On the Uncertainty Modelling for Linear Continuous-Time Systems Utilising Sampled Data and Gaussian Mixture Models

Abstract In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.