# Waypoint error - is it additive?

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Not at all. I'm well versed in both of them.
Well, there you, because that's exactly what it is. The example in your OP can be described as a triangle, two sides are 20 feet long each (your two position errors) and the length of the third side is unknown, which is the distance to the cache. This length can be between 0 feet (the errors cancel each other out) and 40 feet (your "worst case"). Simple trigonometry. The actual answer then depends only on the angle in which the two errors run.

Alternatively you can express it as vector addition. Vector a is 20 feet long and vector b is also 20 feet long. The distance to the cache then is c = a + b. c will then be 40 feet long if a and b are in the same direction, and 0 feet long if they're in opposite direction, and anything in between in all other cases.

Yep, that's how I understood it before I posted, that's how I still understand it.

If Fizzy posted and told you that you couldn't really add the two errors that way when geocaching but didn't explain why, wouldn't you be curious and ask him to explain?

(Not that he would, because what you've said is correct)

That's okay, that's not relevant. I don't CARE what those errors are. I'm not trying to figure them out. I'm just trying to use them to explain why the finder isn't standing on the cache when their GPS says they're at GZ.
So you're just asking how trigonometry/geometry works, right?

Not at all. I'm well versed in both of them. There are some people here that could benefit from learning a bit more about how English works.

I was 100% sure that the two errors added together in the worst case to put you 40 feet away from the cache. Then at some point I read in here that this wasn't the case. Eventually I wanted to know why it wasn't the case bad enough to start a thread about it, just in case there was something I wasn't considering in such a simple explanation. It would have been really cool to find out that in this situation that blah blah blah blah and the numbers aren't additive, they have to be blended. Or whatever.

I've learned that I was correct.

I also learned that probably what I read someone say long ago which was NOT true, was that "you can expect to find the cache 40 feet away". There's a huge difference between "up to 40 feet away" (my version), and "will be 40 feet away" (the version that I probably read about in the past).

... and we also learned in this thread that the probabilty of the error being over 28 feet is, in reality, hardly worth mentioning....

I barely made it through the first page. Math makes my head hurt.

If Fizzy posted and told you that you couldn't really add the two errors that way when geocaching but didn't explain why, wouldn't you be curious and ask him to explain?

(Not that he would, because what you've said is correct)

And I hope I explained it clearly enough. When someone said "error" you thought of a distance, while when I saw "error" I thought of a distribution. I always think of a distribution when considering errors.

So you are correct: it is possible (though generally not useful) to add errors-as-numbers together, but what I originally meant is that you can't add errors-as-distributions together.

When explaining things to newbies, I always try to get to errors-as-distributions as quickly as possible, as it represents what the instrument is doing most accurately.

Yep, that's how I understood it before I posted, that's how I still understand it.

If Fizzy posted and told you that you couldn't really add the two errors that way when geocaching but didn't explain why, wouldn't you be curious and ask him to explain?

(Not that he would, because what you've said is correct)

Well, you got plentiful of explanation in this thread. In your example, you assume that the two position errors are exactly 20 feet, but you make no assumption about the direction of the errors, which is why you say the "worst case" would be 40 feet. While correct, this comes across as strange, because either you know the position errors precisely, in which case you also know in which direction the errors are (in which case you know precisely how far off you are, without the need for a "worst case"), or you don't know the errors at all, in which case you don't know their values either.

When we talk about position errors, we talk about the uncertainty that comes with GPS usage. When you take a GPS reading, you don't only get a set of coordinates, you also get an estimate of accuracy. There's no claim of "this is it", all it tells you is "somewhere around there". This also applies to the posted coordinates of caches, even though it doesn't say so explicitly. You know that they will be off by an unknown amount and in an unknown direction, and you know that your GPS will be off by an unknown amount and in an unknown direction (both of which are subject to change over time). You can guess that each of them could be up to 20 feet off, but you can't make any guess about their direction at all. People think "+- 20 feet here plus +- 20 feet there, so that means the cache could be up to 40 feet away". This is not how it works and this is what fizzymagic was posting about.

Edited by dfx
Yep, that's how I understood it before I posted, that's how I still understand it.

If Fizzy posted and told you that you couldn't really add the two errors that way when geocaching but didn't explain why, wouldn't you be curious and ask him to explain?

(Not that he would, because what you've said is correct)

Well, you got plentiful of explanation in this thread. In your example, you assume that the two position errors are exactly 20 feet, but you make no assumption about the direction of the errors, which is why you say the "worst case" would be 40 feet. While correct, this comes across as strange, because either you know the position errors precisely, in which case you also know in which direction the errors are (in which case you know precisely how far off you are, without the need for a "worst case"), or you don't know the errors at all, in which case you don't know their values either.
I've tried unsuccessfully several times to say that the hider and finder don't know the errors, the values or the direction, only that there ARE errors. The numbers of 20 and 40 were given only as an example, but I stated over and over that it didn't matter specifically what the errors were, I just wanted to verify that they do add together as I thought they did.

When we talk about position errors, we talk about the uncertainty that comes with GPS usage. When you take a GPS reading, you don't only get a set of coordinates, you also get an estimate of accuracy.
Okay. But when you're given a set of coordinates, they're specific, and they represent a specific location. Nothing fuzzy about them.

There's no claim of "this is it", all it tells you is "somewhere around there". This also applies to the posted coordinates of caches, even though it doesn't say so explicitly.
I disagree. Posted coordinates point to a specific spot. In my example in the OP, they pointed exactly to B.

You know that they will be off by an unknown amount and in an unknown direction
I know that the cache will be an unknown amount and direction from that specific spot.

, and you know that your GPS will be off by an unknown amount and in an unknown direction (both of which are subject to change over time).
Correct. But in my example I was only talking about the instance when the newbie looks up and asks why they weren't on the cache when they reached what they thought was GZ. I'm not talking about what happens to the GPSr readings over the course of a cache search.

You can guess that each of them could be up to 20 feet off, but you can't make any guess about their direction at all. People think "+- 20 feet here plus +- 20 feet there, so that means the cache could be up to 40 feet away". This is not how it works and this is what fizzymagic was posting about.
But that IS how it works.

If the hider was 20 feet off, in an unknown direction, and the finder was off 20 feet in an unknown direction, the finder could (in worst case) be reading GZ but be 40 feet away from the cache. I'm not saying that the 20 feet errors are known whenever you're looking for a cache, or that they're the EPE readings from your GPS, I'm saying they're the actual errors in one specific example designed to ask if errors can add.

Fizzy explained that it's not likely for the cache to be located at 40 feet away, and it shouldn't be expected since it's the worst case, but it IS possible. The expected error (statistically what would should expect) is 28 feet, but worst case is still 40 feet.

If Fizzy posted and told you that you couldn't really add the two errors that way when geocaching but didn't explain why, wouldn't you be curious and ask him to explain?

(Not that he would, because what you've said is correct)

And I hope I explained it clearly enough. When someone said "error" you thought of a distance, while when I saw "error" I thought of a distribution. I always think of a distribution when considering errors.

So you are correct: it is possible (though generally not useful) to add errors-as-numbers together, but what I originally meant is that you can't add errors-as-distributions together.

When explaining things to newbies, I always try to get to errors-as-distributions as quickly as possible, as it represents what the instrument is doing most accurately.

I understand that you can't add the EPE numbers. I also understand that while you can add the errors-as-numbers together you won't ever know the values so you can't actually add them together to come up with a specific number in a cache hunt. However, the fact that there ARE errors in where the GPSr tells you that you are vs where you actually are, in both hiding and finding a cache, is the reason your GPSr doesn't lead you straight to the cache.

I've tried unsuccessfully several times to say that the hider and finder don't know the errors, the values or the direction, only that there ARE errors. The numbers of 20 and 40 were given only as an example, but I stated over and over that it didn't matter specifically what the errors were, I just wanted to verify that they do add together as I thought they did.

