Role of nonlinearity of the measurement model and its interactions with quality of measurements and geometry of the problem is coarsely examined. It is shown that for problems in astrodynamics several important conclusions can be drawn by an examination of the transformations of density function in various coordinate systems and choices of variables. Probability density transformations through nonlinear, smooth and analytic functions are examined and the role of change of variables in calculus of random variables is elucidated. It is shown that the transformation of probability density functions through mappings provides insight in to problems, a priori providing the analyst with an insight on the interaction of nonlinearity, uncertainty and geometry of estimation problems. Examples are presented to highlight salient aspects of the discussion. Finally, a sequential orbit determination problem is analyzed and the transformation formula is shown to be helpful in making the choice of coordinates for estimation of dynamic systems.
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