Filtering, smoothing and prediction using a control-loop spectral factorization method for coloured noise

SUMMARY

A method for the linear least-squares estimation of random signals contaminated with random noise that uses a new method of spectral factorization is shown. It is shown that the optimal filter can be written entirely in terms of the two spectral factors of signal plus noise and noise-alone, and can be applied to the general case of coloured and white additive noise. The method of spectral factorization used is novel and uses control-system methodology. Copyright © 2012 John Wiley & Sons, Ltd.