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    This study introduces optimized unscented particle filters (UPFs) using geometric principles for improved navigation systems. The enhanced UPFs offer comparable performance with significantly better computational efficiency, even with intermittent measurements.

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    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.