Fit a least squares ellipse

I am trying to fit a least square ellipse to to the 'ellipse' data set that i have attached

I feel like i have everything correct (i might not have) but i am struggling plottting the ellipse function 'f'. i keep getting the following error

Warning: Error updating ImplicitFunctionLine.

Arrays have incompatible sizes for this operation.

Any help would be appreciated, Thanks in advance

load ellipse  % loads x and y

%least squares fit to an ellipse
% A x^2 + B xy + C y^2 + Dx + Ey = 1
% Returns coefficients A..F
%A x^2 + B xy + C y^2 + Dx + Ey + F = 0
% where F = -1
M = [x.^2 x.*y y.^2 x y]; % design matrix
b1=ones(size(x));
MTM=M'*M;MTb=M'*b1; %normal equation
R=rref([MTM MTb]); % the coefficent are found in the last collunm
A=R(1:6);
B=R(2,6);
C=R(3,6);
D=R(4,6);
E=R(5,6);
f= @(x,y) A.*x.^2 + B.*x.*y+C.*y.^2+D.*x+E.*y-1; % ellipse function
figure, plot(x, y, '.')
hold on
fimplicit(f)

[Alex Sha]

Function: A*x^2 + B*x*y + C*y^2 + D*x + E*y + 1 = 0
Parameter: 
A: -0.550741506585047
B: -0.46781995608367
C: -0.804115378029277
D: -0.163329836528614
E: 2.72555198327659

Answer 1

[KSSV]

Replace this line:

A=R(1:6);

with

A=R(1,6);

There is a typo error in getting A. A is a vector in your case, you arenot getting the ellipse.

Answer 2

[Matt J]

I feel like i have everything correct (i might not have)

Your ordinary least squares method is not ideal because your design matrix has stochastic errors in it (iterative total least squares is the gold standard). The method used by this toolbox is a bit better,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

and also has utility functions to let you plot directly,

load ellipse

fitobj=ellipticalFit([x,y]')

fitobj =

ellipticalFit with properties:

center: [-0.9975 1.9968]

a: 3.0246

b: 1.9954

angle: -30.0868

plot(fitobj)