Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction

This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.     

采用整体最小二乘法的条纹图配准方法

针对共光路菲索型动态干涉仪采集到的4幅条纹图的空间一致性问题,本文提出一种新的条纹图配准思路,将条纹图与图像配准在关联度上人为分开,搭建了专用的图像配准装置,避免将条纹与十字丝标志点混在一幅图像内而影响干涉仪的测量精度。首先通过本文搭建的条纹图配准装置对4台CMOS相机进行物理配准,然后利用整体最小二乘法对采集到的同一十字丝刻划板图像进行十字丝提取、交点计算以及旋转量计算,实现共光路菲索型动态干涉仪条纹图像的点点对应。最后通过试验对比验证,证明了本文算法的配准精度优于模板重心法的配准结果,互相关度达到96%以上。     

A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction

A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.     

MRI quantification of diffusion and perfusion in bone marrow by intravoxel incoherent motion (IVIM) and non-negative least square (NNLS) analysis

Object

To assess the feasibility of measuring diffusion and perfusion fraction in vertebral bone marrow using the intravoxel incoherent motion (IVIM) approach and to compare two fitting methods, i.e., the non-negative least squares (NNLS) algorithm and the more commonly used Levenberg–Marquardt (LM) non-linear least squares algorithm, for the analysis of IVIM data.

Materials and Methods

MRI experiments were performed on fifteen healthy volunteers, with a diffusion-weighted echo-planar imaging (EPI) sequence at five different b-values (0, 50, 100, 200, 600 s/mm²), in combination with an STIR module to suppress the lipid signal. Diffusion signal decays in the first lumbar vertebra (L1) were fitted to a bi-exponential function using the LM algorithm and further analyzed with the NNLS algorithm to calculate the values of the apparent diffusion coefficient (ADC), pseudo-diffusion coefficient (D*) and perfusion fraction.

Results

The NNLS analysis revealed two diffusion components only in seven out of fifteen volunteers, with ADC = 0.60 ± 0.09 (10^− 3 mm²/s), D* = 28 ± 9 (10^− 3 mm²/s) and perfusion fraction = 14% ± 6%. The values obtained by the LM bi-exponential fit were: ADC = 0.45 ± 0.27 (10^− 3 mm²/s), D* = 63 ± 145 (10^− 3 mm²/s) and perfusion fraction = 27% ± 17%. Furthermore, the LM algorithm yielded values of perfusion fraction in cases where the decay was not bi-exponential, as assessed by NNLS analysis.

Conclusion

The IVIM approach allows for measuring diffusion and perfusion fraction in vertebral bone marrow; its reliability can be improved by using the NNLS, which identifies the diffusion decays that display a bi-exponential behavior.     

Evaluation of dimension of fractal time series with the least square method

<正>Properties of fractional Brownian motions(f Bms)have been investigated by researchers in different fields,e.g.statistics,hydrology,biology,finance,and public transportation,which has helped us better understand many complex time series observed in nature[1-4].The Hurst exponent H(0H1)is the most important parameter characterizing any given time series F(t),where t represents the time steps,and the fractal     

Bilateral two-dimensional least mean square filter for infrared small target detection

The basic TDLMS (Two-Dimensional Least Mean Square) filter fails to detect infrared small targets consistently, especially under conditions of heavy noise and distinct cloud edges. This paper proposes a robust and efficient small-target detection method based on the basic TDLMS filter. The method first smooths the input image with a Gaussian filter of adaptive variance, and then employs TDLMS with a selected step size to filter the image with rightward and leftward iterations. Two prediction error images are obtained by subtracting the prediction images of the bilateral filtering from the original input image. Each prediction error image is separated into positive and negative prediction error images. That is, four images are generated in the bilateral filtering. The final image is obtained by fusing these four images. Experimental results show that the proposed method achieves significant improvement in background suppression and detection performance over the basic TDLMS filter and other improved TDLMS filters.     

