Hierarchical Variational Kalman Filter boosts convergence and accuracy

Traditional variational Kalman filters often suffer from inconsistent process covariance estimation and slow convergence due to the iterative nature of coordinate ascent variational inference (CAVI). To overcome these limitations, researchers from Beijing Institute of Technology and Hong Kong University of Science and Technology introduce a novel Hierarchical Variational Kalman Filter. Their key innovation is introducing a surrogate variable representing the process-noise-free state, which allows explicit modeling of process noise statistics. They then reformulate CAVI as a marginalized maximum a posteriori (MAP) problem followed by a single-step hyperparameter fitting. This decouples covariance tracking filter design from the main inference loop, eliminating the need for multiple inner iterations.

The new architecture supports deploying higher-order filters for covariance tracking and enables sliding-window hyperparameter estimation. Notably, when the sliding window covers all historical data, the covariance estimator becomes a zero-phase filter, preventing lag-induced distortions. Numerical simulations validate the framework, showing enhanced convergence speed and superior estimation accuracy compared to existing methods. This work, published on arXiv under ID 2607.00877, represents a significant practical improvement for state estimation in systems with unknown noise statistics.