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}
}