Robust Fusion Kalman Filter For Clustered Sensor Networks

In recent years, with the development of sensor network technology, network estimation and control problem received extensive attention, in network systems, packet dropouts, measurement delay, model parameter and noise variance uncertainties and other problems are unavoidable. As we all know, the classical Kalman filtering requires exactly known mathematical model of system; these problem of state estimation based on the classical Kalman filtering is facing greater challenges. Hence, in the network monitoring and control systems, the robust state estimation problem of uncertain network system is particularly important. In particular, the problem of information fusion robust estimation is paid more and more attention. Information fusion methods are divided into centralized fusion and distributed fusion, depending on whether raw data are used directly for fusion or not. By the centralized fusion approach, all sensor measurement data is sent to fusion center for processing, and the obtained state estimator is globally optimal in the sense of unbiased linear minimum variance, but the disadvantages of this method are that communication and computing burden are larger. The distributed fusion approach is divided into distributed state fusion and distributed measurement fusion. By distributed state fusion method, measurement data of each sensor are first processed by corresponding local processer, and can obtain local fusion estimators, the local fusion estimators are sent to fusion center, and can obtain global fusion estimators. The fusion estimators by decentralized combination methods are the global optimal, the fusion estimators by the different weighting methods(matrix weighted, scalars weighted and diagonal matrix weighted) are global suboptimal. By the distributed measurement fusion approach, the fusion measurement equation is obtained via weighted local measurement equations, and can obtain weighted measurement fusion estimator by combining fusion measurement equation with state equation, which is global optimal. Compared with the centralized fuser, the advantage of the distributed measurement fusion method is to reduce the computation and communication burden, and to reduce energy consumption.Sensor network systems are consists of a series of sensor nodes with computing power, storage capacity and transmission capacity, in many areas have very important applications, such as military, environmental monitoring, medical, industrial, agricultural, construction, logistics and transportation etc.. In order to save energy and reduce the burden of communication, the sensor network is partitioned as clusters by the nearest neighbor rule, each cluster is consists of a cluster head and a number of sensor nodes; the local estimators obtained from the sensor nodes and measurement data are communicated to the corresponding cluster heads; the local fused estimators obtained from each cluster head and measurement data are communicated to the base station to give a global fused estimators. This is two-level clustering fusion structure.In summary, we consider a clustering sensor network system with the uncertain noise variances in the paper, using the least squares method, according to the minimax estimation principles, based on weighted measurement fusion algorithm, the two-level weighted measurement fusion robust Kalman filter and predictor are presented, the main works of this paper are as follows:Using full-rank decomposition of matrix method, the two two-level weighted measurement fusion robust time-varying Kalman filter and predictor are respectively presented, and using indirect methods of taking the limit, the two-level weighted measurement fusion robust steady-state Kalman filter and predictor are respectively presented, the robustness is proved by a Lyapunov equation method.Using the information filter, it is proved that the robust accuracies of the two-level weighted measurement fusion Kalman filter and predictor are respectively equal to those of the global centralized fusion robust Kalman filter and predictor and are higher than those of every local robust Kalman filter and predictor. The convergences in a realization between the time-varying and steady-state two-level weighted measurement fusion robust Kalman filter and predictor are respectively proved by the dynamic error system analysis(DESA) method and the dynamic variance error system analysis(DVESA) method.Using full-rank decomposition of matrix method, by directly method, the two two-level weighted measurement fusion robust steady-state Kalman filter and predictor are respectively presented, the robustness is proved by a Lyapunov equation method.Several simulation examples show the correctness and effectiveness of the proposed results.