最小二乘法怎么分段拟​合一条曲线？如何确定​分段点？。

一条曲线由圆弧+直线+圆弧组成，想用最小二乘法拟合这条曲线，分段点怎么确定？确定之后怎么拟合？已知测量数据入下

-0.0080,0.0000

0.0829,0.8670

0.2931,1.7132

0.6751,2.4970

1.1621,3.2204

1.7893,3.8264

2.5010,4.3284

3.2933,4.6891

4.1309,4.9290

5.0000,5.0040

6,5.0060

7,4.9950

8,5.0080

9,4.9950

10,5.0030

11,4.9960

12,5.0060

13,4.9970

14,5.0050

15,4.9900

16,5.0100

17,4.9980

18,5.0040

19,4.9950

20,5.0070

21,4.9970

22,5.0040

23,4.9910

24,5.0020

25,4.9920

26,5.0020

27,4.9960

28,5.0020

29,4.9950

30.0000,4.9920

30.8695,4.9309

31.7070,4.6900

32.5030,4.3353

33.2075,3.8226

33.8341,3.2172

34.3284,2.4990

34.7079,1.7135

34.9191,0.8674

35.0040,0.0000

Answer 1

[thyboe]

SSy = 95.91

fx=@(b,x)sqrt(b(3)*x+b(4)*x.^2+b(5)*x.^3).*(x<=b(1))+(x>b(1)).*b(6).*(x<=b(2))+(x>b(2)).*(sqrt(b(3)*(x-b(2)+b(1))+b(4)*(x-b(2)+b(1)).^2+b(5)*(x-b(2)+b(1)).^3));

b =[4.1454 28.699 9.8202 -0.93995 2.7233e-05 4.9984]

RSS = 0.0906461108591

MSe = 0.0024499

R^2 = 0.99905

如图。