response by using, for example, the `lsim` command in MATLAB. Although this approach has provided a quick procedure to compute the filtered regressor and instrument vectors, it is prone to approximation errors that can jeopardise the statistical properties of the method.

\[algorithm1\]

Input: $\{(u(t_k),y(t_k))\}_{k=1}^N$, model order $(n,m)$, initial vector estimate $\theta_1$, tolerance $\epsilon$ and maximum number of iterations $M$ Using $\theta_1$, form the estimated system polynomials $A_1(p)$ and $B_1(p)$ $j\gets 1$, $\textnormal{flag}\gets 1$ Reflect the unstable poles of $1/A_j(s)$ into the stable region of the complex $s$-plane Prefilter the (DT) input $\{u(t_k)\}_{k=1}^N$ and output $\{y(t_k)\}_{k=1}^N$ by CT filters to form

\_f(t\_k) & \^,&\
\_f(t\_k) & \^, &\
\[filteredoutput\] y\_f(t\_k) &y(t\_k)&

Compute the parameter estimate $$\label{iterations}
        \theta_{j+1} \gets \hspace{-0.05cm}\left[\sum_{k=1}^N  \hat{\varphi}_f(t_k) \varphi_f^\top(t_k)\right]^{-1}\hspace{-0.1cm}\left[ \sum_{k=1}^N \hat{\varphi}_f(t_k) y_f(t_k)  \right]$$ $\textnormal{flag} \gets 0$ $j \gets j+1$ Output: $\theta_{j}$ and its associated model $B_j(p)/A_j(p)$.

\[algorithm1\]

**.** In the SRIVC method, the user has several choices regarding the intersample behaviour assumptions. In particular, the intersample behaviour of the input in both and can be chosen, as well as the reconstruction of the output signal for the filtering steps in  and . Usually the output is selected to have a FOH behaviour, since it is argued that it typically 