A Maximum Likelihood Method for Estimating EEG Evoked Potentials

The problem of EEG evoked potential (EP) estimation is basically one of estimating a transient signal embedded in nonstationary mostly additive noise; and as such it is well suited to a nonstationary estimation approach utilizing, for example, the Kalman filter. The method presented in this paper is based on a model of the EEG response which is assumed to be the sum of the EP and independent correlated Gaussian noise representing the spontaneous EEG activity. The EP is assumed to vary in both shape and latency; the latter is assumed to be governed by some unspecified probability density; and no assumption on stationarity is needed for the noise. With the model described in state-space form, a Kalman filter is constructed, and the variance of the innovation process is derived; a maximum likelihood solution to the EP estimation problem is then obtained via this innovation process. The method was tested on simulated as well as real EEG data.     

Estimation of neural dynamics from MEG/EEG cortical current density maps: application to the reconstruction of large-scale cortical synchrony

There is a growing interest in elucidating the role of specific patterns of neural dynamics--such as transient synchronization between distant cell assemblies--in brain functions. Magnetoencephalography (MEG)/electroencephalography (EEG) recordings consist in the spatial integration of the activity from large and multiple remotely located populations of neurons. Massive diffusive effects and poor signal-to-noise ratio (SNR) preclude the proper estimation of indices related to cortical dynamics from nonaveraged MEG/EEG surface recordings. Source localization from MEG/EEG surface recordings with its excellent time resolution could contribute to a better understanding of the working brain. We propose a robust and original approach to the MEG/EEG distributed inverse problem to better estimate neural dynamics of cortical sources. For this, the surrogate data method is introduced in the MEG/EEG inverse problem framework. We apply this approach on nonaveraged data with poor SNR using the minimum norm estimator and find source localization results weakly sensitive to noise. Surrogates allow the reduction of the source space in order to reconstruct MEG/EEG data with reduced biases in both source localization and time-series dynamics. Monte Carlo simulations and results obtained from real MEG data indicate it is possible to estimate non invasively an important part of cortical source locations and dynamic and, therefore, to reveal brain functional networks.     

Sampled-data filtering framework for cardiac motion recovery: optimal estimation of continuous dynamics from discrete measurements

Quantitative and noninvasive estimation of cardiac kinematics has significant physiological and clinical implications. In this paper, a sampled-data filtering framework is presented for the recovery of cardiac motion and deformation functions from periodic medical image sequences. Cardiac dynamics is a continuously evolving physical/physiological process, whereas the imaging data can provide only sampled measurements at discrete time instants. Given such a hybrid paradigm, stochastic multiframe filtering frameworks are constructed to couple the continuous dynamics with the discrete measurements, and to coordinately deal with the parameter uncertainty of the biomechanical constraining model and the noisy nature of the imaging data. The state estimates are predicted according to the continuous-time biomechanically constructed state equation between observation time points, and then updated with the new imaging-derived measurements at discrete time instants, yielding physically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data Hinfinity filter are applied for motion recovery. While Kalman filter is the optimal estimator under Gaussian noises, the Hinfinity scheme can give robust estimation results when the types and levels of model uncertainties and data disturbances are not available a priori. The strategies are validated through synthetic data experiments to illustrate their advantages and on canine MR phase contrast images and human MR tagging data to show their clinical potential.     

Inference life-models of electrical insulating materials by using aKalman filter

A Kalman filter is applied to life tests for characterizing electrical or thermal endurance of electrical insulating materials. This recursive estimator provides updated life model parameter values after each life test. The life models are: (1) inverse power law and the exponential law, used for electrical or multi-stress ageing; and (2) Arrhenius model, used for thermal ageing. The state, prediction, and updating equations of the Kalman filter algorithm are specified for insulation endurance inference. Insight into the definition of the state variables, which are directly related to the model parameters, and determination of system and observation errors are developed. A recursive breakdown test detects important changes in the prevailing ageing process. The range of validity of the life model, as well as information on electrical and thermal threshold are considered. A flow chart of the filtering algorithm is presented. Example experimental results relevant to insulating materials and systems subjected to electrical and thermal life tests are processed according to the algorithm     

