Explain the limited empirical separation among curvature-aware estimators

Determine why the improved curvature information in the iterated extended Kalman filter and Laplace approximation does not separate their performance as clearly as in the simulated experiments.

Background

The paper compares constrained recursive least squares, a constrained MAP estimator, the extended Kalman filter, the iterated extended Kalman filter, and the Laplace approximation for tracking time-varying simplicial complexes. In the real-data experiment, the iterated extended Kalman filter and Laplace approximation incorporate richer curvature information from nonlinear constraint pseudo-measurements, but their differences in relative error are marginal. The authors explicitly leave unresolved why this additional curvature information does not produce the clearer performance separation observed in simulation.