Version 1
: Received: 16 April 2023 / Approved: 17 April 2023 / Online: 17 April 2023 (07:25:11 CEST)
How to cite:
Gilani, S.A.A.; Mihaylova, L.S.; Bhutta, M.F. Mixture Culver Filter for Space Object Orbit Determination. Preprints2023, 2023040421. https://doi.org/10.20944/preprints202304.0421.v1
Gilani, S.A.A.; Mihaylova, L.S.; Bhutta, M.F. Mixture Culver Filter for Space Object Orbit Determination. Preprints 2023, 2023040421. https://doi.org/10.20944/preprints202304.0421.v1
Gilani, S.A.A.; Mihaylova, L.S.; Bhutta, M.F. Mixture Culver Filter for Space Object Orbit Determination. Preprints2023, 2023040421. https://doi.org/10.20944/preprints202304.0421.v1
APA Style
Gilani, S.A.A., Mihaylova, L.S., & Bhutta, M.F. (2023). Mixture Culver Filter for Space Object Orbit Determination. Preprints. https://doi.org/10.20944/preprints202304.0421.v1
Chicago/Turabian Style
Gilani, S.A.A., Lyudmila S Mihaylova and Maheen Fatima Bhutta. 2023 "Mixture Culver Filter for Space Object Orbit Determination" Preprints. https://doi.org/10.20944/preprints202304.0421.v1
Abstract
Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
