ICCK Transactions on Advanced Computing and Systems
ISSN: 3068-7969 (Online)
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TY - JOUR AU - Fu, Heran AU - Jin, Xuebo PY - 2025 DA - 2025/12/25 TI - VNNPF: A Variational Neural Network with Planar Flow for Robust IMU-GPS Fusion and Trajectory Estimation JO - ICCK Transactions on Advanced Computing and Systems T2 - ICCK Transactions on Advanced Computing and Systems JF - ICCK Transactions on Advanced Computing and Systems VL - 2 IS - 1 SP - 25 EP - 41 DO - 10.62762/TACS.2025.570823 UR - https://www.icck.org/article/abs/TACS.2025.570823 KW - state estimation KW - bayesian recurrent neural networks KW - variational autoencoders KW - planar flow KW - kalman filter KW - IMU-GPS fusion AB - Accurate state estimation for dynamic targets is essential in fields such as target tracking, navigation, and autonomous driving. However, traditional estimation models struggle to handle the nonlinear motion patterns and sensor noise prevalent in real-world environments. To address these challenges, this paper proposes a novel end-to-end estimation model named Variational Neural Network with Planar Flow (VNNPF). The model integrates a Bayesian Gated Recurrent Unit (BGRU) as the process model, a planar flow-based variational autoencoder (PFVAE) as the measurement model, and a Bayesian hyperparameter optimization module inspired by Kalman filtering. The BGRU captures nonlinear temporal dependencies and enhances robustness by modeling parameters as distributions. PFVAE transforms simple latent distributions into more complex posteriors, enabling more accurate modeling of colored noise in sensor data. The Kalman-inspired update module computes a learnable gain to fuse prior and posterior information effectively. Experiments on the KITTI IMU–GPS benchmark demonstrate that VNNPF consistently achieves lower state-estimation errors than several state-of-the-art neural network baselines. These results indicate that VNNPF can provide accurate and robust trajectory estimation for nonlinear dynamic systems with complex sensor noise. SN - 3068-7969 PB - Institute of Central Computation and Knowledge LA - English ER -
@article{Fu2025VNNPF,
author = {Heran Fu and Xuebo Jin},
title = {VNNPF: A Variational Neural Network with Planar Flow for Robust IMU-GPS Fusion and Trajectory Estimation},
journal = {ICCK Transactions on Advanced Computing and Systems},
year = {2025},
volume = {2},
number = {1},
pages = {25-41},
doi = {10.62762/TACS.2025.570823},
url = {https://www.icck.org/article/abs/TACS.2025.570823},
abstract = {Accurate state estimation for dynamic targets is essential in fields such as target tracking, navigation, and autonomous driving. However, traditional estimation models struggle to handle the nonlinear motion patterns and sensor noise prevalent in real-world environments. To address these challenges, this paper proposes a novel end-to-end estimation model named Variational Neural Network with Planar Flow (VNNPF). The model integrates a Bayesian Gated Recurrent Unit (BGRU) as the process model, a planar flow-based variational autoencoder (PFVAE) as the measurement model, and a Bayesian hyperparameter optimization module inspired by Kalman filtering. The BGRU captures nonlinear temporal dependencies and enhances robustness by modeling parameters as distributions. PFVAE transforms simple latent distributions into more complex posteriors, enabling more accurate modeling of colored noise in sensor data. The Kalman-inspired update module computes a learnable gain to fuse prior and posterior information effectively. Experiments on the KITTI IMU–GPS benchmark demonstrate that VNNPF consistently achieves lower state-estimation errors than several state-of-the-art neural network baselines. These results indicate that VNNPF can provide accurate and robust trajectory estimation for nonlinear dynamic systems with complex sensor noise.},
keywords = {state estimation, bayesian recurrent neural networks, variational autoencoders, planar flow, kalman filter, IMU-GPS fusion},
issn = {3068-7969},
publisher = {Institute of Central Computation and Knowledge}
}
Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 
ICCK Transactions on Advanced Computing and Systems
ISSN: 3068-7969 (Online)
Email: [email protected]
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