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 Wiener.

A smoother is an algorithm or implementation that implements a solution to such problem.

Not to be confused with blurring and smoothing using methods such as moving average. See smoothing.

The Smoothing problem and Filtering problem are often considered a closely-related pair of problems.

Bayesian smoothing theory

Example smoothers

Some variants include :

• Rauch–Tung–Striebel (RTS) smoother
• RTS smoother (ERTSS)
• Gauss–Hermite RTS smoother (GHRTSS)
• Cubature RTS smoother (CRTSS)