Least squares approximation for two circles and two lines

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arisish roy 2016-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/270104-least-squares-approximation-for-two-circles-and-two-lines

评论： Torsten 2016-2-26

Can anyone please tell me how to do a least squares approximation for two circles and two(or one) line to find their approximate intersection point? Thank you.

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Answer 1

Torsten 2016-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/270104-least-squares-approximation-for-two-circles-and-two-lines#answer_211292

编辑：Torsten 2016-2-26

在 MATLAB Online 中打开

Use fmincon to solve the optimization problem

min: sqrt((x*-x1*)^2+(y*-y1*)^2)+sqrt((x*-x2*)^2+(y*-y2*)^2)+sqrt((x*-x3*)^2+(y*-y3*)^2)+sqrt((x*-x4*)^2+(y*-y4*)^2)
under the constraints
(x1*-x1)^2+(y1*-y1)^2=R1^2
(x2*-x2)^2+(y2*-y2)^2=R2^2
x3*=x3+lambda*l_x3
y3*=y3+lambda*l_y3
x4*=x4+mu*l_x4
y4*=y4+mu*l_y4

Here,

x1,y1,R1,x2,y2,R2,x3,l_x3,y3,l_y3,x4,l_x4,y4,l_y4

are known parameters and

x1*,y1*,x2*,y2*,x3*,y3*,x4*,y4*,lambda, mu, x*,y*

are the unknowns to be solved for.

(x*,y*) will be the approximate intersection point.

Best wishes

Torsten.

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arisish roy 2016-2-26

Thank you for the solution but can you please tell me what lambda and mu are? (x1*-x1)^2+(y1*-y1)^2=R1^2 (x2*-x2)^2+(y2*-y2)^2=R2^2 are circle equations but I can't understand what lambda and mu are? Are they derived from line equations? My lines are of the form y=mx+b. Can you please tell me how to derive the parameters from that?