观测噪声为分式布朗单的单侧递归滤波方程-概率论与数理统计专业论文.docxVIP

华中科技 大学硕士 学 华 中 科 技 大 学 硕 士 学 位 论 文 II II Abstract In 1940, based on the needs of the fire control,one of the creations of the control theory Wiener proposed the Statistics optimal filtering in the frequency domain, this method is called filtering. During the same period, Kolmogrov proposed and soluted the discrete stationary random sequence’s prediction and extrapolation. Wiener filtering and Kolmogrov filtering have created a new field which uses statistical estimation method to solut stochastic control problem. Since then, after more than 50 years’ development, filtering theory has been gradually improved, from one-dimensional filtering to multi-dimensional filtering, from linear filtering to nonlinear filtering and the observation noise from Brownian motion to two-dimensional random field. At the same time, filtering theory has been widely used in the signal, navigation, control, sensing data processing, missile-tracking and so on. In recent years, filtering theory has been more widely used in the computer image processing, such as human face recognition, image segmentation, image edge detection, etc. The core content of this paper is the one-sided recursive filtering equation in the presence of fractional Brownian sheet observation noise by using multi-parameter martingale theory and the relationship between Brownian sheet and fractional Brownian sheet. In this article，the main content of the first chapter is the background, the theoretical foundation and the development of the filtering theory. The second chapter introduces the generation of the filtering and the one-dimensional linear filtering. In the end of this chapter, the nonlinear filtering under normal circumstances and nonlinear filtering under Gauss circumstances are introduced. Based on Wong[34] and combined the results of Amirdjamova[24],the last chapter gives the one-sided recursive filtering equation in the presence of fractional Brownian sheet observation noise by using multi-parameter