An Example of an Infinite Dimensional Filtering Problem: Filtering for Gyroscopic Noise.

摘要

An infinite-dimensional model is given for the generation of gryroscopic noise, which exhibits power spectral density proportional to (1/f) over a wide frequency range. The optimal filter is given for separating a statistically described signal from additive gyroscopic noise, using discrete-time observations. This filter is expressed as a discrete-time infinite-dimensional Kalman-Bucy filter, with an associated Riccati covariance operator equation. Sufficient conditions are specified such that this Kalman-Bucy filter will possess various desired properties. (Author)