  This paper proposes a new algorithm for linear system identification from
noisy measurements. The proposed algorithm balances a data fidelity term with a
norm induced by the set of single pole filters. We pose a convex optimization
problem that approximately solves the atomic norm minimization problem and
identifies the unknown system from noisy linear measurements. This problem can
be solved efficiently with standard, freely available software. We provide
rigorous statistical guarantees that explicitly bound the estimation error (in
the H_2-norm) in terms of the stability radius, the Hankel singular values of
the true system and the number of measurements. These results in turn yield
complexity bounds and asymptotic consistency. We provide numerical experiments
demonstrating the efficacy of our method for estimating linear systems from a
variety of linear measurements.
