A parallel processing solution to the adaptive Kalman filtering problem with vector measurements

The adaptive Kalman filtering problem with vector measurements is considered. A computational algorithm is derived which gives estimates of the state of a linear dynamic system driven by additive white Gaussian noise with unknown covariance Q and observed by a linear function of the state contaminated by additive white Gaussian noise with unknown covariance R. The computational algorithm is inherently parallel in nature and it is noted that the algorithm should be implemented in a special purpose parallel processing digital computer made up of a number of filters similar to steady state Kalman filters each with a different gain. It is shown that the estimates of the state and the estimates of the unknown covariances Q and R can be made arbitrarily close to the optimal nonlinear Bayesian estimates by an appropriate choice for the number of parallel paths in the computer. When the filtering algorithm is implemented in a parallel processing computer the total processing time for state estimation in the unknown noise environment is only slightly increased over that required for a steady state Kalman filter. A numerical example with a five dimensional state and two dimensional measurement vector is presented.     

非加性噪声情形下卡尔曼滤波器的推广

在数字信号处理中,得到的信号总是或多或少伴随着噪声。如何去除噪声,恢复真实的信号,是信号处理面临的首要问题。一般情形下我们都假定噪声是加性的,即噪声是不依赖于信号的,此时,卡尔曼滤波器是一种非常简便的降噪方法,它是一个最优化自回归数据处理算法,是用前一个估计值和最近一个观察数据来估计信号的当前值,是用状态方程和递推的方法进行估计的,而且它在均方误差意义下是最优的。本文将噪声推广到一般的乘性噪声的情形,利用卡尔曼滤波的基本思想,同样可以得到均方误差意义下的最优滤波,最后通过一个模拟的例子验证了该方法的有效性。     

卡尔曼滤波系统和量测噪声自适应估计的关联性

卡尔曼滤波是惯导系统(INS)/GPS组合导航的主要算法之一,Sage-Husa算法是在卡尔曼滤波基础上,为减少系统噪声和量测噪声的不确定性对误差估计的影响而采用的自适应估计方法.对Sage-Husa算法提出了4条改进措施;并通过在3种数据扰动情形下的仿真计算发现,只对一类噪声做自适应估计更容易产生较大的偏差,对系统噪声和量测噪声两类噪声同时做自适应估计,其效果要优于只对一类噪声做自适应估计,把此现象定义为卡尔曼滤波的系统和量测噪声自适应估计的关联性.这个结果不同于一些文献的观点.此项研究对自适应卡尔曼滤波在INS/GPS组合导航的工程化应用有较高的实用价值.     

白噪声Wiener反卷积滤波器

应用现代时间序列分析方法,基于ARMA新息模型提出了白噪声Wiener反卷积滤波器。该滤波器可统一处理滤波、平滑和预报问题,可用ARMA递推滤波器实现,适用于石油地震勘探数据处理。同多项式方法和Kalman 滤波方法相比,避免了求解Diophantine方程和Riccati方程,减少了计算负担。Bernoulli-Gaussian白噪声反卷积的仿真例子说明了其有效性。     

混合式自适应Kalman滤波算法

采用虚拟噪声补偿模型误差和有偏的噪声方差估值器、滤波器收敛性判据相结合的方法来解决自适应Kalman滤波发散的问题。首先若模型不准确,则引入虚拟噪声对模型误差进行虚拟补偿,然后采用有偏的噪声方差估值器、滤波器收敛性判据对噪声方差估计值进行监控,阻止滤波器发散。采用混合式自适应Kalman滤波算法对Gill公司的风向风速仪实时采集的数据进行处理,实验结果表明,该方法能有效的提高性能、抑制滤波发散,具有较强的实用性、自适应能力。     

