Deterministic filtering and dimensionality reduction for optimal attitude estimation on SO(3)

TL;DR

This paper introduces min/max-plus techniques to efficiently solve the optimal attitude estimation problem on SO(3), enabling deterministic filtering for nonlinear systems with improved computational performance.

Contribution

It applies min/max-plus methods to develop computationally efficient deterministic filters for nonlinear attitude estimation on SO(3).

Findings

Validated techniques with attitude estimation examples on SO(3).

Demonstrated improved computational efficiency over traditional methods.

Provided a new approach for nonlinear filtering on Lie groups.

Abstract

In this article we introduce the use of recently developed min/max-plus techniques in order to solve the optimal attitude estimation problem in filtering for nonlinear systems on the special orthogonal (SO(3)) group. This work helps obtain computationally efficient methods for the synthesis of deterministic filters for nonlinear systems -- i.e. optimal filters which estimate the state using a related optimal control problem. The technique indicated herein is validated using a set of optimal attitude estimation example problems on SO(3).