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 .

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 :

• 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 .

In the Filtering Problem the information from observation up to the time of the current sample is used. In smoothing all observation samples are used (from future). Filtering is causal but smoothing is batch processing of the same problem, namely, estimation of a time-series process based on serial incremental observations.

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