Objectives : Finite time-transfer records can preserve several parameter decompositions that assign different values to propagation delay. This study determines which delay functionals a record identifies and which closure equations make the full delay vector unique. Methods: The finite record is written as \(y = A\tau + B\kappa\). Record-preserving perturbations are projected onto the delay coordinates to form \(\Pi_\tau(\ker J)\). Closure is analysed through its induced action on delay-changing equivalence classes, and a projected Moore–Penrose inverse quantifies sensitivity to closure error. Results: A linear delay functional is identifiable exactly when it annihilates the projected null space. Its identifiable subspace has codimension \(\dim \Pi_\tau(\ker J)\). Full delay identification under closure is equivalent to \(\Pi_\tau(\ker J \cap \ker G) = \{0\}\), with effective closure rank computed after zero-delay null directions are removed. The criterion is realised in a standard two-way transfer model, verified by synthetic operator tests, and traced through raw and residualised GNSS/RINEX records. Conclusion: Propagation delay has a unique record-based meaning when the target functional is invariant on the record-equivalence class. Closure can supply the information that creates this invariance; stable reconstruction alone does not establish it.
- Open Access
- Article
Identifiability of Propagation Delay from Finite Time-Transfer Records
Author Information
Received: 25 August 2026 | Revised: 14 September 2026 | Accepted: 23 October 2026 | Published: 27 October 2026
Abstract
Keywords
structural identifiability | inverse problems | time transfer | propagation delay | closure constraints | GNSS
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