iPhone / iOS GPS Accuracy Statistical Confidence

Question

When you request a GPS CLLocation from iOS, it has a horizontalAccuracy field, which is a radius in meters from the reported location where the user is likely to actually be.

My question is this: With what statistical confidence (i.e. a percentage) can we say that the phone is within the "horizontalAccuracy" distance from the given location?

Some background on why I care:

1. I'm working with data coming from both Android and iOS and I would like to know how confident I can be about any given piece of location data.

2. On Android, this data is explicit: 68%. From the docs:

   We define accuracy as the radius of 68% confidence. In other words, if you draw a circle centered at this location's latitude and longitude, and with a radius equal to the accuracy, then there is a 68% probability that the true location is inside the circle.

3. In general, when dealing with GPS data, there are a number of standard error reporting methods including RMS (68%, likely the method Android uses), 2DRMS (95%), CEP (50%), Error Ellipse (95%). You can read more about these methods here.

Answer 1

Since any documentation doesn't describe this, you have to do your own research... Or hope that someone did the job for you :)

I'm not sure what FileMaker is, but it doesn't matter: it's definitely built on CoreLocation. Somebody gathered a lot of samples from users and filed a report on his blog:

http://scarpettagroup.com/location-whats-accuracy/

FileMaker is not reporting CEP, R95, 2DRMS, or anything else consistent. For some reported accuracies, FileMaker appears to be reporting the 90% confidence radius (true position is within that radius 90% of the time); for others, it looks like the 75% confidence radius. For some positions, the reported accuracy is orders of magnitude bigger than the actual variation in the coordinate positions.

Read the whole blog article for more. Unfortunately it's not very specific, and the blogger doesn't share his data so you can calculate some minimum accuracy.

You can try contacting this person and ask him to share his data with you. Maybe you'll be able to gather something from this. You can try in this thread:

http://fmforums.com/forum/topic/89502-which-measure-of-accuracy-is-used-by-location-functions/

jbante is the user that did that research.

If you want a specific answer, you'd have to do extensive testing, like this one here:

http://blog.oplopanax.ca/2012/11/measuring-smartphone-gps-accuracy/

Answer 2

The value of horicontal accuracy is not calculated by ios (or android). it is directly delivered by the GPS (GNSS) chip with their cutom, binary protocol. You may download ublox binary protocol specification and read that horciontal acc estim, documentation, too. The chip manufactures usually call it "horicontal accuracy estimate". Further the chip manufactures (e.g uBlox) do not give the info of such a confidence (radius), related to that estimation.

To answer your question:"With what statistical confidence (i.e. a percentage) can we say that the phone is within the "horicontalAccuracy" distance from the given location".

It is simply unknown, the chip manufacturers do not specify that. Since much calculation slike the hdop value are based on the 1-sigma value, I just asume it will be no better than 1-sigma which is the 68% mentioned by android.

Further, pleaes note that the manufacturers call it horicontal accurcay estimate, so it is even not a statistical size, it cannot be such, since the correct location is unknown.

Next to note: since GPS radial position deviations are only long term normal distributed (24h) such short term estimations are even more doubtfull.