  Subspace identification is revisited in the scope of nuclear norm
minimization methods. It is shown that essential structural knowledge about the
unknown data matrices in the data equation that relates Hankel matrices
constructed from input and output data can be used in the first step of the
numerical solution presented. The structural knowledge comprises the low rank
property of a matrix that is the product of the extended observability matrix
and the state sequence and the Toeplitz structure of the matrix of Markov
parameters (of the system in innovation form). The new subspace identification
method is referred to as the N2SID (twice the N of Nuclear Norm and SID for
Subspace IDentification) method. In addition to include key structural
knowledge in the solution it integrates the subspace calculation with
minimization of a classical prediction error cost function. The nuclear norm
relaxation enables us to perform such integration while preserving convexity.
The advantages of N2SID are demonstrated in a numerical open- and closed-loop
simulation study. Here a comparison is made with another widely used SID
method, i.e. N4SID. The comparison focusses on the identification with short
data batches, i.e. where the number of measurements is a small multiple of the
system order.
