A subspace algorithm for identifying 2-D CRSD systems with deterministic inputs

In this paper, the class of subspace system identification algorithms is used to derive a new identification algorithm for 2-D causal, recursive, and separable-in-denominator (CRSD) state space systems in the Roesser model form. The algorithm take a given deterministic input-output pair of 2-D signals and computes the system order (n) and system parameter matrices {A;B;C;D}. Since the CRSD model can be treated as two 1-D systems, the proposed algorithm first separates the vertical component from the state and output equations and then formulates an equivalent set of 1-D horizontal subspace equations. The solution to the horizontal subspace identification subproblem contains all the information necessary to compute the system order and parameter matrices, including those from the vertical subsystem.