Fast Time-Invariant Implementations for Linear Least-Squares Smoothing Filters
1978 (English)In: Proceedings of the 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, 1978, 1156-1159 p.Conference paper (Refereed)
We present a new solution for the fixed interval linear least-squares smoothing of a stationary random signal in additive white noise. By using the generalized Sobolev identity for the Fredholm resolvent of a covariance kernel, the smoothed estimate is expressed entirely in terms of time-invariant causal and anticausal filtering operations. These operations are interpreted from a stochastic point of view as giving some constrained (time-invariant) filtered estimates of the signal. From a computational point of view, the implementation presented here is particularly convenient, not only because time-invariant filters can be used to find the smoothed estimate, but also because a fast algorithm based on Levinson recursions can be used to compute the time-invariant filters themselves.
Place, publisher, year, edition, pages
1978. 1156-1159 p.
Least-squares, Smoothing, Linear, Fredholm resolvent, Levinson recursions
IdentifiersURN: urn:nbn:se:liu:diva-101006DOI: 10.1109/CDC.1978.268116OAI: oai:DiVA.org:liu-101006DiVA: diva2:664732
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, San Diego, CA, USA, January, 1979