Least Squares Realization of Complex-Valued Multiple-Output Autonomous LTI Systems via the Riemannian Singular Value Decomposition*

We present a generalization of least squares realization of multiple-output linear time-invariant models to the complex domain, thereby enabling broader applicability in areas such as signal processing, control, and system identification. We discuss the challenges inherent to optimization over complex variables and formulate the realization problem as a structured total least squares problem. A key contribution is the derivation of a complex-valued nonlinear generalized singular value decomposition. We adapt an existing heuristic algorithm that works over the real domain to solve the complex nonlinear generalized singular value decomposition. We validate our framework through illustrative examples and demonstrate its use in a nuclear magnetic resonance modeling problem and a direction of arrival estimation problem.