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How were the space shuttle's rate gyro and accelerometer outputs converted into reliable position and velocity vectors before being fed into GNC software? Is there a document detailing those calculations?

I know that velocity often comes from integrating an acceleration signal---after some signal processing to filter out high-frequency noise---and that position normally comes from twice integrating acceleration.

But they must account for nonideal effects such as gyro friction and precession as well as sensor and integration errors. I'm curious about the actual implementation of the calculations or at least a detailed explanation of them---though NASA documents are normally very very generous with calculations details for people who seek them, so I suspect there is a document out there that has exactly this info?

Also interested in these calculations as they were done on the Saturn V if by chance they are lacking for the space shuttle.

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    $\begingroup$ This might also interest you. Here's a video demonstrating how the accelerometers worked with the Apollo Guidance Computer (not Saturn V): youtu.be/-f7SE-dDNA0?t=208 $\endgroup$ – Bret Copeland Feb 5 at 16:09
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Mostly I'll treat this as a reference-request since the topic is lengthy. But you are correct, it's all there in publicly available documents.

Summary

  • Ascent: The three IMUs are calibrated and aligned before liftoff. Ascent navigation onboard software is initialized at liftoff minus eight seconds. During a nominal ascent, only the IMU data is processed by PASS and BFS navigation [McHenry, 1979]. One state vector is maintained by selecting the middle value acceleration data from the three IMUs. No external sensor measurements are processed, and there is no on-board Kalman filter logic that runs during ascent.

  • Orbit: During the orbit phase, the on-board navigation state vector is monitored and maintained by Mission Control via state vector uplinks. A vent force may also be uplinked by Mission Control for use by the GPCs to help reduce error growth in the on-board state vector. The vent force takes into account non-propulsive forces acting on the orbiter that cannot be detected by the High-Accuracy Inertial Navigation System (HAINS) IMUs. Vent values are based on flight history for specific orbiter attitudes. The MCC can also uplink a drag K-Factor, although the orbiter has never used this procedure. Alignment of the HAINS IMUs is periodically performed using star sightings [Smith, 1983]. Two star trackers with near orthogonal lines-of-sight are located on the nose of the orbiter. Data from star sightings can also be used by Mission Control to determine IMU gyro biases. The ground determined biases are then uplinked for use in the Shuttle PASS flight software. If the orbiter cannot maneuver to a star-sighting attitude due to excessive IMU misalignment, a rough alignment can be executed by a crewmember sighting on a star using the Heads-Up Display (HUD) or the COAS. A HUD or COAS alignment would be followed by a precise star alignment using the star trackers.

  • Entry: During entry, three independent navigation state vectors are maintained in the PASS [Ewell, 1982]. Each uses accumulated, sensed velocity data from a different IMU to protect against IMU failures. The Kalman filter uses external sensor data to improve the accuracy of the three state vectors. ... A selection filter selects one navigation state vector (position and velocity) as the selected navigation state vector.

Source: JSC-63653 Navigation Technical History with Lessons Learned

For Apollo check out Apollo Guidance Navigation and Control Systems

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    $\begingroup$ Thanks @OrganicMarble! Document 2 had a surprise for me---the clearest layout of the PEG algorithm that I've seen so far. The section on state propagation answered questions I had and confirmed things I thought I knew. Thanks a bunch for listing all this here. $\endgroup$ – user36480 Feb 6 at 10:12

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