• DOI:10.48550/arXiv.2204.13089
• Corpus ID: 248405699

Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensions

@article{Das2022VariationalKF,
  title={Variational Kalman Filtering with Hinf-Based Correction for Robust Bayesian Learning in High Dimensions},
  author={Niladri Das and Jed A. Duersch and Thomas A. Catanach},
  journal={ArXiv},
  year={2022},
  volume={abs/2204.13089}
}

• Niladri Das, J. Duersch, T. Catanach
• Published 27 April 2022
• Computer Science
• ArXiv

— In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and H ∞ -norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually in the form of a diagonal covariance approximation. The challenge is to retain convergence and correct for biases intro-duced by the sequential VIF steps. We desire a frame- work that improves feasibility while still maintaining reasonable proximity to the optimal Kalman filter as data is assimilated. To accomplish this goal, a H ∞ norm based optimization perturbs the VIF covariance matrix to improve robustness. This yields a novel VIF-H ∞ recursion that employs consecutive variational inference and H ∞ based optimization steps. We explore the development of this method and investigate a numerical example to illustrate the effectiveness of the proposed filter.