Potential-energy gating for robust state estimation in bistable stochastic systems

Abstract: We introduce potential-energy gating, a method for robust state estimation in systems governed by double-well stochastic dynamics. The observation noise covariance of a Bayesian filter is modulated by the local value of a known or assumed potential energy function: observations are trusted when the state is near a potential minimum and progressively discounted as it approaches the barrier separating metastable wells. This physics-based mechanism differs from purely statistical robust filters, which treat all regions of state space identically, and from constrained filters, which impose hard bounds on states rather than modulating observation trust. We implement the gating within Extended, Unscented, Ensemble, and Adaptive Kalman filters and particle filters, requiring only two additional hyperparameters. Synthetic benchmarks on a Ginzburg-Landau double-well process with 10% outlier contamination and Monte Carlo validation over 100 replications show 57-80% RMSE improvement over the standard Extended Kalman Filter, all statistically significant (p < 10^{-15}, Wilcoxon signed-rank test). A naive topological baseline using only distance to the nearest well achieves 57%, confirming that the continuous energy landscape adds an additional ~21 percentage points. The method is robust to misspecification: even when assumed potential parameters deviate by 50% from their true values, improvement never falls below 47%. Comparing externally forced and spontaneous Kramers-type transitions, gating retains 68% improvement under noise-induced transitions whereas the naive baseline degrades to 30%. As an empirical illustration, we apply the framework to Dansgaard-Oeschger events in the NGRIP delta-18O ice-core record, estimating asymmetry parameter gamma = -0.109 (bootstrap 95% CI: [-0.220, -0.011], excluding zero) and demonstrating that outlier fraction explains 91% of the variance in filter improvement.