大失准角下SINS的KF/EKF2混合滤波对准

针对捷联惯导系统(SINS)大失准角下滤波对准过程中非线性滤波器状态维数过大的问题,提出了一种基于模型分解的卡尔曼滤波/二阶扩展卡尔曼滤波(KF/EKF2)混合滤波方法,将基于欧拉平台误差角的非线性滤波模型分解为线性部分和非线性部分,分别采用线性KF滤波和非线性EKF2滤波处理,并且设计了混合滤波的滤波步骤。实验结果表明,KF/EKF2混合滤波算法在计算量、实时性及精度等方面优于最常用的无迹卡尔曼滤波(UKF)和EKF2滤波。     

两阶段高维容积信息滤波及其在目标跟踪中的应用

非线性系统估计的过程是一个多传感器信息融合的过程,在集中处理量测数据的过程中,Kalman滤波具有很高的计算复杂度.尤其当系统模型中存在随机偏差时,扩维后计算量大幅增大,容易造成系统溢出和运行失败的问题.通过将两阶段容积Kalman滤波嵌入到扩展信息滤波框架的方式,提出了一种两阶段高维容积信息滤波算法.该算法初始化容易,计算量较小,直接利用协方差矩阵的逆与信息矩阵之间的等价关系参与滤波递推的过程,减少了对滤波增益阵的计算.在协方差矩阵的解算过程中,两阶段算法的协方差矩阵之间存在有耦合关系,因此在信息滤波中,两阶段信息矩阵之间也存在着某种耦合关系,算法中通过将非线性T变换和矩阵求逆应用于信息矩阵,得到了两阶段信息矩阵与协方差矩阵之间的耦合关系.通过纯方位跟踪系统的仿真实验,验证了两阶段高维容积信息滤波算法在精度上高于容积Kalman滤波算法,在运行时间上也短于容积Kalman滤波算法,证明了该算法的可用性.     

三状态样条Kalman滤波与目标机动检测

基于样条方法和Kalman滤波理论，给出了一种新的三状态样条Kalman滤波方法及对目标进行机动检测的方法。该滤波方法用样条函数建立目标运动模型，应用Kalman滤波进行状态估计；该机动检测方法通过检测滤波新息来对目标机动发生或消除进行判断。由于考虑了加速度的实时估计，该滤波方法尤其适用于对弹道式目标的机动跟踪。仿真计算与实测数据计算表明：该滤波具有较高的精度；该机动检测方法具有较高的检测效率。     

无线电静默下数据链端机的时间同步守时优化

在无线电静默的情况下所有数据链端机无法进行往返校时,这会导致端机间时间同步精度的降低。国内外普遍使用卡尔曼滤波的方法来实现守时优化,但当模型建立不准确时,容易出现滤波发散的现象。提出了一种改进的卡尔曼滤波算法,在自适应渐消卡尔曼滤波渐消因子计算方法的基础上,将其与奇异点剔除技术相结合来防止滤波的发散。该方法计算过程比较简单,满足工程所需的实时性要求。多次仿真实验证明数据链端机可以满足10 m测距所要求的33 ns以内的时间同步精度要求,使得数据链端机在静默结束后可以完成更高要求的任务。     

基于分层采样粒子滤波的麦克风阵列说话人跟踪方法

针对噪声与混响环境下的说话人跟踪问题,本文提出了一种基于粒子滤波的麦克风阵列声源定位与跟踪方法.该方法在粒子滤波框架下,将无混响影响的语音建立信号作为观测信息,通过计算麦克风阵列波束形成器的输出能量来构建似然函数,同时考虑语音信号不同频率成分在声源定位中的作用,利用分层采样方法提高粒子的采样效率.实验结果表明,本文方法提高了说话人声源跟踪系统的抗噪声与抗混响能力.     

