Accurate calculation of time to go until impact is an essential component in coordinating multiple precision-guided munitions for a simultaneous strike. Conventional means for calculating time to go contain potential errors, due in part to the trajectory curvatures, and may fall short on the accuracy required to achieve a desired impact time, especially if velocity changes rapidly due to atmospheric drag and gravity. A closed-loop guidance law will be presented in which an optimized, piecewise continuous, and smooth family of polynomial trajectories is parameterized in terms of downrange distance and has a closed-form solution of arc length for improved calculation of time to go.
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Snyder et al. (2016) studied this question.
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