A subspace algorithm for identifying 2-D separable in denominator filters

In this paper, we extend the 1-D linear subspace identification algorithm to the class of 2-D causal, recursive, and separable in denominator filters (CRSD). The new 2-D subspace identification algorithm uses the input/output data directly to identify the system matrices, while classical algorithms first deconvolve the impulse response and then perform a realization step to obtain the system matrices. The identified models are in balanced form, which makes the 2-D subspace algorithm directly comparable to Hankel-based methods. Other advantages of the subspace algorithm are the automatic structure identification (system order), geometrical insights (notions of angle between subspaces), and the fact that it relies on robust numerical procedures (singular value decomposition)