An effective implementation for kernel‐based positive system identification using Gibbs sampling

Abstract Recently, the kernel‐based method has been applied for the positive system identification where the hyperparameter estimation is a crucial and critical part. The regularized identification problem for the positive system is first formulated. Due to the nonnegative constraint of the positive system, the Bayesian interpretation chooses the truncated Gaussian distribution as the prior of the system parameter. The hyperparameters estimation is cast as a marginal likelihood optimization. A Bayesian network for the positive system is established to construct a probabilistic framework for handling the hyperparameter estimation. Based on the derived conditional distributions, this paper develops a Markov chain Monte Carlo method to sample according to the likelihood function, where the Gibbs sampling is available to improve the sampling efficiency. The proposed sampling‐based algorithm facilitates searching for hyperparameters globally. The simulation results demonstrate that the proposed algorithm provides more precise and efficient identification compared to the conventional method.