Exactly Sparse Gaussian Variational Inference with Application to Derivative-Free Batch Nonlinear State Estimation

Understand

We present a Gaussian Variational Inference (GVI) technique that can be applied to large-scale nonlinear batch state estimation problems.

• The main contribution is to show how to fit both the mean and (inverse) covariance of a Gaussian to the posterior efficiently, by exploiting factorization of the joint likelihood of the state and data, as is common in practical problems.
• This is different than Maximum A Posteriori (MAP) estimation, which seeks the point estimate for the state that maximizes the posterior (i.e., the mode).
• The proposed Exactly Sparse Gaussian Variational Inference (ESGVI) technique stores the inverse covariance matrix, which is typically very sparse (e.g., block-tridiagonal for classic state estimation).