容积Rauch-Tung-Striebel平滑器

针对离散非线性系统的状态平滑问题,基于Rauch-Tung-Striebel(RTS)理论设计了一种容积卡尔曼平滑器(Cubature Kalman Smoother,CKS),即容积Rauch-Tung-Striebel平滑器(RTSCKS)。首先,基于经典贝叶斯状态估计理论框架,推导了状态概率密度分布形式的非线性系统最优平滑算法;其次,基于Rauch-Tung-Striebel理论,建立了相应的最优平滑递推算法;然后,将其与容积卡尔曼滤波算法相结合,建立了递推形式的RTS-CKS平滑器;最后,通过典型的纯方位跟踪模型验证了该平滑器的可行性和有效性。该平滑器为非线性系统的状态估计提供了新的估计算法。     

Optimal information fusion distributed smoother for discrete multichannel ARMA signals

Based on the multisensor optimal information fusion criterion weighted by matrices in the linear minimum variance sense, using estimators of white measurement noise, an optimal information fusion distributed Kalman smoother is given for discrete time multichannel autoregressive moving average (ARMA) signals with correlated noise. It has a three-layer fusion structure with a fault tolerant property. The first and the second fusion layers both have netted parallel structures to determine cross-covariance matrices between any two faultless sensors. The third fusion layer is the fusion centre to determine the optimal weights and obtain the optimal fusion smoother. The fusion smoother has higher precision than that of any local smoother. Its effectiveness is shown by applying it to a double-channel signal system with three sensors.     

Optimal data-based kernel estimation of evolutionary spectra

Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain. First, a tapered Fourier transform, y_v(f, t), is calculated. Then the log-spectral estimate, is smoothed. As the characteristic widths of the kernel smoother increase, the bias from the temporal and frequency averaging increases while the variance decreases. The demodulation parameters, such as the order, length, and bandwidth of spectral taper and the kernel smoother, are determined by minimizing the expected error. For well-resolved evolutionary, spectra, the optimal taper length is a small fraction of the optimal kernel halfwidth. The optimal frequency bandwidth, w, for the spectral window scales as w²~λ/τ, where τ is the characteristic time and λ_F is the characteristic frequency scalelength. In contrast, the optimal halfwidths for the second stage kernel smoother scales as h~1/(τλ_F )¹(p+2)/ where p is the order of the kernel smoother. The ratio of the optimal-frequency halfwidth to the optimal-time halfwidth is determined     

A self-tuning filter for fixed-lag smoothing

The problem of estimating a discrete-time stochastic signal which is corrupted by additive white measurement noise is discussed. How the stationary solution to the fixed-lag smoothing problem can be obtained is shown. The first step is to construct an innovation model for the process. It is then shown how the fixed-lag smoother can be determined from the polynomials in the transfer function of the innovation model. In many applications, the signal model and the characteristics of the noise process are unknown. It is shown that it is possible to derive an algorithm which on-line finds the optimal fixed-lag smoother, a self-tuning smoother. The self-tuning smoother consists of two parts: an on-line estimation of the parameters in the one-step ahead predictor of the measured signal, and a computation of the smoother coefficients by simple manipulation of the predictor parameters. The smoother has good transient, as well as good asymptotic, properties.     

Outline designs for stable continuous-time fixed-lag smoothers

Three basic methods for constructing suboptimal continuous-time linear fixed-lag smoothers are described. In contrast to the optimal smoother, all the suboptimal smoothers are stable. The degree of complexity allowed in the suboptimal smoothers determines how closely they perform to the limit obtainable from the theoretical optimal linear fixed-lag smoother.     

Optimal and robust noncausal filter formulations

The paper describes an optimal minimum-variance noncausal filter or fixed-interval smoother. The optimal solution involves a cascade of a Kalman predictor and an adjoint Kalman predictor. A robust smoother involving H/sub /spl infin// predictors is also described. Filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error. These bounds lead to a priori estimates for the scalar /spl gamma/ in the H/sub /spl infin// filter and smoother design. The results of simulation studies are presented, which demonstrate that optimal, robust, and extended Kalman smoothers can provide performance benefits.     

