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Adaptive sparse grid quadrature filter for spacecraft relative navigation
Institution:1. Shri Vishnu Engineering College for Women, Bhimavaram 534 202, Andhra Pradesh, India;2. Space Physics Laboratory, Dept. of Physics, Andhra University, Visakhapatnam 530 003, India;1. The Center for Exascale Simulation of Plasma-coupled Combustion, Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana IL 61801, USA;2. Mechanical Science & Engineering, University of Illinois at Urbana–Champaign, Urbana IL 61801, USA;3. Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana IL 61801, USA;1. Department of Electronic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China;2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, China;1. Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Republic of Korea;2. BK21+Transformative Training Program for Creative Mechanical and Aerospace Engineers, Seoul National University, Seoul 08826, Republic of Korea;3. Automation and Systems Research Institute, Seoul 08826, Republic of Korea;4. Institute of Advanced Aerospace Technology, Seoul 08826, Republic of Korea
Abstract:This paper explores a novel adaptive sparse grid quadrature filter. The sparse grid quadrature approach has been recently developed for nonlinear estimation problems to alleviate the curse-of-dimensionality issue of the Gauss–Hermite quadrature filter. Accuracy level of the sparse grid quadrature filter is an important tuning factor that affects desired performance. The proposed filter autonomously adjusts the accuracy level of the sparse grid quadrature rule in both prediction and update steps by increasing the level gradually until an adaptation criterion is satisfied. The adaptation criterion is derived based on a quadrature error estimator. The nestedness property of sparse grid quadrature rule enables efficient computation in adaptation by reusing quadrature points of the previous level sparse grid quadrature. An application to spacecraft relative navigation has been made to demonstrate the adaptive spare grid quadrature filter outperforming the extended Kalman filter and the unscented Kalman filter.
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