I understand, but the whole assumption of a specific value of error but an unspecific direction makes no sense. Either you know both value and direction, or you know neither.

Okay. But when you're given a set of coordinates, they're specific, and they represent a specific location. Nothing fuzzy about them.

This is only true in theory, in mathematics. In reality, there is no such thing as a perfect set or coordinates for a certain location, or a perfect location for a certain set of coordinates. Either you try to find the coordinates to a specific location, in which case you will end up with a fuzzy set of coordinates, or you try to find the location to a specific set of coordinates, in which case you end up with a fuzzy location. This is true no matter which method of determination is used, GPS or anything else. As soon as you try to apply numbers to the real world, you always end up with a certain amount of uncertainty.

I disagree. Posted coordinates point to a specific spot. In my example in the OP, they pointed exactly to B.

See above, there's no such thing as an exact location for a given set of coordinates in the real world (or an exact set of coordinates for a given location for that matter). Even with the highest possible accuracy with any thinkable way of measurement, there will still be some amout of uncertainty. So now you know that there is some amount of inaccuracy, but you don't know how much since the page doesn't tell you. Obviously you can assume that the coordinates were taken with GPS, so that's how you can take a guess about the amount of inaccuracy.

Correct. But in my example I was only talking about the instance when the newbie looks up and asks why they weren't on the cache when they reached what they thought was GZ.

ok, so what are you gonna tell them if their GPS shows them a distance of 15 feet at the cache location? That the hider's coords are off by X feet and his coords are off by Y feet, both in an unknown direction, and the triangulation of those numbers results in 15 feet? I don't think they're gonna be satisfied with that. If anything, the logical next question from them would be "why is it like that?" at which point you'll have to start explaining about general GPS inaccuracies and how EPE tries to give an estimate about the amount of inaccuracy.

You can guess that each of them could be up to 20 feet off, but you can't make any guess about their direction at all. People think "+- 20 feet here plus +- 20 feet there, so that means the cache could be up to 40 feet away". This is not how it works and this is what fizzymagic was posting about.
But that IS how it works.

If the hider was 20 feet off, in an unknown direction, and the finder was off 20 feet in an unknown direction, the finder could (in worst case) be reading GZ but be 40 feet away from the cache. I'm not saying that the 20 feet errors are known whenever you're looking for a cache, or that they're the EPE readings from your GPS, I'm saying they're the actual errors in one specific example designed to ask if errors can add.

Fizzy explained that it's not likely for the cache to be located at 40 feet away, and it shouldn't be expected since it's the worst case, but it IS possible. The expected error (statistically what would should expect) is 28 feet, but worst case is still 40 feet.

You're not listening. There's no way of knowing the actual errors, which makes them completely irrelevant. All you can do is guess and estimate based on the available information. You don't know how far off the hider was. You can guess it's up to 20 feet, but you don't know. Most likely it's less, but maybe it's more. You don't know how far off you are right now. It may be up to 20 feet, but you don't know. It's probably less, but could be more. You don't know and can't possibly know. Nobody can know, it's impossible to tell. And that doesn't only apply to value, it also applies to direction. And that's the thing: if you're estimating that the hider is probably less than 20 feet off, and you are probably currently less than 20 feet off, then the conclusion is that the cache is currently probably less than 28 feet away when your GPS says zero. And not 40. It's not the "worst case" either, because you're just estimating. And you're estimating because there's no possible way to know any better.

In other words: of course the errors add, but the fact that you can't ever possibly know any of them, especially their direction, simply adding their values is not how it works. You must consider the errors as a statistical entity and treat them as such. Nothing else makse sense in the real world.

I've tried unsuccessfully several times to say that the hider and finder don't know the errors, the values or the direction, only that there ARE errors. The numbers of 20 and 40 were given only as an example, but I stated over and over that it didn't matter specifically what the errors were, I just wanted to verify that they do add together as I thought they did.
I understand, but the whole assumption of a specific value of error but an unspecific direction makes no sense. Either you know both value and direction, or you know neither.
How many times do I need to say it??? You know neither! It's not important WHAT the error is, just that they add together, and therefore is the reason the person standing at what they're told by their GPS is GZ is not on the cache.

Okay. But when you're given a set of coordinates, they're specific, and they represent a specific location. Nothing fuzzy about them.
This is only true in theory, in mathematics. In reality, there is no such thing as a perfect set or coordinates for a certain location, or a perfect location for a certain set of coordinates. Either you try to find the coordinates to a specific location, in which case you will end up with a fuzzy set of coordinates, or you try to find the location to a specific set of coordinates, in which case you end up with a fuzzy location. This is true no matter which method of determination is used, GPS or anything else. As soon as you try to apply numbers to the real world, you always end up with a certain amount of uncertainty.
What the heck are you talking about???? If I tell you to go to N 0.00 W00.000 that is a very specific location. What can possibly be fuzzy about that?

I disagree. Posted coordinates point to a specific spot. In my example in the OP, they pointed exactly to B.

See above, there's no such thing as an exact location for a given set of coordinates in the real world (or an exact set of coordinates for a given location for that matter). Even with the highest possible accuracy with any thinkable way of measurement, there will still be some amout of uncertainty. So now you know that there is some amount of inaccuracy, but you don't know how much since the page doesn't tell you. Obviously you can assume that the coordinates were taken with GPS, so that's how you can take a guess about the amount of inaccuracy.

Wrong again. The posted coordinates point EXACTLY to a point on earth. They probably aren't pointing to the geocache, and getting exactly to the spot they point to will be difficult, but the place is very specific.

Correct. But in my example I was only talking about the instance when the newbie looks up and asks why they weren't on the cache when they reached what they thought was GZ.
ok, so what are you gonna tell them if their GPS shows them a distance of 15 feet at the cache location? That the hider's coords are off by X feet and his coords are off by Y feet, both in an unknown direction, and the triangulation of those numbers results in 15 feet? I don't think they're gonna be satisfied with that. If anything, the logical next question from them would be "why is it like that?" at which point you'll have to start explaining about general GPS inaccuracies and how EPE tries to give an estimate about the amount of inaccuracy.
It doesn't matter if their GPS shows them a distance of 15 feet. That's irrelevant. The discussion isn't about how to find a cache, what EPE is, why the distance shown from the cache is 15 feet, etc. I thought you'd figured this out a few posts back, but you've returned to a discussion of how to measure distances or errors.
You can guess that each of them could be up to 20 feet off, but you can't make any guess about their direction at all. People think "+- 20 feet here plus +- 20 feet there, so that means the cache could be up to 40 feet away". This is not how it works and this is what fizzymagic was posting about.
But that IS how it works.

If the hider was 20 feet off, in an unknown direction, and the finder was off 20 feet in an unknown direction, the finder could (in worst case) be reading GZ but be 40 feet away from the cache. I'm not saying that the 20 feet errors are known whenever you're looking for a cache, or that they're the EPE readings from your GPS, I'm saying they're the actual errors in one specific example designed to ask if errors can add.

Fizzy explained that it's not likely for the cache to be located at 40 feet away, and it shouldn't be expected since it's the worst case, but it IS possible. The expected error (statistically what would should expect) is 28 feet, but worst case is still 40 feet.

You're not listening. There's no way of knowing the actual errors, which makes them completely irrelevant. All you can do is guess and estimate based on the available information. You don't know how far off the hider was. You can guess it's up to 20 feet, but you don't know. Most likely it's less, but maybe it's more. You don't know how far off you are right now. It may be up to 20 feet, but you don't know. It's probably less, but could be more. You don't know and can't possibly know. Nobody can know, it's impossible to tell. And that doesn't only apply to value, it also applies to direction.
Uh.. I'M not listening???? Dude, I've said it a hundred times, the actual error doesn't have to be known in order for the error to exist. If you're 10 feet from the cache then you're 10 feet away. It doesn't matter if you know the value, or even if you're planning on measuring it. I'm going to stop using the value of 20 as an example because you're fixated on it. I'm not at all suggesting that in all caches the errors are 20 feet.

