The code in this page solves the Least Squares problem for the following dynamic model:
where $a$ and $b$ are constants, $u$ is an input. The code is as follow:
t=[0:0.1:10]; m=length(t); y=zeros(m,1); a=-1;b=1;c=1;d=0;u=[100;zeros(m-1,1)]; % u: impulse with magnitude of 100 [ad,bd]=c2d(a,b,0.1); y=dlsim(ad,bd,c,d,u); ym=y+0.08*randn(m,1); %adding Gaussian noise w=inv(0.08^2); h=[ym(1:m-1) u(1:m-1)]; xe=inv(h'*w*h)*h'*w*ym(2:m) ye=dlsim(xe(1),xe(2),c,d,u);
What's is not clear to me is why $a=-1$ and $b=1$. The model as given does not specify a value for either of $a$ and $b$. ($c=1$ and $d=0$ are fine, however).