UD分解与偏差补偿结合用于变量带误差模型辨识

本文提出一种基于UD(upper-diagonal)分解与偏差补偿结合的辨识方法,用于变量带误差(errors-in-variables,EIV)模型辨识.考虑单输入单输出(single input and single output,SISO)线性动态系统,当输入和输出含有零均值、方差未知的高斯测量白噪声时,该类系统的模型参数估计是一种典型的EIV模型辨识问题.为了获得这种EIV模型参数的无偏估计,本文先推导出最小二乘模型参数估计偏差量与输入输出噪声方差以及最小二乘损失函数与输入输出噪声方差的关系,然后采用UD分解方法递推获得模型参数估计值,再利用输入输出噪声方差估计值补偿模型参数估计偏差,以此获得模型参数的无偏估计.本文还讨论了算法实现过程中遇到的一些问题及修补方法,并通过仿真例验证了所提辨识方法的有效性.     

基于Kalman滤波的通用和统一的白噪声估计方法

用射影理论,基于Kalman滤波提出了通用和统一的白噪声估计方法,可统一解决带非零均值相关噪声的线性离散时变随机控制系统的白噪声滤波、平滑和预报问题.提出了输入白噪声估值器和观测白噪声估值器,最优和稳态白噪声估值器,固定点、固定滞后和固定区间白噪声平滑器,白噪声新息滤波器和Wiener滤波器.它可应用于石油地震勘探信号处理和状态估计,为解决信号和状态估计问题,提供了新的途径和工具.关于Bernoulli-Gaussian白噪声估值器的仿真例子说明了其有效性.     

有色噪声干扰下的非线性系统的伪偏差分离估计

本文给出了有色噪声干扰下的一类非线性时变随机系统的伪偏差分析估计方法，偏差允许是非线怀的随机的和时变的，并且时变规律是未知的，与基于扩展状态变量的一类非线性系统的状态估计方法相比本文方法在实时跟踪性方面得到了很大提高。     

带有乘性噪声的线性时滞系统固定步长平滑估计

研究带有乘性噪声的线性时滞系统的固定步长平滑估计问题.通过虚拟噪声补偿技术,将该问题转化为一类带有未知时变噪声的随机系统的估计问题;基于等价系统的新息重组分析及投影定理,通过求解与原系统同维的Riccati方程,得到系统的最优平滑估计器.该方法无需扩维,具有较大的计算优势.仿真实验表明了该算法的有效性.     

基于Kalman滤波的白噪声估计理论

应用Kalman滤波方法,首次提出了一种统一的和通用的白噪声估计理论.它可统一处 理线性离散时变和定常随机系统的输入白噪声和观测白噪声的滤波、平滑和预报问题.提出了最 优和稳态白噪声估值器,且提出了白噪声新息滤波器和Wiener滤波器.它们可应用于石油勘探 地震数据处理,且为解决状态和信号估计问题提供一种新工具.两个仿真例子说明了其有效性.     

一类有输入噪声扰动的逆系统无偏参数辨识算法研究

对逆系统建模时,原系统的输出作为逆系统参数辨识时的输入.由于原系统输出存在测量噪声,且噪声方差未知,采用普通最小二乘法辨识,无法得到逆系统参数的一致无偏估计.为此,本文研究了一种有输入扰动的的逆系统无偏参数辨识算法,该算法先通过小波变换估计输入信号噪声的方差,再由估计得到的方差,通过偏差消除的递推最小_乘法,对逆系统的参数进行无偏辨识.该算法降低了对输入辨识信号为白噪声的要求,具有较强的实用性.由于采用递推运算,该算法也可以用于逆系统参数的在线辨识.最后,通过实验验证了该算法的有效性.     

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.     

