Graphical determination

  • The cost function is \(\displaystyle J(x) = J_b(x) + J_r(x)\) with

    \(\displaystyle J_b(x) = { (x- x^b)^2 \over 2\, \sigma_b^2}\) and \(\displaystyle J_r(x) = { [ y^o + {q \over x -h_L} ]^2 \over2 \, \sigma_r^2}\)

  • The analysis \(x^a\) is the value that minimize the cost function \(J(x)\)