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众所皆知,无论我们所研制的测量设备如何精密,由于它受来自内部和外部的干扰,使得输出信号中参杂着随机噪声的影响,所以观测的数据并非是理想信号。数据平滑就是对观测数据的精加工。应用数据平滑可以较大可能的削弱随机噪声的影响,从而避免了对设备提出过高的要求。数据平滑已广泛地应用在轨道预测、制导、控制、数据处理等方面。关于数据平滑的方法很多,通常的情况下,我们都是利用最小二乘法进行平滑。关于平滑外推也多用线性或非线性一阶或二阶的二点、三点、五点,乃至十一点,至于这方面内容在参考资料[1]、[2]、[3]中都有详细的论述和推证。本文是用资料[4]、[5]、[6]借助Z变换,均方差最小准则,以及差分方程的知识找出的一种数学模型,且将其与最小二乘法推导出的数学模型进行比较,并利用这个数学模型进行多点原始数据平滑外推。
As we all know, no matter how sophisticated the measuring equipment we have developed, the observed data is not ideal because it is affected by internal and external disturbances that make the output signal intermingled with random noise. Data smoothing is the finishing of the observed data. Application data smoothing can greatly reduce the impact of random noise, thus avoiding the high demands placed on the device. Data smoothing has been widely used in orbit prediction, guidance, control, data processing and so on. There are many ways to smooth data. Usually, we use the least-squares method for smoothing. For smooth extrapolation, linear, non-linear first-order or second-order second, third, fifth, and even eleven points are also used. As for this aspect, reference is made to [1], [2] and [3] A detailed discussion and deduction. In this paper, we use a mathematical model of data [4], [5], [6] with the help of Z-transformation, least-mean-square deviation criterion and knowledge of difference equations, and make it with the mathematical model derived from least- Compare and use this mathematical model to smooth extrapolate the original data.