A method and apparatus for estimating the orbits of spacecraft or other
objects relative to primary celestial bodies, given applicable
measurements. The present invention uses the variation of parameters in
universal variables for spacecraft trajectory propagation during operation
of its optimal sequential orbit estimation. This method provides a
universal capability for all three conics: elliptic, parabolic, and
hyperbolic, forward-time and backward-time numerical integration for
filtering and smoothing, respectively. A method for determining local and
global estimates of atmospheric density is also provided. A method for
realistic orbit simulation provides a means for validating an orbit
estimate.