Reduced Nonlinear Model for Orbit Uncertainty Propagation and Estimation
- 1 September 2021
- journal article
- research article
- Published by American Institute of Aeronautics and Astronautics (AIAA) in Journal of Guidance, Control, and Dynamics
- Vol. 44 (9), 1578-1592
- https://doi.org/10.2514/1.g005519
Abstract
This paper presents a novel method for nonlinear uncertainty propagation and estimation in orbital dynamics. The proposed technique relies on a Taylor series expansion of the integral flow to model the dynamics around the reference solution and introduces an approximation of the high-order variational equations that reduces the complexity of evaluating the series. In particular, the high-order state-transition tensors (STTs) are approximated by capturing the dominant secular terms. Simple expressions to compute them are provided. The approximation stems from confining the Lyapunov instability of the motion to the time domain. The result is a time-explicit approximation of the STTs that can be used to predict the evolution of the uncertainty distribution accounting for nonlinear effects with minimal overhead. Finally, a high-order version of the extended Kalman filter is developed by implementing the approximation of the nonlinear terms of the Taylor series into an estimation scheme. The performance of the algorithm is evaluated with several practical examples.Keywords
Funding Information
- Jet Propulsion Laboratory (80NM0018D0004)
This publication has 41 references indexed in Scilit:
- Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial ChaosJournal of Guidance, Control, and Dynamics, 2013
- Non-intrusive MethodsScientific Computation, 2010
- Unscented Filtering and Nonlinear EstimationProceedings of the IEEE, 2004
- A new method for the nonlinear transformation of means and covariances in filters and estimatorsIEEE Transactions on Automatic Control, 2000
- Exact finite-dimensional nonlinear filtersIEEE Transactions on Automatic Control, 1986
- The intermediate anomalyCelestial Mechanics and Dynamical Astronomy, 1977
- Accurate computation of highly eccentric satellite orbitsCelestial Mechanics and Dynamical Astronomy, 1974
- Nonlinear Bayesian estimation using Gaussian sum approximationsIEEE Transactions on Automatic Control, 1972
- Suboptimal state estimation for continuous-time nonlinear systems from discrete noisy measurementsIEEE Transactions on Automatic Control, 1968
- A New Approach to Linear Filtering and Prediction ProblemsJournal of Basic Engineering, 1960