And that's the thing: if you're estimating that the hider is probably less than 20 feet off, and you are probably currently less than 20 feet off, then the conclusion is that the cache is currently probably less than 28 feet away when your GPS says zero. And not 40.
I've always agreed that it was probably less than 28 feet. I've never said it was 40. Do you even read my posts? It sounds like you're arguing what you think I might be saying instead of what I'm actually saying. Are you estimating my replies? What is your Estimated Posting Error? It seems fairly high.

It's not the "worst case" either, because you're just estimating. And you're estimating because there's no possible way to know any better.
I'm not estimating, because I don't care what the error is. I'm only suggesting to the newbie (and asking about in this thread) that two errors have added together to put them somewhere other than the cache. THAT'S ALL. I'm not asking how to measure the errors, or how to avoid them, or anything else.

In other words: of course the errors add, but the fact that you can't ever possibly know any of them, especially their direction, simply adding their values is not how it works. You must consider the errors as a statistical entity and treat them as such. Nothing else makse sense in the real world.
To you. Obviously.

I think in this case context is everything. Let's go back to the original context.

IIRC, my original comment was in response to a thread in which somebody said:

The hider's GPS could have an error up to 20 feet and yours could have an error up to 20 feet, so your GZ could be up to 40 feet away from the cache.

That statement is wrong in a number of ways. I simplified my response to it by saying "you can't add errors that way" and I stand by that statement.

But that original statement has (in one form or another) frequently been made in the forums to "explain" what area one should search for the cache.

Let's look at all the things wrong with it:

• GPS errors are not expressible in the form "the coords are within xx feet of the true location."
• The use of the word "could" implies "likely." No quantification of "likely" is given.
• The statement implies that it is likely that the hider's distance from the true coords is equal to the estimated EPE, and that it is also likely that your measurement will be off by that much.
• The statement implies rather strongly that the probability that the total error would be 40 feet is just the probability that the hider's error was 20 feet times the probability that your error was 20 feet.

Every single one of those things is wrong. Every one.

That's why I was so definitive in my long-ago post. Statements like the above spread misinformation about how GPS units work and where to concentrate your search for a cache.

Yes, it is true that two 20-foot error could (with very low probability) make a 40-foot error. But that statement is not useful for anything.

What the heck are you talking about???? If I tell you to go to N 0.00 W00.000 that is a very specific location. What can possibly be fuzzy about that?

...

Wrong again. The posted coordinates point EXACTLY to a point on earth. They probably aren't pointing to the geocache, and getting exactly to the spot they point to will be difficult, but the place is very specific.

If that's true, then tell me how you or anyone else could ever know where exactly that location is?

Correct. But in my example I was only talking about the instance when the newbie looks up and asks why they weren't on the cache when they reached what they thought was GZ.
ok, so what are you gonna tell them if their GPS shows them a distance of 15 feet at the cache location? That the hider's coords are off by X feet and his coords are off by Y feet, both in an unknown direction, and the triangulation of those numbers results in 15 feet? I don't think they're gonna be satisfied with that. If anything, the logical next question from them would be "why is it like that?" at which point you'll have to start explaining about general GPS inaccuracies and how EPE tries to give an estimate about the amount of inaccuracy.
It doesn't matter if their GPS shows them a distance of 15 feet. That's irrelevant. The discussion isn't about how to find a cache, what EPE is, why the distance shown from the cache is 15 feet, etc. I thought you'd figured this out a few posts back, but you've returned to a discussion of how to measure distances or errors.

Since you didn't answer, but you claim that this is the sole reason for your original question, I'll ask you again: I'm the newbie, I stand at the cache and my GPS shows 15 feet. I ask you why. What's your answer?

Or alternatively (maybe you like this better, even though it's the same thing): I stand where my GPS says 0 but the cache isn't there. I ask you why. What's your answer?

Edited by dfx
What the heck are you talking about???? If I tell you to go to N 0.00 W00.000 that is a very specific location. What can possibly be fuzzy about that?

...

Wrong again. The posted coordinates point EXACTLY to a point on earth. They probably aren't pointing to the geocache, and getting exactly to the spot they point to will be difficult, but the place is very specific.

If that's true, then tell me how you or anyone else could ever know where exactly that location is?
How could anyone know where the location of the posted coordinates are? I'm not sure if you're looking for something other than "Follow your GPS and that will get you close" or not, but that's how I'd get there. I can tell you that your GPS probably won't get you exactly to it, but even if it did you wouldn't know it. You're almost certainly just going to be near it because your GPSr doesn't have perfect accuracy.

Correct. But in my example I was only talking about the instance when the newbie looks up and asks why they weren't on the cache when they reached what they thought was GZ.
ok, so what are you gonna tell them if their GPS shows them a distance of 15 feet at the cache location? That the hider's coords are off by X feet and his coords are off by Y feet, both in an unknown direction, and the triangulation of those numbers results in 15 feet? I don't think they're gonna be satisfied with that. If anything, the logical next question from them would be "why is it like that?" at which point you'll have to start explaining about general GPS inaccuracies and how EPE tries to give an estimate about the amount of inaccuracy.
It doesn't matter if their GPS shows them a distance of 15 feet. That's irrelevant. The discussion isn't about how to find a cache, what EPE is, why the distance shown from the cache is 15 feet, etc. I thought you'd figured this out a few posts back, but you've returned to a discussion of how to measure distances or errors.
Since you didn't answer, but you claim that this is the sole reason for your original question, I'll ask you again: I'm the newbie, I stand at the cache and my GPS shows 15 feet. I ask you why. What's your answer?

Or alternatively (maybe you like this better, even though it's the same thing): I stand where my GPS says 0 but the cache isn't there. I ask you why. What's your answer?

This is from my post, number 90 in this thread. I've changed it a little to try and avoid confusion.

"When the hider measured coordinates for this cache his GPS wasn't showing him exactly where he was because of inaccuracies in the calculation results based on several things. The locations of the satellites as well as interference from trees, buildings, the atmosphere, etc can all make the readings slightly off. So he was standing where the cache was hidden, but wrote down coordinates to an offset somewhere around here. You're trying to put yourself at those coordinates, but because of very similar inaccuracies with your readings your GPS may tell you that you're at those coordinates - but you'd be somewhere else too. These two offsets, depending on what they are, will combine to put you anywhere from on the cache to the sum of the offsets away. Although it's very unlikely you'll be at that worst case distance."

How could anyone know where the location of the posted coordinates are? I'm not sure if you're looking for something other than "Follow your GPS and that will get you close" or not, but that's how I'd get there. I can tell you that your GPS probably won't get you exactly to it, but even if it did you wouldn't know it. You're almost certainly just going to be near it because your GPSr doesn't have perfect accuracy.

Disregard GPS for a moment. I'm asking how you could ever possibly know the exact location for a specific set of coordinates, using whatever way of determination you wish. You say that the coordinates point to a specific location. Obviously GPS can't tell you where exactly it is, but surely there has to be a way to find out?

"When the hider measured coordinates for this cache his GPS wasn't showing him exactly where he was because of inaccuracies in the calculation results based on several things. The locations of the satellites as well as interference from trees, buildings, the atmosphere, etc can all make the readings slightly off. So he was standing where the cache was hidden, but wrote down coordinates to an offset somewhere around here. You're trying to put yourself at those coordinates, but because of very similar inaccuracies with your readings your GPS may tell you that you're at those coordinates - but you'd be somewhere else too. These two offsets, depending on what they are, will combine to put you anywhere from on the cache to the sum of the offsets away. Although it's very unlikely you'll be at that worst case distance."

Ah ok (I'm still the newbie), so how do I know how much those offsets are? And how far from this spot where I'm standing now should I be looking for the cache?

