Adaptations of the classical Wiener–Kolmogorov filters are described that enable them to be applied to short nonstationary sequences. Alternative filtering methods that operate in the time domain and the frequency domain are described. The frequency-domain methods have the advantage of allowing components of the data to be separated along sharp dividing lines in the frequency domain, without incurring any leakage. The paper contains a novel treatment of the start-up problem that affects the filtering of trended data sequences.

The purpose of this paper is to provide a systematic treatment of the problem of estimation in systems of linear stochastic equations where some of the disturbances are uncorrelated and where the identifying equations are equivalent to a linear system.