A1 Jindřich Duník

A1 Ondřej Straka

A1 Benjamin Noack

A1 Jannik Steinbring

A1 Uwe D. Hanebeck

PB iet

T1 Directional splitting of Gaussian density in non-linear random variable transformation

JN IET Signal Processing

AB 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.

K1 probability density function

K1 fault detection

K1 numerical simulations

K1 approximate GM distribution

K1 Gaussian distribution

K1 design parameter selection

K1 directional splitting

K1 automatic control

K1 error minimisation

K1 to-be-transformed random variable distribution approximation

K1 nonlinear random variable transformation

K1 Gaussian density

K1 Gaussian mixture distribution

K1 signal processing

K1 GM splitting directions

DO http://dx.doi.org/10.1049/iet-spr.2017.0286

UL http://digital-library.theiet.org/;jsessionid=1mbt9gnrgu8tg.x-iet-live-01content/journals/10.1049/iet-spr.2017.0286

LA English

SN 1751-9675

YR 2018

OL EN