扩展自适应中值滤波器的原理与实现

在图像处理领域中噪声滤除是图像预处理阶段一项必不可少的工作。在许多场合都会遇到高强度噪声的图像，特别是椒盐噪声的滤除非常困难。本文对空间域的常用噪声滤波技术的不足进行了分析，提出了一种新的滤波器技术——扩展自适应中值滤波器技术。该技术不仅继承了原自适应中值滤波器技术的优点，而且还弥补了它的不足，解决了高强度噪声干扰下图像的滤波问题，滤波效果相当理想。最后，给出了几种滤波技术的滤波效果比较图，验证了本文提出的滤波新方法对椒盐噪声的滤除能力。     

自适应噪声抵消技术的仿真与应用研究

从有用信号中剔除噪声是信号处理中一个重要研究课题.在金属矿区进行地震勘探数据采集时,经常会受到矿区内机械设备的强噪声干扰,常规的滤波方法对于淹没在强机器噪声下的有效地震信号的提取已经不适用,而随着计算机和信号处理技术的发展,自适应噪声抵消技术已广泛的应用于各个领域.通过对自适应噪声抵消器原理的研究,结合地震数据信噪模型分析,重点研究利用自适应噪声抵消技术来消除机器噪声.针对基于NLMs算法的常规技术存在的不足,提出了一种改进的算法,并运用MATLAB进行仿真试验,仿真结果表明自适应噪声抵消技术可以有效抵消机器噪声的干扰,大大提高地震资料的信噪比,使有效地震信号失真小.     

基于卡尔曼滤波的数据融合算法与应用研究

针对无人机飞控系统对输入的多传感器信息融合时传统卡尔曼滤波算法容易出现滤波发散,滤波精度和系统的实时性降低的问题,研究了一种改进的自适应滤波算法,可以让数据融合后的信息精度更高,实时性更强。改进的算法是在Sage-Husa滤波的基础上引入滤波收敛性判据,并提出了基于改进的Sage-Husa滤波算法的联邦卡尔曼滤波器的设计,可以抑制滤波发散,提高滤波精度和稳定性。同时引入强跟踪滤波算法的思想,调整增益矩阵,改进滤波算法,提高系统突变情况下的滤波处理能力。最后,通过对特定的自主避障系统用改进后的算法与传统卡尔曼滤波算法进行MATLAB仿真比较,仿真结果显示改进的自适应滤波算法在系统模型参数失配和实变噪声情况未知时,可以较好地保持滤波的精度和实时性。     

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.     

Kalman滤波技术在地球化学数据处理中的应用

针对传统地球化学数据处理问题,引入Kallman滤波对地球化学数据进行降噪预处理,并对Kalman滤波技术应用于地球化学数据误差校正的可行性进行了系统研究,并以铜绿山1：5万水系中Cu的测量数据为例进行了验证分析,试验结果表明,Kalman滤波技术在对地球化学数据处理方面具有优势,适用于地球化学数据的误差校正。     

Hierarchical bayesian models for regularisation in sequential learning

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise estimation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not possible. The Bayesian approach, with extended Kalman filtering at the parameter estimation level, allows for regularization within a minimum variance framework. A multilayer perceptron is used to generate the extended Kalman filter nonlinear measurements mapping. We describe several algorithms at the noise estimation level that allow us to implement on-line regularization. We also show the theoretical links between adaptive noise estimation in extended Kalman filtering, multiple adaptive learning rates, and multiple smoothing regularization coefficients.     

基于自适应卡尔曼滤波器的MEMS陀螺零点漂移的研究

随机噪声是影响MEMS陀螺精度的一个重要因素。本文基于时间序列分析方法建立MEMS陀螺的随机漂移AR模型后,使用自适应卡尔曼滤波器对信号进行滤波。通过比较陀螺原始信号和自适应卡尔曼滤波后的信号,可以得出结论：自适应卡尔曼滤波器在处理MEMS陀螺零点漂移中具有良好的滤波效果。     

Specail Feature Computer-Aided Seismic Analysis and Discrimination

The tremendous amount of data generated in the three branches of seismic activity–nuclear test discrimination, earthquake research, and geophysical exploration–places extraordinary demands on digital processing for extracting significant information. Faced with this heavy workload, the seismic community has from the start led in the development of analytical methods such as compositing (extracting a signal from noise) and digital filtering. More recently, seismic analysts have been using automatic-pattern-recognition techniques to discriminate between underground nuclear explosions and earthquakes.     

