实现闭环系统参数─致估计的直接辨识方法

为了实现闭环系统参数的一致估计，提出了一种一致辨识闭环系统模型参数的偏差补偿最小二乘法。这种方法不需要事先假设系统模型阶次和通道时延满足一定的不等式，允许前向通道和反馈通道之一中的噪声为有色噪声，并且在其辨识过程中不需要对有色噪声建模。     

实现闭环系统参数一致估计的直接辨识方法

为了实现闭环系统参数的一致估计，提出了一种一致辨识闭环系统模型参数的偏差补偿最小二乘法，这种方法不需要事先假设系统模型阶次和通道时延满足一定的不等式，允许前向通道的反馈通道一中的噪声为有色噪声，并且在其辨识过程中不需要对有色噪声建模。     

有色噪声条件下的子空间辨识改进方法及应用

针对工业生产过程中噪声往往为有色噪声的情况,提出一种改进的子空间辨识方法。传统的子空间辨识方法在系统存在有色噪声时辨识效果不佳,改进方法则采用变换系统模型形式来克服有色噪声对系统的影响,在辨识时直接利用变换系统模型后的数据得到系统较为准确的状态空间模型,实践证明,状态空间模型更适用于工业过程。连续搅拌反应釜（CSTR）系统是一类典型的工业生产系统,将子空间辨识方法应用于CSTR过程的仿真实验,通过比较改进前和改进后的系统预测误差,验证了所提方法的有效性。     

有色噪声干扰下Hammerstein非线性系统两阶段辨识

针对实际工业过程中普遍存在有色噪声,提出了有色噪声干扰下Hammerstein非线性系统两阶段辨识方法。采用设计的组合式信号实现Hammerstein系统各模块参数辨识分离,简化了辨识过程。在第一阶段,基于可分离信号的输入输出数据,利用相关分析算法估计线性模块参数,减少了有色噪声对辨识的干扰。在第二阶段,基于随机信号的输入输出数据,在最小二乘算法中引入滤波技术,推导了滤波递推增广最小二乘算法,提高了非线性模块参数和噪声模型参数的辨识精度。仿真结果表明：提出的两阶段辨识方法提高了辨识精度,有效地抑制了有色噪声的干扰。     

有色噪声中非线性动态系统的BP网络辨识

前馈多层神经网络为复杂的非线性系统提供了一种极具吸引力的模型结构。本文不利用仅含一个隐层的前馈多层神经网络来拟合离散时间非线性动态系统的问题进行了探讨。由于有色噪声的存在会导致网络模型偏差产生，文中引入了一种对噪声建模的方案。借助于非线性模型检验技术，本文给出了在有色噪声存在的情况下，利用ＢＰ网络辨识离散时间非线性动态系统的一般方法，仿真结果亦表明该方法行之有效。     

有色噪声背景下的正交子空间辨识

针对传统子空间辨识中存在的有色噪声干扰问题,本文提出一种正交子空间辨识方法.首先,根据子空间辨识算法机制构建含有色噪声的扩展状态空间模型.然后,结合有色噪声的相关性分析,研究了传统子空间辨识方法的有偏性问题,并重新设计了投影向量和正交投影方式,用以消除有色噪声干扰.最后,对投影后的数据矩阵进行奇异值分解,获取广义能观测矩阵,进而求得系统的状态空间模型参数.仿真结果表明该方法在有色噪声干扰下是一致无偏的,并且具有渐进二阶统计特性.结合陀螺仪的具体实验结果表明,该算法在实际应用中具有比传统子空间辨识法更高的辨识精度.     

含有有色噪声的非线性分数阶系统自适应扩展卡尔曼滤波器

研究了含有未知参数的情况下，分别含有分数阶有色过程噪声和有色测量噪声的连续时间非线性分数阶系统状态估计问题.采用Grünwald-Letnikov （G-L）差分方法和1阶泰勒展开公式，对描述连续时间非线性分数阶系统的状态方程进行离散化和线性化.构造由状态量、未知参数和分数阶有色噪声的增广向量，设计自适应分数阶扩展卡尔曼滤波算法实现对有色噪声情况下的连续时间非线性分数阶系统的状态和参数的估计.最后，通过分析两个仿真实例，验证了提出算法的有效性.     

过程控制常用连续模型的直接辨识法及应用

针对工业过程中最常用的一阶加滞后、二阶加滞后、二阶加零点、二阶加零点及滞后、积分惯性加滞后等环节，给出了基于阶跃响应的连续模型参数直接辨识算法。由传递函数的拉普拉斯逆变换式和对象阶跃响应的采样数据构成模型参数回归表达式，用最小二乘法或辅助变量法直接辨识对象的连续时间传递函数模型参数。仿真与实际应用结果表明，该算法提高了模型辨识精度，减小了对过程的扰动，并且对输出测量噪声不敏感，鲁棒性强，容易编程实现，可提高实际PID控制器参数整定质量。     

基于人工神经网络的Hammerstein模型辨识

证明了Ｈａｍｍｅｒｓｔｅｉｎ模型在有色噪声情况下，可利用系统的稳态信息辨识模型的非线性增益，并提出了神经元网络的辨识方法。利用系统的动态信息，运用一般的辅助变量法可辨识Ｈ模型的线性子系统。仿真结果表明该方法辨识精度高，具有一定的实用性。     

