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

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).