Bayesian positive system identification: Truncated Gaussian prior and hyperparameter estimation

Bayesian methods have been extended for the linear system identification problem in the past ten years. The traditional Bayesian identification selects a Gaussian prior and considers the tuning of kernels, i.e., the covariance matrix of a Gaussian prior. However, Gaussian priors cannot express the system information appropriately for identifying a positive finite impulse response (FIR) model. This paper exploits the truncated Gaussian prior and develops Bayesian identification procedures for positive FIR models. The proposed parameterizations in the truncated Gaussian prior can reflect the decay rate and the correlation of the impulse response of the system to be identified. The expectation-maximization (EM) algorithm is tailored to the hyperparameter estimation problem of positive system identification with the truncated Gaussian prior. Numerical experiments compare the truncated Gaussian prior to the traditional Gaussian prior for positive FIR system identification. The simulation results demonstrate that the truncated Gaussian prior outperforms the Gaussian prior. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces a new method for Bayesian identification of positive finite impulse response (FIR) models by using a truncated Gaussian prior. The parameterization in the truncated Gaussian prior can better reflect the characteristics of the impulse response of the system to be identified. Compared to the traditional Gaussian prior, the truncated Gaussian prior outperforms in positive FIR system identification.