Application of Pseudorandom Maximum Length Binary Signals to Nonlinear Kernel-Based Estimation

Abstract

This paper considers the identification of nonlinear systems using kernel-based estimation. Recent literature has presented interesting results employing a linear kernel and a nonlinear kernel. It was shown that, via careful design of the kernels, high accuracy can be achieved. However, long data records are required and the hyperparameter optimization is computationally intensive. In the current work, the identification problem is explored from a perturbation signal design viewpoint. In particular, the pseudorandom maximum length binary signal is applied to identify the nonlinear terms present in the system. Such an experiment may be useful as a preliminary test as insights gained can potentially simplify the subsequent identification problem and shorten the required data record.