Improved absorbing boundary condition based on linear interpolation for ADI-FDTD method

With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.

An osculatory rational interpolation method of model reduction in linear system

A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.

LINEAR SYSTEMS AND LINEAR INTERPOLATION I

The linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.

Tri-linear interpolation-based cerebral white matter fiber imaging

Diffusion tensor imaging is a unique method to visualize white matter fibers three-dimensionally, non-invasively and in vivo, and therefore it is an important tool for observing and researching neural regeneration. Different diffusion tensor imaging-based fiber tracking methods have been already investigated, but making the computing faster, fiber tracking longer and smoother and the details shown clearer are needed to be improved for clinical applications. This study proposed a new fiber tracking strategy based on tri-linear interpolation. We selected a patient with acute infarction of the right basal ganglia and designed experiments based on either the tri-linear interpolation algorithm or tensorline algorithm. Fiber tracking in the same regions of interest （genu of the corpus callosum） was performed separately. The validity of the tri-linear interpolation algorithm was verified by quan- titative analysis, and its feasibility in clinical diagnosis was confirmed by the contrast between tracking results and the disease condition of the patient as well as the actual brain anatomy. Statis- tical results showed that the maximum length and average length of the white matter fibers tracked by the tri-linear interpolation algorithm were significantly longer. The tracking images of the fibers indicated that this method can obtain smoother tracked fibers, more obvious orientation and clearer details. Tracking fiber abnormalities are in good agreement with the actual condition of patients, and tracking displayed fibers that passed though the corpus callosum, which was consistent with the anatomical structures of the brain. Therefore, the tri-linear interpolation algorithm can achieve a clear, anatomically correct and reliable tracking result.

Analysis and Comparison of Time Replica and Time Linear Interpolation for Pilot Aided Channel Estimation in OFDM Systems

This paper analyzes and compares two time interpolators, i.e., time replica and time linear interpolator, for pilot aided channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The mean square error (MSE) of two interpolators is theoretically derived for the general case. The equally spaced pilot arrangement is proposed as a special platform for these two time interpolators. Based on this proposed platform, the MSE of two time interpolators at the virtual pilot tones is derived analytically;moreover, the MSE of per channel estimator at the entire OFDM symbol based on per time interpolator is also derived. The effectiveness of the theoretical analysis is demonstrated by numerical simulation in both the time-invariant frequency-selective channel and the time varying frequency-selective channel.

Shifted Linear Interpolation Filter

Linear interpolation has been adapted in many signal and image processing applications due to its simple implementation and low computational cost. In standard linear interpolation the kernel is the second order B-spline. In this work we show that the interpolation error can be remarkably diminished by using the time-shifted B-spline as an interpolation kernel. We verify by experimental tests that the optimal shift is. In VLSI and microprocessor circuits the shifted linear interpolation (SLI) algorithm can be effectively implemented by the z-transform filter. The interpolation error of the SLI filter is comparable to the more elaborate higher order cubic convolution interpolation.

A Linear Interpolation-Based Algorithm for Path Planning and Replanning on Girds

Field D* algorithm is widely used in mobile robot navigation since it can plan and replan any-angle paths through non-uniform cost grids. However, it still suffers from inefficiency and sub-optimality. In this article, a new linear interpolation-based planning and replanning algorithm, Update-Reducing Field D*, is proposed. It employs different approaches during initial planning and replanning respectively in order to reduce the number of updates of the rhs-values of vertices. Experiments have shown that Update-Reducing Field D* runs faster than Field D* and returns smoother and lower-cost paths.

