# FW-NKF: Frequency-Weighted Neural Kalman Filters

arXiv: https://arxiv.org/abs/2606.02251 · HTML: https://mlsanity.com/paper/2606.02251/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [HuMoR: 3D Human Motion Model for Robust Pose Estimation](https://mlsanity.com/paper/2105.04668/) (2021)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Composable Deep Reinforcement Learning for Robotic Manipulation](https://mlsanity.com/paper/1803.06773/) (2018)
- [TOCH: Spatio-Temporal Object-to-Hand Correspondence for Motion Refinement](https://mlsanity.com/paper/2205.07982/) (2022)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [IONet: Learning to Cure the Curse of Drift in Inertial Odometry](https://mlsanity.com/paper/1802.02209/) (2018)
- [MuProp: Unbiased Backpropagation for Stochastic Neural Networks](https://mlsanity.com/paper/1511.05176/) (2015)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [How to Train Your Differentiable Filter](https://mlsanity.com/paper/2012.14313/) (2020)
- [Ultra Inertial Poser: Scalable Motion Capture and Tracking from Sparse Inertial Sensors and Ultra-Wideband Ranging](https://mlsanity.com/paper/2404.19541/) (2024)
- [Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification](https://mlsanity.com/paper/2506.11639/) (2025)
- [Perceptual Kalman Filters: Online State Estimation under a Perfect Perceptual-Quality Constraint](https://mlsanity.com/paper/2306.02400/) (2023)

## Abstract (arXiv)

Robust state estimation is central to robotic autonomy, yet classical Kalman filters struggle with frequency-dependent disturbances and model mismatch such as sensor vibrations, electromagnetic interference, and periodic noise. Although Deep Kalman Filter (DKF) variants extend the Extended Kalman Filtering (EKF) framework by learning latent transitions, they lack explicit mechanisms to suppress band-limited noise components that typically corrupt sensor measurements in real-world scenarios. We introduce the Frequency-Weighted Neural Kalman Filter (FW-NKF), a unified hybrid approach that embeds a causal spectral-shaping operator into the Kalman measurement residual and jointly learns observation, and transition networks. By adapting both the filter spectrum and the latent state representation, FW-NKF attenuates the noise-dominated frequency bands while capturing complex residual structures. We conduct extensive experiments on four heterogeneous benchmarks, including chaotic systems such as multi-dimensional Lorenz systems and full-body inertial pose estimation, and find a reduction in localization error of up to 10% as well as marked improvements in orientation accuracy. Our ablation studies confirm that frequency weighting and deep latent-state modeling contribute to overall performance.