The Influence of Model Parameters on BEG/MEG Single Dipole Source Estimation

This paper deals with source localization and strength estimation based on EEG and MEG data. It describes an estimation method (inverse procedure) which uses a four-spheres model of the head and a single current dipole. The dependency of the inverse solution on model parameters is investigated. It is found that sphere radii and conductivities influence especially the strength of the EEG equivalent dipole and not its location or direction. The influence on the equivalent dipole of the gradiometer is investigated. In general the MEG produces better location estimates than the EEG whereas the reverse is found for the component estimates. An inverse solution simultaneously based on EEG and MEG data appears slightly better than the average of separate EEG and MEG solutions. Variances of parameter estimators which can be calculated on the basis of a linear approximation of the model, were tested by Monte Carlo simulations.     

Standardized shrinking LORETA-FOCUSS (SSLOFO): a new algorithm for spatio-temporal EEG source reconstruction

This paper presents a new algorithm called Standardized Shrinking LORETA-FOCUSS (SSLOFO) for solving the electroencephalogram (EEG) inverse problem. Multiple techniques are combined in a single procedure to robustly reconstruct the underlying source distribution with high spatial resolution. This algorithm uses a recursive process which takes the smooth estimate of sLORETA as initialization and then employs the re-weighted minimum norm introduced by FOCUSS. An important technique called standardization is involved in the recursive process to enhance the localization ability. The algorithm is further improved by automatically adjusting the source space according to the estimate of the previous step, and by the inclusion of temporal information. Simulation studies are carried out on both spherical and realistic head models. The algorithm achieves very good localization ability on noise-free data. It is capable of recovering complex source configurations with arbitrary shapes and can produce high quality images of extended source distributions. We also characterized the performance with noisy data in a realistic head model. An important feature of this algorithm is that the temporal waveforms are clearly reconstructed, even for closely spaced sources. This provides a convenient way to estimate neural dynamics directly from the cortical sources.     

基于FPGA的Kalman滤波器实现研究

卡尔曼（Kalman）滤波计算精度和速度是工程应用中是否成功的决定性条件,为进一步提高Kalman滤波算法在更复杂的环境下使用的性能,并能够同时满足实时性和精度的要求,采用现场可编程逻辑阵列（FPGA）技术,设计了Kalman滤波算法在FPGA上的实现方案,选择了一种可以同时满足精度和实时性的方案进行实现,对算法中的矩阵相乘、状态机的应用以及资源分时复用等关键技术进行了设计。通过与Matlab及DSP的计算结果相对比,验证了在FPGA内实现Kalman滤波器的优势。     

FIR Filtering for Discrete-Time Markov Jump Linear Systems

This paper is concerned with finite impulse response (FIR) filtering problem for discrete-time linear system which possesses stochastically jumping parameters described by a finite-state Markov process. An FIR filter processes the measured inputs and outputs on a finite receding horizon linearly and the filter gain is obtained by minimizing variance of the error between real state and estimated one. According to inverse computation, system matrix is always assumed to be non-singular. In terms of engineering application, we must have complete access to the current time jump mode. The FIR filter is presented in batch form and recursive form, respectively, and Kalman filter is also addressed for comparison. Finally, a numerical example is given to illustrate the design procedure and their effectiveness.     

