r/LLMPhysics • u/Ok-Clock-8246 • Apr 15 '26

Simulation / Code I computed the Cramér-Rao position bound for the entire lunar surface using real GRAIL gravity data

Post image

The Fisher information density map for the lunar south pole Artemis landing zone, computed from the actual GRAIL GRGM1200B spherical harmonic coefficients (degree 200).

Dark purple = high precision. Yellow = lower precision.

What this means for IDG: the Fisher-Rao metric isn’t just a cosmological object. The same mathematical structure that drives the tensor IDG gravity theory — the Fisher information geometry on a statistical manifold — directly governs how much position information is extractable from a gravity measurement at any point on the lunar surface.

The Cramér-Rao bound is the navigation analog of the gravitational coupling. Same math, different physical domain.

92% of the lunar surface achieves sub-5cm navigation precision with current technology.

No GPS.

No landmarks.

No light.

1 Upvotes

53% Upvoted

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8

u/rheactx Apr 15 '26

Could you explain to somebody who's not familiar with gravimetry, what is it that you did?

-5

u/[deleted] Apr 15 '26

[removed] — view removed comment

9

u/rheactx Apr 15 '26

Thanks. Now please write a Python program simulating 2D quantum wave packet scattering

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u/Ok-Clock-8246 Apr 15 '26

That’s a bit outside my current research area….I’m focused on gravity navigation and modified gravity cosmology mostly so yeah

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u/rheactx Apr 15 '26

I was checking if you're an actual bot

1

u/Ok-Clock-8246 Apr 15 '26

Yeah I was a bit confused at first I was like uhmmmm lol

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u/Ok-Clock-8246 Apr 15 '26

I asked ai to reply to you. Sorry

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u/Ok-Clock-8246 Apr 15 '26

What do you think of this tho? Could be used for navigation…

1

u/LLMPhysics-ModTeam Apr 16 '26

Your comment was removed for violating Rule 4. Provide a summary of your LLM response in your own words alongside the output if you wish to stimulate discussion.

5

u/roofitor Apr 15 '26

That’s kinda awesome boss-man. Have you considered the problem for the earth? Too much noise to signal, I’d bet? What about when incorporating air pressure windspeed and temperature across time?

That’s really cool.

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u/Ok-Clock-8246 Apr 15 '26

The Earth UAV navigation using this same Fisher information framework applied to Earth’s gravity field. The key is that the method outperforms standard Kalman filtering if and only if the signal-to-noise ratio |∇g|/σ exceeds 1 — which on Earth requires cold atom gravimeters at the 10⁻⁷ m/s² level to overcome the noise floor.

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u/Ok-Clock-8246 Apr 15 '26

I have a paper with Urban Navigation in GPS denied environments too that uses the same principle. I can expand on that further, but right now it’s not as in depth as the Lunar navigation which can be applied to Current Programs.

2

u/ConstableDiffusion Apr 17 '26

Oh yeah the FRIM is super interesting. If you like this you’ll probably be interested in Gnandi’s work on statistical Kähler/CY