Comparison of uncertainty propagation techniques in small-body environment

The paper’s claims and scenario-by-scenario findings (LinCov accurate for simple arcs and flybys; UT generally overestimates in nonlinear regimes; 4th-order PCE most accurate with ≈10× lower CPU than MC) are consistent with their equations and results (Eqs. 3–6, 7–9, 10–15, 22; Scenarios 1–7) and are well-supported by figures and timing tables. By contrast, the model’s keystone theoretical claim—“LinCov systematically underestimates dispersion via a positive semidefinite O(Σ0^2) correction” derived from a second-order Taylor expansion—omits the O(Σ0^2) linear–cubic cross term and incorrectly treats the quadratic-only correction as exhaustive at that order. In general, cubic contributions produce O(Σ0^2) terms of indefinite sign (e.g., 1D y = aξ + cξ^3 gives Var(y) = a^2σ^2 + 6acσ^4 + …), so the model’s asserted always-underestimation is false without extra assumptions. The model also mislabels Q as the covariance (off by a factor 1/2). Although many of the model’s qualitative scenario conclusions align with the paper, its central “rigorous” proof is flawed.