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

Abstract

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.