Geometric Unscented Particle Filters on Lie Groups for State Estimation

Area of Science:

• Robotics and Control Systems
• Navigation and Positioning
• Signal Processing

Background:

• Unscented particle filters (UPFs) are crucial for state estimation in complex systems.
• Existing UPFs face challenges with computational efficiency and stability, especially with intermittent measurements.
• Geometric methods offer a novel perspective for improving filter performance.

Purpose of the Study:

• To develop geometrically-inspired unscented particle filters (UPFs) for enhanced state estimation.
• To address computational demands and stability issues in UPFs, particularly with intermittent data.
• To optimize UPF performance for applications like Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integration.

Main Methods:

• Developed an unscented particle filter (UPF) on Lie groups, performing propagation on Lie groups and updates on Lie algebra.
• Introduced the log-linear property of group elements to streamline particle propagation and reduce redundant computations.
• Incorporated intermittent measurements into the UPF update process, proving bounded estimation error under specific assumptions.

Main Results:

• The proposed UPF framework demonstrates comparable estimation performance to existing methods.
• Achieved significant improvements in computational efficiency compared to the original UPF.
• Established a critical threshold for intermittent measurement arrival rates and derived an upper bound for expected state error covariance.

Conclusions:

• The redesigned UPF offers a computationally efficient and stable solution for state estimation, particularly in GNSS/INS integrated navigation.
• The geometric approach effectively handles intermittent measurements, maintaining bounded estimation errors.
• The optimized UPF framework presents a viable alternative for real-time navigation applications demanding high performance and efficiency.