# Geometric Symmetry Reduction of the Unobservable Subspace for Kalman Filtering

## TL;DR

This paper introduces a geometric approach to reduce the unobservable subspace in Kalman filtering for invariant dynamical systems, improving accuracy and robustness in orientation and position estimation.

## Contribution

It presents a novel reduction technique for unobservable subspaces in Kalman filters using geometric symmetry, enhancing estimation accuracy and robustness.

## Key findings

- Improved orientation and position estimation accuracy.
- Enhanced robustness to measurement noise.
- Effective decomposition of state space into observable and unobservable parts.

## Abstract

In this article, we consider the implications of unobservable subspaces in the construction of a Kalman filter. In particular, we consider dynamical systems which are invariant with respect to a group action, and which are therefore unobservable in the group direction. We obtain reduced propagation and measurement equations that are invariant with respect to the group action, and we decompose the state space into unobservable and observable parts. Based on the decomposition, we propose a reduced Bayesian inference method, which exhibits superior accuracy for orientation and position estimation, and that is more robust to large measurement noise.