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1/3 of a second in 100 hours is basically 1ppm, or TXCO levels of accuracy, so pretty good i'd have thought, even for a submarine INS?

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USN ballistic missile submarines deploy the most accurate INS in the world (ESGN), and that system is used in conjunction with another advanced gyro.

Here is a 2 RU atomic clock on ebay for context: https://www.ebay.com/itm/Antelope-Audio-Isochrone-10M-Rubidi...

Not sure about that. ESGN is old technology, since submarines don't need that much accuracy. For example, space probes, ballistic missiles, smart artillery shells/rockets/missiles and so on would all appear to have multiple orders of magnitude better accuracy than submarines, in the fractional ppb ranges, rather than tens of ppm. [0][1]

0. https://www.sto.nato.int/publications/STO%20Meeting%20Procee...

1. http://users.cecs.anu.edu.au/~Jonghyuk.Kim/teaching/Inertial...

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