Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions

TL;DR

This paper introduces a novel robust sequential inference method that uses bounded information geometry and non-parametric field actions to effectively handle structured outliers, improving estimation stability across diverse applications.

Contribution

It proposes a new theoretical framework that truncates infinite tails in parameter spaces, enabling robust inference without infinite-tailed assumptions.

Findings

Outperforms traditional estimators in outlier-rich scenarios

Successfully applied to LiDAR, cryptocurrency, and quantum state data

Ensures finite, normalizable probability measures for robust estimation

Abstract

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 \nu) 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.