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.

翻译：本文提出势能门控方法，用于在双阱随机动力学系统中实现鲁棒状态估计。该方法通过已知或假设的势能函数局部值来调制贝叶斯滤波器的观测噪声协方差：当状态接近势能极小值时信任观测数据，随着状态接近分隔亚稳态势阱的势垒而逐步降低观测权重。这种基于物理机制的方案既不同于对所有状态空间区域进行统一处理的纯统计鲁棒滤波器，也不同于对状态施加硬约束而非调制观测信任度的约束滤波器。我们在扩展卡尔曼滤波器、无迹卡尔曼滤波器、集合卡尔曼滤波器、自适应卡尔曼滤波器以及粒子滤波器中实现了门控机制，仅需引入两个超参数。在包含10%离群值污染的Ginzburg-Landau双阱过程上的合成基准测试表明，经过100次重复的蒙特卡洛验证，该方法相比标准扩展卡尔曼滤波器实现了57-80%的均方根误差改进，所有结果均具有统计显著性（p < 10^{-15}，Wilcoxon符号秩检验）。仅使用最近势阱距离的朴素拓扑基线方法实现了57%的改进，证实连续能量景观带来了额外的约21个百分点改进。该方法对模型误设具有鲁棒性：即使假设势能参数偏离真实值50%，改进幅度仍不低于47%。对比外部驱动与自发Kramers型跃迁，在噪声诱导跃迁场景下门控方法保持68%的改进，而朴素基线方法则降至30%。作为实证示例，我们将该框架应用于NGRIP冰芯δ-18O记录中的Dansgaard-Oeschger事件，估计得到不对称参数γ = -0.109（自助法95%置信区间：[-0.220, -0.011]，排除零值），并证明离群值比例可解释滤波器改进幅度91%的方差。