How could anyone know where the location of the posted coordinates are? I'm not sure if you're looking for something other than "Follow your GPS and that will get you close" or not, but that's how I'd get there. I can tell you that your GPS probably won't get you exactly to it, but even if it did you wouldn't know it. You're almost certainly just going to be near it because your GPSr doesn't have perfect accuracy.
Disregard GPS for a moment. I'm asking how you could ever possibly know the exact location for a specific set of coordinates, using whatever way of determination you wish. You say that the coordinates point to a specific location. Obviously GPS can't tell you where exactly it is, but surely there has to be a way to find out?

This is a very off topic question. I guess maybe using maps, benchmarks and surveying equipment?? Why would you ask me how to find where a set of coordinates point to but not to use a GPS?

"When the hider measured coordinates for this cache his GPS wasn't showing him exactly where he was because of inaccuracies in the calculation results based on several things. The locations of the satellites as well as interference from trees, buildings, the atmosphere, etc can all make the readings slightly off. So he was standing where the cache was hidden, but wrote down coordinates to an offset somewhere around here. You're trying to put yourself at those coordinates, but because of very similar inaccuracies with your readings your GPS may tell you that you're at those coordinates - but you'd be somewhere else too. These two offsets, depending on what they are, will combine to put you anywhere from on the cache to the sum of the offsets away. Although it's very unlikely you'll be at that worst case distance."
Ah ok (I'm still the newbie), so how do I know how much those offsets are? And how far from this spot where I'm standing now should I be looking for the cache?
I don't think you can know how much those offsets are. Again, why are you asking? This thread isn't about how to find a cache once you're wherever your GPS tells you it should be. It's about whether or not the offsets of the two GPSrs are additive, and way way way back on the first page I found out that they were.

Please don't post anything else off topic. If you want to discuss how to locate a specific set of coordinates, or how to look for a cache near GZ, start a new thread. If you want to discuss the possible addition of GPS inaccuracies, get to the point.

This is a very off topic question. I guess maybe using maps, benchmarks and surveying equipment?? Why would you ask me how to find where a set of coordinates point to but not to use a GPS?

It's not off topic at all. I'm asking for a specific reason, one that you'd eventually understand if didn't evade the question.

I don't think you can know how much those offsets are. Again, why are you asking? This thread isn't about how to find a cache once you're wherever your GPS tells you it should be. It's about whether or not the offsets of the two GPSrs are additive, and way way way back on the first page I found out that they were.

Unfortunately you're evading the question again. Your refusal to play along only demonstrates your resistance to learning anything and your unwillingness to admit that you might not be totally right. Which is why I will leave you with your flawed understanding of how GPS errors work and won't post any more here.

Edited by dfx

It's about whether or not the offsets of the two GPSrs are additive, and way way way back on the first page I found out that they were.

I think the problem is that a GPSr doesn't have an offset. If you take one measurement, then a GPSr reading will have a certain error. It will give you coordinates that are not the actual coordinates of the point where you took the the measurement. The finder then uses his GPSr to go to these "wrong" coordinates. When his GPSr shows the same coordinates, there will also be a certain error. The true position of this coordinate may be some distance away from the place where his GPSr says these coordinates are.

If the coordinates returned by the first GPSr were for a point ( that was 20 feet from the actual position of the GPSr (A), and if the 2nd GPSr was also 20 feet from the actual position of these coordinates © when it displays those coordinates (, you want to know the maximum distance the position of the cache (A) is from where the 2nd GPSr is © when it read the coordinates return by the 1st GPSr. I've added the letters from your diagram in the OP. The maximum distance is of course 40 feet.

The problem is that in the real world the finder does not know what the error of the hider's measurement is. Nor does he know the error of his GPSr for any one reading. He can look at the EPE and know a little bit about the distribution for the error on his unit. As he wanders around he can expect to be within a certain distance from B a certain percentage of the time. But he still doesn't know the error of the hider. When he finally finds the cache his GPS says he is 40 feet from the posted coordinates. If his EPE shows only 20 feet, he may wonder why is the cache so far from the posted coordinates. So we tell newbies a story that the hider also had 20 feet EPE and what's more, that the coordinates he posted could have 20 feet of error. Then we "explain" the 40 feet by adding the 20 feet of the hider to the 20 feet of the finder. This is just a made up scenario, one that is not very likely, that is used to explain 40 feet of error. It is very unlikely that both GSPr readings had 20 feet of error; it is even more unlikely that the direction of the errors were 180 degrees apart so that the distances added. We want to get newbies to start looking for caches to be up to 40 feet (or more) from where their GPSr zeros out. So we tell them this unlikely scenario. But it's really easy to understand and therefore it works. Newbies start looking for caches 40 feet from where they zeroed out.

This is a very off topic question. I guess maybe using maps, benchmarks and surveying equipment?? Why would you ask me how to find where a set of coordinates point to but not to use a GPS?
It's not off topic at all. I'm asking for a specific reason, one that you'd eventually understand if didn't evade the question.
If you're leading to something on topic, then post the on topic question. If you're leading to something by asking off topic questions and I try to answer but can't, that's not evading the question. My best guess was to use maps, benchmarks, and surveying equipment.

I don't think you can know how much those offsets are. Again, why are you asking? This thread isn't about how to find a cache once you're wherever your GPS tells you it should be. It's about whether or not the offsets of the two GPSrs are additive, and way way way back on the first page I found out that they were.
Unfortunately you're evading the question again. Your refusal to play along only demonstrates your resistance to learning anything and your unwillingness to admit that you might not be totally right.
Again, I didn't evade, I answered. My answer was that I didn't think you can know how much the offsets are. The reason I thought it was off topic is because I've said several times that I didn't think anyone would know what they are, and it's not necessary to know what they are in order for them to add or not add. But I did answer.

Which is why I will leave you with your flawed understanding of how GPS errors work and won't post any more here.
I guess that's one less person that will be telling me that I'm asking about EPE.
It's about whether or not the offsets of the two GPSrs are additive, and way way way back on the first page I found out that they were.
I think the problem is that a GPSr doesn't have an offset. If you take one measurement, then a GPSr reading will have a certain error. It will give you coordinates that are not the actual coordinates of the point where you took the the measurement. The finder then uses his GPSr to go to these "wrong" coordinates. When his GPSr shows the same coordinates, there will also be a certain error. The true position of this coordinate may be some distance away from the place where his GPSr says these coordinates are.
What you've just described is what I started the thread calling "error" because the coordinates returned weren't for exactly the coordinates the GPSr was located. But I changed it to "offset" to try and avoid confusion with EPE.

If the coordinates returned by the first GPSr were for a point that was 20 feet from the actual position of the GPSr (A), and if the 2nd GPSr was also 20 feet from the actual position of these coordinates [C] when it displays those coordinates , you want to know the maximum distance the position of the cache (A) is from where the 2nd GPSr is [C] when it read the coordinates return by the 1st GPSr. I've added the letters from your diagram in the OP. The maximum distance is of course 40 feet.
Agreed. It seemed obvious to me before I posted, but I just wanted to make sure I wasn't missing something important.

The problem is that in the real world the finder does not know what the error of the hider's measurement is. Nor does he know the error of his GPSr for any one reading.
That's not a problem at all. The person at [C] can be 40 feet from [A] without knowing it. Knowing what the value is wasn't the question. The question was if the person could end up 40 feet away by following their GPSr. The answer is yes, although it's very unlikely.

