NASA NTRS2006
This paper explores techniques that can be used to adapt the standard linearized propagation of an orbital covariance matrix to the case where there is a maneuver and an associated execution uncertainty. A Monte Carlo technique is used to construct a final orbital covariance matrix for a 'prop-burn-prop' process that takes into account initial state uncertainty and execution uncertainties in the maneuver magnitude. This final orbital covariance matrix is regarded as 'truth' and comparisons are made with three methods using modified linearized covariance propagation. The first method accounts for the maneuver by modeling its nominal effect within the state transition matrix but excludes the execution uncertainty by omitting a process noise matrix from the computation. The second method does not model the maneuver but includes a process noise matrix to account for the uncertainty in its magnitude. The third method, which is essentially a hybrid of the first two, includes the nominal portion of the maneuver via the state transition matrix and uses a process noise matrix to account for the magnitude uncertainty. The first method is unable to produce the final orbit covariance except in the case of zero maneuver uncertainty. The second method yields good accuracy for the final covariance matrix but fails to model the final orbital state accurately. Agreement between the simulated covariance data produced by this method and the Monte Carlo truth data fell within 0.5-2.5 percent over a range of maneuver sizes that span two orders of magnitude (0.1-20 m/s). The third method, which yields a combination of good accuracy in the computation of the final covariance matrix and correct accounting for the presence of the maneuver in the nominal orbit, is the best method for applications involving the computation of times of closest approach and the corresponding probability of collision, PC. However, applications for the two other methods exist and are briefly discussed. Although the process model ("prop-burn-prop") that was studied is very simple - point-mass gravitational effects due to the Earth combined with an impulsive delta-V in the velocity direction for the maneuver - generalizations to more complex scenarios, including high fidelity force models, finite duration maneuvers, and maneuver pointing errors, are straightforward and are discussed in the conclusion.