Common dynamic estimation via structured low-rank approximation with multiple rank constraints

We consider the problem of detecting the common dynamic among several observed signals. It has been shown in (Markovsky et al., 2019) that the problem is equivalent to a generalization of the classical Hankel low-rank approximation to the case of multiple rank constraints. We propose an optimization method based on the integration of ordinary differential equations describing a descent dynamic for a suitable functional to be minimized. We show how the proposed algorithm improves the numerical solutions computed by existing subspace methods which solve the same problem.