滤波是利用观察信息来估计信号的一种方法，有着广泛的应用。目前非线性滤波是滤波理论的研究重点。关于非线性滤波，人们已经取得了十分丰富的结果,写了好几部专著。但是到目前为止，人们对非线性滤波的研究主要集中在连续观测的情形，对带跳观测的非线性滤波的研究相对较少。然而，对带跳观测的非线性滤波的研究有其必要性，因为它们已经被应用到通讯与控制、生命科学与金融等领域。我们相信正如连续观测的情形，带跳观测的非线性滤波必将被应用到更加广泛的领域。从上世纪90年代开始，非线性滤波领域中的一个十分重要的问题"滤波的稳定性问题"受到了人们的高度关注，研究该问题具有重要的理论与实际意义。本项目拟主要研究几类带跳观测的非线性滤波的稳定性以及某些奇异信号在带跳观测下的非线性滤波。

Filtering is a kind of method to estimate the signal by the observation information and it has extensive applications. Now nonlinear filtering is the focus of filtering theory. About nonlinear filtering, so many achievements have been obtained and several monographs have been written. But up to now, the study on nonlinear filtering is focused on the case with continuous observations and the work on the nonlinear filterings with jump observations is fewer. While, it's necessary to study the nonlinear filterings with jump observations, because they have been applied to communication and control, life science and finance etc. We believe that they are certain to be applied to more extensive fields as the case with continuous observations. From 90s of last century, an important problem `stability of filter' in the field of nonlinear filtering has been payed high attension to by people and the research on this problem has important theoretic and practical significance. The main goal of this project is to explore the stability of several classes of nonlinear filters with jump observations, and the nonlinear filterings of some singular signals with jump observations.