Least-Squares Approach to Determine Coefficients of Calibration Function (Hot Wire Anemometry Data)

I have a list of 50,000 Voltages (taken over time) for 7 Velocities. From this, I calculated the overall mean of the Voltage.

I am supposed to use: 1) a least-squares approach 2) the Voltage mean - to find a calibration function to convert the Voltages into Velocities.

I have been provided with the following (which is based off of King's law) - U = a0 + a1*E + … + ai*E^i + … aM*E^M (in which U = velocity, E = voltage (which I calculated), and I'm assuming the a values are the calibration coefficients)

And have been asked to perform this calibration across values of M and discuss its accuracy as a function of M.

My question is: how can I determine these calibration coefficients / a values in MATLAB?

Answer 1

[Star Strider]

It appears to be a polynomial regression in powers of ‘E’. See if the polyfit function will do what you want. (If so, pay close attention ot the order of the coefficients that the function returns.)

[C W]

I tried to use the polyfit function but it returned the error message that X and Y vectors must be the same size (one is [1x7], the other is [50,000x7] .... not sure what to do from there.

[Star Strider]

It will likely be necessary to use a for loop to regress each of the rows. All the corfficient vector sizes will be the same for each row, so either save them in a matrix, or save them in a cell array. That choiice is yours, as is the analysis you want to do on them later.

[C W]

I'm struggling to understand how you would set that for loop up. I understand the basic structure of a for loop but am unclear on how you would indicate to go row by row through the [50,000 x 7], making it [1 x 7] and for each time reference the existing [1 x 7] - would you be able to give an example of how to do this?

[Star Strider]

I was thinking:

for k = 1:size(E,1)
    B(k,:) = polyfit(U, E(k,:),  ... );
end

I leave the rest to you.