Subspace methods for multi-channel sum-of-exponentials common dynamics estimation

Estimation of common dynamics among several observed signals occurs in signal processing, system theory, and computer algebra problems. In this paper, we propose subspace methods for common linear time-invariant dynamics detection and estimation. First, we consider the deterministic problem of detection of common dynamics when the data is exact (noise free). Then, we consider the stochastic estimation problem when the data is corrupted by white Gaussian noise. The subspace identification methods proposed have a system theoretic interpretation of finding the intersection of autonomous linear time-invariant behaviors. They are computationally fast but statistically less accurate than alternative optimization methods. Development of local optimization-based methods for common dynamics estimation is a topic of future work.