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

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.

[Matt J]

You mean an 8th order smoothing spline?

[Mohammad Shafi Nikzada]

Does Spline return coefficients?

[dpb]

An 8th order polynomial through 9 points is exact through the points -- of course, it may be give completely unreasonable responses/predictions between those points and will not be continuously differentiable at the breakpoints.

In general this is aBadIdea™

As Matt J says, an interpolating or smoothing spline would likely be a better choice and a lot less cumbersome to deal with than a zillion separate 8-degree polynomials as the spline toolset will encapsulate the breakpoints and all much more neatly for you.

But, no, you don't get a set of coefficients just like the polynomial coefficients; they're in there but built into the spline object.

What use do you think you'll be making of the coefficients, themselves, anyways, other than plugging into the equation to evaluate?

[Mohammad Shafi Nikzada]

This is what our assistant prof. wants. Find the coefficients, plug it into the equation and then calculate Velocity and acceleration. :D

[Matt J]

Your data looks very sinuisoidal. Are you sure you couldn't convince your assistant prof. just to fit a sinusoid?

Answer 1

[Walter Roberson]

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.

Answer 2

[David Hill]

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