Solving a linear equation using least-squares (Calibration Matrix)

Question

Omar Alahmad 2019-5-8

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https://ww2.mathworks.cn/matlabcentral/answers/460929-solving-a-linear-equation-using-least-squares-calibration-matrix

编辑： Matt J 2019-5-9

采纳的回答： Matt J

Hi,

I need to find the calibration matrix C and offset A in the equation:

F = A + CX

F is a [2x1] vector and X is [3x1] vector. These are known from experimental data.

The offset vector A is [2x1] and the calibration matrix C is [2x3].

I have multiple data such that F becomes a matrix of size [2xn] and X becomes a matrix of size [3xn].

I need to find a way to approximate matrices A and C using a least-squares approach.

It is not clear to me how to proceed however.

Thanks!

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Answer 1

Matt J 2019-5-8

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https://ww2.mathworks.cn/matlabcentral/answers/460929-solving-a-linear-equation-using-least-squares-calibration-matrix#answer_374123

在 MATLAB Online 中打开

W=[ones(1,n);X];
Z=F/W;
A=Z(:,1);
C=Z(:,2:end);

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Omar Alahmad 2019-5-9

Thanks Matt, it seems to have done the job. Although I still do not have a complete understanding of how it worked. I will have to look a bit further.

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Answer 2

Matt J 2019-5-8

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https://ww2.mathworks.cn/matlabcentral/answers/460929-solving-a-linear-equation-using-least-squares-calibration-matrix#answer_374126

编辑：Matt J 2019-5-9

Are these equations for projective transformations? If so, they are not really linear equations. They are accurate only up to some multiplicative factor. You would need to use methods from projective geometry like the DLT to solve it,

https://en.wikipedia.org/wiki/Direct_linear_transformation