  This paper proposes a novel model inference procedure to identify system
matrix from a single noisy trajectory over a finite-time interval. The proposed
inference procedure comprises an observation data processor, a redundant data
processor and an ordinary least-square estimator, wherein the data processors
mitigate the influence of observation noise on inference error. We first
systematically investigate the comparisons with naive least-square-regression
based model inference and uncover that 1) the same observation data has
identical influence on the feasibility of the proposed and the naive model
inferences, 2) the naive model inference uses all of the redundant data, while
the proposed model inference optimally uses the basis and the redundant data.
We then study the sample complexity of the proposed model inference in the
presence of observation noise, which leads to the dependence of the processed
bias in the observed system trajectory on time and coordinates. Particularly,
we derive the sample-complexity upper bound (on the number of observations
sufficient to infer a model with prescribed levels of accuracy and confidence)
and the sample-complexity lower bound (high-probability lower bound on model
error). Finally, the proposed model inference is numerically validated and
analyzed.
