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.

在过去的十年中，贝叶斯方法已经扩展到线性系统识别问题。传统的贝叶斯识别选择高斯先验并考虑内核的调整，即高斯先验的协方差矩阵。但是，高斯先验不能正确表达系统信息以识别正有限冲激响应（FIR）模型。本文利用截断的高斯先验并为正FIR模型开发了贝叶斯识别程序。截断的高斯先验中建议的参数化可以反映衰减率和待识别系统的脉冲响应的相关性。期望最大化（EM）算法针对截断的高斯先验正系统识别的超参数估计问题而定制。数值实验比较了截断的高斯和传统的高斯先验，以进行正FIR系统识别。仿真结果表明，截断的高斯先验优于高斯先验。