Connections between H 2 optimal filters and unknown input observers – performance limitations of H 2 optimal filtering

For linear time invariant continuous-time systems with either unknown or white noise input, two well-known filtering problems are considered. These are the unknown input observer problem and the Kalman filtering problem. Most of the available literature on Kalman filtering considers the so-called regular filtering problem. We consider here the general singular filtering problem. We show that such a Kalman filtering problem for a given system can be transformed to the unknown input observer problem for an auxiliary system constructed from the data of the given system. Such transformations between these two filtering problems enable us to study various properties of Kalman filtering, including existence and uniqueness of Kalman filters, computation of performance indices of Kalman filtering, and performance limitations of Kalman filtering as related to the structural properties of the given system.     

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.     

带模型误差系统自适应Kalman滤波的虚拟噪声补偿技术

本文讨论了带模型误差系统的自适应 Kalman 滤波问题。通过引入虚拟噪声,应用带未知时变噪声统计系统的自适应 Kalman 滤波器,提出了补偿模型误差、改进滤波器性能的虚拟噪声补偿新技术。三个不同类型的数值仿真例子证明了本文结果的有效性。     

基于信息补偿的自适应联邦滤波算法

针对采用标准卡尔曼滤波器必须知道系统噪声统计特性的局限性,研究了一类系统噪声未知情况下的自适应联邦滤波方法,指出了自适应滤波方法应用于联邦结构时应当注意的问题,提出了一种基于信息补偿的自适应联邦滤波算法。SINS／BDS／GPS组合导航系统的仿真结果表明,该方法可以有效抑制系统噪声未知情况下的滤波发散现象,提高了滤波的稳定性和估计性能。     

Digital signal processing methods for impedance microfluidic cytometry

Impedance microfluidic cytometry is a non-invasive, label-free technology that can characterize the dielectric properties of single particles (beads/cells) at high speed. In this paper we show how digital signal processing methods are applied to the impedance signals for noise removal and signal recovery in an impedance microfluidic cytometry. Two methods are used; correlation to identify typical signals from a particle and for a noisier environment, an adaptive filter is used to remove noise. The benefits of adaptive filtering are demonstrated quantitatively from the correlation coefficient and signal-to-noise ratio. Finally, the adaptive filtering method is compared to the Savitzky–Golay filtering method.     

Estimation of atmospheric CO2 concentration using Kalman filtering

Using a dynamic state model for the observed upward trend and sinusoidal variation, a Kalman filter is constructed to estimate the atmospheric CO₂ concentration, The process noise is assumed to be white with an unknown covariance, so an adaptive scheme is used to estimate the steady-state Kalman gain matrix. Several tests for optimality are performed on the adaptive filter. Measured data are then filtered using the Kalman algorithm. The filtering results are shown to reduce the variability of the airborne fraction of fossil-fuel-produced atmospheric CO₂.     

基于支持向量机的自适应卡尔曼滤波技术研究

针对卡尔曼滤波(KF)中噪声的统计特性与实际不符时滤波精度严重降低甚至引起滤波器发散的问题,提出一种基于支持向量机的自适应卡尔曼滤波算法(SVMAKF).根据新息理论方差与实际方差的比值,应用支持向量机产生自适应因子对卡尔曼滤波器的噪声方差阵进行在线修正,使噪声方差阵能够根据实际噪声的变化得到调整.通过对雷达目标跟踪系统的仿真表明,该算法对噪声有较强的自适应性,能够提高滤波精度和滤波器的鲁棒性.