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.     

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。     

快速对角阵权系数协方差交叉融合容积卡尔曼滤波器

针对互协方差信息未知的多传感器系统,本文提出了一种快速对角阵权系数协方差交叉融合算法(FDCI).本文首先提出了一种对角阵权系数协方差交叉融合(DCI)方案,并证明了所提出DCI算法在融合估计精度上高于经典批处理CI融合(BCI)算法.在此基础之上,针对非线性等复杂的互协方差未知的多传感器系统,提出FDCI算法,并证明了所提出FDCI算法的无偏性及鲁棒精度. FDCI融合算法虽然在融合估计精度上低于DCI,但FDCI无需进行多权系数的非线性代价函数的优化问题,进而大大降低了计算负担,提高了系统的实时性.最后,结合容积卡尔曼滤波算法(CKF)提出了快速对角阵权系数协方差交叉融合容积卡尔曼滤波算法.仿真实例验证了所提出算法的正确性和有效性.     

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.     

基于卡尔曼滤波器的雷达跟踪

卡尔曼滤波是一种统计估算方法,通过处理一系列带有误差的实际测量数据而得到所需要的物理参数的最佳估算值.对于每一个估计量,就使贝叶斯MSE最小而言,卡尔曼滤波器是最佳的。本文介绍了卡尔曼滤波器在雷达跟踪问题上的应用,说明卡尔曼滤波器在建模和计算机仿真上有着重要的现实意义。     

卡尔曼滤波器用于发动机传感器故障检测

讨论了采用卡尔曼滤波器对发动机传感器故障进行检测，分离问题，当传感器参与控制过程时，必须避免故障传感器输出对其它传感器的影响，并有效地检测出已故障的传感器，还就实时控制时信号重构过程进行了全数字仿真，结果表明所采用方法能有效检测，分离故障，并进行信号的重构与切换。     

基于MATLAB的卡尔曼滤波器设计

针对传统的维纳滤波器实现过程中存在的运算量过于复杂且只能处理平稳和一维信号的缺点,结合卡尔曼滤波相关理论,使用MATLAB软件,设计算法,实现了可以用来处理多维和非平稳的随机信号的卡尔曼滤波器。测试结果表明,卡尔曼滤波器在语音去噪、目标追踪中效果更为显著,功能更加强大。该研究为信号处理技术的进一步发展提供了价值。     

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.     

确保状态估计性能的离散时间鲁棒Kalman滤波器

讨论了一类具有不确定噪声的离散时间线性系统的鲁棒Kalman滤波器的设计思想和方法.文中给出确保估计误差性能指标的不确定噪声协方差矩阵的扰动上界,并在此界限内采用最坏情况下最优滤波器实现对状态的估计,它不仅能极小化不确定下的最坏性能,而且还能确保估计误差性能指标达到给定的某个自由度.     

Modal Kalman Filter

In the Extended Kalman Filter (EKF), only the first‐order term of the Taylor series is employed. Hence, the nonlinearities in the system dynamics are not fully considered. In the proposed method, to overcome this drawback, the higher‐order terms of the Taylor series are considered and a new filter, based on the Modal series, is designed. In this paper, based on the Modal series and careful approximations, a nonlinear filter is converted to a series of linear filters, and the extracted filter is named the Modal Kalman Filter (MKF). The efficiency and advantage of MKF are analytically proven and its applicability examined with some simulations.     

基于卡尔曼滤波的谐波检测分析

针对日益严重且复杂的电网谐波问题,提出了一种基于卡尔曼滤波的谐波检测方法.阐述了卡尔曼滤波器的跟踪估计原理,并建立了基于卡尔曼滤波器谐波分析的数值模型,结合Matlab仿真平台对算法检测稳态谐波和暂态谐波信号的性能进行了分析.通过对比研究表明该算法在准确度、快速性、暂态谐波分析等方面均优于快速傅里叶变换(FFT),仿真和试验结果表明该算法在分析复杂的电网电能质量事件中具有较高的实用性.     

Inertial Parameter Estimation of an Excavator with Adaptive Updating Rule Using Performance Analysis of Kalman Filter

International Journal of Control, Automation and Systems - This paper presents a rotational inertia estimation algorithm for excavators based on recursive least-squares with forgetting and an...     

