How to use solve function

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Tompak 2017-6-29

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评论： Richard Marveldoss 2017-7-7

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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] ...

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Torsten 2017-6-29

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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 2017-7-7

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.

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