He can look at the EPE and know a little bit about the distribution for the error on his unit. As he wanders around he can expect to be within a certain distance from B a certain percentage of the time. But he still doesn't know the error of the hider. When he finally finds the cache his GPS says he is 40 feet from the posted coordinates. If his EPE shows only 20 feet, he may wonder why is the cache so far from the posted coordinates. So we tell newbies a story that the hider also had 20 feet EPE and what's more, that the coordinates he posted could have 20 feet of error. Then we "explain" the 40 feet by adding the 20 feet of the hider to the 20 feet of the finder. This is just a made up scenario, one that is not very likely, that is used to explain 40 feet of error. It is very unlikely that both GSPr readings had 20 feet of error; it is even more unlikely that the direction of the errors were 180 degrees apart so that the distances added. We want to get newbies to start looking for caches to be up to 40 feet (or more) from where their GPSr zeros out. So we tell them this unlikely scenario. But it's really easy to understand and therefore it works. Newbies start looking for caches 40 feet from where they zeroed out.
And as I've said before, I wasn't asking about EPE, so if the EPE says 20 feet it's just a coincidence in my opinion. This also isn't about what's the best way to hunt for a cache, what is the best story to tell a newbie about how it works, or anything else. I can understand why these subjects are mentioned here, but it's not relevant to answering the question I asked.

I wasn't asking about EPE, so if the EPE says 20 feet it's just a coincidence in my opinion. This also isn't about what's the best way to hunt for a cache, what is the best story to tell a newbie about how it works, or anything else. I can understand why these subjects are mentioned here, but it's not relevant to answering the question I asked.

However in your OP, you repeated the story you were told as a newbie to explain why the cache might be 40 ft. from where the GPSr zeros out. You then mention that you recalled someone in forums stating this wasn't true but not explaining it.

Two ways to look at the this.

Fist of all is to look at the simplistic example and say of course this is true. Be sure to tell this to your friend so they won't expect to find the cache spot on every time.

The second is to get to the bottom of why you recalled someone saying this wasn't true. All the discussion about error being a distribution and not being able to combine distributions by addition is to explain why someone might have said that the story wasn't true. I doubt that you ever read that the story is untrue, only that it isn't a very likely to be the reason the cache is that far from ground zero.

For those who are interested in a more complete and accurate explanation of why caches are often pretty far from ground zero, I hope the discussions in this thread have been educational. I suspect that the simple story will remain useful in getting newbies to understand the cache might not be where the GPSr zeros out.

I wasn't asking about EPE, so if the EPE says 20 feet it's just a coincidence in my opinion. This also isn't about what's the best way to hunt for a cache, what is the best story to tell a newbie about how it works, or anything else. I can understand why these subjects are mentioned here, but it's not relevant to answering the question I asked.
However in your OP, you repeated the story you were told as a newbie to explain why the cache might be 40 ft. from where the GPSr zeros out. You then mention that you recalled someone in forums stating this wasn't true but not explaining it.

Two ways to look at the this.

Fist of all is to look at the simplistic example and say of course this is true. Be sure to tell this to your friend so they won't expect to find the cache spot on every time.

That's the way I look at it.

The second is to get to the bottom of why you recalled someone saying this wasn't true. All the discussion about error being a distribution and not being able to combine distributions by addition is to explain why someone might have said that the story wasn't true.
I understand that. Honestly, I do understand why people read the word "error" in my OP and assumed I was talking about the EPE of 20' that the GPSr reports as an estimate of the error in position. But it wasn't. I was talking about the actual distance between the cache and the published coordinates, and the actual distance between the published coordinates and the Newbie standing there asking the question.

I've explained this more times than I can count. But for some reason people continue to suggest that the error is EPE shown on the unit, and that this is the number that I am suggesting be used as an absolute known value. I'm not saying it is, and I'm not suggesting that it has anything to do with the question asked.

I doubt that you ever read that the story is untrue, only that it isn't a very likely to be the reason the cache is that far from ground zero.
I'm now confident that whoever said that the story was untrue was either talking about adding EPE numbers, or was talking about the worst case being what should be expected. But when I posted I wanted to make sure there wasn't a problem with inaccuracies in GPS readings being added.

For those who are interested in a more complete and accurate explanation of why caches are often pretty far from ground zero, I hope the discussions in this thread have been educational. I suspect that the simple story will remain useful in getting newbies to understand the cache might not be where the GPSr zeros out.
I, for one, have definitely learned several things, and reading this thread has been as entertaining and educational at times, as it has been frustrating.
The hider's GPS could have an error up to 20 feet and yours could have an error up to 20 feet, so your GZ could be up to 40 feet away from the cache.

That statement is wrong in a number of ways. I simplified my response to it by saying "you can't add errors that way" and I stand by that statement.

Yes, it is true that two 20-foot error could (with very low probability) make a 40-foot error. But that statement is not useful for anything.

I'm having trouble reconciling these two statements. "Could" to me, says that it is in the realm of possibility. I'm reading your analysis to be that "could" is within the realm of probability and that because something is unlikely to happen it is not true.

So you start off saying that the statement is wrong in a number of ways, admit that it is also right in one potential way and then conclude that the unlikely outcome is irrelevant.

Am I the only one confused by this?

I'm now confident that whoever said that the story was untrue was either talking about adding EPE numbers, or was talking about the worst case being what should be expected.

No, not really (trying once more here), not directly anyway. The reason why I and others here are insisting so badly is that while your original example, assumption, question and answer, are all correct, they lead to an incorrect assumption that many geocachers still believe in. Let me try to explain:

Your OP was about how to add two position offsets. You have one offset X here and another offset Y there, so the combined offset Z would be X+Y away in the worst case. Correct, and is perfectly suitable as explanation to a newbie about how two position offsets add to each other.

However, without further explanation beyond that, the newbie will automatically draw a seemingly logical conclusion: Both offsets are obviously unknown when hunting for a cache, so they have to make a guess. If they guess that both offsets are probably less then 20 feet (or "could be up to 20 feet" - see below), then their conclusion would be that they could find the cache up to 20+20=40 feet away from where they get zero. This is not correct, but is exactly what so many geocachers believe, simply because they were never told otherwise. If you give your newbie only the simple explanation of error X + error Y = X+Y maximum error, then that's exactly what they will start believing and that's exactly what we want to avoid.

I'm having trouble reconciling these two statements. "Could" to me, says that it is in the realm of possibility. I'm reading your analysis to be that "could" is within the realm of probability and that because something is unlikely to happen it is not true.

So you start off saying that the statement is wrong in a number of ways, admit that it is also right in one potential way and then conclude that the unlikely outcome is irrelevant.

Am I the only one confused by this?

When you say "the GPS could be off by up to 20 feet", then it doesn't really mean what it says. Strictly speaking it would mean that the error could be anything between 0 and 20 feet, but not more. That's not how GPS works. More precisely you'd have to say "the GPS is probably off by less than 20 feet", which means that there's the unlikely (but possible) case that it's off by more. Even that still doesn't tell the full story because it doesn't say how probable it is, and how the probabilities are distributed within that range. And it's exactly this distribution of probabilities that makes the "up to 20 feet plus up to 20 feet equals up to 40 feet" statement incorrect.

Of course the OP is gonna insist that this is all off topic. Oh well.

Edited by dfx

When you say "the GPS could be off by up to 20 feet", then it doesn't really mean what it says. Strictly speaking it would mean that the error could be anything between 0 and 20 feet, but not more. That's not how GPS works. More precisely you'd have to say "the GPS is probably off by less than 20 feet", which means that there's the unlikely (but possible) case that it's off by more. Even that still doesn't tell the full story because it doesn't say how probable it is, and how the probabilities are distributed within that range. And it's exactly this distribution of probabilities that makes the "up to 20 feet plus up to 20 feet equals up to 40 feet" statement incorrect.

Of course the OP is gonna insist that this is all off topic. Oh well.

Yes, but in a statement of undefined terms (ie "could"), to then say that something is definitively "wrong" isn't that kind of... wrong?

I understand that the upward range of 40' is unlikely, but in the simple binary sense it is not "wrong".

It seems like you're trying to flesh out answer with probabilities and distributions when the simple answer is "it could happen" followed by the qualifier of "most times it won't".

Yes, but in a statement of undefined terms (ie "could"), to then say that something is definitively "wrong" isn't that kind of... wrong?

I understand that the upward range of 40' is unlikely, but in the simple binary sense it is not "wrong".

