Truncated Gaussian Noise Estimation in State-Space Models

Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which can lead to inaccuracies when the noise follows bounded distributions. With the aim of generalizing the Gaussian noise assumption to potentially truncated densities, this paper introduces a method for estimating the noise parameters in a state-space model subject to truncated Gaussian noise. Our proposed data-driven approach is rooted in maximum likelihood principles combined with the Expectation-Maximization algorithm. The efficacy of the proposed approach is supported by a simulation example.