Differentiable Adaptive Kalman Filtering via Optimal Transport
This addresses noise-statistics drift in learning-based filtering for applications such as robotics or sensor networks, but it is incremental as it builds on existing adaptive Kalman filtering methods.
The paper tackles the problem of noise-statistics drift in learning-based Kalman filtering for non-linear dynamical systems, which degrades performance in real-world deployments like changing environmental conditions. It proposes OTAKNet, an online solution using optimal transport, and demonstrates improved performance on synthetic and real-world datasets, particularly with limited training data.
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.