How to use solve function

Hi

I am trying to make a manual calculation of least square errors. This procedure involves a symbolic variable "n".

Here is my code:

syms n;
f = 0;
for i=1:length(distanceVal)
    estimateCoeff = (meanVal(1,1) - 10*log10((distanceVal(1,i)+2)/2));
    f = (f + sqrt((estimateCoeff*n - meanVal(1,i))^2));
end
f

dMSE = diff(f,n);
result = solve(dMSE,n)

Where meanVal is the mean of my measured values, distanceVal is the distance corresponding to each meanVal and estimateCoeff is the estimated coefficient for each estimated value (estimated value = n*estimatedCoeff = n*10*log(d/d_ref))

However the output of result = solve(dMSE,n) is: "Empty sym: 0-by-1" What does that mean? I expect result for n=[2,4] ...

[Torsten]

Are you sure the "sqrt" is at the right place ?

You want to do L1-minimization and not L2-minimization ?

Best wishes

Torsten.

[Tompak]

Thanks for the answer! I did not know there were two different methods. I am not sure what I did expect adding the L2 version in the code

      syms n;
      f = 0;
      for i=1:length(distanceVal)
         estimateCoeff = (meanVal(1,1) - 10*log10((distanceVal(1,i)+2)/2))

         f = (f + (estimateCoeff*n - meanVal(1,i))^2);
         y = (f + sqrt((estimateCoeff*n - meanVal(1,i))^2));
      end

      dMSE = diff(f,n);
      result = solve((dMSE==0),n)
      dMSE = diff(y,n);
      result = solve((dMSE==0),n)

Both ways give similar result: n = 0.9446 and n = 0.9444

However none of them are really what I expected. Do you see any flaws in my code, or do you know any other way of estimating n?

[Torsten]

You can check the result of the L2 minimization since it has an analytical solution:

n = sum_{i=1}^{N} ((a_i)*(b_i)) / sum_{i=1}^{N} ((a_i)^2)

with

N = length(distanceVal)
a_i = meanVal(1,1) - 10*log10((distanceVal(1,i)+2)/2)
b_i = meanVal(1,i)

Best wishes

Torsten.

[Richard Marveldoss]

Could you help me in understanding your code as it doesn't seem like the typical least square errors? Can you explain more about the different variables used and maybe give a sample input dataset for the above code.