An Algorithm for Optimally Fitting a Wiener Model

Algorithm 2

Levenberg-Marquardt algorithm used.

Set 𝛼.

Let 𝜈=2

For  𝑖=1 to 5  do

 Calculate the Jacobian 𝐽.

 if  𝑖=1  then

  𝜆=max(𝐽′𝐽)⋅𝛼

 else

  𝜆=𝜆⋅max(13,1−(2𝜂−1)³)

 end if

 𝐺=𝐽′𝐟

 ℎ=(𝐽′𝐽+𝜆𝐼)⁻¹𝐺

 𝜃̂=𝜃̂+ℎ

 𝜂=𝐹(𝜃̂−ℎ)−𝐹(𝜃̂)ℎ′(𝜆ℎ−𝐺)

 if  𝜂>0  then

  𝜈=2

 else

  𝜆=𝜆⋅𝜈

  𝜈=2𝜈

  if  𝜈>128  then

   break

  end if

 end if

end for