含有分数阶有色关联噪声的分数阶系统的卡尔曼滤波器设计

提出基于Tustin生成函数的分数阶卡尔曼滤波器设计方法,以解决含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计问题.通过Tustin生成函数方法,对连续时间线性分数阶系统进行离散化,将分数阶系统的微分方程转化为差分方程.利用增广向量法,将分数阶状态方程和分数阶有色噪声作为新的增广状态向量,从而将分数阶有色噪声转化为高斯白噪声.然后,提出一种基于Tustin生成函数的分数阶卡尔曼滤波算法,有效地实现对含有相互关联的分数阶有色过程噪声和分数阶有色测量噪声的连续时间线性分数阶系统的状态估计.与基于Grddotunwald-Letnikov差分的离散化方法相比,所提出的基于Tustin生成函数的卡尔曼滤波算法得到的状态估计精度更高,状态估计效果更好.最后,通过仿真结果验证所提出算法的有效性.     

Fractional-order Kalman filters for continuous-time linear and nonlinear fractional-order systems using Tustin generating function

This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using the Tustin generating function, the differential equation model is obtained by discretising the investigated continuous-time fractional-order system. The two kinds of fractional-order Kalman filters are given for the correlated and uncorrelated cases in terms of the process noise and measurement noise for linear fractional-order system, respectively. In addition, based on the first-order Taylor expansion formula, the extended fractional-order Kalman filter using Tustin generating function is proposed to improve the accuracy of state estimation. Finally, three examples are illustrated to verify the effectiveness of the Tustion fractional-order Kalman filters for linear and nonlinear fractional-order systems.     

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.     

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.     

Kalman Filters for Continuous-time Fractional-order Systems Involving Fractional-order Colored Noises Using Tustin Generating Function

This study presents fractional-order Kalman filers for linear fractional-order systems with colored noises using Tustin generating function. A continuous-time fractional-order system with the fractional-order colored process noise is discretized by Tustin generating function. The augmented vector consists of the state and the colored noise is offered to construct an augmented system based on the discretized state equation of a fractional-order system and the colored process noise. The Tustin fractional-order Kalman filter is designed based on the augmented system to obtain the state estimation, effectively. Besides, the colored noise involved in the measurement of a continuous-time fractional-order system is also discussed, and the corresponding Tustin fractional-order Kalman filter is provided in this study. Two illustrative examples are given to verify the effectiveness of Tustin fractional-order Kalman filters for the colored process and measurement noises.     

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.     

Robust multiple-model LPV approach to nonlinear process identification using mixture t distributions

In this paper, we propose a robust multiple-model linear parameter varying (LPV) approach to identification of the nonlinear process contaminated with outliers. The identification problem is formulated and solved under the EM framework. Instead of assuming that the measurement noise comes from the Gaussian distribution like conventional LPV approaches, the proposed robust algorithm formulates the LPV solution using mixture t distributions and thus naturally addresses the robust identification problem. By modulating the distribution tails through degrees of freedom, the proposed algorithm can handle various outliers. Two simulated examples and an experiment are studied to verify the effectiveness of the proposed approach.     

基于信息压缩矩阵交替变换的分数阶系统结构、阶次与参数的同时辨识方法

在愈来愈被关注的分数阶控制研究中,分数阶系统辨识的理论与方法是一个重要方向. 目前相关研究极少涉及分数阶系统的结构和阶次辨识. 首先讨论了分数阶线性SISO系统辨识的有色噪声模型,然后构造了具有"移位性质"的信息向量和信息压缩矩阵,并给出了信息压缩矩阵分解变换的理论分析及其证明;在此基础上,提出了一种利用信息压缩矩阵交替变换提取相关信息的算法,论述了最优估计模型结构与阶次的判定准则,从而同时辨识分数阶系统时域模型的结构、阶次与参数;仿真研究表明,本文方法能够获得满意的辨识结果,具有良好的抑制噪声干扰能力;不仅能够准确地辨识系统模型的结构与阶次,而且能够辨识噪声模型的结构与阶次.     

A cumulant based algorithm for the identification of input-output quadratic systems

The identification of a special class of polynomial models is pursued in this paper. In particular a parameter estimation algorithm is developed for the identification of an input-output quadratic model excited by a zero mean white Gaussian input and with the output corrupted by additive measurement noise. Input-output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm. Simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms, the output error method and a combination of the instrumental variables and the output error approach. The proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator.     

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.     

Consistent parameter estimation and convergence properties analysis of hammerstein output-error models

This paper presents an on-line bias-compensating recursive least squares (BCRLS) identification algorithm for Hammerstein output-error models disturbed by non-martingale difference sequence noise. By introducing an auxiliary vector uncorrelated with the noise, the consistent parameter estimation is obtained without the strictly positive real (SPR) condition. Convergence analysis of the recursive algorithm is performed using the ordinary differential equation (ODE) method. The simulation results validate the algorithm proposed.     

具有噪声方差及多种网络诱导不确定系统鲁棒Kalman估计

对不确定噪声方差乘性噪声,同时带观测缺失、丢包和一步随机观测滞后三种网络诱导特征的混合不确定网络化系统,应用带虚拟噪声的扩维方法和去随机参数方法,将其转化为带不确定虚拟噪声方差的时变系统.基于极大极小鲁棒估计原理,对带虚拟噪声方差保守上界的最坏情形系统,设计了鲁棒时变和稳态Kalman估值器.对所有容许的不确定性,保证实际Kalman估计误差方差有最小上界.应用扩展的Lyapunov方程方法和矩阵分解方法证明了所设计估值器的鲁棒性.证明了实际和保守估值器的精度关系,以及时变和稳态估值器间的按实现收敛性.应用于F-404航空发动机系统的仿真验证了所提出结果的正确性和有效性.     

