# A Hybrid Model and Learning-Based Adaptive Navigation Filter

arXiv: https://arxiv.org/abs/2207.12082 · HTML: https://mlsanity.com/paper/2207.12082/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [RoNIN: Robust Neural Inertial Navigation in the Wild: Benchmark, Evaluations, and New Methods](https://mlsanity.com/paper/1905.12853/) (2019)
- [RIDI: Robust IMU Double Integration](https://mlsanity.com/paper/1712.09004/) (2017)
- [Collapse of Deep and Narrow Neural Nets](https://mlsanity.com/paper/1808.04947/) (2018)
- [Denoising IMU Gyroscopes with Deep Learning for Open-Loop Attitude Estimation](https://mlsanity.com/paper/2002.10718/) (2020)
- [Deep Learning based Pedestrian Inertial Navigation: Methods, Dataset and On-Device Inference](https://mlsanity.com/paper/2001.04061/) (2020)
- [Learning Vehicle Trajectory Uncertainty](https://mlsanity.com/paper/2206.04409/) (2022)

## Built on by (most cited first, 12 of 12)

- [Inertial Navigation Meets Deep Learning: A Survey of Current Trends and Future Directions](https://mlsanity.com/paper/2307.00014/) (2023)
- [Adaptive Kalman-Informed Transformer](https://mlsanity.com/paper/2401.09987/) (2024)
- [LiBeamsNet: AUV Velocity Vector Estimation in Situations of Limited DVL Beam Measurements](https://mlsanity.com/paper/2210.11572/) (2022)
- [Data-Driven Meets Navigation: Concepts, Models, and Experimental Validation](https://mlsanity.com/paper/2210.02930/) (2022)
- [Deep Learning for Inertial Sensor Alignment](https://mlsanity.com/paper/2212.11120/) (2022)
- [A Hybrid Adaptive Velocity Aided Navigation Filter with Application to INS/DVL Fusion](https://mlsanity.com/paper/2211.01329/) (2022)
- [Surface Recognition for e-Scooter Using Smartphone IMU Sensor](https://mlsanity.com/paper/2302.12720/) (2023)
- [Learning Position From Vehicle Vibration Using an Inertial Measurement Unit](https://mlsanity.com/paper/2303.03942/) (2023)
- [Selection-Induced Contraction of Innovation Statistics in Gated Kalman Filters](https://mlsanity.com/paper/2512.18508/) (2025)
- [Overcoming the Intrinsic Performance Limitations of MEMS IMU via Diffusion-Based Generative Learning](https://mlsanity.com/paper/2605.16391/) (2026)
- [Can Predicted Dynamics Exist in the Physical World?](https://mlsanity.com/paper/2606.00089/) (2026)
- [One Residual with Three Reuses: A Wristband Front End for Gesture Sensing](https://mlsanity.com/paper/2608.16542/) (2026)

## Abstract (arXiv)

The fusion between an inertial navigation system and global navigation satellite systems is regularly used in many platforms such as drones, land vehicles, and marine vessels. The fusion is commonly carried out in a model-based extended Kalman filter framework. One of the critical parameters of the filter is the process noise covariance. It is responsible for the real-time solution accuracy, as it considers both vehicle dynamics uncertainty and the inertial sensors quality. In most situations, the process noise is covariance assumed to be constant. Yet, due to vehicle dynamics and sensor measurement variations throughout the trajectory, the process noise covariance is subject to change. To cope with such situations, several adaptive model-based Kalman filters were suggested in the literature. In this paper, we propose a hybrid model and learning-based adaptive navigation filter. We rely on the model-based Kalman filter and design a deep neural network model to tune the momentary system noise covariance matrix, based only on the inertial sensor readings. Once the process noise covariance is learned, it is plugged into the well-established, model-based Kalman filter. After deriving the proposed hybrid framework, field experiment results using a quadrotor are presented and a comparison to model-based adaptive approaches is given. We show that the proposed method obtained an improvement of 25% in the position error. Furthermore, the proposed hybrid learning method can be used in any navigation filter and also in any relevant estimation problem.