# Differentiable Adaptive Kalman Filtering via Optimal Transport

arXiv: https://arxiv.org/abs/2508.07037 · HTML: https://mlsanity.com/paper/2508.07037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 9 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024)
- [Online Learning of the Kalman Filter with Logarithmic Regret](https://mlsanity.com/paper/2002.05141/) (2020)
- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Adaptive Adjustment of Noise Covariance in Kalman Filter for Dynamic State Estimation](https://mlsanity.com/paper/1702.00884/) (2017)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Kalman-Inspired Feature Propagation for Video Face Super-Resolution](https://mlsanity.com/paper/2408.05205/) (2024)
- [Adaptive KalmanNet: Data-Driven Kalman Filter with Fast Adaptation](https://mlsanity.com/paper/2309.07016/) (2023)
- [Unsupervised Cross-Domain Image Retrieval via Prototypical Optimal Transport](https://mlsanity.com/paper/2402.18411/) (2024)
- [Optimal-state Dynamics Estimation for Physics-based Human Motion Capture from Videos](https://mlsanity.com/paper/2410.07795/) (2024)
- [CTD4 -- A Deep Continuous Distributional Actor-Critic Agent with a Kalman Fusion of Multiple Critics](https://mlsanity.com/paper/2405.02576/) (2024)
- [Data-driven Optimal Filtering for Linear Systems with Unknown Noise Covariances](https://mlsanity.com/paper/2305.17836/) (2023)

## Abstract (arXiv)

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.