Differentiable Adaptive Kalman Filtering via Optimal Transport

TL;DR

OTAKNet introduces an online, optimal transport-based adaptive Kalman filtering method that effectively manages noise-statistics drift in non-linear systems without requiring retraining or ground truth labels.

Contribution

It is the first online adaptive Kalman filter leveraging optimal transport to handle noise-statistics drift without offline training or ground truth labels.

Findings

Outperforms classical adaptive Kalman filters in noisy, real-world scenarios.

Effective in limited training data conditions.

Demonstrated on synthetic and NCLT datasets.

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.