Application of the transformation of variables technique for uncertainty mapping in nonlinear filtering

This paper addresses the impact nonlinear observations of state variables have on uncertainty accuracy associated with state estimation algorithms. The transformation of variables technique is applied to exactly map probability density functions (PDFs) between domains completely spanned by different...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2014-02, Vol.118 (2), p.129-164
Main Authors: Weisman, R. M., Majji, M., Alfriend, K. T.
Format: Article
Language:English
Subjects:
Aerospace engineering
Aerospace Technology and Astronautics
Astrophysics and Astroparticles
Bayesian analysis
Classical Mechanics
Dynamical Systems and Ergodic Theory
Geophysics/Geodesy
Kalman filters
Mapping
Original Article
Physics
Physics and Astronomy
Probability distribution
Variance analysis
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Summary:This paper addresses the impact nonlinear observations of state variables have on uncertainty accuracy associated with state estimation algorithms. The transformation of variables technique is applied to exactly map probability density functions (PDFs) between domains completely spanned by different combinations of basis vectors. The technique allows for proper generation of the likelihood density when converting from measurement to state variable space and for association of a present state distribution with prior observation data. The exact mapping of probability distribution functions between domains and proper characterization of prior knowledge allows for Bayesian estimation to be appropriately carried out. A Bayes filter utilizing the technique is developed which uses the technique to map the uncertainty in time for generation of the prior density and in space for generation of the likelihood density. The filter is compared with conventional nonlinear filtering techniques in multiple scenarios to demonstrate the utility and insight offered for object tracking and parameter estimation applications.
ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-013-9527-2