History and Usage of a Figure of Merit for Injection Covariances

This paper provides some background and definition for the Figure of Merit (FOM) used by flight projects at JPL to evaluate injection covariance matrices describing launch dispersions.The FOM described here represents the square root of the expected value of the square of the magnitude of the ∆V required to correct target errors arising from injection errors.This metric is preferred because, although the description is long, the implementation is actually rather simple.It only requires a covariance matrix, a trajectory propagation with partial derivatives, and a choice for the time of a midcourse correction; it does not require Monte Carlo simulations.The focus is on the traditional case of a ballistic trajectory culminating in a hyperbolic planetary encounter while other cases are briefly discussed.