Suppose there are two vector signals $x$, $z$. The observer 1 receives a linear version of $x$ plus Gaussian noise. Observer 2 receives a linear sum of both $x$ and $z$ plus Gaussian noise as shown below; $$y_1(t)=A_1(t)x(t)+n_1(t),$$ $$y_2(t)=A_2(t)x(t)+B_2(t)z(t)+n_2(t).$$ But observer 2 is only interested in estimating $z$ so ideally he would like to cancel the whole term $A_2x$. Furthermore $A_2$ is changing slowly over time. Slowly in the sense the changes are correlated over time. Suppose observer 1 can provide his estimates of $x$ say $x_1$ to observer 2. Is there any way for observer 2 to use that information to better estimate $z$? The matrices $A_1,A_2,B_2$ are independent.
Edit: Suppose $A_2(t+1)= \sum_{n=0}^{n=t}\alpha_nA_2(n) + z_t(t+1)$ where $z_(t)$ are independent Gaussian noise.
