Reliable truncation parameter selection and model order estimation for stochastic subspace identification

Stochastic subspace identification (SSID) is a fundamental technique for the analysis and prediction of dynamic systems influenced by stochastic processes. This paper addresses critical challenges in SSID, focusing on two steps of SSID, the estimation of truncation hyperparameters and the model order selection, which are pivotal for accurate and robust system parameter estimation. While the existing approaches for truncation hyperparameter estimation mostly rely on arbitrary choices in practice, a new fully automated approach, denoted as Multivariate Reconstruction Error Modelling (MREM), is introduced that is based on a solid theory of measurement errors. Similarly, the existing order selection approaches utilize different penalty terms. However, in application, the optimum approach is chosen by trial and error, and as the data length increases, the methods seem to perform worse, which alarms the issue of consistency. A new method for model order estimation, called Advanced Mean Square Eigenvalue Error (AMSEE) Minimization, is proposed in this work, which is not only consistent as the data length grows but also shows superiority over these existing methods. Instead of a penalty term, the method focuses on the mean square error of the singular value decomposition (SVD) and provides a method that, unlike existing ones, is robust to noise variation. The combination of MREM and AMSEE collectively denoted as MRSEE, achieves rapid convergence to the true model order, maintaining accuracy even as the data length increases. Simulation results consistently confirm these properties and the superiority of MRSEE over the existing approaches, exhibiting better accuracy and robustness against overfitting and underfitting in varying measurement noise conditions. In experiments with synthesized electroencephalogram (EEG) data, MRSEE reduces estimation and true error rates up to 43.44% and 41.16%, respectively, compared to the state-of-the-art approaches. These results highlight MRSEE’s capability to provide robust and reliable solutions for SSID applications, particularly in scenarios with relatively shorter data lengths and lower signal-to-noise ratio (SNR).