自动化学报2015，Vol.41Issue(11)：1877-1892,16.DOI:10.16383/j.aas.2015.c150278
一种带有色量测噪声的非线性系统辨识方法
An Identification Method for Nonlinear Systems with Colored Measurement Noise
摘要
Abstract
In this paper, an identification method for nonlinear systems with colored measurement noise is proposed by using the maximum likelihood criterion. Firstly, the colored measurement noise is decorrelated based on the measurement differencing approach, and a new measurement equation is derived. Thus, the nonlinear system identification problem with colored measurement noise is transformed into the nonlinear system identification problem with white measurement noise and one-step delayed state. Secondly, a new nonlinear system identification method with maximum likelihood estimation is proposed based on the expectation maximization (EM) algorithm, which consists of expectation step (E-step) and the maximization step (M-step). In the E-step, the expectation of the complete data log-likelihood function is approximately calculated based on currently estimated parameters and the Gaussian approximated filter and smoother for nonlinear system with colored measurement noise. In the M-step, the approximately calculated expectation value is maximized, and noise parameter estimations are updated analytically and model parameter estimations are updated approximately by using Newton method. Finally, the efficiency of the proposed algorithm is illustrated in numerical simulations.关键词
非线性系统辨识/最大似然判据/有色量测噪声/期望最大化算法/量测差分方法/非线性状态估计器Key words
Nonlinear system identification/maximum likelihood criterion/colored measurement noise/expectation maximization (EM) algorithm/measurement differencing approach/nonlinear state estimator引用本文复制引用
黄玉龙,张勇刚,李宁,赵琳..一种带有色量测噪声的非线性系统辨识方法[J].自动化学报,2015,41(11):1877-1892,16.基金项目
国家自然科学基金(61001154, 61201409, 61371173), 中国博士后科学基金(2013M530147, 2014T70309), 黑龙江省博士后基金(LBH-Z13052, LBH-TZ0505), 哈尔滨工程大学中央高校基本科研业务费专项基金(HEUCFQ20150407) 资助Supported by National Natural Science Foundation of China (61001154, 61201409, 61371173), China Postdoctoral Science Foundation (2013M530147, 2014T70309), Heilongjiang Postdoc-toral Fund (LBH-Z13052, LBH-TZ0505), and Fundamental Re-search Funds for the Central Universities of Harbin Engineering University (HEUCFQ20150407) （61001154, 61201409, 61371173）
