Analytic assessment of sensor uncertainty for application to space object tracking and correlation

Acceptable accomplishment of reliable tracking and correlation of space objects is predicated upon correct assessment of the impact measurement uncertainty has on the observed object's state estimate and a posteriori probability density function. The nonlinear mapping from measurement variables to state variables can render the Gaussian assumption of state uncertainty invalid, requiring state estimation methods to account for the shape distorting effect of the nonlinear transform. This research applies the transformation of variables technique to map the measurement error probability density function directly and exactly from sensor frame to the desired state variable frame. The exact mapping enables direct application of Bayes' Theorem for space object sequential state estimation in addition to covariance initialization automation for conventional nonlinear extensions of the Kalman filter. Comparison with existing architectures for state estimation and covariance initialization of conventional nonlinear filters are presented to show the utility of the technique for both position and velocity state observation as well as position only observation where the transformation of variables technique is applied to estimate the uncertainty associated with the Herrick-Gibbs initial orbit determination routine. Copyright 2011 by Ryan M. Weisman, Manoranjan Majji, and Kyle T. Alfriend. Published by the IAF with permission and released to the IAF to publish in all forms.

Analytic assessment of sensor uncertainty for application to space object tracking and correlation Conference Paper