Hello everyone, anyone knows how to approximate a data with polynomial of degree 8 using least square method?

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Mohammad Shafi Nikzada
回答： Walter Roberson 2021-6-25
Polynomial degree is 8 and it should be approximated piecewise.
  • y = a0t0 + a1t1 + a2t2 +… + antn ………………………….. (1)
Data description:
The first column is Time(GPS format) unit is seconds.
Second column is y values, so I have to find the coefficients (a0, a1...). And this should be done peicewise (9 points), then iterate this method till the end of the data.
Data is attached.
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Mohammad Shafi Nikzada
Mohammad Shafi Nikzada 2021-6-25
This is what our assistant prof. wants. Find the coefficients, plug it into the equation and then calculate Velocity and acceleration. :D
Matt J
Matt J 2021-6-25
编辑：Matt J 2021-6-25
Your data looks very sinuisoidal. Are you sure you couldn't convince your assistant prof. just to fit a sinusoid?

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回答（2 个）

Walter Roberson
Walter Roberson 2021-6-25
Loop, moving one point at a time. At each location use polyfit on 9 points to create coefficients. polyder() https://www.mathworks.com/help/matlab/ref/polyder.html and evaluate to get velocity. polyder() again and evaluate to get acceleration.
Then move one point further on.
David Hill
David Hill 2021-6-25
编辑：David Hill 2021-6-25
Use polyfit, place the x and y columns of your data into the function.
p=polyfit(x,y,8);%you will need to convert time using datenum and likely normalize

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