∆V Control Distance with Dynamics Parameter Uncertainty

Increasing quantities of active spacecraft and debris in the space environment pose substantial risk to the continued safety of specific orbit regimes. Successful quantification of space object state knowledge is a fundamental prerequisite in ensuring operational safety and continuity. However, uncertainty in orbit dynamics such as atmospheric drag, solar radiation pressure, and other effects can confound track association efforts and thereby decrease object state knowledge. Errors in dynamics modeling can cause objects to become lost or incorrectly associated with maneuvers, and need to be accounted for. This paper demonstrates how existing optimal control ∆V object correlation approaches can be modified to account for distributions in dynamics parameters (e.g. atmospheric density, drag coefficients, and surface areas). The method involves linearizing about a nominal connecting trajectory and computing the variation in the required ∆V cost of equivalent maneuvers due to variations in the dynamics parameters and boundary conditions. The resulting variations are then considered to be drawn from distributions, and finally distributions of possible ∆V expenditures are computed. An example of debris in Low Earth Orbit (LEO) is given to demonstrate the utility of the approach and conclusions are made.