Smoothing problem (stochastic processes)
The Smoothing problem (not to be confused with smoothing in signal processing and other contexts) refers to Recursive Bayesian estimation also known as Bayes filter is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems defined by Norbert Wiener [1] [2].
A smoother is an algorithm or implementation that implements a solution to such problem. Please refer to the article Recursive Bayesian estimation for more information. The Smoothing problem and Filtering problem are often considered a closely-related pair of problems. They are studied in Bayesian smoothing theory.
Note: Not to be confused with blurring and smoothing using methods such as moving average. See smoothing.
Example smoothers
Some variants include [3]:
- Rauch–Tung–Striebel (RTS) smoother
- RTS smoother (ERTSS)
- Gauss–Hermite RTS smoother (GHRTSS)
- Cubature RTS smoother (CRTSS)
Relation between Filtering and Smoothing problems
Both smoothing problems and filtering problems are often confused with smoothing and filtering in other contexts (especially non-stochastic signal processing). These names are used in the context of World War 2 defined by people like Norbert Wiener [1][2].
See Also
- Smoothing problem is closely related to the Filtering problem.
- Filtering (disambiguation)
- Filtering problem
- Not to be confused with Filter (signal processing)
- Kalman filter most famous filtering algorithm in the sense of 'filtering problem' and 'smoothing problem'.
- Smoothing (not to be confused with the Smoothing problem)
- Smoothing (disambiguation)
- Smoothing problem
References
- ^ a b 1942, Extrapolation, Interpolation and Smoothing of Stationary Time Series. A war-time classified report nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject. Published postwar 1949 MIT Press. http://www.isss.org/lumwiener.htm])
- ^ a b Wiener, Norbert (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. New York: Wiley. ISBN 0-262-73005-7.
- ^ Simo Särkkä. Bayesian Filtering and Smoothing. Publisher: Cambridge University Press (5 Sept. 2013) Language: English ISBN-10: 1107619289 ISBN-13: 978-1107619289