一种带有色量测噪声的非线性系统辨识方法

黄玉龙; 张勇刚; 李宁; 赵琳

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

doi: 10.16383/j.aas.2015.c150278

1.
哈尔滨工程大学自动化学院哈尔滨 150001

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

详细信息

作者简介:
黄玉龙哈尔滨工程大学自动化学院博士研究生.主要研究方向为惯性导航,滤波算法,组合导航.E-mail:heuedu@163.com

李宁哈尔滨工程大学自动化学院副教授.主要研究方向为自适应滤波,组合导航.E-mail:ningli@hrbeu.edu.cn

赵琳哈尔滨工程大学自动化学院教授.主要研究方向为惯性导航,卫星导航,组合导航.E-mail:zhaolin@hrbeu.edu.cn

通讯作者:
张勇刚哈尔滨工程大学自动化学院研究员.2007年获得英国Cardiff大学博士学位.主要研究方向为光纤陀螺,惯性导航,滤波算法,组合导航.本文通信作者.E-mail:zhangyg@hrbeu.edu.cn

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出版历程
- 收稿日期: 2015-05-11
- 修回日期: 2015-08-18
- 刊出日期: 2015-11-20

An Identification Method for Nonlinear Systems with Colored Measurement Noise

1.
College of Automation, Harbin Engineering University, Harbin 150001

Funds:

Supported by National Natural Science Foundation of China (61001154, 61201409, 61371173), China Postdoctoral Science Foundation (2013M530147, 2014T70309), Heilongjiang Postdoctoral Fund (LBH-Z13052, LBH-TZ0505), and Fundamental Research Funds for the Central Universities of Harbin Engineering University (HEUCFQ20150407)

摘要

摘要: 利用最大似然判据, 本文提出了一种带有色量测噪声的非线性系统辨识方法. 首先, 利用量测差分方法将有色量测噪声白色化, 获得新的量测方程, 从而将带有色量测噪声的非线性系统辨识问题转化成带白色量测噪声和一步延迟状态的非线性系统辨识问题. 其次, 利用期望最大化(Expectation maximization, EM)算法提出了一种新的基于最大似然估计的非线性系统辨识方法, 该算法由期望步骤(Expectation step, E-step)和最大化步骤(Maximization step, M-step)两部分组成. 在期望步骤中, 基于当前估计的参数并利用带有色量测噪声的高斯近似滤波器和平滑器, 近似计算完整的对数似然函数的期望. 在最大化步骤中, 近似计算的似然函数期望值被最大化, 并且通过解析更新获得噪声参数估计, 通过Newton更新方法获得模型参数的估计. 最后, 数值仿真验证了本文提出算法的有效性.
- 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
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.
- Nonlinear system identification /
- maximum likelihood criterion /
- colored measurement noise /
- expectation maximization (EM) algorithm /
- measurement differencing approach /
- nonlinear state estimator

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