Open AccessDirectional splitting of Gaussian density in non‐linear random variable transformation
Author(s) -
Duník Jindřich,
Straka Ondřej,
Noack Benjamin,
Steinbring Jannik,
Hanebeck Uwe D.
Publication year - 2018
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2017.0286
Subject(s) - gaussian , random variable , transformation (genetics) , probability density function , mathematics , gaussian process , algorithm , variable (mathematics) , gaussian random field , gaussian function , computer science , statistics , mathematical analysis , biochemistry , physics , chemistry , quantum mechanics , gene
Transformation of a random variable is a common need in a design of many algorithms in signal processing, automatic control, and fault detection. Typically, the design is tied to an assumption on a probability density function of the random variable, often in the form of the Gaussian distribution. The assumption may be, however, difficult to be met in algorithms involving non‐linear transformation of the random variable. This paper focuses on techniques capable to ensure validity of the Gaussian assumption of the non‐linearly transformed Gaussian variable by approximating the to‐be‐transformed random variable distribution by a Gaussian mixture (GM) distribution. The stress is laid on an analysis and selection of design parameters of the approximate GM distribution to minimise the error imposed by the non‐linear transformation such as the location and number of the GM terms. A special attention is devoted to the definition of the novel GM splitting directions based on the measures of non‐Gaussianity. The proposed splitting directions are analysed and illustrated in numerical simulations.