The multi-state Kalman Filter in medical monitoring

In order to gain the best advantage from a computer database the way in which the information is displayed is vitally important. On-line statistical techniques could prove to be a great bonus to medical monitoring but have been limited by the methodology available. The Kalman Filter is one of the most powerful methods for time series analysis, and we have now shown it to be useful in a variety of settings, including the detection of kidney transplant rejection, where detection in some patients precedes that of experienced clinicians.     

The eXogenous Kalman Filter (XKF)

It is well known that the time-varying Kalman Filter (KF) is globally exponentially stable and optimal in the sense of minimum variance under some conditions. However, nonlinear approximations such as the extended KF linearises the system about the estimated state trajectories, leading in general to loss of both global stability and optimality. Nonlinear observers tend to have strong, often global, stability properties. They are, however, often designed without optimality objectives considering the presence of unknown measurement errors and process disturbances. We study the cascade of a global nonlinear observer with the linearised KF, where the estimate from the nonlinear observer is an exogenous signal only used for generating a linearised model to the KF. It is shown that the two-stage nonlinear estimator inherits the global stability property of the nonlinear observer, and simulations indicate that local optimality properties similar to a perfectly linearised KF can be achieved. This two-stage estimator is called an eXogeneous KF (XKF).     

卡尔曼滤波器在PLC系统中的实现

卡尔曼滤波器涉及大量矩阵运算。针对PLC系统不支持矩阵存储问题,采用PLC的数据块（DB）和数组（ARRAY）类型,实现矩阵元素的存储;针对PLC系统不支持矩阵运算问题,采用拆分方法将矩阵运算拆分为PLC系统可以支持的加、减、乘、除运算,从而通过PLC系统基本指令实现矩阵运算。并将典型矩阵运算编写为若干功能（FC）,通过多次功能的嵌套调用,在PLC系统中实现了卡尔曼滤波算法。将该算法实际运用于信号滤波和小球跟踪实验。实验结果表明,PLC系统实现的卡尔曼滤波器具有滤波和跟踪功能,提高了PLC的智能化程度。     

卡尔曼滤波在自动驾驶的应用

卡尔曼滤波是一种估值算法,用估计与测量对模型的状态进行较为准确的监控和预判,同样可以用于汽车自动驾驶的领域,来进行对动态模型的计算。自动驾驶是当前正在被突破的一个创新领域,以我国目前迅猛发展的科技实力,在这个新兴领域也能冲在前面。这个过程的研究中运用了数学、物理学、统计学等多方面的知识,包括动态模型的建立和监测,速度控制以及运动路线的规划等等。运用卡尔曼滤波可以帮助自动驾驶的研究和发展,更好地进行车辆间距离的监测和控制。     

Fractionally Delayed Kalman Filter

The conventional Kalman filter is based on the assumption of non-delayed measurements. Several modifications appear to address this problem, but they are constrained by two crucial assumptions: 1) the delay is an integer multiple of the sampling interval, and 2) a stochastic model representing the relationship between delayed measurements and a sequence of possible non-delayed measurements is known. Practical problems often fail to satisfy these assumptions, leading to poor estimation accuracy and frequent track-failure. This paper introduces a new variant of the Kalman filter, which is free from the stochastic model requirement and addresses the problem of fractional delay.The proposed algorithm fixes the maximum delay(problem specific), which can be tuned by the practitioners for varying delay possibilities. A sequence of hypothetically defined intermediate instants characterizes fractional delays while maximum likelihood based delay identification could preclude the stochastic model requirement. Fractional delay realization could help in improving estimation accuracy. Moreover, precluding the need of a stochastic model could enhance the practical applicability. A comparative analysis with ordinary Kalman filter shows the high estimation accuracy of the proposed method in the presence of delay.     

一种有效的分布式离散Kalman滤波器

运用一致性检验原理,提出了一种有效的分布式离散Kalman滤波器;分析了用于多传感器数据融合的分布式Kalman滤波方法,并将经过一致性检验的量测数据引入分布式Kalman滤波器进行数据融合;当干扰噪声的统计特征发生变化时,仿真结果表明该滤波器可以大大提高数据融合的精度。