一种线性最小二乘法的声源目标精确定位方法

在分析了声音能量距离衰减模型的基础上,提出了一种声源发射能量未知下的声源目标位置精确定位计算方法。将声音能量定位模型转化为非约束线性最小二乘法估计问题,其定位结果直接用代数解表示。同时对非约束线性最小二乘法下的参数进一步优化,提出了约束线性最小二乘法以提高定位精度。对信标节点位置坐标存在高斯噪声下的定位计算方法进行了改进以减少定位误差。仿真验证了该定位计算方法的有效性,数值模拟了不同观测信号噪声和信标节点位置噪声对定位误差的影响。结果同时表明,约束线性最小二乘法比非约束线性最小二乘法的定位误差更小,更接近于定位误差的克拉美罗下界值。     

一种线性最小二乘法的声源目标精确定位方法

在分析了声音能量距离衰减模型的基础上,提出了一种声源发射能量未知下的声源目标位置精确定位计算方法。将声音能量定位模型转化为非约束线性最小二乘法估计问题,其定位结果直接用代数解表示。同时对非约束线性最小二乘法下的参数进一步优化,提出了约束线性最小二乘法以提高定位精度。对信标节点位置坐标存在高斯噪声下的定位计算方法进行了改进以减少定位误差。仿真验证了该定位计算方法的有效性,数值模拟了不同观测信号噪声和信标节点位置噪声对定位误差的影响。结果同时表明,约束线性最小二乘法比非约束线性最小二乘法的定位误差更小,更接近于定位误差的克拉美罗下界值。     

自适应滤波技术在激光多普勒测速仪中的应用

激光多普勒测速仪检测系统提取的光电信号中存在较大的噪声信号。为了消除这些噪声干扰, 提高激光多普勒测速仪的测量精度,提出一种新的信号处理方法,将最小均方差自适应滤波技术应用于激光多普勒测量中,利用多普勒信号和噪声信号的统计特性,以最小均方误差估计为准则,最大程度地滤除噪声信号。阐述了最小均方差自适应滤波算法的基本原理,在MATLAB平台上将其应用于理想正弦信号进行仿真,并将其应用于实测多普勒信号的处理中。仿真和实验均表明,该技术可以有效抑制激光多普勒测量中的多频率噪声的干扰,大大提高多普勒信号的信噪比和测量精度,为设计高精度的激光多普勒测速仪创造了条件。     

Minimum mean square error method for stripe nonuniformity correction

Stripe nonuniformity is very typical in line infrared focal plane (IRFPA) and uncooled starring IRFPA. We develop the minimum mean square error (MMSE) method for stripe nonuniformity correction (NUC). The goal of the MMSE method is to determine the optimal NUC parameters for making the corrected image the closest to the ideal image. Moreover, this method can be achieved in one frame, making it more competitive than other scene-based NUC algorithms. We also demonstrate the calibration results of our algorithm using real and virtual infrared image sequences. The experiments verify the positive effect of our algorithm.     

主动光学中阻尼最小二乘法的精度估计

阻尼最小二乘法在主动光学研究中有重要的作用。针对主动光学的需要,就阻尼最小二乘法求解过程中参数进行精度估计,对待求量进行精度估计,以及将待求量代入原方程后的所得进行精度估计,对它们的方差进行了推导。     

Application of least mean square algorithm to suppression of maglev track-induced self-excited vibration

Track-induced self-excited vibration is commonly encountered in EMS (electromagnetic suspension) maglev systems, and a solution to this problem is important in enabling the commercial widespread implementation of maglev systems. Here, the coupled model of the steel track and the magnetic levitation system is developed, and its stability is investigated using the Nyquist criterion. The harmonic balance method is employed to investigate the stability and amplitude of the self-excited vibration, which provides an explanation of the phenomenon that track-induced self-excited vibration generally occurs at a specified amplitude and frequency. To eliminate the self-excited vibration, an improved LMS (Least Mean Square) cancellation algorithm with phase correction (C-LMS) is employed. The harmonic balance analysis shows that the C-LMS cancellation algorithm can completely suppress the self-excited vibration. To achieve adaptive cancellation, a frequency estimator similar to the tuner of a TV receiver is employed to provide the C-LMS algorithm with a roughly estimated reference frequency. Numerical simulation and experiments undertaken on the CMS-04 vehicle show that the proposed adaptive C-LMS algorithm can effectively eliminate the self-excited vibration over a wide frequency range, and that the robustness of the algorithm suggests excellent potential for application to EMS maglev systems.     

Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting(NLSF) method and the linear regression of the sum(LRS) method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.     

最小二乘B样条函数在火箭发动机数据处理中的应用

在固体火箭发动机地面试验数据处理中,通过应用最小二乘三次B样条函数拟合的方法,进行野值辨识和修复。文中阐述了实际应用中的步骤及应注意的几点问题。为避免常规的控制序列中含有野值而影响数据辨识的问题,提出差别选取控制点循环过滤的方法,实现精度更高的野值辨识。进而采用门限判别方法,实现野值的修复。通过实测数据处理的应用表明,该算法对单个和成片野值的辨识度都很高,适用于火箭发动机地面试验数据处理。     

用最小二乘法测弹簧的有效质量

在气垫层轨上组装一简谐振动系统，利用最小二乘法测出弹簧的有效质量，并与理论值进行比较。     

A meshless Galerkin method with moving least square approximations for infinite elastic solids

Combining moving least square approximations and boundary integral equations, a meshless Galerkin method, which is the Galerkin boundary node method （GBNM）, for twoand three-dimensional infinite elastic solid mechanics problems with traction boundary conditions is discussed. In this numerical method, the resulting formulation inherits the symmetry and positive definiteness of variational problems, and boundary conditions can be applied directly and easily. A rigorous error analysis and convergence study for both displacement and stress is presented in Sobolev spaces. The capability of this method is illustrated and assessed by some numerical examples.     

多尺度变步长最小均方自适应算法在光纤陀螺数据处理中的应用

为有效抑制光纤陀螺(FOG)随机噪声,提出将一种多尺度变步长最小均方(MVSLMS)自适应算法应用于FOG数据处理中。根据FOG输出数据的特点,构建了MVSLMS自适应滤波器,提出了FOG信号滤波算法的实现步骤。对FOG实测静态数据、振动数据和速率测试数据进行了滤波实验,结果表明所提算法对FOG随机噪声的抑制效果明显,相比LMS滤波,MVSLMS自适应滤波后的静态数据零偏稳定性数值减小了72.0%,振动数据在振前、振中、振后零偏稳定性数值分别减小91.5%,77.4%和96.5%,速率测试数据标准差减小了54.4%。摇摆测试滤波实验结果表明所用算法对FOG真值信号具有较好的跟踪能力。     

多尺度变步长最小均方自适应算法在光纤陀螺数据处理中的应用

为有效抑制光纤陀螺(FOG)随机噪声,提出将一种多尺度变步长最小均方(MVSLMS)自适应算法应用于FOG数据处理中。根据FOG输出数据的特点,构建了MVSLMS自适应滤波器,提出了FOG信号滤波算法的实现步骤。对FOG实测静态数据、振动数据和速率测试数据进行了滤波实验,结果表明所提算法对FOG随机噪声的抑制效果明显,相比LMS滤波,MVSLMS自适应滤波后的静态数据零偏稳定性数值减小了72.0%,振动数据在振前、振中、振后零偏稳定性数值分别减小91.5%,77.4%和96.5%,速率测试数据标准差减小了54.4%。摇摆测试滤波实验结果表明所用算法对FOG真值信号具有较好的跟踪能力。     

Restricted linear least square treatment processing of heteronuclear spectra of biomolecules using the ANAFOR strategy

We explore the use of a processing procedure based on restricted least square minimization as a tool for reducing the time versus resolution dilemma often encountered for biomolecular multidimensional spectra. Using a 2D spectrum as a reference, we obtain the necessary input of frequency components and linewidths. Combined even with a limited time evolution in the indirect dimension, the amplitudes of the correlation peaks in all planes of the 3D spectra can be extracted, and can be used to reconstruct the interferograms in the third dimension. Parameters such as number of lines, threshold choice, resolution, lineshape, number of experimental data points and finally signal to noise ratio of the spectrum are examined starting from a triple-resonance HNCA spectrum of ubiquitin.