A unified approach to smoothing formulas
(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)
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- author
- Ljung, Lennart and Kailath, Thomas
- organization
- publishing date
- 1976
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Automatica
- volume
- 12
- issue
- 2
- pages
- 147 - 157
- publisher
- Pergamon Press Ltd.
- 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
- 2021-01-03 08:12:00
@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 Press Ltd.}}, series = {{Automatica}}, title = {{A unified approach to smoothing formulas}}, url = {{http://dx.doi.org/10.1016/0005-1098(76)90078-9}}, doi = {{10.1016/0005-1098(76)90078-9}}, volume = {{12}}, year = {{1976}}, }