Kernel-based system identification using generalized orthogonal basis functions and meta-heuristic techniques

The kernel-based regularization method (KRM), emerging as a paradigm for system identification, has found widespread application in both causal and non-causal system identification. Its main challenges are the design of the kernel and the estimation of the hyperparameters. In this paper, we give some approaches to address these challenges. Specifically, we introduce a framework for causal kernel design based on generalized orthogonal basis functions (GOBFs) and successfully extend it to the non-causal scenario. In addition, using the grey wolf optimization (GWO) algorithm as an example, we explore the potential of using meta-heuristic techniques for hyperparameter estimation in KRM. To further enhance the search accuracy of the algorithm, we improve the GWO algorithm by adopting a nonlinear weight update strategy and incorporating crossover and mutation strategies inspired by the genetic algorithm (GA). Numerical simulations demonstrate that the kernel regularized identification method proposed in this paper exhibits good model estimation performance.