图像处理中非加性噪声情形下维纳滤波的推广

在图像处理中,噪声问题是经常会遇到的问题。一般情形下都假定噪声是加性的,此时,维纳滤波器是一种最简便的降噪方法,而且它在均方误差意义下是最优的。将噪声推广到非加性的情形,利用维纳滤波的基本思想,同样可以得到均方误差意义下的最优滤波。     

适用处理非高斯观测噪声的强跟踪卡尔曼滤波器

在高斯噪声条件下,卡尔曼滤波器(KF)能够获得系统状态的一致最小方差线性无偏估计.但当噪声非高斯,KF性能将严重下降.观测噪声非高斯现象在深空探测自主导航中经常遇到,然而现有模型可能存在着精度不高、稳定性不强或者计算复杂度较高的缺点.针对这种现状,本文在传统强跟踪卡尔曼滤波器(STKF)中新息正交原则的基础上,推导了适用处理非高斯观测噪声的强跟踪卡尔曼滤波器(STKFNO),并将其嵌入到无迹卡尔曼滤波(UKF)框架下形成适用处理非线性系统非高斯观测噪声的强跟踪无迹卡尔曼滤波器(STUKFNO).所提出的算法被应用到深空光学自主导航系统中,仿真结果表明所提出的算法能够较好地应对观测噪声的非高斯性.     

基于卡尔曼滤波器组的多重故障诊断方法研究

针对缺乏有效的用于处理多重(两重及以上)加性故障隔离问题的诊断方法的现状,本文提出了一种新的基于卡尔曼滤波器组的控制系统多重故障的检测与隔离算法.通过构造多个结构不同的卡尔曼滤波器并设计相应的残差,使得每个残差仅对执行机构或传感器某个故障敏感而对其余故障不敏感,最终实现多重故障检测与隔离.除此之外,通过理论推导以及仿真分析,证明了所提出的故障检测与隔离算法的优越性.     

局域自适应卡尔曼滤波器的图像复原

本文提出了一种新的图像复原算法,通过局域自适应卡尔曼滤波将被附加白噪声劣化的二维图像复原。首先根据图像局域统计特性用区域分裂与合并算法将图像分割为一系列不连续的局域簇,然后对边界像素进行邻域均匀随机填充计算,之后进行独立的交向矩形窗扫描,并对扫描信号进行自回归建模及滤波,分割后的处理过程可并行进行并考虑了人的视觉特性。     

基于卡尔曼滤波器的PID控制仿真研究

针对工业过程中常见的二阶滞后对象的PID参数调节问题,采用KALMAN滤波器同常规PID控制相结合的方法对系统进行仿真研究。结果表明:同没有加卡尔曼滤波器的常规PID控制相比,卡尔曼滤波器很好的抑制了白噪声的污染,控制效果明显改善。     

带噪声统计估计器的Unscented卡尔曼滤波器设计

针对传统Unscented卡尔曼滤波器(UKF)在噪声先验统计未知或不准确时滤波精度下降甚至发散的问题,基于极大后验(MAP)估计原理,设计了一种带噪声统计估计器的UKF.该UKF滤波算法在进行状态估计的同时,能实时估计和修正噪声均值和协方差.相比于传统UKF,所提出的UKF具有应对噪声统计变化的自适应能力.仿真结果表明了该UKF滤波算法的有效性.

Abstract：

For the problem that the accuray of the conventional UKF declines and further diverges when the prior noise statistic is unknown or inaccurate, an unscented Kalman filter (UKF) with noise statistic estimator is designed.This UKF filtering algorithm based on maximum a posterior (MAP) estimation can estimate and correct the mean and covariance of the noise in real time while it estimates the states.The proposed UKF has the adaptive capability of dealing with variable noise statistic.The simulation results show the effectiveness of the proposed UKF filtering algorithm.     

