How to implement otimization on function that depends on other functions

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Rafael 2022-9-24

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https://ww2.mathworks.cn/matlabcentral/answers/1811445-how-to-implement-otimization-on-function-that-depends-on-other-functions

编辑： Torsten 2022-9-25

I am trying to implement this equations, but cant figure out how, im thinking of using anonymous functions and fminsearch() to get the estimation of my paramater (equation 30), but not sure how i would actually do it.

As you can see, to implement equation 30 I need all of the other three eqs.

"p" is the only unkown variable in my program.

Im not sure how to implement equation 24 and 30, due to those sums and this " nesting of equations". Any ideas?

This is the code that i have right now ( i have a lot more code, relating to other coefficents present in the above mentioned equations, they are all stored in matrixes, i index refers to k):

bdpfunH = ...
    @(p_,n,i) eta * sqrt(G_R)* f_n(n,2) / (4*pi*norm(p_- pk(i))) * exp(-j*2*pi*f_n(n,1)/3e8*norm(p_- pk(i)));
gdpfunH = ...
    @(n,i) xi_k * (sqrt(G_T*G_R*TX_pwr_sub) * f_n(n,2))/(4*pi*norm(ptx-pk(i))) * exp(-j*2*pi*f_n(n,1)/3e8*normtxk(ptx-pk(i)) + j*2*pi*f_n(n,1)*t_0 + j*phi_0);
hdpfunH = ...
    @(gdpfunH,bdpfunH) gdpfunH * bdpfunH;
phi_t = ...
    @(hdpfunH) 
  
p_est = ...
    @(phi_t) 
      

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Rafael 2022-9-25

编辑：Rafael 2022-9-25

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Hi again, i implemented the function and it compiles so thats good, but the value returned by fminsearch is always the initial value i give to fminsearch, im not sure why is that, do you think i messed something up coding my function is is there another reason to fminsearch do that?

In my main file:

pestimation = zeros(N,3);
x0 = [10 10 10];
for n = 1:N
  p_ = fminsearch(@(p_)functionslibv3.objective(p_,n,K,T,y,gdp,G_R,f_n,p_k,BETAt_k,sig2,phi_0),x0);
  pestimation(n,:) = p_(1,:);
  
 end

In my function file:

 function phat = objective(p_,n,K,T,y,gdp,G_R,f_n,p_k,BETAt_k,sig2,phi0)   %in main, call this function n times.
          eta = 1;
          bnkdp = zeros(1,K);
          gnkdp = zeros(1,K);
          hnkdp = zeros(1,K);
          phi_t = zeros(T,1);
          for i = 1:K
              bnkdp(1,i) = eta * sqrt(G_R)* f_n(n,2) / (4*pi*norm(p_- p_k(i,:))) * exp(-1i*2*pi*f_n(n,1)/3e8*norm(p_- p_k(i,:)));
          end
          for i = i:K
              gnkdp(1,i) = gdp(n,i);
          end
          for i = 1:K
              hnkdp(1,i) = gnkdp(1,i) * bnkdp(1,i);
          end
          for t = 1:T
              sumbh = 0;
              for i = 1:K
                  sumbh = sumbh + BETAt_k(t,i) * hnkdp(1,i); 
              end
              phi_t(t) = angle(sumbh);
          end
          sump = 0;
          for t= 1:T
              sump = sump + abs(y(n,t)^2)/sig2^2 * sin(angle(y(n,t)) - phi_t(t) - phi0)^2;
          end
          phat = sump;
      end