An example of an infinite dimensional filtering problem: Filtering for gyroscopic noise

An infinite-dimensional model is given for the generation of gyroscopic 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 form 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.