Density Criteria for the Identification of Linear Time-Varying Systems

TL;DR

This paper establishes a density criterion for identifying linear time-varying systems with delays and Doppler shifts, linking system identifiability to Beurling density and interpolation in the Bargmann-Fock space, and proposes a subspace method for system identification.

Contribution

It introduces a density-based criterion for stable identifiability of LTV systems and connects it to complex analysis, along with a practical subspace identification method.

Findings

Stable identifiability when density < 1/2

Impossible identifiability when density > 1/2

Proposed subspace method for system identification

Abstract

This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform Beurling density of the delay-Doppler support set is strictly smaller than 1/2 and stable identifiability is impossible for densities strictly larger than 1/2. The proof of this density theorem reveals an interesting relation between LTV system identification and interpolation in the Bargmann-Fock space. Finally, we introduce a subspace method for solving the system identification problem at hand.