Estimating Closed-Loop Multiple-Input Single-Output Dynamic Systems using Gaussian Processes
This paper extends complex Gaussian process regression-based transfer function (TF) estimation from the single-input single-output setting to closed-loop multiple-input single-output (MISO) systems. Accurate estimation of individual TFs in closed-loop MISO systems is challenging as feedback and correlation between measured signals can obscure the contributions of each input. We formulate a Gaussian process-based estimator for MISO systems, provide analytical conditions under which each system module can be separately identified, and show that the estimator converges to the true TFs in the zero noise limit. Moreover, we demonstrate how conventional closed-loop bias handling techniques relying on external excitation can be employed to construct appropriate regressors. Monte Carlo simulations support the analytical identifiability results and highlight the trade-off between closed-loop bias and error introduced by constructing exogenous regressors partly from endogenous signals. The presented work offers an expressive, nonparametric alternative to existing estimation approaches for MISO systems, while providing a probabilistic characterization of the estimation uncertainty.