Realization of orientation interpolation of 6-axis articulated robot using quaternion

In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point （so-called Gimbal Lock）. However, quaternion interpolation has the advantage of natural （specifically smooth） orientation interpolation without Gimbal Lock. This work presents the application of quatemion interpolation, specifically Spherical Linear IntERPolation （SLERP）, to the orientation control of the 6-axis articulated robot （RS2） using LabVIEW and RecurDyn. For the comparison of SLERP with linear Euler interpolation in the view of smooth movement （profile） of joint angles （torques）, the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn. Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional （linear） Euler interpolation.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

A modified time domain interpolation method for LS channel estimation in OFDM systems

A modified time domain interpolation method is proposed for orthogonal frequency division multiplexing(OFDM)systems to address the problem that time domain interpolation in the least square(LS)channel estimation method based on comb-type pilots cannot choose the pilot spacing flexibly.Firstly,the estimated channel frequency response(CFR)at pilot positions in the frequency domain is obtained by LS channel estimation based on comb-type pilots,and the estimated channel impulse response(CIR)in the time domain is obtained by linear interpolation and inverse fast Fourier transform(IFFT).Secondly,the error of the estimated CIR obtained by linear interpolation is analyzed by theoretical deduction,and a method for correcting it is proposed.Finally,an estimated CFR at all subcarrier positions in the frequency domain is obtained by performing zero padding in the time domain and fast Fourier transform(FFT)on the modified CIR.The simulation results suggest that the proposed method gives similar performance to time domain interpolation,yet it does not need to meet the condition of time domain interpolation that the number of subcarriers must be an integral multiple of pilot spacing to use it.The proposed method allows for flexible pilot spacing,reducing the number of pilots and the consumption of subcarriers used for channel estimation.

Seismic ray-tracing calculation based on parabolic travel-time interpolation

A new seismic ray-tracing method is put forward based on parabolic travel-time interpolation(PTI) method, which is more accurate than the linear travel-time interpolation (LTI) method. Both PTI method and LTI method are used to compute seismic travel-time and ray-path in a 2-D grid cell model. Firstly, some basic concepts are introduced. The calculations of travel-time and ray-path are carried out only at cell boundaries. So, the ray-path is always straight in the same cells with uniform velocity. Two steps are applied in PTI and LTI method, step 1 computes travel-time and step 2 traces ray-path. Then, the derivation of LTI formulas is described. Because of the presence of refraction wave in shot cell, the formula aiming at shot cell is also derived. Finally, PTI method is presented. The calculation of PTI method is more complex than that of LTI method, but the error is limited. The results of numerical model show that PTI method can trace ray-path more accurately and efficiently than LTI method does.

MRF-Based Multispectral Image Fusion Using an Adaptive Approach Based on Edge-Guided Interpolation

In interpretation of remote sensing images, it is possible that some images which are supplied by different sensors become incomprehensible. For better visual perception of these images, it is essential to operate series of pre-processing and elementary corrections and then operate a series of main processing steps for more precise analysis on the images. There are several approaches for processing which are depended on the type of remote sensing images. The discussed approach in this article, i.e. image fusion, is the use of natural colors of an optical image for adding color to a grayscale satellite image which gives us the ability for better observation of the HR image of OLI sensor of Landsat-8. This process with emphasis on details of fusion technique has previously been performed;however, we are going to apply the concept of the interpolation process. In fact, we see many important software tools such as ENVI and ERDAS as the most famous remote sensing image processing tools have only classical interpolation techniques (such as bi-linear (BL) and bi-cubic/cubic convolution (CC)). Therefore, ENVI- and ERDAS-based researches in image fusion area and even other fusion researches often don’t use new and better interpolators and are mainly concentrated on the fusion algorithm’s details for achieving a better quality, so we only focus on the interpolation impact on fusion quality in Landsat-8 multispectral images. The important feature of this approach is to use a statistical, adaptive, and edge-guided interpolation method for improving the color quality in the images in practice. Numerical simulations show selecting the suitable interpolation techniques in MRF-based images creates better quality than the classical interpolators.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

A Virtual Walk along Street Based on View Interpolation

Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walking view needs to create new appearing scene in the vision-vanishing point and disappearing scene beyond the scope of view. To attain these two aims we use two enhanced position parameters to match pixels of source images and target images. One enhanced position parameter is the angular coordinates of pixels. Another enhanced position parameter is the distances from pixels to the vision-vanishing point. According to the parameter values, pixels beyond the scope of view can be ＂moved＂ out in linear interpolation. Result demonstrates the validity of the algorithm. Another advantage of this algorithm is that the enhanced position parameters are based on real locations and walking distances, so it is also an approach to online virtual tour by satellite maps of virtual globe applications such as Google Earth.

