Given a model $y_k=A_kx$, we can estimate $x$ by RLC method,
$$\hat x_k= \hat x_{k-1}+P_k A^T_k (y_k-A_k \hat x_{k-1})$$
where $P_k$ is the Riccati equation.
$$P_k = P_{k-1} - P_{k-1} A^T_k (I + A_kP_{k-1}A^T_k)^{-1}A_kP_{k-1}$$
My homework is to estimate $x$ in matlab with RLS, which I already did and seem to work fine. What I don't understand is that I can basically pick anything for $\hat x_0$ to start with. However $P_0$ only can be the identity matrix, other than that, RLS won't give my the correct estimation. Can someone explain to me how to pick initial conditions.