gives rise to a satisfactory approximation if the sampling period is small [@chen2017robust].

Consistency Analysis of the SRIVC estimator
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Previous works [@young2008refined; @young2015refined] have suggested that the SRIVC estimator uses the optimal instrumental variable terms, and that it minimises the prediction error and maximises the likelihood function, but they lack rigorous theoretical analysis regarding the influence of the interpolation of the input and output for the prefiltering step. Only recently [@pan2020consistency] has the intersample behaviour of the signals been taken into account for the consistency analysis. In [@pan2020consistency Theorem 1], the generic consistency of the SRIVC estimator was proven for inputs that can be exactly interpolated by FOH or ZOH devices. More precisely, under mild assumptions regarding the sampling period and persistence of excitation of the input, the following statements are true for an input that is exactly reconstructible with FOH or ZOH interpolation:

1.  The matrix $E\{\hat{\varphi}(t_k)\varphi^\top(t_k)\}$ is generically non-singular.[^1]

2.  The true parameter $\theta^*$ is the unique converging point.

3.  As the sample size $N$ approaches infinity, $\theta_{j+1}$ in  converges to $\theta^*$ for $j\geq 1$.

Also, the effect of choosing a different intersample behaviour than that of the system input was also analysed in [@pan2020consistency Corollary 3]. 