Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Carlos C. Rodriguez

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 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.

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

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 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.
Paper Structure (11 sections, 11 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 11 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction: The Normalizability Crisis in Sequential Tracking
  2. Descending from Geometric Ignorant Priors: The Abstraction Sequence
  3. Resolution via Non-Parametric Field Actions
  4. The Infinite-Dimensional Mandate and the Dirac Analogy
  5. The Base Measure: Feynman-Kac and Reproducing Kernel Banach Spaces
  6. Bridging the Field Action to Finite Gaussians
  7. Empirical Applications of Bounded Geometry
  8. LiDAR Kinematic Tracking: Monte Carlo Benchmarks
  9. High-Frequency Cryptocurrency Order Flow and Turnover Loss
  10. Quantum State Tomography
  11. Conclusion

Figures (3)

  • Figure 1: The thermodynamic geometry of the Non-Parametric Field Action over the statistical manifold. An unconstrained estimator (red wireframe) acts as an infinite-volume gas, assigning non-zero probability mass across the entire manifold and succumbing to infinite Euclidean drag from the extreme outlier. By enforcing the strictly invariant Delta Information Separation constraint, the Information Tracker creates a rigid surface tension. The geometry collapses into a finite, normalizable probability droplet (solid surface), structurally truncating the reflection ghost entirely because the probability mass at that location is identically zero.
  • Figure 2: Head-to-head tracking benchmark of a maneuvering target under severe reflection ghost contamination ($+40$m offset). The Information Tracker analytically truncates the outliers and maintains a zero-residual path, while the unconstrained Gaussian MAP estimator succumbs to infinite-volume drag.
  • Figure 3: Head-to-head tracking benchmark of ETH-USD. The raw 1-minute tick data (grey) contains severe liquidation wicks. The SOTA Kalman filter (orange, dashed) statistically digests every anomaly, resulting in a highly volatile state estimate that triggers high trading turnover. The Information Tracker (blue, solid) analytically truncates these wicks, holding the consensus price and structurally adapting to genuine regime shifts.