Parameter Estimation of Linear Dynamical Systems with Gaussian Noise

Léo Simpson, Andrea Ghezzi, Jonas Asprion, Moritz Diehl

Published 2022-11-22Version 1

We present a novel optimization-based method for parameter estimation of a time-varying dynamic linear system. This method optimizes the likelihood of the parameters given measured data using an optimization algorithm tailored to the structure of this maximum likelihood estimation problem. Some parameters of the covariance of process and measurement noise can also be estimated. This is particularly useful when offset-free Model Predictive Control with a linear disturbance model is performed. To reduce the complexity of the maximum likelihood estimation problem we also propose an approximate formulation and show how it is related to the actual problem. We present the advantages of the proposed approach over commonly used methods in the framework of Moving Horizon Estimation. We also present how to use Sequential Quadratic Programming efficiently for the optimization of our formulations. Finally, we show the performance of the proposed methods through numerical simulations. First, on a minimal example with only one parameter to be estimated, and second, on a system with heat and mass transfer. Both methods can successfully estimate the model parameters in these examples.