It seems like you're trying to flesh out answer with probabilities and distributions when the simple answer is "it could happen" followed by the qualifier of "most times it won't".

No, the statement is wrong because the original assumption ("the error could be up to X") is wrong to begin with. There is no absolute upper limit to each individual error, which means that there's also no upper limit to the combined error.

Nobody's saying that the combined error can't be 40 feet, that's not the part that's wrong. The wrong part is the assumption that each GPS could have an error of up to 20 feet and not more. All you can say is that's it's probably less than 20 feet (or whatever other value you wanna use), and if you have two errors of probably less than 20 feet, then the combined error is probably less than 28 feet, and not 40 feet (which is the second part that's wrong). It could still be 40 feet, but it could also be more (which is the third part that's wrong, but who's counting), such as 60 feet or 200 feet. 40 as the sum of the two numbers really has no meaning in this context.

Edited by dfx

Perhaps a better story to tell newbies is:

One possibility is that the hider's GPSr gave a reading that was 20 feet from the actual position. You then go to that location, but your GPSr is also giving a reading that is 20 feet from the actual location except in the opposite direction. Then you will be 40 feet away from the the cache.

Of course this is just one possibility and an unlikely one at that. If you want to know more about how the error of hider's GPSr and the finder's GPSr combine then look at this thread in the Groundspeak forums.

I'm now confident that whoever said that the story was untrue was either talking about adding EPE numbers, or was talking about the worst case being what should be expected.
No, not really (trying once more here), not directly anyway. The reason why I and others here are insisting so badly is that while your original example, assumption, question and answer, are all correct, they lead to an incorrect assumption that many geocachers still believe in. Let me try to explain:

Your OP was about how to add two position offsets. You have one offset X here and another offset Y there, so the combined offset Z would be X+Y away in the worst case. Correct, and is perfectly suitable as explanation to a newbie about how two position offsets add to each other.

So once again you start your post by agreeing with me that the answer I think is the correct answer, is correct.

However, without further explanation beyond that, the newbie will automatically draw a seemingly logical conclusion: Both offsets are obviously unknown when hunting for a cache, so they have to make a guess. If they guess that both offsets are probably less then 20 feet (or "could be up to 20 feet" - see below), then their conclusion would be that they could find the cache up to 20+20=40 feet away from where they get zero. This is not correct, but is exactly what so many geocachers believe, simply because they were never told otherwise.
If someone assumes that the offset is 20 feet for some reason how does that change the fact that there IS an offset? They're going to go away and make a lot of other bogus assumptions too I suppose. But that doesn't explain your incorrect statement here. I think that the cache could be at 40 feet away, and you're saying it can't be 40 feet away. Could does not equal "probably will". I agree that it's wrong to expect the cache at 40 feet, but you're saying that it's not possible for the cache to be at 40 feet. I think you're wrong about that. It's less likely, but still possible.

If you give your newbie only the simple explanation of error X + error Y = X+Y maximum error, then that's exactly what they will start believing and that's exactly what we want to avoid.
Unless you're once again talking about EPE and a range of possibilities of errors, how can you say that X+Y=Maximum error isn't worth believing? That's exactly what you say above is correct in the worst case.

I'm having trouble reconciling these two statements. "Could" to me, says that it is in the realm of possibility. I'm reading your analysis to be that "could" is within the realm of probability and that because something is unlikely to happen it is not true.

So you start off saying that the statement is wrong in a number of ways, admit that it is also right in one potential way and then conclude that the unlikely outcome is irrelevant.

Am I the only one confused by this?

When you say "the GPS could be off by up to 20 feet", then it doesn't really mean what it says. Strictly speaking it would mean that the error could be anything between 0 and 20 feet, but not more. That's not how GPS works. More precisely you'd have to say "the GPS is probably off by less than 20 feet", which means that there's the unlikely (but possible) case that it's off by more. Even that still doesn't tell the full story because it doesn't say how probable it is, and how the probabilities are distributed within that range. And it's exactly this distribution of probabilities that makes the "up to 20 feet plus up to 20 feet equals up to 40 feet" statement incorrect.
This is definitely about EPE, which is fine to discuss and is great to learn more about I suppose. But I don't know anyone that has suggested that "up to 20 feet plus up to 20 feet equals up to 40 feet".

Of course the OP is gonna insist that this is all off topic. Oh well.
No, you did that for me. But I'll point out that just a few posts ago you said you were done with this topic and wouldn't post again, and I when I read it I knew you were wrong about that too.
I'm now confident that whoever said that the story was untrue was either talking about adding EPE numbers, or was talking about the worst case being what should be expected. But when I posted I wanted to make sure there wasn't a problem with inaccuracies in GPS readings being added.

Then you still do not understand. When I say that the error is a distribution, I am NOT talking about EPE. I am talking about the ACTUAL ERROR, just like you say you are. The actual error is a distribution and should be treated as such. That's because there is no way to know the exact value and direction of the error, as has been pointed out many times.

EPE is an estimate of the width of the error distribution; it is not the error distribution. In fact, EPE has an error associated with it! But there is some "true" distribution from which the error is drawn. For the purposes of this discussion, that distribution (which you do not know exactly) is what I call the error.

So when I wrote that you cannot add errors the way you add regular numbers, I was not referring to EPE. I was referring to the actual error distribution.

Treating errors like regular numbers and adding them is just wrong. It has no conceivable use.

Edited by fizzymagic
Yes, but in a statement of undefined terms (ie "could"), to then say that something is definitively "wrong" isn't that kind of... wrong?

I understand that the upward range of 40' is unlikely, but in the simple binary sense it is not "wrong".

It seems like you're trying to flesh out answer with probabilities and distributions when the simple answer is "it could happen" followed by the qualifier of "most times it won't".

No, the statement is wrong because the original assumption ("the error could be up to X") is wrong to begin with. There is no absolute upper limit to each individual error, which means that there's also no upper limit to the combined error.

Nobody's saying that the combined error can't be 40 feet, that's not the part that's wrong. The wrong part is the assumption that each GPS could have an error of up to 20 feet and not more. All you can say is that's it's probably less than 20 feet (or whatever other value you wanna use), and if you have two errors of probably less than 20 feet, then the combined error is probably less than 28 feet, and not 40 feet (which is the second part that's wrong). It could still be 40 feet, but it could also be more (which is the third part that's wrong, but who's counting), such as 60 feet or 200 feet. 40 as the sum of the two numbers really has no meaning in this context.

Huh. At this point I'm going to admit that I don't understand and walk away slowly from the thread. It sounds to me like there are two different definitions in regard to the "20' error" and maybe even two different basis of understanding for that number. But you've made my brain hurt and I'm over my head so I bid you good day.

Huh. At this point I'm going to admit that I don't understand and walk away slowly from the thread. It sounds to me like there are two different definitions in regard to the "20' error" and maybe even two different basis of understanding for that number. But you've made my brain hurt and I'm over my head so I bid you good day.

Here, I created a quick script to simulate the GPS error, for you and for the OP: http://dfx.at/rand.php

It uses a Gaussian distribution formula and gives the statistical breakdown at the bottom.

This is a list of 500 (well, 1000, as it's pairs) randomly generated actual errors. The distances are randomly generated with a standard deviation of 10, but there is no hard upper limit to them. If you keep reloading the page and look through the list, you can see single errors of 30 feet or even more (max value given in the last line - can fluctuate quite a bit). Most of the errors are much smaller though, and I chose the arbitrary number of 18 feet to show that 90-95% of the errors are under that value (second line from bottom). The mean error comes out at around 8 feet. The directions of the errors are completely random.

The 18 feet is what you could consider as the GPS error. You'd say "the coordinates could be up to 18 feet away", even though that's not really true.

The third column is the combined error. If the two angles are about the same, you can see that the errors add to each other, while when the angles are in opposite directions, they cancel each other out. I didn't bother calculating the direction of the combined error.

