A Robust and Global Hybrid Complementary Filter on SO(3) using Morse Functions on RP3

This paper addresses the problem of global attitude filtering on the special orthogonal group SO(3). A hysteresis-based hybrid switching strategy is used to switch between two filters that operate in different regions of SO(3). The first filter is the passive complementary filter, whereas the second filter is designed using an appropriately chosen Morse function. To this end, a novel approach to design Morse functions on SO(3) is proposed. The proposed hybrid filter is shown to be input-to-state stable with respect to measurement noise. Simulations validate the stability properties of the hybrid filter.