含噪声驱动阵的相关噪声卡尔曼滤波及稳定性

探讨相关噪声下离散时变线性系统的卡尔曼滤波模型。借助广义逆和最小模最小二乘解的思想,在Frobenius范数意义下,获得基于偏差最优估计的转换系数矩阵,将相关噪声系统转化为不相关噪声系统,获得相应的卡尔曼滤波模型。理论上,在误差协方差矩阵有界前提下,获证该滤波模型是全局渐近稳定的,数值实验获该模型的合理性。理论和实验结果表明,该模型是稳定的,且可有效解决含相关噪声和时变量测噪声驱动阵的离散时变系统的状态估计问题。     

带时间相关乘性噪声多传感器系统的分布式融合估计

研究带时间相关乘性噪声多传感器系统的分布式融合估计问题,其中时间相关的乘性噪声满足一阶高斯-马尔科夫过程.通过引入虚拟状态和虚拟过程噪声,构建了虚拟状态的递推方程.首先,基于新息分析方法,分别对系统状态和虚拟状态设计局部一步预报器.然后,基于一步预报器设计状态的局部线性滤波器、多步预报器和平滑器.推导了任意两个局部状态估计误差之间的互协方差矩阵.接着,基于线性最小方差意义下的矩阵加权、对角矩阵加权和标量加权融合算法,给出相应的分布式融合状态估值器.最后,分析算法的稳定性.仿真研究验证了该算法的有效性.     

双线性状态空间系统的状态观测器设计

针对受过程噪声和量测噪声干扰的双线性状态空间系统,研究其状态估计算法.借助双线性系统的特殊结构,将其等价表示为线性时变模型,推导基于Kalman滤波的状态估计算法.针对线性时变模型中存在的未知变量,基于辅助模型辨识思想,通过构造一个辅助模型,将未知变量用该模型的输出代替,提出基于辅助模型的双线性系统状态估计算法.构造双线性状态观测器,引入delta算子极小化状态估计误差协方差矩阵,从而得到最优状态估计增益,并提出基于delta算子的双线性系统状态估计算法.所提出的算法能够避免线性化过程带来的估计精度差的问题,提高双线性系统的状态估计精度.通过仿真实验验证了所提出算法的有效性,并对比分析了不同噪声情况下所提出算法的估计效果.     

不完全量测下估计误差协方差与传感器精度上–下确界的关系

在不完全量测下估计系统状态时,状态的稳态误差协方差与各个传感器精度指标有关.今提出一种新算法.可以根据估计误差协方差确定出传感器精度的上-下确界.算法根据稳态卡尔曼滤波的估计误差协方差表达式,推出传感器探测概率以及量测噪声方差指标的容差,并结合线性矩阵不等式求出传感器量测噪声方差的上-下界.根据这些结果,可以对给定的估计误差协方差,采用传感器精度指标的下界,从而在满足其他工程要求的前提下,放宽采样频率,降低传感器成本.     

WLS-SVM算法用于DCSK通信系统降噪

本文提出了基于加权最小二乘支撑矢量机（WLS-SVM）学习算法的一种DCSK混沌通信系统降噪方法。给定接收信号为训练样本集,首先用最小二乘支撑矢量机（LS-SVM）对样本数据进行估计得到估计误差,根据估计误差的统计分布特性获得一个加权系数,然后再求解WLS-SVM,得到优化的接收信号的估计值,达到降噪的目的。仿真结果表明,优化后的系统误码率（BER）性能与DCSK系统的理论噪声性能相比得到改善。     

一种考虑非高斯L´evy 量测噪声下的改进分数阶卡尔曼滤波

针对量测噪声模型为非高斯L´evy 噪声, 研究离散线性随机分数阶系统的卡尔曼滤波设计问题. 通过剔除极大值的方法得到近似高斯白噪声的L´evy 噪声, 基于最小二乘原理, 提出一种考虑非高斯L´evy 量测噪声下的改进分数阶卡尔曼滤波算法. 与传统的分数阶卡尔曼滤波相比, 改进的分数阶卡尔曼滤波对非高斯L´evy 噪声具有更好的滤波效果. 最后, 通过模拟仿真验证了所提出算法的正确性和有效性.

