The closer you get, the worse the map gets

In short

A phone's position error does not shrink as you get closer to each other. It stays the same — but it covers a wider and wider angle as the distance falls. Measured in an urban setting, a phone lands within about 10 metres (7–13 m average horizontal error, iPhone 6, 955 observations, Merry & Bettinger 2019). Two phones are wrong independently of each other, so the error between them is around 14 metres. 14 metres is a 1.6-degree bearing error at 500 metres — and 25 degrees at 30 metres, 54 degrees at 10 metres. That is why two people, each following their own dot, can walk past each other over and over on the last twenty metres.

The first article on this blog ended on a claim that sounds wrong: the problem of finding each other gets worse the closer you get.

This article is about that.

The dot wobbles just as much however close you are

Suppose it worked. All four friends on the festival site are sharing their position, and all four can see each other's dots on a map.

At 400 metres it is an excellent experience. The dot says northeast, you walk northeast, and the distance drops. The map does exactly what you expect a map to do.

Then you get within 30 metres of each other, and the experience falls apart. The dot is right next to your own, but "right next to" on the screen is three metres in one direction and thirty in the other, and there are 8,000 people in between. You turn on the spot. The dot moves a little. You take five steps to the left. Now it is on your right.

The intuitive explanation is that the phone must get less precise up close. It doesn't. The phone is exactly as precise as it was before. All that has changed is the distance.

What a phone actually knows about where it is

There are two numbers in circulation, and both are correct — they were just measured under wildly different conditions.

Under open sky, with nothing in the way, a modern phone lands within a couple of metres. That is impressive, and it is also not the situation most of us are in when we need it.

As soon as there is something solid nearby, it degrades. Merry and Bettinger found that what mattered most for accuracy was proximity to multistorey buildings — not activity on the wifi network, which was what they set out to investigate. The signal from the satellite arrives by two routes: the direct one, and the one that hits a surface first and carries on from there. The phone cannot tell them apart, and a signal that has taken a detour is the same thing as a wrong distance measurement.

A festival site is not a university campus. What it does have is steel stages, sound towers, video screens, food stalls, containers and tens of thousands of bodies, all of which are wet bags of salt — about the best thing you could find for attenuating a satellite signal. As far as we can tell, nobody has measured GPS accuracy in the middle of a festival crowd. So we use the urban number, about 10 metres per phone, and say plainly that it is borrowed from a different situation and probably on the optimistic side.

Two phones are wrong independently of each other, and the number that matters is not how well your phone knows its own position, but how well the two phones know each other's. It is the difference between the two errors, not the sum.

And the errors are not purely harmful here. If they point the same way — both dots displaced ten metres north — the error cancels itself out: you are both in equally wrong places, but the distance and direction between you are right. If they point towards or away from each other, they stack, and the error between you is worse than either phone's own. The two cases are equally likely, and reality mostly sits between them.

That is why you don't add the deviations, you add the variances — the squared deviations. Two independent errors of about 10 metres each give 10² + 10² = 200, and the square root of that is around 14 metres. The 20 metres you would reach by adding them is the worst case, not the typical one; 14 is what it comes to once you average over all the directions the errors can point in.

The arithmetic that turns it all around

Now there is only geometry left. A sideways error of 14 metres at a distance of 500 metres is a very small angle. The same error at 30 metres is a very large one.

Draw it as a triangle. The true line to your friend is the long side — the distance between you. The error pushes her dot sideways off that line and forms the short side. The bearing error is the angle between the two, where you are standing, and it is given by the ratio of the short side to the long one: the error divided by the distance.

Only the ratio matters. If the two sides are the same length — a 14-metre error at 14 metres' distance — the angle is 45 degrees, whether the units are metres or millimetres:

These figures are calculated from the measured errors above, not measured in themselves, and they show the worst case, where the whole error lies across the direction you need to go. If it lies along that direction instead, the arrow points correctly and lies about the distance.

Note the optimistic column. Even with open sky and the best figures from 2025, the direction is 26 degrees off at 10 metres. The problem does not go away with a better phone. It is not a hardware problem, it is a fraction: the numerator holds still, and the denominator goes to zero.

And that is before the arrow has to point anywhere. For the screen to show "that way", the phone also has to know which way you are facing, and that is the magnetometer — the compass. Our own field measurements on an iPhone running iOS 26 on 1 August 2026 had the phone reporting its own compass accuracy as ±14 to ±16 degrees, on the drive where the heading was actually right. That error stacks on top of the table. There is an article coming about that number alone.

Why you walk past each other

Put the two together and the behaviour follows.

You are 20 metres apart. Your arrow points 30 degrees too far to the left. Hers points 30 degrees too far the other way. You both walk that way, honestly and trustingly, and you pass each other twelve metres apart with a stage in between.

Now both phones update their position — a couple of seconds late, because that is what they do. Both arrows now point back. You turn around. You pass each other again, the other way.

It is not because either of you is doing anything wrong. It is two people each following an instrument that is precise enough to be trusted and imprecise enough to be wrong, and that updates more slowly than you walk.

What we do about it

The radar. When the distance is short, we stop pretending to a precision we don't have. Instead of two dots on a map that both look exact, Raduno shows direction and approximate distance, rotated to the phone's compass, so "up" on the screen is the way you are looking. An instrument showing an arrow and about 30 metres promises something it can keep. Two dots three metres apart promise something else.

The near zone (not built). The table above also says what has to happen at the end: below roughly 15 metres the direction is effectively arbitrary, and at that point the right message is not an arrow but a sentence — you're close to each other now, look up and wave.

There is another route as well, and we haven't built it either. This whole article is about GPS, that is, about two phones each asking some satellites where they are and then comparing the answers. But two phones standing twelve metres apart can actually hear each other directly — over Bluetooth, with nobody having to pair anything. It doesn't solve the same problem: signal strength is a poor distance measurement, and a single body between two phones can move the reading a long way. What is far more robust than the absolute value is whether the signal is getting stronger or weaker as you walk. And warmer/colder happens to be the question left on the last ten metres — not "which way exactly". For us that is research, not a feature: we have read about it, done the arithmetic, and not measured a single thing ourselves yet. We'll write about it when we have.

That is why this article does not end with a solution. It ends with the reason the last stretch is hard: a phone can tell you where your friend is, give or take about half a house front. At 500 metres that is nothing. At twelve metres it is the whole difference.

What we don't know

• Neither study was done at a festival. One is a campus, the other is open sky over peatland. We borrow the urban figure because it is the closest analogy we can find to a dense crowd with metal in it, not because anyone has checked it there.
• We have not measured position accuracy ourselves. The numbers in the tables are other people's measurements plus our arithmetic. Our own measured figure in this article is the compass accuracy, and that was measured on one iPhone, not on Android.
• The table is an upper bound, not an average. It assumes the entire error lies perpendicular to the direction between you. In practice it is spread out, and the arrow is more often slightly wrong than completely wrong.