%0 Electronic Article
%A Jindřich Duník
%A Ondřej Straka
%A Benjamin Noack
%A Jannik Steinbring
%A Uwe D. Hanebeck
%K probability density function
%K numerical simulations
%K fault detection
%K approximate GM distribution
%K Gaussian distribution
%K design parameter selection
%K directional splitting
%K automatic control
%K error minimisation
%K to-be-transformed random variable distribution approximation
%K nonlinear random variable transformation
%K Gaussian density
%K Gaussian mixture distribution
%K signal processing
%K GM splitting directions
%X 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.
%@ 1751-9675
%T Directional splitting of Gaussian density in non-linear random variable transformation
%B IET Signal Processing
%D December 2018
%V 12
%N 9
%P 1073-1081
%I Institution of Engineering and Technology
%U https://digital-library.theiet.org/;jsessionid=1nbe798t5tm84.x-iet-live-01content/journals/10.1049/iet-spr.2017.0286
%G EN