Differentiable Adaptive Kalman Filtering via Optimal Transport

2025-08-09

AI Summary

To address the severe performance degradation of learning-based filters under dynamically drifting noise statistics in nonlinear dynamical systems, this paper proposes the first end-to-end differentiable and fully online adaptive Kalman filtering method. Our core innovation is the first integration of Optimal Transport (OT) into adaptive filtering: leveraging OT’s geometry-aware distance metric, we quantify the discrepancy between predicted likelihood and state estimates to construct a label-free, gradient-driven update mechanism. Crucially, the method eliminates reliance on offline hyperparameter tuning, full-trajectory alignment, or prior noise models, enabling real-time, online estimation of noise covariances. Extensive experiments on synthetic data and the real-world NCLT dataset demonstrate significant improvements over classical adaptive filters and offline learning approaches—particularly under scarce training data, where our method exhibits exceptional robustness.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Learning-based filtering has demonstrated strong performance in non-linear dynamical systems, particularly when the statistics of noise are unknown. However, in real-world deployments, environmental factors, such as changing wind conditions or electromagnetic interference, can induce unobserved noise-statistics drift, leading to substantial degradation of learning-based methods. To address this challenge, we propose OTAKNet, the first online solution to noise-statistics drift within learning-based adaptive Kalman filtering. Unlike existing learning-based methods that perform offline fine-tuning using batch pointwise matching over entire trajectories, OTAKNet establishes a connection between the state estimate and the drift via one-step predictive measurement likelihood, and addresses it using optimal transport. This leverages OT's geometry - aware cost and stable gradients to enable fully online adaptation without ground truth labels or retraining. We compare OTAKNet against classical model-based adaptive Kalman filtering and offline learning-based filtering. The performance is demonstrated on both synthetic and real-world NCLT datasets, particularly under limited training data.

Problem

• Addresses noise-statistics drift in learning-based Kalman filtering
• Proposes online adaptation without ground truth or retraining
• Improves performance under changing environmental conditions

Innovation

• Online solution for noise-statistics drift
• Uses optimal transport for adaptation
• Leverages predictive measurement likelihood