Fast Time-Invariant Implementations for Linear Least Squares Smoothing Filters
1979 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 24, no 5, 770-775 p.Article in journal (Refereed) Published
We present a new solution for the fixed interval linear least-squares smoothing of a random signal, finite dimensional or not, inadditive white noise. By using the so-called Sobolev identity of radiative transfer theory, the smoothed estimate for stationary processes is expressed entirely in terms of time-invariant causal and anticausal filtering operations; these are interpreted from a stochastic point of view as giving certain constrained (time-invariant) filtered estimates of the signal. Then by using a recently introduced notion of processes close to stationary, these results are extended in a natural way to general nonstationary processes. From a computational point of view, the representations presented here are particularly convenient, not only because time-invariant filters can be used to find the smoothed estimate, but also because a fast algorithm based on the so-called generalized Krein-Levinson recursions can be used to compute the time-invariant filters themselves.
Place, publisher, year, edition, pages
IEEE Control Systems Society , 1979. Vol. 24, no 5, 770-775 p.
Least-squares estimation, Smoothing methods, Time-invariant implementation, Krein-Levinson recursions
IdentifiersURN: urn:nbn:se:liu:diva-102124DOI: 10.1109/TAC.1979.1102152OAI: oai:DiVA.org:liu-102124DiVA: diva2:668556