线性动态系统噪声辨识的非参数贝叶斯推理算法研究

Bayesian Nonparametric Inference Algorithm for Noise Identification of Linear Dynamic System

提出一新的非参数贝叶斯推理算法来辨识任意复杂的多模噪声分布,采用无穷维推理技术,能够较为精确地逼近噪声的后验分布。算法主要引入一随机度量分布满足一预设的先验过程——混合Dirichlet过程(Dirichlet Process Mixture,简称DPM),由于DPM具有形似于Polya urn的采样特性,能够很方便地对噪声数据进行聚类,并导出噪声的后验分布。仿真结果显示,噪声数据似然的Metropolis-Hastings(M-H)的采样算法比点估计的系统分析算法精度高。

In the paper, a novel Bayesian nonparametric inference algorithm for identifying the noise with an arbitrary multi-modal distribution was proposed. The infinite-dimensional inference technique was available to precisely approximate the posterior distribution of the noise. Employing the model of Dirichlet Process Mixture （ DPM）, the noise data could be clustered conveniently, the posterior distribution of the noise could be formulated due to the analogous sampling property of Polya urn for DPM. The results of simulation show that this algorithm has a better precision compared with the system analysis algorithm based on the point estimation.