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In this paper, we address the problem of convergence of sequentialvariational inference filter (VIF) through the application of a robustvariational objective and Hinf-norm based correction for a linear Gaussiansystem. As the dimension of state or parameter space grows, performing the fullKalman update with the dense covariance matrix for a large scale systemrequires increased storage and computational complexity, making it impractical.The VIF approach, based on mean-field Gaussian variational inference, reducesthis burden through the variational approximation to the covariance usually inthe form of a diagonal covariance approximation. The challenge is to retainconvergence and correct for biases introduced by the sequential VIF steps. Wedesire a framework that improves feasibility while still maintaining reasonableproximity to the optimal Kalman filter as data is assimilated. To accomplishthis goal, a Hinf-norm based optimization perturbs the VIF covariance matrix toimprove robustness. This yields a novel VIF- Hinf recursion that employsconsecutive variational inference and Hinf based optimization steps. We explorethe development of this method and investigate a numerical example toillustrate the effectiveness of the proposed filter.

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