Requresive Least Squares(RLS) is a famous algorithm for solving linear system and it's used a lot with system identification for finding parameters for a polynomial function:
$$yA(q) = uB(q) + eC(q)$$
Where $y$ is the output signal, $u$ is the input signal and $e$ is the noise. In RLS-case, we can assume that $e$ is the model error.
The only problem is that $u$ need to varying over time, else, $A(q)$ will be unstable. Why does $u$ not to varying over time. Why can't $u$ be a fixed value?