基于时变盲混合高斯白噪声干扰的卫星姿态随机自学习控制

本文提出一种基于统计模式识别,针对盲混合高斯白噪声干扰下卫星姿态控制的方法.通过对噪声样本进行数据挖掘和模式识别,在线学习噪声的实时特性,获得其概率密度函数的先验知识,应用此先验知识进行样本聚类、分类、无监督学习并对噪声参数进行精确估计.学习系统将干扰白噪声参数的精确估计值传送至随机最优控制器以获得精度优良的控制效果,通过仿真研究表明了方法的有效性.     

色噪声激励下三势阱系统逻辑随机共振研究

本文利用基于Simulink的数值模拟方法研究了高斯色噪声激励下三势阱系统的逻辑随机共振现象.首先对于独立的加性和乘性高斯色噪声激励下的三势阱系统,发现仅有加性噪声作用不能实现可靠的逻辑操作,但加性噪声和乘性噪声共同作用可诱导良好的逻辑随机共振现象.和高斯白噪声相比较,高斯色噪声激励下能产生可靠逻辑随机共振的（D,Q）平面上的区域范围更大.进一步讨论了加性和乘性噪声之间的关联对于逻辑随机共振现象的影响,发现噪声关联对逻辑随机共振现象起着破坏性的作用.     

离散时间线性时变系统的传感器故障估计滤波器设计

针对一类离散时间线性时变系统提出了一种传感器故障诊断方法.本文首先通过状态增广的方式将被研究的系统转化为描述系统的形式,并且基于该描述系统模型,采用方差最小化原则设计了一种能够同时估计系统状态和传感器故障的故障估计滤波器,然后利用一组故障估计滤波器提出了一种故障诊断方法.本文的主要贡献在于针对离散线性时变系统提出了一种不需要对故障动态进行假设的传感器故障诊断方法.所提出方法的另一个优点是该方法能够在存在过程和测量噪声的情况下实现故障检测、分离与估计.仿真结果说明了所提出方法的有效性.     

非线性时变系统的一种即时局部模型及参数估计算法

针对包含未知和不可测量的确定性扰动的非线性时变系统的辨识和预测,提出了一种简便实用的线性化即时局部模型,给出并证明了这种即时模型的存在性定理。为了跟踪快速变化的模型参数,利用最新的多个线性局部模型进行外推,提出了一种滚动多模型加权平均参数估计算法。仿真结果表明了这种即时局部模型和参数估计算法的可行性。     

Active fault tolerant control using state-space self-tuning control approach

This paper presents a new fault tolerant control scheme for unknown multivariable stochastic systems by modifying the conventional state-space self-tuning control approach. For the detection of faults, a quantitative criterion is developed by comparing the innovation process errors occurring in the Kalman filter estimation algorithm, which, for faulty system recovery, a weighting matrix resetting technique is developed by adjusting and resetting the covariance matrices of the parameter estimate obtained in the Kalman filter estimation algorithm to improve the parameter estimation of the faulty systems. The proposed method can effectively cope with partially abrupt and/or gradual system faults and/or input failures with fault detection. The modified state-space self-tuning control scheme can be applied to the multivariable stochastic faulty system without requiring prior knowledge of system parameters and noise properties.     

Augmented instrumental variable method for position and heading estimation with RDOA measurements

In this paper, we proposed a position and heading estimation algorithm using only range difference of arrival (RDOA) measurements. Based on RDOA measurements, an uncertain linear measurement model is derived and both position and heading are estimated with the instrumental variable (IV) method which can show unbiased estimation results for the uncertainty of the model. In addition, to remove the unknown bias included in the measurement model error, we augment the bias to the state vector of the model. Since the proposition inherits the characteristic of the IV method, it does not need the stochastic information of the RDOA measurement excepting the assumption that the RDOA measurement noise is zero mean and white, and the zero mean error performance can be guaranteed when variances of RDOA measurement noises are identical. Through simulations, the performance of the proposed algorithm is verified at various positions and headings in the sensor network and compared with the robust least squares method which shows a zero mean error performance under the assumption that the stochastic information is known exactly.     

