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 statistical robust filters, which treat all state-space regions identically, and from constrained filters, which bound states rather than modulating observation trust. The approach is especially relevant in non-ergodic or data-scarce settings where only a single realization is available and statistical methods alone cannot learn the noise structure. We implement gating within Extended, Unscented, Ensemble, and Adaptive Kalman filters and particle filters, requiring only two additional hyperparameters. Monte Carlo benchmarks (100 replications) on a Ginzburg-Landau double-well with 10% outlier contamination show 57-80% RMSE improvement over the standard Extended Kalman Filter, all statistically significant (p < 10^{-15}, Wilcoxon test). A naive topological baseline using only well positions achieves 57%, confirming that the continuous energy landscape adds ~21 percentage points. The method is robust to misspecification: even with 50% parameter errors, 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 gamma = -0.109 (bootstrap 95% CI: [-0.220, -0.011]) and showing 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调制贝叶斯滤波器的观测噪声协方差：当系统状态接近势能最小值时充分信任观测数据，当状态接近分隔亚稳态势阱的势垒时则逐步降低观测权重。这种基于物理机制的调控方式与统计鲁棒滤波器（对所有状态空间区域采用统一处理）和约束滤波器（直接限制状态而非调节观测可信度）存在本质区别。该方法特别适用于非遍历性或数据稀缺场景——当仅能获取单次实现且统计方法无法独立学习噪声结构时。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。基于金兹堡-朗道双阱模型的蒙特卡洛基准测试（100次重复实验）显示，在10%异常值污染条件下，相比标准扩展卡尔曼滤波器均方根误差降低57-80%，所有结果均具有统计显著性（p < 10^{-15}，Wilcoxon检验）。仅使用势阱位置的朴素拓扑基线方法实现57%的改进，证实连续能量景观可带来约21个百分点的额外增益。该方法对参数失配具有鲁棒性：即使存在50%参数误差，改进幅度始终不低于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%的改进幅度，而朴素基线方法则降至30%。作为实证案例，我们将该框架应用于NGRIP冰芯δ-18O记录中的Dansgaard-Oeschger事件，估计得到不对称系数γ = -0.109（自助法95%置信区间：[-0.220, -0.011]），并证明异常值比例可解释滤波器改进幅度91%的方差。