SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 1, Page 483-509, January 2020.
A stable filter has the property that it asymptotically “forgets" initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words approximations that are uniformly convergent in the time variable. As uniform approximations are ideal from a practical perspective, finding criteria for filter stability has been the subject of many papers. In this paper, we seek to construct approximate filters that stay close to a given (possibly) unstable filter. Such filters are obtained through a general truncation scheme and, under certain constraints, are stable. The construction enables us to give a characterization of the topological properties of the set of optimal filters. In particular, we introduce a natural topology on this set, under which the subset of stable filters is dense.

中文翻译：

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最优滤波器的稳定逼近方案

SIAM / ASA不确定性量化期刊，第8卷，第1期，第483-509页，2020年1月。
稳定的滤波器具有渐近地“忘记”初始扰动的特性，因此，可以构造这样的滤波器的近似值，这些滤波器的误差在时间上仍然很小，也就是说，近似值在时间变量中始终收敛由于从实际的角度来看均匀近似是理想的，因此寻找滤波器稳定性的标准已成为许多论文的主题，在本文中，我们试图构造近似于给定（可能）不稳定滤波器的近似滤波器。通过一般的截断方案，并且在一定的约束下是稳定的，该结构使我们能够表征最佳滤波器组的拓扑特性，尤其是在该组滤波器上引入自然拓扑，在此之下，稳定滤波器的子集是密集的。