Simultaneous Spherical Divergence Correction and Optima Deconvolution

The effects of spherical divergence on reflection seismograms destroys the stationarity assumption implicit in Weiner smoothing by distorting the amplitudes of the reflection coefficient sequence. The traditional correction for spherical divergence consists of an immediate scaling of the observed signal by an expected attenuation factor. It is this correction that violates the stationarity assumption, for it distorts the amplitudes of the observation noise process. Attempts to adapt the Weiner smoother to time-varying signals by time gating are cumbersome and suboptimal. In this paper, we show how to implement a Kalman deconvolution smoother which compensates for the effects of spherical divergence. The implementation is simple and straightforward, and estimates of the reflection coefficient sequence are optimal and corrected in amplitude. A computational example which compares our approach to an ad hoc Weiner smoother is provided for a simulated seismic signal. By means of this example, we demonstrate better performance for our approach over the Weiner smoother approach.     

Can the zero-lag filter be a good smoother?

The problem of constructing low complexity suboptimal fixed-lag estimators is discussed. First, it is shown that any optimal fixed-lag estimator structure generally performs better if more delay is accepted than the designed lag. As this holds for any design lag including zero-lag, it is demonstrated that the zero-lag filter treated as a suboptimal fixed-lag smoother has an error considerably lower than the conventional zero-lag error. A near optimal fixed-lag smoother is then found by a straightforward extention of the zero-lag filter. Several examples are considered. Finally, the usefulness of the conventional fixed-lag mmse criterion is discussed.     

An expectation-maximization algorithm based Kalman smoother approach for event-related desynchronization (ERD) estimation from EEG

We consider the problem of event-related desynchronization (ERD) estimation. In existing approaches, model parameters are usually found manually through experimentation, a tedious task that often leads to suboptimal estimates. We propose an expectation-maximization (EM) algorithm for model parameter estimation that is fully automatic and gives optimal estimates. Further, we apply a Kalman smoother to obtain ERD estimates. Results show that the EM algorithm significantly improves the performance of the Kalman smoother. Application of the proposed approach to the motor-imagery EEG data shows that useful ERD patterns can be obtained even without careful selection of frequency bands.     

Estimation of nonstationary EEG with Kalman smoother approach: an application to event-related synchronization (ERS)

An adaptive spectrum estimation method for nonstationary electroencephalogram by means of time-varying autoregressive moving average modeling is presented. The time-varying parameter estimation problem is solved by Kalman filtering along with a fixed-interval smoothing procedure. Kalman filter is an optimal filter in the mean square sense and it is a generalization of other adaptive filters such as recursive least squares or least mean square. Furthermore, by using the smoother the unavoidable tracking lag of adaptive filters can be avoided. Due to the properties of Kalman filter and benefits of the smoothing the time-frequency resolution of the presented Kalman smoother spectra is extremely high. The presented approach is applied to estimation of event-related synchronization/desynchronization (ERS/ERD) dynamics of occipital alpha rhythm measured from three healthy subjects. With the Kalman smoother approach detailed spectral information can be extracted from single ERS/ERD samples.     

Monte Carlo smoothing with application to audio signal enhancement

We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao-Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. All the algorithms suggested are tested with real speech and audio data, and the results are shown and compared with those generated using the generic particle smoother and the extended Kalman filter (EKF). It is found that the proposed Rao-Blackwellized particle smoother improves on the standard particle smoother and the extended Kalman smoother. In addition, the proposed block-based smoother algorithm enhances the efficiency of the proposed Rao-Blackwellized smoother by significantly reducing the storage capacity required for the particle information     

多传感器分布式融合白噪声反卷积滤波器

基于Kalman滤波方法和白噪声估计理论,在按矩阵加权线性最小方差最优融合准则下,提出了带ARMA有色观测噪声系统的多传感器分布式融合白噪声反卷积滤波器,其中推导出用Lyapunov方程计算最优加权的局部估计误差互协方差公式。与单传感器情形相比,可提高融合估值器精度。它可应用于石油地震勘探信号处理。一个三传感器分布式融合Bernoulli-Gauss白噪声反卷积平滑器的仿真例子说明了其有效性。     

多通道ARMA信号信息融合Wiener滤波器

应用Kalman滤波方法,基于白噪声估计理论,在线性最小方差最优信息融合准则下,提出了多通道ARMA信号的两传感器信息融合稳态最优Wiener滤波器、平滑器和预报器;给出了最优加权阵和最小融合误差方差阵.与单传感器情形相比,可提高滤波精度.一个雷达跟踪系统的仿真例子说明了其有效性.     

