Projecting High-Dimensional Parametric Uncertainties for Improved State Estimation Error Confidence


The navigation of vehicles oftentimes involves the use of key environment and vehicle parameters in the forward evolution of the state estimate and its associated uncertainty. Given the objective of achieving precision navigation, it is critical that the full effect of the parameters, including their uncertainties, is taken into account in the estimation process. When the parameter set is of high dimension, the computational complexity involved in projecting the parametric uncertainties into state uncertainties can make the navigation solution intractable for onboard computation. A method is presented that projects the uncertainties in the parameters through an equivalent process-noise structure leading to real-time computations supporting precision navigation. Having first shown that the procedure works for linear systems, the method is applied to generating a process-noise-like term that accounts for the uncertainty present in the spherical harmonics coefficients of a high-order gravitational acceleration model. Simulation studies are performed to show that the method can be applied to the conversion of the uncertainty in spherical harmonics gravity coefficients, which can be of dimension 10,000 and higher, to a process-noise representation that accurately predicts the position and velocity uncertainties for spacecraft navigation.


Mechanical and Aerospace Engineering

Keywords and Phrases

Amphibious vehicles; Harmonic analysis; Linear systems; Navigation; State estimation; Tracking (position); Uncertainty analysis; Gravitational accelerations; Gravity coefficients; Navigation of vehicles; Parametric uncertainties; Precision navigation; Real-time computations; Spacecraft navigation; Velocity uncertainty; Parameter estimation

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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© 2015 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

01 Sep 2015