用势能控制观测信任度，提升双阱系统状态估计的鲁棒性。
Potential-energy gating for robust state estimation in bistable stochastic systems
- 根据势能高低动态调整观测可信度，靠近势阱时信任高，接近壁垒时逐步降低。
- 在含10%异常值的模拟中，均方误差降低57%至80%，显著优于标准卡尔曼滤波。
- 适用于数据稀疏或非遍历场景，适合气候突变等物理系统状态追踪。
我们提出势能门控方法，用于由双阱随机动力学支配的系统中的鲁棒状态估计。通过已知或假设的势能函数局部值调节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，接近分离两稳态井的势垒时逐步降低信任。该基于物理机制的方法不同于统计鲁棒滤波（对所有状态空间区域同等处理）和约束滤波（仅限制状态范围）。该方法在仅有单个实现且统计方法无法学习噪声结构的非遍历或数据稀缺场景中尤为适用。我们在扩展、无迹、集合及自适应卡尔曼滤波器与粒子滤波器中实现了该门控，仅需两个额外超参数。蒙特卡洛基准测试（100次重复）显示，在含10%异常值的Ginzburg-Landau双阱系统中，均方误差较标准扩展卡尔曼滤波器改善57%-80%，全部统计显著（p < 10^{-15}，Wilcoxon检验）。仅使用井位置的朴素拓扑基线达到57%，表明连续势能景观贡献约21个百分点提升。方法对参数误设具鲁棒性：即使参数误差达50%，改进仍不低于47%。对比外力驱动与自发的Kramers型跃迁，门控在噪声诱导跃迁下仍保持68%改进，而基线降至30%。以NGRIP δ¹⁸O冰芯记录中的丹斯加德-奥舍格事件为例，估计不对称性γ = -0.109（置信区间[-0.220, -0.011]），并发现异常值比例解释了91%的滤波性能提升方差。
原文摘要 · Abstract (English)
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.
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