  This paper considers the problem of linear time-invariant (LTI) system
identification using input/output data. Recent work has provided non-asymptotic
results on partially observed LTI system identification using a single
trajectory but is only suitable for stable systems. We provide finite-time
analysis for learning Markov parameters based on the ordinary least-squares
(OLS) estimator using multiple trajectories, which covers both stable and
unstable systems. For unstable systems, our results suggest that the Markov
parameters are harder to estimate in the presence of process noise. Without
process noise, our upper bound on the estimation error is independent of the
spectral radius of system dynamics with high probability. These two features
are different from fully observed LTI systems for which recent work has shown
that unstable systems with a bigger spectral radius are easier to estimate.
Extensive numerical experiments demonstrate the performance of our OLS
estimator.
