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It's my understanding that in 2008, the US government published GPS standards for civilian applications (including cellphones) of rms 4m.

  1. Is it correct that this applies to cellphones? and
  2. Has this 4m rms been improved since 2008?

http://www.gps.gov/technical/ps/2008-SPS-performance-standard.pdf

What is the maximum Theoretical accuracy of GPS?

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    all depends on hardware the device is using. accuracy can get way better than 4m. If you mean the default standard GPS locators on a phone then that will depend on the model and the year the phone was built. – NULL.Dude Aug 7 '17 at 14:35
  • Do you have an estimate on a particular model, say the iphone 7 with a BCM4774 chip? I cannot find specific accuracy specs online. Thanks – user140531 Aug 7 '17 at 15:06
  • I have a Sony Xperia Z3 (released in 2015 I think) and it's ~ 5m – TurboGraphxBeige Aug 7 '17 at 20:49
  • I don't have straight answer to your question but I used geotagged photos tool in ArcMap to embed the photos from my cell phone in the map. I have recorded the same points with Trimble Juno 3B GPS. I have noticed Trimble nailed locations with very good accuracy while geotagged photos were not accurate and 4-5 m off. My phone was Samsung Galaxy Note 4. – Amadeus Aug 7 '17 at 21:44
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GPS SPS does not apply to cellphones or to any other receivers, it only applies to the signal in space (SIS) that is broadcast by GPS satellites. So the 4m accuracy does not mean that the user position will have that accuracy, since the US government does not impose any restriction to end users. What it means is that the satellites will send information such that their pseudorange has an accuracy of at least 4m rms (or 7.8m 95% of the time under certain conditions) excluding ionosopheric errors, multipath, etc. From https://www.gps.gov/systems/gps/performance/accuracy/:

The accuracy commitments do not apply to GPS devices, but rather to the signals transmitted in space. For example, the government commits to broadcasting the GPS signal in space with a global average user range error (URE) of ≤7.8 m (25.6 ft.), with 95% probability. Actual performance exceeds the specification. On May 11, 2016, the global average URE was ≤0.715 m (2.3 ft.), 95% of the time.

To be clear, URE is not user accuracy. User accuracy depends on a combination of satellite geometry, URE, and local factors such as signal blockage, atmospheric conditions, and receiver design features/quality.

Nevertheless, Appendix B from the SPS contains an interesting discussion on how to calculate accuracy at user level.

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