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Robust Unscented Kalman Filtering via Recurrent Meta-Adaptation of Sigma-Point Weights

Kenan Majewski, Michał Modzelewski, Marcin Żugaj, Piotr Lichota

TL;DR

The Meta-Adaptive UKF (MA-UKF) is introduced, a framework that reformulates sigma-point weight synthesis as a hyperparameter optimization problem addressed via memory-augmented meta-learning and significantly outperforms standard baselines.

Abstract

The Unscented Kalman Filter (UKF) is a ubiquitous tool for nonlinear state estimation; however, its performance is limited by the static parameterization of the Unscented Transform (UT). Conventional weighting schemes, governed by fixed scaling parameters, assume implicit Gaussianity and fail to adapt to time-varying dynamics or heavy-tailed measurement noise. This work introduces the Meta-Adaptive UKF (MA-UKF), a framework that reformulates sigma-point weight synthesis as a hyperparameter optimization problem addressed via memory-augmented meta-learning. Unlike standard adaptive filters that rely on instantaneous heuristic corrections, our approach employs a Recurrent Context Encoder to compress the history of measurement innovations into a compact latent embedding. This embedding informs a policy network that dynamically synthesizes the mean and covariance weights of the sigma points at each time step, effectively governing the filter's trust in the prediction versus the measurement. By optimizing the system end-to-end through the filter's recursive logic, the MA-UKF learns to maximize tracking accuracy while maintaining estimation consistency. Numerical benchmarks on maneuvering targets demonstrate that the MA-UKF significantly outperforms standard baselines, exhibiting superior robustness to non-Gaussian glint noise and effective generalization to out-of-distribution (OOD) dynamic regimes unseen during training.

Robust Unscented Kalman Filtering via Recurrent Meta-Adaptation of Sigma-Point Weights

TL;DR

The Meta-Adaptive UKF (MA-UKF) is introduced, a framework that reformulates sigma-point weight synthesis as a hyperparameter optimization problem addressed via memory-augmented meta-learning and significantly outperforms standard baselines.

Abstract

The Unscented Kalman Filter (UKF) is a ubiquitous tool for nonlinear state estimation; however, its performance is limited by the static parameterization of the Unscented Transform (UT). Conventional weighting schemes, governed by fixed scaling parameters, assume implicit Gaussianity and fail to adapt to time-varying dynamics or heavy-tailed measurement noise. This work introduces the Meta-Adaptive UKF (MA-UKF), a framework that reformulates sigma-point weight synthesis as a hyperparameter optimization problem addressed via memory-augmented meta-learning. Unlike standard adaptive filters that rely on instantaneous heuristic corrections, our approach employs a Recurrent Context Encoder to compress the history of measurement innovations into a compact latent embedding. This embedding informs a policy network that dynamically synthesizes the mean and covariance weights of the sigma points at each time step, effectively governing the filter's trust in the prediction versus the measurement. By optimizing the system end-to-end through the filter's recursive logic, the MA-UKF learns to maximize tracking accuracy while maintaining estimation consistency. Numerical benchmarks on maneuvering targets demonstrate that the MA-UKF significantly outperforms standard baselines, exhibiting superior robustness to non-Gaussian glint noise and effective generalization to out-of-distribution (OOD) dynamic regimes unseen during training.
Paper Structure (23 sections, 22 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 23 sections, 22 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Problem Definition
  4. Standard Unscented Kalman Filter Formulation
  5. The Paradigm of Differentiable Filtering
  6. Context-Driven Meta-Policy Formulation
  7. Meta-Adaptive Unscented Kalman Filter
  8. Innovation Feature Extraction
  9. Recurrent Context Encoding
  10. Convex Sigma-Point Weight Synthesis
  11. Algorithm and Computational Flow
  12. Computational Complexity Analysis
  13. Training via End-to-End Analytical Gradients
  14. Experimental Evaluation
  15. Simulation Environment and Datasets
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Architecture of the Meta-Adaptive UKF (MA-UKF). A Recurrent Context Encoder processes the innovation history to generate a latent context embedding, which drives a policy network to modulate the sigma-point weights in real-time.
  • Figure 2: Trajectory tracking performance on the OOD maneuver. The optimized UKF$^{\star}$ (Blue) suffers catastrophic divergence, while the IMM-UKF$^{\star}$ (Green) exhibits violent corrections. The MA-UKF (Red) sustains robust track continuity for longer, and closely hugs the underlying ground truth despite the simultaneous model mismatch and severe glint noise.
  • Figure 3: Temporal evolution of the learned sigma-point weights ($W_0$ to $W_{10}$) during the maneuver. The distinct impulsive spiking behavior across the entire geometry, contrasted with the continuous micro-modulation between events, indicates that the policy dynamically expands and contracts the local geometric spread to accommodate rapid directional changes and reject anomalies.