function [logl] = kalmanforward(y,theta,p,v_sim)



  [T,n]=size(y);
  
  logl=0;

  
  r = v_sim(1:3,1:3);

  c = v_sim(4:15,1:3);

  q = v_sim(4:15,4:15);

  
  for t = 2:T

%       definition of X
      x = [1, y(t-1,:), zeros(1,8);

         zeros(1,4), 1, y(t-1,:), zeros(1,4);

         zeros(1,8), 1, y(t-1,:)]';

     % p t|t-1
     p = p+q;
     k = (p*x+c)*inv(x'*p*x+r+x'*c+c'*x);
     % theta t+1|t
     theta = theta+k*(y(t,:)'-x'*theta);
     
     % omega t|t-1
     var=x'*p*x+r;
     % innovation yt-Eyt|t-1
     inov=y(t,:)'-x'*theta;
     logl=log((2*pi)^(-n/2)*det(var)^(-1/2)*exp(-0.5*(inov'*var*inov)))+logl;
     p = p-k*(x'*p+c');

  end