     

时变系统有限数据窗最小二乘辨识的有界收敛性

利用随机过程理论证明了有限数据窗最小二乘法的有界收敛性,给出了参数估计误差 上界的计算公式,阐述了获得最小均方参数估计误差上界时数据窗长度的选择方法.分析表明, 对于时不变随机系统,数据窗长度越大,均方参数估计误差上界越小;对于确定性时变系统,数 据窗长度越小,均方参数估计误差上界越小.因此,对于时变随机系统,一个折中方案是寻求一 个最佳数据窗长度,以使均方参数估计误差最小.该文的研究成果对于提高辨识算法的实际应 用效果有重要意义.     

受多随机噪声和多随机脉冲干扰的非线性系统稳定性分析

针对一类受多有色噪声和多随机脉冲干扰的非线性系统(其中系统连续动态中的多随机噪声包含乘性和加性有色噪声且离散动态中多随机脉冲幅值的类型由一个齐次不可约非周期Markov链决定),分别提出概率意义和矩意义下的噪声-状态稳定性、概率意义下的全局渐近稳定性、矩意义下的指数稳定性判据.在脉冲数量受模态依赖平均脉冲区间约束下,首先基于乘性随机噪声的估计和Lyapunov函数方法,分别研究系统在矩意义下的噪声到状态稳定性和指数稳定性判据;然后基于乘性随机噪声满足大数定律的假设和Lyapunov函数方法,分别给出系统在概率意义下的噪声-状态稳定和全局渐近稳定的充分条件;最后通过仿真结果验证所提出稳定性判别准则的有效性.     

相关白噪声激励下双稳态Duffing-Van der Pol系统的随机分岔

研究了相关乘性和加性高斯白噪声激励下,双稳态Duffing-Van der Pol系统的随机P-分岔和D-分岔;利用随机平均法,得出系统幅值稳态概率密度的理论表达式,以及随机P-分岔发生的临界参数条件;通过分析概率密度曲线形状的变化,发现阻尼系数、加性和乘性噪声强度均可诱导系统出现随机P-分岔,但对系统分岔区域的影响有着明显的不同,同时Monte-Carlo数值模拟验证了理论分析的有效性.此外,利用Wolf算法得到系统的最大Lyapunov指数,并分析了系统的稳定性和随机D-分岔,发现加性和乘性噪声强度以及阻尼系数α_1的增大,均会使系统趋于不稳定,而阻尼系数ε,α_2的增大,可以增强系统的稳定性.     

加速度计几种模型辨识方法的比较研究

加速度计离心试验中,为了更精确的得到加速度计的模型系数,比较研究了3种辨识方法:最小二乘方法(加权最小二乘)、总体最小二乘方法和EV模型方法.通过仿真得出在输出噪声和输入噪声为白噪声或者近似白噪声且离心机精度优于1×10-5的情况下,最小二乘与其他2种辨识方法辨识精度相当.最后通过试验对比了最小二乘方法与加权最小二乘方...     

Extended state space recursive least squares

A new extended state space recursive least squares (ESSRLS) algorithm is proposed for state estimation of nonlinear systems. It is based on state space recursive least squares (SSRLS) approach and uses first order linearization of the system. It inherits the capability of obtaining state estimate without knowledge of process and measurement noise covariance matrices (Q and R respectively). The proposed approach is considered to provide new design option for scenarios where noise statistics and system dynamics vary. ESSRLS is initialized using delayed recursion method and a forgetting factor λ is employed to optimize the performance. The selection of λ can be problem specific as shown through experimental validations. However a value closer to and less than unity is generally recommended. Theoretical bases are validated by applying this algorithm to problems of tracking a non-conservative oscillator, a damped system with amplitude death and a signal modeled by mixture of Gaussian kernels. Simulation results show an MSE performance gain of 20 dB and 23 dB over extended Kalman filter (EKF) and unscented Kalman filter (UKF) while tracking van der Pol oscillator without knowledge about noise variances. The computational complexity of ESSRLS falls within that of EKF and UKF.     

广义时滞系统的时滞依赖L2-L∞滤波

讨论广义时滞系统的L2-L∞滤波问题. 目的是设计全阶滤波器保证滤波误差系统的时滞依赖指数允许性和给定的L2-L∞性能指标. 通过解线性矩阵不等式获得所需的滤波器. 数值例子表明结果具有较小的保守性.     

