Regularized Basis Function Estimation of Volterra Kernels for the Cascaded Tanks Benchmark

Abstract In the nonlinear setting, nonparametric estimation methods are convenient because they do not require a detailed model structure selection and can be used with limited prior knowledge on the system of interest. In this paper, we consider the cascaded tanks benchmark dataset, and estimate Volterra series models using a regularized basis function approach. By directly regularizing the basis function expansions of each Volterra kernel in a Bayesian framework, the resulting model has a more compact form and can be estimated far more quickly than the equivalent time domain method, while achieving comparable prediction accuracy with respect to the validation data.