Sequential Gaussian Variational Inference for Nonlinear State Estimation and Its Application in Robot Navigation

TL;DR

This work proposes a Sequential Gaussian Variational Inference (S-GVI) method to address nonlinearity and provide efficient sequential inference processes, and demonstrates significant improvements in state estimation over the Maximum A Posteriori (MAP) estimation method.

Abstract

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.

Figures (5)

• Figure 1: RMSE of the proposed S-GVI and MAP estimation over all Monte Carlo runs for different sets of $\{Q, R\}$. The mean values are provided in ($\cdot$). The S-GVI significantly outperforms the MAP estimation in all simulation sets, indicating that S-GVI is robust against high nonlinearity.
• Figure 2: Experimental setup and $4$ experiments with $300$ time steps.
• Figure 3: Position RMSE plots of the proposed S-GVI and MAP estimation in each experiment.
• Figure 4: Number of iterations for the proposed S-GVI and MAP estimations in each experiment. The S-GVI requires fewer iterations than MAP most of the time.
• Figure 5: Error with $3$-sigma bounds for the $x$ and $y$ positions of the proposed S-GVI and MAP estimation in each experiment.

Theorems & Definitions (1)

• Remark II.1