基于MATLAB的最小二乘曲线拟合仿真研究

在科学实验及应用中,需要在分析一组测试数据的基础上,求出自变量与应变量之间近似函数关系表达式,以便计算机或其他设计人员利用它来方便地进行其他设计计算,这类问题就是由测得的点求曲线拟合的问题。在系统辨识领域中,最小二乘法作为曲线拟合最常用的方法,因其更为准确、实用而被广泛应用。在介绍基于最小二乘法的曲线拟合原理基础上,结合MATALB软件具体举例分析函数拟合方法和图形界面拟合方法以及MATALB工具箱拟合,并比较分析各种方法拟合效果与特点。通过具体分析可见,函数拟合需要对拟合函数有比较好的了解、编写相关程序,使用较灵活,而图形界面拟合以及曲线拟合工具箱cftool拟合直观、简洁,通过分析得到拟合方程参数及残差,可见拟合精度高、效果好。

MATLAB simulation of curve fitting based onleast-squares

In scientific experiments and applications, based on analyzing a set of test data to seek approximate function relational expression between the independent variables and the dependent variable is often necessary. So that it can easily be used in computer or by other designer for other design or calculation, such problem is the curve fitting by the set of test data. In the field of system identification, because more accurate and practical, least squares curve fitting is widely used as the most commonly used method. The principle of curve fitting based on least squares method is introduced in this paper. The method of curve fitting by function, the method of curve fitting by graphical interface and the method of curve fitting by Fitting Toolbox are analyzed by examples specifically. The effects and characteristics of various methods of fitting are compared and analyzed in this paper. The following conclusions by analyzing, there is need for a better understanding of fitting function and the related programs are written used the method of curve fitting by function. This method is more flexible. The characteristics are intuitive, simple and the parameters and residuals of fitting equation can be obtained by using the method of curve fitting by graphical interface or by Fitting Toolbox. Fitting accuracy is high and the effect is good.