提出几何约束方法，让追踪模型自动过滤极端异常值。
Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions
- 用非参数场和不变信息分离，构建有界参数空间
- 实测三领域中异常值被精确截断，估计更稳定
- 适合处理高噪声、强异常的实时追踪任务
标准序列推断架构在面对极端结构性异常值时会遭遇可归一化危机。由于在无界参数空间中运行，现有估计算法缺乏合适的内在几何结构来有效切断异常，导致协方差无限膨胀和均值发散。本文从元先验层面（S_2）分析推理抽象序列，证明在无限维空间极值化作用量需依赖由预先验锚定的非参数场，因均匀体积元在数学上不存在。通过在统计流形上使用严格不变的Delta（或ν）信息分离，物理截断空间分布的无限尾部。当作为相对于基测度的Radon-Nikodym导数评估时，活跃参数空间压缩为严格有限、可归一化的概率小滴。在三个领域——LiDAR机动目标追踪、高频加密货币订单流、量子态层析——的实证基准测试表明，该有界信息几何能解析地截断异常值，确保鲁棒估计，无需依赖无穷尾分布假设。
原文摘要 · Abstract (English)
Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry required to appropriately sever anomalies, resulting in unbounded covariance inflation and mean divergence. This paper resolves this structural failure by analyzing the abstraction sequence of inference at the meta-prior level (S_2). We demonstrate that extremizing the action over an infinite-dimensional space requires a non-parametric field anchored by a pre-prior, as a uniform volume element mathematically does not exist. By utilizing strictly invariant Delta (or ν) Information Separations on the statistical manifold, we physically truncate the infinite tails of the spatial distribution. When evaluated as a Radon-Nikodym derivative against the base measure, the active parameter space compresses into a strictly finite, normalizable probability droplet. Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this bounded information geometry analytically truncates outliers, ensuring robust estimation without relying on infinite-tailed distributional assumptions.
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