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Maximum A Posteriori Estimation of Hamiltonian Systems with High Order Taylor Polynomials

Abstract

This paper presents a new approach to Maximum A Posteriori (MAP) estimation for Hamiltonian dynamic systems. By representing probability density functions through Taylor polynomials and using Differential Algebra techniques, this work proposes to derive the MAP estimate directly from high order polynomials. The polynomial representation of the posterior probability density function leads to an accurate approximation of the true a posterior distribution, that describes the uncertainties of the state of the system. The new method is applied to a demonstrative orbit determination problem.

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Acknowledgements

This work was sponsored in part by the Air Force Office of Scientific Research under grant number FA9550-18-1-0351

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Correspondence to Renato Zanetti.

Appendix

Appendix

The DAMAP algorithm for the orbit determination application summed up in Algorithm 1.

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Servadio, S., Zanetti, R. & Armellin, R. Maximum A Posteriori Estimation of Hamiltonian Systems with High Order Taylor Polynomials. J Astronaut Sci 69, 511–536 (2022). https://doi.org/10.1007/s40295-022-00304-4

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  • DOI: https://doi.org/10.1007/s40295-022-00304-4

Keywords

  • Filtering problem
  • Halo orbits
  • Maximum a posteriori
  • Nonlinear estimation
  • Orbit determination