一种基于插值和卡尔曼滤波的接收机钟差预测方法

针对多模多频接收机面临同时处理大量数据的压力,提出了一种基于插值和卡尔曼滤波的接收机钟差预测方法。插值方法分别用拉格朗日和三次样条,三次样条端点的一阶导数采用“差分法代替求导法”来确定。首先由插值方法得出每隔1s的卫星坐标、速度、钟差、频漂和伪距测量值,然后基于单星授时方法计算出静止接收机钟差,接着用卡尔曼滤波算法对接收机钟差和频漂进行预测,最后将预测的接收机钟差与加拿大空间参考系统( CSRS )提供的精密接收机钟差数据进行比较。结果表明,拉格朗日插值由于存在龙格效应,其接收机钟差的抖动幅度比三次样条略大,它们与CSRS钟差数据相比,均方根误差在3 ns之内。     

Mobile WiMAX系统中一种改进的信道估计算法

在Mobile WiMAX OFDMA系统下,研究了线性插值、二阶多项式插值和三次样条插值等几种经典的内插拟合的信道估计方法,仿真发现它们不能很好地支持高速移动性,基于分段线性插值算法提出了一种改进方法。在ITUVA60和Va120信道环境下,对这几种内插算法的误比特率和均方误差性能进行了仿真。仿真结果证明,在高速移动环境下,提出的改进方法要比其他几种算法的性能要好。     

基于改进型B样条分层插值的汽车零件检测研究

在汽车零件的在线装配过程中,为了减小由理论数模与实际位置之间的偏差导致的装配误差,设计了改进型B样条分层插值算法。首先,根据点云重建曲面的曲率分布对初始数据进行分层,然后再通过三次B样条插值算法获得实际零件点云与数模点云的偏差分布,最后由绝对距离偏差值推导得到路径补偿归一化系数,从而实现对汽车零件自动检测的扫描路径优化。仿真对包含直角、棱边及孔洞特征的零件进行分析,结果显示点云去噪效果良好,重建曲面形貌符合实体零件特征。实验对比了直接重建与采用三次B样条分层插值算法优化后的重建效果,通过对300个测试点的数据统计,三个坐标轴方向的位置优化前后平均误差分别为3.345 mm和0.599 mm。可见,优化后位置预测精度得到了较好的提升,为提高扫描路径精度奠定了基础。     

基于虚拟仪器技术的点云数据反求

在点云反求中,采取分段样条插值法拟合曲线,是非常实用和有效的处理方法.应用插值法的目的是使样条函数为低次多项式,确保拟合的曲线光滑连接.设计中,选取了具有优良数学特征的三次样条插值法,利用虚拟仪器技术,编写算法,使曲线通过所有扫描点后快速生成并显示.这种技术及方法可广泛应用于曲线设计与反求之中.     

楔顶双孔受感器试验数据处理方法研究

楔顶双孔压力受感器可以用来获取三维动态流场数据.本文分别采用三次样条插值、最小二乘法拟合和线性插值等三种方法,对基于楔顶双孔高频压力受感器试验数据进行了分析研究,结果表明线性插值法较样条插值、最小二乘法具有更高的精度.     

基于三次Hermite插值的OFDM信道估计

主要研究基于导频的正交频分复用（OFDM）信道估计的插值方法,提出三次Hermite插值信道估计算法,目的是利用该插值算法在不同信噪比的环境下,缩短运算时间和降低误码率（BER）。通过Matlab仿真实验说明,该算法相对于传统的信道估计算法具有较良好的性能。相对于改进的二项插值,具有较低的BER,相对于三次样条插值算法,具有运算时间较短、大信噪比环境下BER较低的优点。     

Polynomial spline-approximation of Clarke's model

We investigate polynomial spline approximation of stationary random processes on a uniform grid applied to Clarke's model of time variations of path amplitudes in multipath fading channels with Doppler scattering. The integral mean square error (MSE) for optimal and interpolation splines is presented as a series of spectral moments. The optimal splines outperform the interpolation splines; however, as the sampling factor increases, the optimal and interpolation splines of even order tend to provide the same accuracy. To build such splines, the process to be approximated needs to be known for all time, which is impractical. Local splines, on the other hand, may be used where the process is known only over a finite interval. We first consider local splines with quasioptimal spline coefficients. Then, we derive optimal spline coefficients and investigate the error for different sets of samples used for calculating the spline coefficients. In practice, approximation with a low processing delay is of interest; we investigate local spline extrapolation with a zero-processing delay. The results of our investigation show that local spline approximation is attractive for implementation from viewpoints of both low processing delay and small approximation error; the error can be very close to the minimum error provided by optimal splines. Thus, local splines can be effectively used for channel estimation in multipath fast fading channels.     

OFDM系统中基于导频信道估计方法的研究

对基于导频的信道估计中的插值算法,包括线性、高斯、变换域、低通滤波及三次样条插值算法的性能、特点进行分析比较。其中,三次样条插值算法在对复杂信道的估计方面,具有更好的性能和灵活性。最后,给出三次样条插值利于工程实现的简便算法。     

On the comparison of interpolation methods

A study of different cubic interpolation kernels in the frequency domain is presented that reveals novel aspects of both cubic spline and cubic convolution interpolation. The kernel used in cubic convolution is of finite support and depends on a parameter to be chosen at will. At the Nyquist frequency, the spectrum attains a value that is independent of this parameter. Exactly the same value is found at the Nyquist frequency in the cubic spline interpolation. If a strictly positive interpolation kernel is of importance in applications, cubic convolution with the parameter value zero is recommended.     

求最平坦的三次样条插值的粒子群优化算法

在分析了样条函数插值基础上，提出最平坦的三次样条插值问题，并提出了利用粒子群优化算法解决该问题。最后给出了一个实例。