Advanced

A unified approach to smoothing formulas

Ljung, Lennart and Kailath, Thomas (1976) In Automatica 12(2). p.147-157
Abstract
Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major previous approaches are obtained as special cases, and their relationships are clarified. The set of solutions also contains as a fourth special case a (new) backwards analog of the innovations solution. The Mayne-Fraser two-filter formula belongs to the set of backwards solutions, and within this framework certain difficulties with its... (More)
Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major previous approaches are obtained as special cases, and their relationships are clarified. The set of solutions also contains as a fourth special case a (new) backwards analog of the innovations solution. The Mayne-Fraser two-filter formula belongs to the set of backwards solutions, and within this framework certain difficulties with its interpretation can be resolved. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Automatica
volume
12
issue
2
pages
147 - 157
publisher
Pergamon
external identifiers
  • scopus:49549133160
ISSN
0005-1098
DOI
10.1016/0005-1098(76)90078-9
language
English
LU publication?
no
id
bffed25f-a7a2-4176-a49e-4200bbfb65e3
date added to LUP
2018-12-27 11:16:18
date last changed
2019-01-06 14:21:18
@article{bffed25f-a7a2-4176-a49e-4200bbfb65e3,
  abstract     = {Based on various approaches, several different solutions to the smoothing problem have been given. The relationships between these solutions are not immediate, although they solve the same problem. Making use of a certain framework from scattering theory, we derive two families of solutions, with equations evolving forwards and backwards in time, respectively. Within these families three major previous approaches are obtained as special cases, and their relationships are clarified. The set of solutions also contains as a fourth special case a (new) backwards analog of the innovations solution. The Mayne-Fraser two-filter formula belongs to the set of backwards solutions, and within this framework certain difficulties with its interpretation can be resolved.},
  author       = {Ljung, Lennart and Kailath, Thomas },
  issn         = {0005-1098},
  language     = {eng},
  number       = {2},
  pages        = {147--157},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {A unified approach to smoothing formulas},
  url          = {http://dx.doi.org/10.1016/0005-1098(76)90078-9},
  volume       = {12},
  year         = {1976},
}