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arXiv 0903.0324gr-qcphysics.data-an
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离散导数估计在LISA Pathfinder数据简化中的应用

Discrete derivative estimation in LISA Pathfinder data reduction

Luigi Ferraioli, Mauro Hueller, Stefano Vitale

摘要:

LISA技术包(LTP)实验的数据分析将搭载LISA探路者任务飞行,需要从干涉仪位置数据出发,求解系统动力学,以计算作用在测试质量(TM)上的力。这个问题的解决方案的需要,促使我们实现一个离散的时域导数估计适合LTP实验的要求。我们首先报告的两种方法的定义的数学程序;第一个基于抛物线拟合近似和第二个基于泰勒级数展开。这两种方法,然后推广,并纳入一个更一般的类五点离散导数估计。用于二阶导数的相同过程可以应用于一阶导数的估计和数据平滑器的估计,允许为两者定义一类简单的五点估计。用模拟的噪声数据分析了五点二阶导数估计器的三种具体实现的性能。分析指出,引入大量高频噪声的估计器可确定低频噪声水平估计中的系统误差。

英文摘要:

Data analysis for the LISA Technology package (LTP) experiment to be flown aboard the LISA Pathfinder mission requires the solution of the system dynamics for the calculation of the force acting on the test masses (TMs) starting from interferometer position data. The need for a solution to this problem has prompted us to implement a discrete time domain derivative estimator suited for the LTP experiment requirements. We first report on the mathematical procedures for the definition of two methods; the first based on a parabolic fit approximation and the second based on a Taylor series expansion. These two methods are then generalized and incorporated in a more general class of five point discrete derivative estimators. The same procedure employed for the second derivative can be applied to the estimation of the first derivative and of a data smoother allowing defining a class of simple five points estimators for both. The performances of three particular realization of the five point second derivative estimator are analyzed with simulated noisy data. This analysis pointed out that those estimators introducing large amount of high frequency noise can determine systematic errors in the estimation of low frequencies noise levels.

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