Suboptimal anisotropic filtering in a finite horizon

Consideration was given to the problem of robust stochastic filtering in a finite horizon for the linear discrete time-varying system. A random disturbance with inaccurately known probabilistic distribution is fed to the system input. Uncertainty of the input disturbance is defined in the information-theoretical terms by the anisotropy functional of a random vector. The sufficient condition for strict boundedness of the anisotropic norm of linear discrete timevarying system assigned by the threshold value (lemma of real boundedness) was proved in terms of the matrix inequalities. Sufficient conditions for boundedness of the anisotropic norm of two limiting cases of the anisotropy levels of the input disturbance (a = 0 and a → ∞) were established. A sufficient existence condition for the estimator guaranteeing boundedness of the anisotropic norm of the estimation error operator by the given threshold value was formulated and proved. Sufficient existence conditions for the estimators of two limiting cases of the anisotropy levels of input disturbance were obtained. The estimation algorithm relies on the recurrent solution of a system of matrix inequalities.     

Guest Editorial

The identification of continuous time models from non-uniformly sampled data records is investigated and a new identification algorithm based on the state variable filter approach is derived. It is shown that the orthogonal least squares estimator can be adapted for the identification of continuous time models from non-uniformly sampled data records and instrumental variables are introduced to reduce the bias in stochastic system identification. Multiplying the filtered variables obtained from the state variable filter, with higher powers of the noise free output signal prior to the estimation, is shown to enhance the parameter estimates. Simulated examples are included to illustrate the models.     

Adaptive Iterated Extended KALMAN Filter for Relative Spacecraft Attitude and Position Estimation

This paper presents a novel adaptive iterated extended Kalman filter (AIEKF) for relative position and attitude estimation, taking into account the influence of model uncertainty. Considering a nonlinear stochastic discrete‐time system with unknown disturbance, the AIEKF algorithm adopts the Gauss‐Newton iterative optimization steps to implement a maximum a posteriori (MAP) estimation, and the switch‐mode combination technique is used to achieve the adaptive capability. The mean‐square estimation error (MSE) of the state estimate is derived. It is proved that the AIEKF can yield a smaller MSE than that of the traditional extended Kalman filter (EKF) or iterated extended Kalman filter (IEKF). The performance advantage of the AIEKF is illustrated via Monte Carlo simulations on a typical relative position and attitude estimation application. Through comparisons in different scenarios, the presented algorithm is shown to improve adaptability and ensure estimation accuracy.     

Subspace model identification under load disturbance with unknown transient and periodic dynamics

To overcome the influence from load disturbance with unknown transient and periodic dynamics, as often encountered when performing identification tests in engineering applications, a bias-eliminated subspace model identification method is proposed to realize consistent estimation, which can be used for both open- and closed-loop systems. By decomposing the output response into disturbed and undisturbed components, an oblique projection is subtly introduced to eliminate the disturbance and noise impact so as to obtain unbiased estimation on the deterministic system state matrices, while the disturbance response dynamics could be estimated. In particular, a specific algorithm based on minimizing the output prediction error is given to find out the disturbance period if exists, such that the disturbance effect can be eliminated by the above projection regardless of the disturbance waveform and magnitude. A shift-invariant approach is then given to retrieve the deterministic state matrices. Consistent estimation on the deterministic system matrices is analyzed with a proof. A benmark example from the literature and an industrial injection molding process are used to demonstrate the effectiveness and merit of the proposed method.     

基于混合系统状态估计的故障诊断

如果将故障的发生视为一个离散事件,则存在故障可能的系统可以看作随机混合系 统,那么故障诊断问题就可转化为混合系统的离散状态估计问题.文中试图从这个角度研究 在非高斯噪声环境下非线性系统的故障诊断问题.在发生故障后的系统模型是已知的假定条 件下,使用随机混合自动机对系统建模,并利用基于粒子滤波的混合估计算法估计出混合状 态,从而完成故障诊断.仿真结果表明,所提的方法是可行的,可以处理某类故障诊断.