A Survey of Infinite-Dimensional Filtering

In the last few years there has been quite a lot of literature on the problem of filtering for infinite-dimensional systems. The class of systems studied has been wide, including both linear and nonlinear distributed parameter systems, with partial-integro-differential operators, with delays, with boundary noise and even coupled with lumped parameter systems. However, the mathematical problem of rigorously modeling distributed noise is a fundamental and difficult one which has been ignored by most of the, authors, who have been content to proceed with a formal analysis. As this theoretical problem has now been solved at least for linear systems and as it gives much insight into the formal analysis, this paper hopes to give a unified survey of the field of infinite-dimensional filtering.