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High Order Nonlinear Least-Squares for Satellite Pose Estimation

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Abstract

This paper introduces a high-order nonlinear least-squares method for solving six-degree-of-freedom (6-DOF) navigation of satellite maneuvers. The approach involves developing first through fourth-order Taylor series models, which provide the necessary conditions that are iteratively adjusted to recover the unknown roots for reducing the errors arising from fitting models to a given set of observations. An initial guess is provided for the unknown parameters in the system, developing a correction vector using Taylor expansion, and then manipulating the necessary conditions to provide the least-squares algorithm. Computational differentiation (CD) tools generate the Taylor expansion partial derivative models. This paper presents an experimental work conducted using a 6-DOF platform to demonstrate the performance of the developed high-order nonlinear least-squares navigation method. An initial calibration of the sensing systems is performed in an operationally relevant ground-based environment. The experiments demonstrate that accelerated convergence is achieved for the second-, third-, and fourth-order expansions with various initial guess conditions.

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Authors and Affiliations

  1. Department of Aerospace Engineering, San Diego State University, San Diego, CA, 92182, USA

    Ahmad Bani Younes & Ahmed M. Atallah

  2. Jordan University of Science and Technology, Irbid, Jordan

    Mohammad Alhulayil

  3. Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, 92093, USA

    Ahmed M. Atallah

  4. Aerospace Engineering Department, Texas A&M University, College Station, TX, USA

    James D. Turner

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  1. Ahmad Bani Younes
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  2. Mohammad Alhulayil
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  3. James D. Turner
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  4. Ahmed M. Atallah
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Correspondence to Ahmad Bani Younes.

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Bani Younes, A., Alhulayil, M., Turner, J.D. et al. High Order Nonlinear Least-Squares for Satellite Pose Estimation. J Astronaut Sci 70, 15 (2023). https://doi.org/10.1007/s40295-023-00378-8

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