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    This study introduces a computational relaxation for the unscented transformation (UT), reducing CPU time in Unscented Kalman filter applications. This method enhances performance in robotics and autonomous systems by optimizing calculations for nonlinear models.

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    Area of Science:

    • Robotics and Autonomous Systems
    • Control Theory
    • Computational Mathematics

    Background:

    • Advanced robotics and autonomous vehicles heavily depend on filtering and sensor fusion.
    • Onboard computations in these mobile applications face limited computing capacities.
    • Efficient filtering is crucial for accurate control and extended battery life.

    Purpose of the Study:

    • To introduce a generic computational relaxation for the unscented transformation (UT).
    • To reduce the computational demand of Unscented Kalman filter (UKF) applications.
    • To demonstrate the practical benefits of the proposed relaxation method.

    Main Methods:

    • Developed a computational relaxation technique for the unscented transformation (UT).
    • The core idea involves separating the linear component of the filtering model.
    • Avoided complex calculations for the nonlinear part of the model.
    • Implemented and tested the method in a simultaneous localization and mapping (SLAM) scenario.

    Main Results:

    • The proposed relaxation significantly reduces computational demand, by up to 50%.
    • Accuracy of the approximation is maintained without degradation.
    • Superior performance demonstrated in SLAM implementations, especially when nonlinearities affect an affine subspace.
    • The method is validated in practically relevant scenarios.

    Conclusions:

    • The computational relaxation of the UT offers a significant improvement for UKF-based applications.
    • This optimization is particularly beneficial for resource-constrained mobile systems like robots and autonomous vehicles.
    • The open-source C++ library 'RelaxedUnscentedTransformation' is available for practical implementation.