The Interacting Multiple Model Filter and Smoother on Boxplus-Manifolds.

Area of Science:

• Robotics
• Control Systems
• State Estimation

Background:

• Hybrid systems require estimating multiple dynamic models (modes).
• Estimating mode sequences leads to computational complexity.
• Interacting Multiple Model (IMM) filters are standard but limited in state space applicability.

Purpose of the Study:

• To generalize the IMM filter and smoother to manifold state spaces.
• To address limitations of existing methods for non-Euclidean states like quaternions.
• To introduce a principled framework for hybrid system state estimation on manifolds.

Main Methods:

• Developed a novel generalization of the IMM filter and smoother using the boxplus method.
• Proposed a linear approximation for Gaussian mixing on boxplus-manifolds.
• Derived a Rauch-Tung-Striebel smoother for single models on boxplus-manifolds.

Main Results:

• Introduced three novel algorithms for manifold state spaces.
• Algorithms demonstrated comparable performance to specialized quaternion-based methods in simulations.
• The generalized approach offers significant benefits in terms of applicability to diverse manifold state spaces.

Conclusions:

• The proposed generalized IMM framework effectively handles hybrid systems with manifold state spaces.
• This principled approach enhances the versatility of state estimation techniques.
• Open-source implementations facilitate adoption and further research.