value for people to control time-delay systems effectively. In this paper, we study the distributed optimal weighted information fusion estimation, including systems with delayed measurements, delayed states, and delayed measurements and states.Based on the modern time series analysis method, a distributed fusion filter for multi-sensor stochastic systems with delayed measurements and correlated noise is studied. The system with delayed measurements can be transferred to an equivalent system without delayed measurements. The output predictor, white noise estimators and state estimator for the systems with a single sensor are given. The cross-covariance matrix of different-step prediction errors between any two sensor subsystems is derived. And then based on distributed optimal weighted fusion estimation algorithms, distributed weighted fusion Wiener filter for multi-sensor systems with delayed measurements is given.Based on Kalman filtering method, the non-augmented distributed weighted fusion optimal estimators are given for multi-sensor multi-delay systems with correlated noises. The estimation error cross-covariance matrix between local estimators based on any two sensors is derived. We use two approaches to derive distributed weighted fusion optimal estimators for systems with multi-delay states and measurements. One is to use projection theory directly for systems with correlated noise. The other is to transfer multi-delay systems with correlated noises to multi-delay systems with uncorrelated noises and then derive the distributed weighted fusion optimal estimators, which avoids the complexity in theory derivation for systems with correlated noise. Compared with the local estimator based on a single sensor, the distributed fusion estimator has higher accuracy. Compared with the centralized optimal estimator by augmentation, it has the better reliability due to its parallel structure and avoids the high-dimensional computation and the large space memory by augmentation though there is the accuracy loss. Then, we compare the computation burden and performance between non-augmented and augmented methods as well as between distributed and centralized methods.Based on Kalman filtering method, the non-augmented distributed weighted fusion optimal estimator for multi-sensor multi-delay systems with colored measurement noise is derived by two approaches. One is to transfer the filtering problem for multi-delay systems with colored measurement noise to the prediction problem for multi-delay systems with correlated white noises. The other is to transfer multi-delay systems with colored measurement noise to multi-delay systems with uncorrelated white noise. The filter of the new system is that of the original system. Then, the advantages and disadvantages between these two approaches are analyzed. At last, the information fusion Kalman filter for multi-delay systems with AR(autoregressive) colored measurement noise is given.