Are Powered Explicit Guidance calculations done before or during launch?

Question

Space shuttle orbital insertion was done using a powered explicit guidance algorithm.

At the surface, the algorithm is simple, as it gives the instantaneous pitch as a linear function of time:

$\phi = \arctan(at + b )$ which is ~$at + b$ at small pitch angles.

Sadly, the simplicity is illusion, as the coefficients a and b aren't trivial to find. The calculations are fairly elaborate---so elaborate, in fact, they I wonder if they did them all in real time during launch...

...or if they instead did the calculations on the ground in order to get the Powered Explicit Guidance trajectory they would need to feed their attitude controllers.

Thing is... the calculations seem to require knowledge of your instantaneous state vector, which is a variable known with reasonable certainty only in flight. You could simulate on the ground and get some approximate numbers that way, and if you can live with the error that comes with conditions that are not nominal---unexpected differences in wind, engine performance, etc...

Does anyone know where/when the P.E.G. calculations were done? On the ground before flight or in the rocket computers during launch?

Answer 1

It was in the onboard flight software, at least for shuttle.

The second stage guidance software uses a cyclic, closed loop scheme to calculate the necessary commands to take the mated vehicle to a specified set of target MECO conditions. These conditions include cutoff velocity, radius from the Earth, flight path angle, orbital inclination, and longitude of the ascending node. The name of the targeting scheme is PEG (powered explicit guidance) 1. The predicted time of MECO (TMECO) is calculated by both PASS and BFS and displayed on their respective ASCENT TRAJ displays for the crew to evaluate. (A discrepancy between PASS and BFS may indicate a guidance error, requiring the crew to take manual control.) Following SRB separation, it may take the PEG 1 guidance algorithm several cycles to converge and for TMECO to become stable. Forty seconds prior to MECO, guidance begins targeting only for the desired cutoff velocity.

Shuttle Crew Operations Manual page 2.13-56

PASS and BFS were names of the onboard computer software systems. Primary Avionics Software System in the 4 primary onboard computers and Backup Flight System in the backup.