Now when you have two errors with a mean of around 8 feet, and the errors add to each other, does that make the mean of the combined error 16 feet? No it doesn't, it's much smaller. The same is true for the majority of the errors, if 90% of the single errors are under 18 feet, does that mean that 90% of the combined errors are under 36 feet? No, it's more samples in a much smaller range.

Again, there's no upper limit to either of the individual errors and thus no upper limit to the combined error, which is why you can't give an "up to ..." value. This is (I believe) a good simulation of how actual GPS errors work, how they add up and what they mean for a cache hunt.

Edited by dfx
I'm now confident that whoever said that the story was untrue was either talking about adding EPE numbers, or was talking about the worst case being what should be expected. But when I posted I wanted to make sure there wasn't a problem with inaccuracies in GPS readings being added.
Then you still do not understand. When I say that the error is a distribution, I am NOT talking about EPE. I am talking about the ACTUAL ERROR, just like you say you are. The actual error is a distribution and should be treated as such. That's because there is no way to know the exact value and direction of the error, as has been pointed out many times.
But doesn't the distribution only matter if you're either trying to determine the possible values of the actual error, or use the values in the actual error in a calculation? If the posted coordinates are not exactly where the cache is located, then there is a very specific distance between the two locations. We don't know the value, or care what it is, and we're not trying to describe it. That distance will be the same number until the cache is moved. Is this distance not a fixed amount?

EPE is an estimate of the width of the error distribution; it is not the error distribution. In fact, EPE has an error associated with it! But there is some "true" distribution from which the error is drawn. For the purposes of this discussion, that distribution (which you do not know exactly) is what I call the error.

So when I wrote that you cannot add errors the way you add regular numbers, I was not referring to EPE. I was referring to the actual error distribution.

Treating errors like regular numbers and adding them is just wrong. It has no conceivable use.

This is exactly what I wanted to get into by post 3 or 4. I promise I'm trying to look at this with an open mind and I'm not trying to convince you that I'm right or change your mind. I'm trying to figure out what this all means. If I'd just emailed you instead of posting I'm sure I would have saved myself a lot of trouble.

So let me try and clear something up for myself by looking at a different situation.

I throw a dart at a dartboard and aim for the bulls-eye. You can't see the dartboard and don't know where the dart hit, but you DO know that I'm not very good at darts and you know that I very rarely hit what I'm aiming at. I guess you've watched me play a lot.

Later I throw a second dart at the first one. You can't see it either.

I think all the following are true (even if they're not useful):

1. You can assume neither dart hit the bulls-eye, although it's possible that either one or both did. The reason you can assume they didn't, is because you know how I play and you've watched me miss almost always.
2. If you know that I normally don't miss by really far, maybe 8" on average, then you also know there is a high probability that both darts are somewhere on the board.
3. Someone may ask you why my second dart didn't hit the bulls-eye. You can answer it's because I wasn't a very accurate dart thrower, and I'm almost always off by some amount.
4. There is an exact location of that first dart. If you were at the dartboard perhaps you could measure it and find out what that location was, but you're not there. You not knowing the location of the dart doesn't change that it's in a fixed location. You can only describe it's location as a distribution, but that doesn't mean that the dart itself is moving around and may or may not end up somewhere else. It's location is fixed.
5. You can tell someone that IF my first throw was off by 6", and IF my second throw was also off by 6", it's possible that second dart might be as far away from the bulls-eye by as much as a foot, but it's highly unlikely, and you wouldn't expect it to be exactly a foot away.
6. You can tell them also, that you don't know how far off I actually was with either throw, so there's no way to tell with any degree of certainty where the second one hit. However, knowing I'm off by 8" on average you can discuss the probabilities that it was at various distances, even beyond 16" (with diminishing possibilities).

If anything in there is wrong, then I've failed to understand something and would love to know what I'm missing. Help me to figure this out and I'll buy you a beer.

Edited by Mushtang
Huh. At this point I'm going to admit that I don't understand and walk away slowly from the thread. It sounds to me like there are two different definitions in regard to the "20' error" and maybe even two different basis of understanding for that number. But you've made my brain hurt and I'm over my head so I bid you good day.
Here, I created a quick script to simulate the GPS error, for you and for the OP: http://dfx.at/rand.php

It uses a Gaussian distribution formula and gives the statistical breakdown at the bottom.

This is a list of 500 (well, 1000, as it's pairs) randomly generated actual errors. The distances are randomly generated with a standard deviation of 10, but there is no hard upper limit to them. If you keep reloading the page and look through the list, you can see single errors of 30 feet or even more (max value given in the last line - can fluctuate quite a bit). Most of the errors are much smaller though, and I chose the arbitrary number of 18 feet to show that 90-95% of the errors are under that value (second line from bottom). The mean error comes out at around 8 feet. The directions of the errors are completely random.

The 18 feet is what you could consider as the GPS error. You'd say "the coordinates could be up to 18 feet away", even though that's not really true.

The third column is the combined error. If the two angles are about the same, you can see that the errors add to each other, while when the angles are in opposite directions, they cancel each other out. I didn't bother calculating the direction of the combined error.

Now when you have two errors with a mean of around 8 feet, and the errors add to each other, does that make the mean of the combined error 16 feet? No it doesn't, it's much smaller. The same is true for the majority of the errors, if 90% of the single errors are under 18 feet, does that mean that 90% of the combined errors are under 36 feet? No, it's more samples in a much smaller range.

Again, there's no upper limit to either of the individual errors and thus no upper limit to the combined error, which is why you can't give an "up to ..." value. This is (I believe) a good simulation of how actual GPS errors work, how they add up and what they mean for a cache hunt.

I didn't look at the link but I did read your description. I agree that it sounds like a good model to describe the errors in how a GPS reports coordinates of a location.

Run it again and instead of 500 initial points let it only randomly pick ONE point. Don't look at it though.

I say that this one point is analogous to the published coordinates of a cache. I know you can't tell me the value of the error, or really make a good guess as to how far off it is, but realize that I'm not asking you for that information. However, the value of the error does exist, doesn't it? It's very precise and not changing. The value of the error is a specific number regardless of the fact that you haven't looked at it.

Looking at the value won't change what it is. But it will change what it could be. It will change the possibilities of where it might be.

Mushtang, it seems to me that you asked a question, to which you expect a certain answer. So far no one has given you that expected answer, so you are continuing to argue trying to meld our opinion into the answer you want. I don't think that's going to happen.

Is what I've explained above true for worst case error in a pair of GPS readings?

Yes, but it would happen so rarely that the "statement is not useful for anything."

Mushtang, it seems to me that you asked a question, to which you expect a certain answer. So far no one has given you that expected answer, so you are continuing to argue trying to meld our opinion into the answer you want. I don't think that's going to happen.

Is what I've explained above true for worst case error in a pair of GPS readings?
Yes, but it would happen so rarely that the "statement is not useful for anything."

Actually I asked a question that I expected a certain answer to, and I've been given that answer several times.

But then someone comes along and gives me a different answer. So I discuss with them why they think otherwise.

Or someone will come along and say the equivalent of, "What you actually are trying to ask is..." and then they'll tell me something totally different than what I really asked. This is strange to me but it keeps happening.

So I feel that it's okay to reply to these people. I'm not just jumping in here and posting without it being a reply to someone. It's a discussion on what values can be added when talking about GPS errors.

I'm sorry that this thread is bothering you as much as it appears to. I've learned a few things and am enjoying the discussions. Are you saying you want me to stop posting in here? I'm not sure I understand.

Are you saying you want me to stop posting in here?

No, not at all. I guess I read the answer I believe to be correct several pages ago, and everything since appears to be argumentative (and wrong IMO). Maybe I am being bothered. I suppose I need to stop looking at this thread. Sorry I said anything.

5. You can tell someone that IF my first throw was off by 6", and IF my second throw was also off by 6", it's possible that second dart might be as far away from the bulls-eye by as much as a foot, but it's highly unlikely, and you wouldn't expect it to be exactly a foot away.

