# Adaptive Kalman-Informed Transformer

arXiv: https://arxiv.org/abs/2401.09987 · HTML: https://mlsanity.com/paper/2401.09987/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 58 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Backprop KF: Learning Discriminative Deterministic State Estimators](https://mlsanity.com/paper/1605.07148/) (2016)
- [AI-IMU Dead-Reckoning](https://mlsanity.com/paper/1904.06064/) (2019)
- [Inertial Navigation Meets Deep Learning: A Survey of Current Trends and Future Directions](https://mlsanity.com/paper/2307.00014/) (2023)
- [Adaptive Adjustment of Noise Covariance in Kalman Filter for Dynamic State Estimation](https://mlsanity.com/paper/1702.00884/) (2017)
- [BeamsNet: A data-driven Approach Enhancing Doppler Velocity Log Measurements for Autonomous Underwater Vehicle Navigation](https://mlsanity.com/paper/2206.13603/) (2022)
- [A Hybrid Model and Learning-Based Adaptive Navigation Filter](https://mlsanity.com/paper/2207.12082/) (2022)
- [Learning Vehicle Trajectory Uncertainty](https://mlsanity.com/paper/2206.04409/) (2022)
- [VIO-DualProNet: Visual-Inertial Odometry with Learning Based Process Noise Covariance](https://mlsanity.com/paper/2308.11228/) (2023)
- [ProNet: Adaptive Process Noise Estimation for INS/DVL Fusion](https://mlsanity.com/paper/2212.08882/) (2022)
- [Adaptive Step Size Learning with Applications to Velocity Aided Inertial Navigation System](https://mlsanity.com/paper/2206.13428/) (2022)

## Built on by (most cited first, 11 of 11)

- [Seamless Underwater Navigation with Limited Doppler Velocity Log Measurements](https://mlsanity.com/paper/2404.13742/) (2024)
- [DCNet: A Data-Driven Framework for DVL Calibration](https://mlsanity.com/paper/2410.08809/) (2024)
- [DVL Calibration using Data-driven Methods](https://mlsanity.com/paper/2401.12687/) (2024)
- [Data-Driven Strategies for Coping with Incomplete DVL Measurements](https://mlsanity.com/paper/2401.15620/) (2024)
- [Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation](https://mlsanity.com/paper/2509.04154/) (2025)
- [Gaussian Process Regression for Improved Underwater Navigation](https://mlsanity.com/paper/2502.16510/) (2025)
- [AUV Acceleration Prediction Using DVL and Deep Learning](https://mlsanity.com/paper/2503.16573/) (2025)
- [ICD-Net: Inertial Covariance Displacement Network for Drone Visual-Inertial SLAM](https://mlsanity.com/paper/2512.00037/) (2025)
- [Neural-Assisted in-Motion Self-Heading Alignment](https://mlsanity.com/paper/2604.00168/) (2026)
- [Information-Aided DVL Calibration](https://mlsanity.com/paper/2606.31216/) (2026)
- [Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter](https://mlsanity.com/paper/2609.32640/) (2026)

## Abstract (arXiv)

The extended Kalman filter (EKF) is a widely adopted method for sensor fusion in navigation applications. A crucial aspect of the EKF is the online determination of the process noise covariance matrix reflecting the model uncertainty. While common EKF implementation assumes a constant process noise, in real-world scenarios, the process noise varies, leading to inaccuracies in the estimated state and potentially causing the filter to diverge. Model-based adaptive EKF methods were proposed and demonstrated performance improvements to cope with such situations, highlighting the need for a robust adaptive approach. In this paper, we derive an adaptive Kalman-informed transformer (A-KIT) designed to learn the varying process noise covariance online. Built upon the foundations of the EKF, A-KIT utilizes the well-known capabilities of set transformers, including inherent noise reduction and the ability to capture nonlinear behavior in the data. This approach is suitable for any application involving the EKF. In a case study, we demonstrate the effectiveness of A-KIT in nonlinear fusion between a Doppler velocity log and inertial sensors. This is accomplished using real data recorded from sensors mounted on an autonomous underwater vehicle operating in the Mediterranean Sea. We show that A-KIT outperforms the conventional EKF by more than 49.5% and model-based adaptive EKF by an average of 35.4% in terms of position accuracy.