一种带有色量测噪声的非线性系统辨识方法

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.

An Identification Method for Nonlinear Systems with Colored Measurement Noise

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.