不确定多传感器系统鲁棒观测融合Kalman 预报器

对于带不确定模型参数和噪声方差的线性离散时不变多传感器系统, 用虚拟噪声补偿不确定参数, 系统转化为仅带噪声方差不确定性的多传感器系统. 用加权最小二乘法和极大极小鲁棒估计准则, 基于带噪声方差保守上界的最坏情形保守系统, 提出一种鲁棒加权观测融合稳态Kalman 预报器, 并应用Lyapunov 方程方法证明了它的鲁棒性, 同时给出了与鲁棒局部和集中式融合Kalman 预报器的精度比较. 最后通过一个仿真例子说明了如何搜索参数扰动的鲁棒域, 并验证了所提出的理论结果的正确性和有效性.

     

On-line system identification with an adjustable estimation interval

On-line system identification with an adjustable estimation interval based on a continuous-time model is developed. The algorithm of interval selection depends on measurement noise, adaptive gain, and modelling error. Parameter estimation is carried out using recursive formulae via a weighted least-squares estimation. Illustrative examples are presented to show the potential of this method.     

相关观测噪声下的动态定位分析

对车载环境下的定位误差作时间序列分析．得到二阶马尔可夫过程的定位误差模型。将定位误差作为观测噪声．以此建立的观测方程中的观测噪声具有时间相关性。利用观测量相差法，把相邻两次观测量的相关部分消去，建立起观测噪声为白噪声的观测方程，并推导出状态估计的递推方程。避免了高阶矩阵的求逆，有效地减少了计算量，并降低了对内存的需求，提高了车载动态定位系统的实时性和定位精度。仿真结果进一步证明了算法的有效性。     

Blind equalization using a predictive radial basis function neural network

In this paper, we propose a novel blind equalization approach based on radial basis function (RBF) neural networks. By exploiting the short-term predictability of the system input, a RBF neural net is used to predict the inverse filter output. It is shown here that when the prediction error of the RBF neural net is minimized, the coefficients of the inverse system are identical to those of the unknown system. To enhance the identification performance in noisy environments, the improved least square (ILS) method based on the concept of orthogonal distance to reduce the estimation bias caused by additive measurement noise is proposed here to perform the training. The convergence rate of the ILS learning is analyzed, and the asymptotic mean square error (MSE) of the proposed predictive RBF identification method is derived theoretically. Monte Carlo simulations show that the proposed method is effective for blind system identification. The new blind technique is then applied to two practical applications: equalization of real-life radar sea clutter collected at the east coast of Canada and deconvolution of real speech signals. In both cases, the proposed blind equalization technique is found to perform satisfactory even when the channel effects and measurement noise are strong.     

基于小波调制的连续系统模型辨识

介绍了连续模型辨识的调制函数法，其于小波分析理论，提出构造多分辨小波调 制函数的新思路，设计了高斯小波调制函数.以二阶系统为例，研究了调制窗口参数与辨识 精度的关系,并以此得到调制函数参数的设计依据.典型算例表明本文算法的有效性.     

Orthogonal projection based subspace identification against colored noise

In this paper, a bias-eliminated subspace identification method is proposed for industrial applications subject to colored noise. Based on double orthogonal projections, an identification algorithm is developed to eliminate the influence of colored noise for consistent estimation of the extended observability matrix of the plant state-space model. A shift-invariant approach is then given to retrieve the system matrices from the estimated extended observability matrix. The persistent excitation condition for consistent estimation of the extended observability matrix is analyzed. Moreover, a numerical algorithm is given to compute the estimation error of the estimated extended observability matrix. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.     

一种基于改进的暗通道先验的运动模糊核估计方法

传统的暗通道先验已成功地运用于单一图像去模糊问题,但是,当模糊图像具有显著噪声时,暗通道先验无法对模糊核估计起到作用.因此,得益于分数阶计算能够有效地抑制信号的噪声并对信号的低频部分进行增强,将分数阶计算理论与模糊图像的暗通道先验相结合,提出一种基于改进的暗通道先验的运动模糊核估计方法.首先,结合最大后验估计算法与分数阶暗通道先验,构建出运动模糊图像的核估计模型;其次,利用半二次方分裂法解决模型的非凸问题;最后,根据粗糙-精细的策略,利用多尺度迭代框架估计出准确图像的模糊核,进而利用非盲去模糊的方法求解清晰图像.实验结果表明:在有无显著噪声的模糊图像中,所提出的算法虽然所需计算时间较长,但是能够获得较为准确的模糊核,并且能够减少图像噪声以及振铃伪影,提高清晰图像估计的质量;此外,对于不同类型的模糊图像,所提出的算法也同样适用.     

改进粒子群算法优化扩展卡尔曼滤波器电机转速估计

针对感应电机扩展卡尔曼滤波器转速估计中难以取得卡尔曼滤波器系统噪声矩阵和测量噪声矩阵最优值的问题, 提出了一种基于改进粒子群算法优化的扩展卡尔曼滤波器转速估计方法。算法通过融合遗传算法和粒子群算法的优点, 采用可调整的算法模型对粒子群算法进行改进, 将改进的粒子群算法对扩展卡尔曼滤波器中的系统噪声矩阵和测量噪声矩阵进行优化处理, 将优化后的卡尔曼滤波器应用于感应电机转速估计。仿真实验表明, 与试探法、标准粒子群算法及遗传算法比较, 改进粒子群算法优化的扩展卡尔曼滤波器能够有效提高转速估计的精度, 从而提高无速度传感器矢量控制系统的控制性能。