Numerical Solution of Euler-Bernoulli Beam Equation by Using Barycentric Lagrange Interpolation Collocation Method

Euler-Bernoulli beam equation is very important that can be applied in the field of mechanics, science and technology. Some authors have put forward many different numerical methods, but the precision is not enough high. In this paper, we will illustrate the high-precision numerical method to solve Euler-Bernoulli beam equation. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate new algorithm has the following advantages: small computational work, fast convergence speed and high precision.

A Parameterization Method from Conic Spline Interpolation

Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.

基于GRA-GRU的淮河流域水质预测研究

水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。

基于时间序列神经分层插值模型的光伏功率超短期多步预测

针对光伏功率预测准确性受数据质量和外部变量影响的问题,提出一种结合外生变量分析、数据质量控制以及时间序列神经分层插值(N-HiTS)模型的光伏功率超短期多步预测方法。首先,提出用于筛选外生变量的综合相关性度量(ICM)指标,并采用K近邻(KNN)算法与线性插值策略处理数据缺失问题。然后,引入N-HiTS长时间序列预测模型,通过多尺度信号采样和分层插值提高模型对长时间序列数据的处理能力。最后,通过算例对所提方法与传统光伏功率预测方法进行对比分析,验证了所提方法的预测准确性。

线性插值在改善GPS共视时间比对性能中的应用

为了解决GPS共视(CV)时间比对精密度随着基线增长而降低以及在超长基线情况下无法进行共视时间比对计算的问题,利用国际标准GNSS共视归算后星地钟差线性化特性对其进行插值,从而增加可用卫星数量,最后对不同卫星的共视结果进行加权计算,以提高长基线情况下GPS共视时间比对的性能,减少基线长度对共视时间比对的限制。选取中国科学院国家授时中心(NTSC)、韩国计量科学研究院(KRISS)、德国技术物理研究院(PTB)三个守时实验室一个月的星地钟差为数据样本,以300 s为时间间隔对单个卫星的星地钟差数据进行线性插值,随后将所有卫星相同时间的时间比对结果进行等权加权平均,从而获得最终共视时间比对结果。结果表明:NTSC-PTB、KRISS-PTB两条时间比对链路线性插值共视时间比对与GPS精密单点定位时间比对(PPP)结果互差后结果的均方根误差(RMS)分别为0.53 ns、0.8 ns,相比于传统共视,分别提升了48%、54%。

基于多项式回归与线性插值的全场纳米谱学成像背景序列预测

全场纳米谱学成像(TXM-XANES)是将透射X射线显微镜(Transmission X-ray Microscope,TXM)与X射线近边吸收结构(X-ray Absorption Near Edge Structural,XANES)有机结合的成像方法,通过测量感兴趣元素K边前后多个能量点的TXM图像,无损获得样品内部纳米尺度化学元素价态分布,已应用于能源材料、生物医学和地球科学等多个学科领域。常规TXM-XANES数据需要采集每个能量点下的图像和背景图像,数据量大,采集时间长,由于纳米尺度下机械结构的不稳定和样品的移动都会对TXM-XANES数据分析产生一定的影响。基于已知数据,利用机器学习的算法建立了多项式回归与线性插值运算模型,实现了仅通过两张谱学背景图像完成背景图像序列预测建模。利用该方法对标准样品及锂电池正极材料进行谱学成像分析,结果表明:相对于常规TXM-XANES方法,该方法具有数据量少、采集时间短等优势,可显著提升TXM-XANES的实验效率。