正弦曲线三点拟合问题的一种新方法

根据三个样本点拟合一条正弦曲线是计算机仿真和信号测量中的一个基本问题。目前流行的方法是最小二乘法。这种问题是一个三维以上的非线性最小化问题，计算规模与拟合具有三个参数一般曲线的计算规模相当。根据正弦曲线对应于某平面与某圆柱面交线的规律，提出了一种新的用于信号测量的正弦曲线拟合方法，它将原问题转化成为一个关于周期的单变量函数的最小化问题。新方法几何意义明确，算法实现简洁，结果可靠。

A New Algorithm for the Fitting of a Sine Curve with Therr Sample Points

Fitting a sine curve with three sample points is a basic problem encountered in signal measuring and dynamic control fields. Traditionally this kind of problem is solved with minimum squarer error method, B -sample curves based fitting methods and genetic algorithms. The problem is a combined optimal problem in which three variables are involved. A new algorithm is presented which reduces the problem into a minimum problem of an univariate function according to the corresponding relationship between a sine cure and an ellipse on a cylinder surface. The new algorithm has a good geological interpretation. It is more reliable than traditional algorithms.