I have the known measurement: Noise $e(t)$, output $y(k)$, input $u(k)$.
I need to find the Box-Jenkins model:
$$y[k] = \frac{B(q)}{F(q)}u[k] + \frac{C(q)}{D(q)}e[k]$$
Where $B, F, C, D$ are polynomial expressions. Eg.:
$B(q) = 1 + b_1q^{-1} \dots b_nq^{-n}$
Often I have used least square $Ax=b$ to find the parameters inside the polynomial expressions. But in this case, it seems not to work for me.
I have heard that in order to estimate the parameters inside the polynomial, Maximum likelihood estimation must be applied for finding the parameters inside this equation
$$F(q)D(q)y[k] = B(q)D(q)u[k] + F(q)C(q)e[k]$$
How would you do?
