# Hierarchical Variational Kalman Filtering

arXiv: https://arxiv.org/abs/2607.00877 · HTML: https://mlsanity.com/paper/2607.00877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Latent-KalmanNet: Learned Kalman Filtering for Tracking from High-Dimensional Signals](https://mlsanity.com/paper/2304.07827/) (2023)
- [The invariant extended Kalman filter as a stable observer](https://mlsanity.com/paper/1410.1465/) (2014)
- [Generalized Kalman Smoothing: Modeling and Algorithms](https://mlsanity.com/paper/1609.06369/) (2016)
- [Bayesian KalmanNet: Quantifying Uncertainty in Deep Learning Augmented Kalman Filter](https://mlsanity.com/paper/2309.03058/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Adaptive KalmanNet: Data-Driven Kalman Filter with Fast Adaptation](https://mlsanity.com/paper/2309.07016/) (2023)
- [Stochastic Variational Bayesian Inference for a Nonlinear Forward Model](https://mlsanity.com/paper/2007.01675/) (2020)
- [Variational Nonlinear Kalman Filtering with Unknown Process Noise Covariance](https://mlsanity.com/paper/2305.03914/) (2023)
- [Stochastic Event-triggered Variational Bayesian Filtering](https://mlsanity.com/paper/2206.06784/) (2022)
- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)
- [Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation](https://mlsanity.com/paper/2310.19586/) (2023)
- [Consistent and Optimal Solution to Camera Motion Estimation](https://mlsanity.com/paper/2403.01174/) (2024)

## Abstract (arXiv)

Traditional variational Kalman filtering with unknown noise statistics suffers from inconsistent process covariance estimation and slow convergence speed, limiting its practical utility. To address these issues, we introduce a surrogate variable representing the process-noise-free state, which enables explicit modeling and inference of process noise statistics. In addition, we reformulate the conventional coordinate ascent variation inference (CAVI) as a marginalized maximum a posteriori problem, followed by a single-step hyperparameter fitting. This reformulation obviates the need for multiple inner iterations inherent to CAVI and decouples the design of the covariance tracking filters. Consequently, this architecture permits the deployment of higher-order filters for covariance tracking and enables sliding-window hyperparameter estimation. Notably, when this window encompasses all historical data, the covariance tracking estimator intrinsically operates as a zero-phase filter. Numerical simulations validate the theoretical framework, demonstrating the enhanced convergence speed and superior estimation accuracy compared with existing methods.