Identifiability of car-following dynamics

The paper establishes, via the Lie-derivative Observability–Identifiability (OIC) framework and symbolic computation, that all four car-following models (CTH-RV, OV, FTL, IDM) are structurally locally identifiable for almost all initial conditions under admissible inputs; it also isolates equilibrium and other measure-zero cases that lose identifiability, and uses a numerical direct test to study practical identifiability (including measurement noise) . The candidate solution reconstructs these conclusions using explicit input–output derivative manipulations and specialization per model. It matches the paper on: (i) generic structural identifiability for all four models and the required admissible-input smoothness at equilibrium (CTH-RV/OV/IDM need u ∈ C^1; FTL has no admissible input at equilibrium) ; (ii) the CTH-RV loss-of-identifiability cases at equilibrium with constant input and the special relation τ = s0/v0, k2 = v0/s0 (Proposition 3) for which no admissible input exists ; and (iii) practical identifiability via a direct test, where CTH-RV and FTL are unidentifiable even with essentially error-free data, while all models are unidentifiable under measurement error, consistent with the paper’s δ*(ε) evidence and conclusions . Minor issues in the model’s write-up include an over-simplified inversion step for OV using V″/V′ at a single s0 (which depends on b and needs higher derivatives or additional information) and some hand-waving for IDM sensitivities; these do not change the main conclusions, which agree with the paper’s results.