  In this paper, we address the problem of convergence of sequential
variational inference filter (VIF) through the application of a robust
variational objective and Hinf-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 introduced by the sequential VIF steps. We
desire a framework that improves feasibility while still maintaining reasonable
proximity to the optimal Kalman filter as data is assimilated. To accomplish
this goal, a Hinf-norm based optimization perturbs the VIF covariance matrix to
improve robustness. This yields a novel VIF- Hinf recursion that employs
consecutive variational inference and Hinf based optimization steps. We explore
the development of this method and investigate a numerical example to
illustrate the effectiveness of the proposed filter.
