Study On Robust Kalman Filtering For Linear Stochastic Uncertain System

The problem of estimation includes filtering, prediction and smoothing and has been one of the key research topics of control community since the seminal paper by Wiener. But wiener filtering cannot be used in the real time signal processing. Kalman filtering just can fetch up the default, which can give the optimum estimation of signal under the condition of the minimums mean-square. And this method works in the time domain; the processing speed is fast, which make it be use in the real time signal processing. The standard kalman filtering is based on H 2 estimative criterion and need accurate model of system. But there exists stochastic uncertainties in the model of system in case of reality. This paper deals with the problem of robust kalman filtering for a class of stochastic uncertain system, where the uncertainties that satisfy the random uncertain matrices that exist in state matrices and observer matrices. If we still estimate according to the tradinonal kalman filtering, the estimative result will be relatively bad or cause scatteration. We will make further research and analysis for the linear stochastic uncertain system model from two respects separately in this thesis. One is system with time delay; another is system with non-time delay. To the problem of estimation and controlling for system with time delay, we know that there are some methods. for continuous time linear system ,such as prejudicial differential equation,linear matrix inequality ,etc. For discrete time linear systems, the most direct method is augmented system. That is to say, it can only be calculated based on an augmented system. But these methods lead to increasing of calculation when the dimension or time delay in the system is very great. We will adopt a new method in this thesis. The robust kalman filtering will based on two Riccati equations with the same dimension as system. Compared with other existing robust filtering, it is very simple and effective to calculate and is unbiased to the linear stochastic uncertain system. Main idea of the re-organized innovation: We will renew to organize innovation, which comes from different observer measurements, and introduce a re-organized innovation sequence. We also prove that it the innovation sequence which is an uncorrelated white noise and different from the innovation in kalman filtering formulation. Thus robust kalman filtering is derived based on an innovation analysis method together with projection in Hilbert space. In the end a stimulant example shows that the robust filtering method is effective and feasible. The new theory of re-organized innovation will give basic foundation for the problem of robust estimation in the linear system with time-delay. The application prospect of this method is prognosticated at the same time.