  This paper proposes an identification algorithm for Single Input Single
Output (SISO) Linear Time-Invariant (LTI) systems. In the noise-free setting,
where the first $T$ Markov parameters can be precisely estimated, all Markov
parameters can be inferred by the linear combination of the known $T$ Markov
parameters, of which the coefficients are obtained by solving the uniform
polynomial approximation problem, and the upper bound of the asymptotic
identification bias is provided. For the finite-time identification scenario,
we cast the system identification problem with noisy Markov parameters into a
regularized uniform approximation problem. Numerical results demonstrate that
the proposed algorithm outperforms the conventional Ho-Kalman Algorithm for the
finite-time identification scenario while the asymptotic bias remains
negligible.
