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1887

access icon free Directional splitting of Gaussian density in non-linear random variable transformation

© The Institution of Engineering and Technology
Received 15/06/2017, Accepted 21/06/2018, Revised 12/04/2018, Published 16/07/2018

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.

Inspec keywords: approximation theory; minimisation; Gaussian distribution; transforms

Other keywords: nonlinear random variable transformation; Gaussian distribution; directional splitting; Gaussian mixture distribution; design parameter selection; GM splitting directions; approximate GM distribution; Gaussian density; signal processing; numerical simulations; fault detection; probability density function; error minimisation; automatic control; to-be-transformed random variable distribution approximation

Subjects: Other topics in statistics; Optimisation; Probability theory, stochastic processes, and statistics; Other topics in statistics; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Numerical approximation and analysis; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Statistics; Optimisation techniques; Numerical analysis; Optimisation techniques

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