Estimation of Flat-topped Gaussian distribution with application in system identification

Uniformly distributed uncertainty exists in industrial process; additive error introduced by quantization is an example. To be able to handle additive uniform and Gaussian measurement uncertainty simultaneously in system identification, the Flat‐topped Gaussian distribution is considered in this paper as an alternative to the Gaussian distribution. To incorporate this type of uncertainty in the maximum likelihood estimation framework, the explicit form of its density function is of necessity. This work proposes an approach for obtaining both the functional structure and corresponding parameter estimation of Flat‐topped Gaussian distribution by a moment fitting strategy. The performance of the proposed approximation function is verified by comparison to the Flat‐topped Gaussian distributed random variable with different Gaussian and uniform components. Results of numerical simulations and industrial applications in system identification are presented to verify the effectiveness of the Flat‐topped Gaussian distribution for noise distribution in handling additional uniform uncertainty. Flat‐topped Gaussian distribution is considered as the noise distribution in this article in order to handle the uniform and Gaussain measurement uncertainties simultaneously in system identification. This article proposes a parameter estimation approach for the Flat‐topped Gaussian distribution and formulates the system identification problem under maximum likelihood estimation framework. Numerical simulations and industrial case study are presented for its effectiveness.