基于组合式信号源的Hammerstein-Wiener模型辨识方法

针对含有有色噪声的非线性Hammerstein-Wiener模型,提出一种基于组合式信号源的辨识方法.通过利用可分离信号和随机信号组成的组合信号源实现有色噪声干扰下Hammerstein-Wiener模型各串联模块参数辨识的分离,简化辨识过程.首先,基于可分离信号的输入和输出,采用相关分析方法抑制过程噪声的干扰,辨识输出静态非线性模块和动态线性模块的参数;然后,基于辅助模型技术,利用辅助模型的输出和残差的估计值分别取代辨识模型中的不可测中间变量和噪声变量,推导辅助模型递推增广最小二乘方法,根据随机信号的输入输出数据辨识输入静态非线性模块和噪声模型的参数;最后,通过理论分析和仿真结果表明,所提出方法能够有效辨识有色噪声干扰下的非线性Hammerstein-Wiener模型,具有较好的鲁棒性.     

A method for unbiased parameter estimation by means of the equation error input covariance

A method for obtaining an unbiased estimate of the finiteq-dimensional parameter vector defining a time-invariant linear dynamical system in the presence of noise is described. The system is excited by a stationary mean-square bounded process. The method is based on anr geq qparameter "equation error" and is presented in continuous time. The equation error input covariance (EEIC) is equated to zero, and the resulting single linear equation havingr > qunknown parameters provides a necessary condition for their unique identification. From it,r - 1additional independent equations are generated. The resultingrlinear independent equations provide the unbiased estimate of the parameter vector in which the excessr - qcomponents vanish. The method does not require the identification of the noise statistics, and it can be applied without a priori assumption of the order of the system's numerator and denominator. Performance of the method is illustrated by simulated examples demonstrating the convergence of the parameter estimate in on-line recursive identification both in open and closed loop.     

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 effective direct closed loop identification method for linear multivariable systems with colored noise

Multivariable control systems with colored noise widely exist in the most industrial fields, while the system identification under the closed loop conditions is needed in many cases. In view of the above two situations, it needs to find a convenient and effective method to solve the problem. Firstly, the design of the external input signals ensures the identifiability of closed loop system. Secondly, to make the direct method feasible for closed loop identification, the noise model selected is reasonably flexible and independently parameterized. On this basis, this paper proposes an improved method combining the direct closed loop identification approach with the iterative least squares parameter estimation algorithm, which can be an practical solution to the closed loop identification of multivariable systems with colored noise. The presented algorithm based hierarchical identification principle has a strong anti-jamming capability to effectively deal with colored noise existed in the system. Finally, the illustrative examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm.     

基于Haar 小波变换的连续时间系统鲁棒参数辨识

给出用Ｈａａｒ小波对连续时间系统的鲁棒辨识方法。该方法在用Ｈａａｒ小波对系统输入和输入展开时,通过极小化一个鲁棒指标来减少噪声对展开系数的影响。因此对连续时间系统可获得鲁棒参数估计。仿真结果表明了该算法的有效性。     

基于粒子群优化的低阶时滞系统辨识

为了解决低阶时滞系统阶跃响应辨识问题,提出基于粒子群优化的参数估计方法.方法主要包括参数初值计算和参数估计两部分.首先,采用积分方程方法估计时滞系统参数初值,通过设置参数初值估计误差,得到系统参数取值范围.然后,为了减小由观测噪声引起的参数估计误差,采用粒子群优化算法优化模型参数.最后,通过仿真实验分别验证文中方法在不同噪声条件下辨识低阶时滞系统的性能.实验表明,文中方法具有良好的参数估计精度和较强的抗噪能力,可有效解决噪声条件下低阶时滞系统的阶跃响应辨识问题.     

基于小波变换的含噪系统辨识

提出了基于小波变换的含噪声系统辨识方法（COR-WT-LS“三步法”，即“互相关函数—小波变换—最小二乘”）．COR-WT-LS法不仅参数估计值与真实值接近，而且具有较好的预报性能．仿真研究显示，当系统输出的噪信比很高时,该方法仍能获得较准确的参数估计．     

Extended Kalman filters for fractional‐order nonlinear continuous‐time systems containing unknown parameters with correlated colored noises

By using the Grünwald‐Letnikov (G‐L) difference method and the Tustin generating function method, this study presents extended Kalman filters to achieve satisfactory state estimation for fractional‐order nonlinear continuous‐time systems that containing some unknown parameters with the correlated fractional‐order colored noises. Based on the G‐L difference method and the Tustin generating function method, the difference equations corresponding to fractional‐order nonlinear continuous‐time systems are constructed respectively. The first‐order Taylor expansion is used to linearize the nonlinear functions in the estimated system, which provides the system model for extended Kalman filters. Using the augmented vector method, the unknown parameters are regarded as new state vectors, and the augmented difference equation is constructed. Based on the augmented difference equation, extended Kalman filters are designed to estimate the state of fractional‐order nonlinear systems with process noise as fractional‐order colored noise or measurement noise as fractional‐order colored noise. Meanwhile, the extended Kalman filters proposed in this paper can also estimate the unknown parameters effectively. Finally, the effectiveness of the proposed extended Kalman filters is validated in simulation with two examples.     

EM‐based adaptive divided difference filter for nonlinear system with multiplicative parameter

This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E‐)step and Maximization (M‐)step to meet such requirement. Firstly, E‐step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade‐off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete‐data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M‐step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E‐step and M‐step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second‐order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM‐based adaptive version of divided difference filter to the unknown or time‐varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd.