Inverse filtration problem for a moving-mean-like object under the absence of measurement disturbances (Q1287258)

The author considers the problem of linear discrete filtering in the degenerate situation when there is no noise in the observations. Three approaches to solving the filtering problem are examined in the paper: the Kolmogorov-Wiener filter, the Kalman filter, and the decorrelated filter (the idea of the last filter consists in the construction of an estimate such that it is statistically similar to the estimated process: if, for instance, the estimated process is a discrete white noise, the decorrelated filter transforms the observation process in the corresponding discrete white noise).