Researches On Some Model Of Optimal Filtering Theory

As a branch of pre-modern statistics in 20th century, time series nowadays has become one of the most used and the most widely used topics in math, engineering and economic fields. It contains rich content and has wide application domain, whereas, it has become a powerful research tool in many disciplines and engineering.Now there're primarily three kinds of methods to analyze the time series. (1) The Box-Jenkins recursive forecasting method advanced by Box and Jenkins, (2) Projection forecasting method based on the fundamental theory and method of Hilbert space, which is raised by Rockwell and Davis. (3) The optimal filtering theory. Modern time series analysis method is a new method which the time series can be directly researched on by it and it can be connected with the Wiener filtering method and Kalman filtering method for obtaining a new and easily realized Wiener estimator and Kalman estimator. But up to now this kind of estimator is just studied for four models, respectively these models have the corresponding steady-state Kalman estimators. (i.e. Kalman gain matrix doesn't change with time.)Therefore in this thesis it is given four new models. The studying method to the new models is all diverting firstly which makes the model become a particular form of the already-known models. After that ARMA innovation and white noise estimator of models is studied, the state is showed as non-recursive expression of observed white noise, entered white noise and observation( the last three models needs diverting again) for obtaining non-recursive estimator, then recursive projection formula is used to obtain steady-state Kalman estimator.When adopting modern time series analysis method to estimate the state (smoother, filtering and forecasting), these new models can also be estimated besides the already-known four models. Applying the new method of estimating models, some relative problems encountered in reality can be better resolved. It is given in this thesis a example of calculation respectively for the first and the fourth model to demonstrate the application of the algorithm of the estimator of these kinds of models.