卡尔曼滤波器性能分析

本文提出了用实际的估计误差协方差来评价卡尔曼滤波器的性能的思想,并针对单输入单输出系统,分析了在初始条件,误差模型部分或全部不精确已知的情况下,卡尔曼滤波器的性能,得到了一些有用的结论。     

卡尔曼滤波器参数分析与应用方法研究

介绍卡尔曼滤波器及其各种衍生方法.首先给出卡尔曼滤波器的算法流程以及所有参数的含义,并对影响滤波效果的五个主要参数进行了讨论.然后通过仿真实验研究不同的参数取值对于卡尔曼滤波的影响.最后总结在不同应用场景下使用卡尔曼滤波器的宗旨和要点.     

图像处理中维纳滤波器的推广与应用

维纳滤波器是一种最简便的降噪方法,而且它在均方误差意义下是最优的。将噪声推广到一般的乘性噪声的情形,利用维纳滤波的基本思想,同样可以得到均方误差意义下的最优滤波,最后通过两个模拟的例子验证了该方法的有效性。     

迭代无味卡尔曼滤波器

通过对无味卡尔曼滤波器(Unscented Kalman filter,UKF)的误差进行分析,提出了迭代UKF(IUKF)算法.该基本思路是用测量更新后的状态估计去重新对状态量和观测量的一步预测,然后再次应用LMMSE估计子估计状态量的均值和协方差阵,如此多次迭代后的滤波估计输出具有更高的精度和更小的方差,故滤波器表现出更好的一致性.Monte Carlo仿真表明,IUKF主要应用于观测噪声较小的场合,其中的迭代只需进行2～3次即可.     

Unscented Kalman filtering in the additive noise case

The unscented Kalman filter(UKF) has four implementations in the additive noise case,according to whether the state is augmented with noise vectors and whether a new set of sigma points is redrawn from the predicted state(which is so-called resampling) for the observation prediction.This paper concerns the differences of performances for those implementations,such as accuracy,adaptability,computational complexity,etc.The conditionally equivalent relationships between the augmented and non-augmented unscente...     

联合白噪声统计估计和卡尔曼滤波的MIMO信道辨识

提出了一种新的时间选择性衰落环境下MIMO信道辨识算法。为了提高信息传输效率,训练序列被直接叠加于信息序列之上。算法将信息符号输出、接收端AWGN和由于采用零中频接收技术而产生的直流偏移当做虚拟的观测噪声,其均值和自协方差均未知。通过联合的递推白噪声统计估计器和卡尔曼滤波器对时变信道进行跟踪,推导了一种计算简单的次优无偏时变白噪声统计估计器。以简单有效的方法抑制直流偏移对辨识精度的影响。仿真结果表明了算法具有良好的性能。     

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

The presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez–Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez‐Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez–Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non‐Gaussian distributions, is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal filtering for polynomial system states with polynomial multiplicative noise

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state‐independent noise and a conventional extended Kalman–Bucy filter. Copyright © 2006 John Wiley & Sons, Ltd.     

Kalman filtering with faded measurements

This paper considers a sensor network where single or multiple sensors amplify and forward their measurements of a common linear dynamical system (analog uncoded transmission) to a remote fusion center via noisy fading wireless channels. We show that the expected error covariance (with respect to the fading process) of the time-varying Kalman filter is bounded and converges to a steady state value, based on some earlier results on asymptotic stability of Kalman filters with random parameters. More importantly, we provide explicit expressions for sequences which can be used as upper bounds on the expected error covariance, for specific instances of fading distributions and scalar measurements (per sensor). Numerical results illustrate the effectiveness of these bounds.     

Robust Kalman filtering for uncertain systems

This paper studies the problem of Kalman filter design for uncertain systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and measurement matrices. The problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the above problem. Furthermore, a suboptimal covariance upper bound can be computed by a convex optimization.     

Distributed fusion Kalman filtering under binary sensors

Binary sensors are special sensors that only transmit one‐bit information at each time and have been widely applied to environmental awareness and medical monitoring. This paper is concerned with the distributed fusion Kalman filtering problem for a class of binary sensor systems. A novel uncertainty approach is proposed to better extract valid information from binary sensors at switching instant. By minimizing a local estimation error covariance, the local robust Kalman estimates are firstly obtained. Then, the distributed fusion Kalman filter is designed by resorting to the covariance intersection fusion criterion. Finally, a blood oxygen content model is employed to show the effectiveness of the proposed methods.