An Algorithm for Optimally Fitting a Wiener Model

Algorithm 3

Conjugate Gradient algorithm used.

Let 𝑛= number of iterations to be run and 𝜎=1×10⁻⁸.

for  𝑖=1 to 𝑛  do

 if  𝑖=1  then

  ℎ=−∇𝐹

 else

  𝛽=max0,∇𝐹′(∇𝐹−∇𝐹(𝐱∣𝜃̂−ℎ))∇𝐹(𝐱∣𝜃̂−ℎ)′∇𝐹(𝐱∣𝜃̂−ℎ)

  ℎ=−∇𝐹+𝛽ℎ

 end if

 𝑘=−∇𝐹′ℎ

 𝛼=−𝜎⋅𝑘/(∇𝐹(𝐱∣𝜃̂+𝜎ℎ)′ℎ−𝑘)

 𝜃̂=𝜃̂+𝛼ℎ

end for