  Probabilistic state estimation is essential for robots navigating uncertain
environments. Accurately and efficiently managing uncertainty in estimated
states is key to robust robotic operation. However, nonlinearities in robotic
platforms pose significant challenges that require advanced estimation
techniques. Gaussian variational inference (GVI) offers an optimization
perspective on the estimation problem, providing analytically tractable
solutions and efficiencies derived from the geometry of Gaussian space. We
propose a Sequential Gaussian Variational Inference (S-GVI) method to address
nonlinearity and provide efficient sequential inference processes. Our approach
integrates sequential Bayesian principles into the GVI framework, which are
addressed using statistical approximations and gradient updates on the
information geometry. Validations through simulations and real-world
experiments demonstrate significant improvements in state estimation over the
Maximum A Posteriori (MAP) estimation method.