基于卡尔曼滤波的机动目标外推预测的研究

卡尔曼滤波在各个领域都有广泛的应用,如航天器的轨道计算、雷达目标跟踪、生产过程的自动控制等。卡尔曼滤波器在机动目标跟踪中具有良好的性能,是一种最佳估计并能够进行递推计算。为了研究卡尔曼滤波对机动目标的预测,首先用Matlab仿真验证自适应卡尔曼滤波的跟踪滤波能力,根据结果判定目标运动模型,进而在此运动模型下用卡尔曼预测对目标进行外推验证。     

基于容积卡尔曼滤波的自适应IMM算法

在目标跟踪中,针对无迹卡尔曼滤波在高维状态下容易出现滤波精度下降甚至发散的问题,提出了一种自适应交互式多模型容积卡尔曼滤波算法。首先,将容积卡尔曼滤波引入到交互式多模型算法中,提高了算法在高维非线性情况下的滤波精度。然后,结合马尔科夫参数自适应思想,在模型概率更新阶段,利用后验信息修正马尔科夫概率转移矩阵,增大匹配模型的转移概率,进一步提高模型之间的切换速度。最后,在目标跟踪仿真中利用"当前"统计模型对算法进行验证,实验结果证明了算法的有效性。     

基于自适应Kalman滤波的二维有噪子带信号恢复

基于子带信号的多通道表示（multichannel representation)和输入信号的动态特征,本文尝试推出了一种多分辨率状态空间模型,它与带相加子带噪声的滤波器组（Filter Bank)系统是等价的,于是使有噪子带信号的恢复可表述为相应多分辨率态空间模型的最优状态估计问题。进一步又利用信号的向量动态模型,发展了适于二维Kalman滤波的二维多分辨率状态空间模型,根据信号行为的分布,目标平面（object plane)可分割为不同的区域并用不同的向量动态模型来表征信号的非平衡分布,计算机数字仿真结果进一步证实了本文所提出了二维多分辨率Kalman滤波器性能的优越性。     

一种新的机动目标跟踪滤波的模型方法

本文提出了一种新的机动目标跟踪滤波的模型方法。它将目标的机动加速度作为一状态变量引入模型而直接进行估计,并通过卡尔曼滤波器的残差来检测目标机动与否。一旦检测出目标机动,马上重新启动卡尔曼滤波器以适应机动加速度的跳变。新的自适应滤波方法在这种情况下实现了最佳滤波。计算机仿真结果表明,在计算量远少于Moose方法计算量的情况下,本文方法的滤波精度与Moose方法的滤波精度相当。     

Multiresolution modeling and estimation of multisensor data

This paper presents a multiresolution multisensor data fusion scheme for dynamic systems to be observed by several sensors of different resolutions. A state projection equation is introduced to associate the states of a system at each resolution with others. This projection equation together with the state transition equation and the measurement equations at each of the resolutions construct a continuous-time model of the system. The model meets the requirements of Kalman filtering. In discrete time, the state transition is described at the finest resolution and the sampling frequencies of sensors decrease successively by a factor of two in resolution. We can build a discrete model of the system by using a linear projection operator to approximate the state space projection. This discrete model satisfies the requirements of discrete Kalman filtering, which actually offers an optimal estimation algorithm of the system. In time-invariant case, the stability of the Kalman filter is analyzed and a sufficient condition for the filtering stability is given. A Markov-process-based example is given to illustrate and evaluate the proposed scheme of multiresolution modeling and estimation with multiple sensors.     

基于LabVIEW的某导航设备卡尔曼滤波方位解算修正技术

某导航设备信号常使用卡尔曼滤波算法进行方位解算。为改良卡尔曼滤波噪声系数，确保算法在较短的时间内准确解算设备信号方位值，提出一种基于LabVIEW 的卡尔曼滤波方位解算修正技术，通过LabVIEW 快速构建信号模型和卡尔曼滤波方位解算模型，完成对卡尔曼滤波初始参数的修正。经测试，该技术有效缩短卡尔曼滤波噪声系数修正时间，可应用于实装工程。     

基于小波-卡尔曼的语音增强方法研究

提出了一种基于小波变换和卡尔曼滤波相结合的语音增强方法,这样既保留了小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,可以有效地减小非平稳噪声;并引入基于声学模型的感知滤波器,以提高语音信号的可懂度。实验证明该方法对于低信噪比的有色噪声干扰条件下的语音信号的增强效果要优于一般的语音增强系统。