Least Squares Method for best line fitting

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Tharindu Weerakoon
Tharindu Weerakoon 2015-2-26
评论： Tharindu Weerakoon 2015-2-27
I have a set of X and Y coordinates data taken from Laser scanning
X=[x1 x2 x3 x4 .....] Y=[y1 y2 y3 y4 .....]
Elements of both the X and Y include some errors.
I tried to find the best fitting line using polyfit and polyval command in matlab, but it can use only to calculate the Yhat w.r.t. X data.
At the end it will give X and Yhat only.
If I want to know calculate both the Xhat and Yhat, how can I use polyfit and polyval ?

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Torsten
Torsten 2015-2-26
I think you are talking about "orthogonal linear regression".
Try
http://www.mathworks.com/matlabcentral/fileexchange/16800-orthogonal-linear-regression
Polyfit is not suited for this kind of Fitting ; it assumes there are no errors in the independent variable.
Best wishes
Torsten.
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Tharindu Weerakoon
Tharindu Weerakoon 2015-2-27
Yes Torsten. Thanks a lot.
Still the problem is how to compute the Xhat and Yhat from x and y dataset with errors.
Initially I have a data set from LRF (laser scanner): [theta, d] from this data det I compute the x and y.
[theta, d] ---> [d*cos(theta) d*sin(theta)]=[x, y]
It is difficult to use [theta, d], which d is having error only. Because no constrain to use.
So [x y] only be used for segment the data and Orthogonal linear regression to find the best fitted line.

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