Title:
Probability Density Transformations on Admissible Regions for Dynamical Systems
Probability Density Transformations on Admissible Regions for Dynamical Systems
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Author(s)
Worthy, Johnny L., III
Holzinger, Marcus J.
Holzinger, Marcus J.
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Abstract
The admissible region as used for initial orbit determination is often expressed as a
uniform multivariate probability density function (PDF). A multivariate PDF may
be transformed and expressed in an alternate state space if the total probability is
preserved over the transformation. This paper applies the general multivariate PDF
transformation method to an admissible region to develop the conditions required
for such a transformation. Because the probability must be preserved, it is shown
that in general an admissible region PDF may not be transformed by a nonlinear
transformation unless specific mapping conditions are met over all the state space
volume. If this condition is not met then the transformation of an admissible region
PDF yields incorrect probabilities over the state space. Further, it is also shown
that if each state in an admissible region is locally observable then the constant
gradient condition is lifted.
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2015-08
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