Continuation Methods and Non-Linear/Non-Gaussian Estimation for Flight Dynamics
We propose herein to augment current NASA spaceflight dynamics
programs with algorithms and software from two domains. First, we
propose to use numerical parameter continuation methods to assist in
computation of trajectories in complicated dynamical situations.
Numerical parameter continuation methods have been used extensively to
compute a menagerie of structures in dynamical systems including fixed
points, periodic orbits, simple bifurcations (where the structure of
the dynamics changes), Hopf bifurcations (where periodic orbits are
created), invariant manifolds, hetero/homoclinic connections between
invariant manifolds, etc. Perhaps more importantly for the current
work, such methods have already proven their worth in flight dynamics
problems, especially those having to do with the complicated dynamics
near libration points. Second, we propose to use advanced filtering
techniques and representations of probability density functions to
appropriately compute and manage the uncertainty in the trajectories.
While advanced methods for understanding and leveraging the underlying
dynamics are clearly necessary for effective mission design, planning,
and analysis, we contend that they do not suffice. In particular,
they do not, in and of themselves, address the issue of uncertainty.
Herein we discuss methods that balance the accuracy of the uncertainty
representation against computational tractability, including a
discussion of the notorious ``curse of dimensionality'' for problems
with large state vectors. We propose approachs that revolve around
modifications of algorithms such as ``log homotopy'' particle filters
and especially Gaussian sum filters. Finally, we propose to integrate
all of the above algorithms into standard NASA software packages
GEONS, GIPSY, and GMAT.
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