Title:
Probability Density Transformations on Admissible Regions for Dynamical Systems

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Author(s)
Worthy, Johnny L., III
Holzinger, Marcus J.
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Daniel Guggenheim School of Aerospace Engineering
The Daniel Guggenheim School of Aeronautics was established in 1931, with a name change in 1962 to the School of Aerospace Engineering
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Supplementary to
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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Date Issued
2015-08
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Text
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Paper
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