相关观测融合Kalman估值器及其全局最优性

对于带相关观测噪声和带不同观测阵的多传感器线性离散时变随机控制系统, 用加权最小二乘法(WLS)提出了两种加权观测融合Kalman估值器, 它们包括状态滤波、状态预报和状态平滑. 基于信息滤波器形式下的Kalman滤波器, 证明了在相同初值下, 它们在数值上恒等于相应的集中式观测融合Kalman估值器, 因而具有全局最优性. 但是它们可明显减轻计算负担. 数值仿真例子验证了它们在功能上等价于集中式观测融合Kalman估值器.     

自适应Kalman滤波修复六维力传感器下E膜模型误差

为减小动载环境下,噪声信号对六维力传感器测量精度的影响,同时解决因传感器的简化模型误差较大,导致标准Kalman滤波无法获取最优估计的问题,提出一种双因子自适应Kalman滤波算法。算法根据正弦激励力响应和应变之间的关系,建立了下E型膜有色噪声增广状态模型。在标准Kalman滤波的基础上,分析了两种模型误差对滤波效果的影响,采用实时调整状态预测在滤波估计中权重的策略,给出了自适应Kalman滤波准则及递推公式。基于正交性原理和最小二乘法准则,利用三段函数模型构造了双重自适应因子。仿真实例表明,与标准Kalman滤波与强跟踪滤波相比,所提算法具有更好的估计精度和稳定性,能够有效地控制模型误差的影响,从而提高六维力传感器的测量精度。     

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems, when the model parameters and the noise variances are unknown, the consistent fused estimators of the model parameters and noise variances are obtained, based on the system identification algorithm, correlation method and least squares fusion criterion. Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter, a self-tuning weighted measurement fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, the convergence of the self-tuning weighted measurement fusion Kalman filter is proved, i.e., the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization. Therefore, the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality. One simulation example for a 4-sensor target tracking system verifies its effectiveness.     

基于minmaxKKT条件的三维重构方法

机器视觉中, 三维重构是一个重要问题. 基于2范数的最小二乘法速度较快, 但因误差代价函数非凸, 理论上无法获得全局最优解, 即使通过分支限界等方法, 往往也只能获得局部最优. 无穷范数表示的误差代价函数理论上可以获得全局最优, 但是计算速度很慢. 本文提出一种基于最小最大库恩塔克条件(minmaxKKT)的三维重构方法. 该方法利用minmaxKKT条件对基于2范数的三维重构结果进行全局最优判别, 对陷入局部最优的结果运用混合最速下降法进行全局寻优. 该方法可以获得全局最优, 相对于无穷范数算法具有更高的计算效率. 对标准数据集和真实数据的实验结果证明了本文算法的可行性和优点.     

Piece wise linear least–squares approximation of planar curves

Two algorithms for solving the piecewise linear least–squares approximation problem of plane curves are presented. The first is for the case when the L ₂ residual (error) norm in any segment is not to exceed a pre–assigned value. The second algorithm is for the case when the number of segments is given and a (balanced) L ₂ residual norm solution is required. The given curve is first digitized and either algorithm is then applied to the discrete points. For each segment, we obtain the upper triangular matrix R in the QR factorization of the (augmented) coefficient matrix of the resulting system of linear equations. The least–squares solutions are calculated in terms of the R (and Q) matrices. The algorithms then work in an iterative manner by updating the least–squares solutions for the segments via up dating the R matrices. The calculation requires as little computational effort as possible. Numerical results and comments are given. This, in a way, is a tutorial paper.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

A sequential learning algorithm based on adaptive particle filtering for RBF networks

To address the problem of low filtering accuracy and divergence caused by unknown process noise statistics and local linearization in neural network state-space model, this paper proposes an adaptive process noise covariance particle filter algorithm for the radial basis function (RBF) networks. Using the algorithm, the evolution of the weights and centers of RBF networks is achieved sequentially in time by use of the extended Kalman particle filter algorithm, and the process noise covariance matrices are also obtained simultaneously by maximizing the evidence density function with respect to the process noise covariance matrices. Performance of the presented approach is evaluated by two function approximation problems. Experimental results show that the proposed approach obtains better prediction accuracy than other well-known training algorithms.     

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.