Adaptive Fusion Of Kalman Filters For Multi-sensor Fractional-order Systems

At present,the control system mostly considers the differential form of integer order.However,in the actual physical system,due to the special material or time-chemical characteristics of the system,it will show non integer dynamic behavior,such as viscoelastic system,power plant control system and chaotic system.If the integer order is used to describe this kind of system,there will be unknown systematic error.Using fractional order to describe this kind of system can better reveal the essential characteristics and dynamic behavior of things,and will reduce the error caused by the system from the root.If the statistics of the state noise and measurement noise of the system are unknown,the filtering performance will deteriorate.In view of this phenomenon,this dissertation proposes to add a noise estimator in the filtering process.The noise estimator can estimate and correct the noise in real time.At this time,the state estimation problem of the system with unknown noise statistics is transformed into an adaptive state.estimation problem.In order to improve the estimation accuracy of Kalam filter,this dissertation proposes to use multi-sensor information fusion technology to estimate the state of fractional-order system.In this dissertation,the continuous time linear fractional order system is discretized according to the fractional calculus defined by Grunwald letnikov(G-L)and the method of tusin generating function.For the discretized fractional order system,the Kalman filtering algorithm of fractional order system is derived based on the derivation method of classical Kalman filtering.The problem of Kalman filtering estimation for fractional order systems with uncorrelated noise is discussed.Combined with multi-sensor centralized fusion and distributed fusion algorithms,fractional Kalman filtering algorithms for centralized observation fusion and track fusion are proposed respectively.The Kalman filtering estimation problem of fractional order systems with uncorrelated and correlated unknown noise statistics is deeply discussed.By transformation and simplification,the adaptive Kalman filtering problem of fractional order systems with correlated noise can be transformed into the adaptive Kalman filtering problem of fractional order systems with uncorrelated noise.Combined with the same fusion algorithm as above,an adaptive fusion Kalman filtering algorithm for fractional order system is proposed.The results of simulation examples show that the proposed fractional Kalman filter algorithm is correct and feasible.