Optimal smoothing for guaranteed service

We consider the transmission of variable bit rate (VBR) video over a network offering a guaranteed service such as ATM VBR or the guaranteed service of the IETF. The guaranteed service requires that the flow accepted by the network has to be conforming with a traffic envelope σ; in return, it receives a service guarantee expressed by a network service curve β. Functions α and β are derived from the parameters used for setting up the reservation, for example, from the T-SPEC and R-SPEC fields used with the resource reservation protocol (RSVP). In order to satisfy the traffic envelope constraint, the output of the encoder is fed to a smoother, possibly with some look-ahead. The resulting stream is transported by the network; at the destination, the decoder waits for an initial playback delay and reads the stream from the receive buffer. We consider the problem of whether there exists one optimal strategy at the smoother which minimizes the playback delay and the receive buffer size, given the traffic envelope α and the service curve β. We show that there does exist such an optimal smoothing, and give an explicit representation for it. We also obtain a simple expression for the smallest playback delay and playback buffer size which can be achieved over all possible smoothing and playback strategies. We show that the computation of optimal smoothing and minimum playback delay do not depend on the past. We show that separate delay equalization is optimal in the constant bit rate (CBR) case, but not otherwise. We also apply the theory to the analysis of which T-SPEC should be requested by a source-destination pair, given some playback delay and buffer constraint, and given the path characteristics advertised in RSVP PATH messages     

多目标跟踪的多伯努利平滑方法

为提高基于滤波的多目标跟踪方法的性能,提出了一种多伯努利平滑方法.该方法由前向滤波和反向平滑两部分组成,前向滤波采用势平衡多目标多伯努利滤波,反向平滑利用多伯努利概率密度近似多目标平滑状态的概率密度,实现多目标平滑状态概率密度的反向递推计算.仿真结果表明,与滤波相比,多伯努利平滑对目标数量和目标状态的估计精度都有显著提高.     

Continuous-time and continuous–discrete-time unscented Rauch–Tung–Striebel smoothers

This article considers the application of the unscented transformation to approximate fixed-interval optimal smoothing of continuous-time non-linear stochastic dynamic systems. The proposed methodology can be applied to systems, where the dynamics can be modeled with non-linear stochastic differential equations and the noise corrupted measurements are obtained continuously or at discrete times. The smoothing algorithm is based on computing the continuous-time limit of the recently proposed unscented Rauch–Tung–Striebel smoother, which is an approximate optimal smoothing algorithm for discrete-time stochastic dynamic systems.     

Amended Kalman Filter for Maneuvering Target Tracking

The conventional Kalman filter (KF) which uses the current measurement to estimate the current state is a posterior estimation.KF is identified as the optimal estimation in linear models with Gaussian noise.However,the performance of KF with incomplete information may be degraded or diverged.In order to improve the performance of KF,an Amended KF (AKF) is proposed by using more posterior measurements.The principle,derivation and recursive process of AKF are presented.The differences among Kalman smoother,adaptive fading method and AKF are analyzed.The simulation results of target tracking with different covariance of motion model indicate the high precision and robustness of AKF.     

利用单模光纤中调制不稳定性产生超连续激光光谱的研究

根据皮秒光脉冲在光纤中传输时所满足的非线性薛定谔方程,利用数值模拟方法,研究了利用准连续波作为初始输入脉冲、利用单模光纤中的调制不稳定性和光子晶体光纤的高非线性效应产生超连续激光光谱（SC）的新方法。探讨了SC的形成机理,研究了不同条件下SC的形成过程,研究结果表明：准连续波光脉冲峰值功率越高、初始脉宽越宽,越有利于SC的产生;超连续谱向长波长方向的展宽要受到光子晶体光纤长度的影响,要想获得平坦的宽带SC,必须采用合适的光子晶体光纤长度。