Modeling of multiple-input, time-varying systems with recursively estimated basis expansions

We present novel computational schemes for estimating single- (SI) and multiple-input (MI) time-varying (TV) systems, combining a Laguerre-Volterra model formulation with improved recursive schemes based on conventional Recursive Least Squares (RLS) and Kalman Filtering (KF). The proposed recursive estimators achieve superior performance, particularly in the case of TV systems with multiple-inputs or systems that exhibit mixed-mode variations. RLS-based schemes were found to perform better in the case of TV linear systems, while the KF-based schemes were found to perform considerably better in the case of TV nonlinear systems. Model order selection and tuning of the estimator hyperparameters were implemented using Genetic Algorithms (GA), significantly improving performance and reducing computation time. Furthermore, exploiting the search efficiency in hyperparameter space yielded by the proposed GA, we rigorously examined the correlations between the hyperparameter values, the model complexity and the TV characteristics of the true underlying system. The performance of the proposed TV system identification framework was assessed using simulations and experimental data from patients undergoing head-up tilt testing for the diagnosis of vasovagal syncope.