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

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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.
Mohammad Shafi Nikzada
Mohammad Shafi Nikzada on 25 Jun 2021
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 on 25 Jun 2021
Edited: Matt J on 25 Jun 2021
Your data looks very sinuisoidal. Are you sure you couldn't convince your assistant prof. just to fit a sinusoid?

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Answers (2)

Walter Roberson
Walter Roberson on 25 Jun 2021
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 on 25 Jun 2021
Edited: David Hill on 25 Jun 2021
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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