Correct (and everything above). If you know the precise errors, it's a simple matter of trigonometry to figure out the total.

6. You can tell them also, that you don't know how far off I actually was with either throw, so there's no way to tell with any degree of certainty where the second one hit. However, knowing I'm off by 8" on average you can discuss the probabilities that it was at various distances, even beyond 16" (with diminishing possibilities).

Exactly. The problem arises when you don't tell them that. In this case the explanation from #5 is likely to make them believe that with an assumed error of up to 8" on the first throw and an assumed error of up to 8" also on the second throw, the second dart might be up to 16" away from the bullseye. This is wrong because this is not how the errors work and thus the conclusion is wrong as well. Sounds like you understand that part now.

Edited by dfx
Sounds like you understand that part now.

I've understood that part from the beginning. I've been trying to tell you, however, for quite some time, that in order to tell them #5 you don't need to tell them #6.

I'd mention the #5 stuff and you'd come back and try to suggest that the #6 stuff was important, or even required, to enter into the story.

It isn't.

I'd mention the #5 stuff and you'd come back and try to suggest that the #6 stuff was important, or even required, to enter into the story.

It isn't.

So if you don't tell them, what is it that keeps them from making the incorrect assumption that I mentioned just before?

Wow, this dead horse is pounded to a pulp! I learned long ago in these forums that the concept of confidence interval does not work for some folks - and that leads to some long discussions. But no such discussion is complete without at least a mention of the major reason the EPE your GPS gives you (and gave the cache hider) may be a complete lie. That's signal reflection - or signal bounce as I call it. I know of a number of caches where the coords are off 60 to 80 feet - and yet I am quite sure the hider's GPS told him he had something like 15 foot EPE. From my experience you get signal bounce near rocky hillsides or buildings, but it can happen in other places too where there seems to be no good reason. Typically the GPS at different times and conditions will zero out in two locations maybe 60 to 80 feet apart, and it will show a good EPE (e.g. 20 feet) from both locations. Some folks may report the coords are dead-on, and others may say they are way-off. So from my perspective, and from a practical perspective, EPE and the associated statistics is only a rough guide - the actual error may be far greater than the stats indicate.

Wow, this dead horse is pounded to a pulp! I learned long ago in these forums that the concept of confidence interval does not work for some folks - and that leads to some long discussions. But no such discussion is complete without at least a mention of the major reason the EPE your GPS gives you (and gave the cache hider) may be a complete lie. That's signal reflection - or signal bounce as I call it. I know of a number of caches where the coords are off 60 to 80 feet - and yet I am quite sure the hider's GPS told him he had something like 15 foot EPE. From my experience you get signal bounce near rocky hillsides or buildings, but it can happen in other places too where there seems to be no good reason. Typically the GPS at different times and conditions will zero out in two locations maybe 60 to 80 feet apart, and it will show a good EPE (e.g. 20 feet) from both locations. Some folks may report the coords are dead-on, and others may say they are way-off. So from my perspective, and from a practical perspective, EPE and the associated statistics is only a rough guide - the actual error may be far greater than the stats indicate.

multipath error

deleted

Edited by CharlieP
5. You can tell someone that IF my first throw was off by 6", and IF my second throw was also off by 6", it's possible that second dart might be as far away from the bulls-eye by as much as a foot, but it's highly unlikely, and you wouldn't expect it to be exactly a foot away.

Correct (and everything above). If you know the precise errors, it's a simple matter of trigonometry to figure out the total.

6. You can tell them also, that you don't know how far off I actually was with either throw, so there's no way to tell with any degree of certainty where the second one hit. However, knowing I'm off by 8" on average you can discuss the probabilities that it was at various distances, even beyond 16" (with diminishing possibilities).

Exactly. The problem arises when you don't tell them that. In this case the explanation from #5 is likely to make them believe that with an assumed error of up to 8" on the first throw and an assumed error of up to 8" also on the second throw, the second dart might be up to 16" away from the bullseye. This is wrong because this is not how the errors work and thus the conclusion is wrong as well. Sounds like you understand that part now.

Wait a minute... #5 is only correct if you are throwing the 2nd dart AT THE 1ST DART.

In #6, it makes absolutely no difference if you bounced the 1st dart off your own head. If you are still aiming at the original bullseye, there is no relationship between the two darts.

In the geocaching example, you are not looking for the actual bullseye (where the cache is,) but where the hiders 1st dart landed.

After enjoying this thread for several days I am confident of three things:

1) I understand both sides of the debate

2) Someone will tell me I don't

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.

Wait a minute... #5 is only correct if you are throwing the 2nd dart AT THE 1ST DART.

In #6, it makes absolutely no difference if you bounced the 1st dart off your own head. If you are still aiming at the original bullseye, there is no relationship between the two darts.

I guess you missed that part of the OP's example (as I did when reading it first). The example/assumption is that he tries to throw the second dart at the first one.

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.

See, that's the thing. If you think that the hider's error is probably within 20 feet and your own error also also probably within 20 feet, then the conclusion shouldn't be that the total error is probably within 40 feet, and you also shouldn't be telling that to anyone else because it's not right, but they'd believe it anyway because it sounds so logical. You should be telling them that the total error is probably within 28 feet.

5. You can tell someone that IF my first throw was off by 6", and IF my second throw was also off by 6", it's possible that second dart might be as far away from the bulls-eye by as much as a foot, but it's highly unlikely, and you wouldn't expect it to be exactly a foot away.
Correct (and everything above). If you know the precise errors, it's a simple matter of trigonometry to figure out the total.
6. You can tell them also, that you don't know how far off I actually was with either throw, so there's no way to tell with any degree of certainty where the second one hit. However, knowing I'm off by 8" on average you can discuss the probabilities that it was at various distances, even beyond 16" (with diminishing possibilities).
Exactly. The problem arises when you don't tell them that. In this case the explanation from #5 is likely to make them believe that with an assumed error of up to 8" on the first throw and an assumed error of up to 8" also on the second throw, the second dart might be up to 16" away from the bullseye. This is wrong because this is not how the errors work and thus the conclusion is wrong as well. Sounds like you understand that part now.

Wait a minute... #5 is only correct if you are throwing the 2nd dart AT THE 1ST DART.

In #6, it makes absolutely no difference if you bounced the 1st dart off your own head. If you are still aiming at the original bullseye, there is no relationship between the two darts.

In the geocaching example, you are not looking for the actual bullseye (where the cache is,) but where the hiders 1st dart landed.

After enjoying this thread for several days I am confident of three things:

1) I understand both sides of the debate

2) Someone will tell me I don't

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.

As dfx said, the throwing of the 2nd dart AT the 1st dart was, in fact, part of the given situation. Thanks dfx.

I'm also happy to hear that you've actually enjoyed this thread. I know I have, but a couple of vocal readers have obviously not, so I was worried that nobody else was either. It's been a fun thread and I've learned several things.

1) I understand both sides too. And I think some others are beginning to understand my point. However about the time that happens someone else comes in and says, "But the reason the error might be different that what the EPE says is...." and I realize some still think I'm talking about EPE, which I'm not. Maybe I should have said I'm not about 3 dozen times.

2) I hope not. It's frustrating when they do that.

3) No matter what you tell anyone, if you mention it in here someone will think you're wrong.

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.
See, that's the thing. If you think that the hider's error is probably within 20 feet and your own error also also probably within 20 feet, then the conclusion shouldn't be that the total error is probably within 40 feet, and you also shouldn't be telling that to anyone else because it's not right, but they'd believe it anyway because it sounds so logical. You should be telling them that the total error is probably within 28 feet.

Here's another thing. He never said the two errors were "probably within 20 feet". When I read it I thought he was talking about some random situation where the 40 foot statement was true, and the point was that he didn't feel comfortable with the mathematical explanation enough to get into that conversation with someone else.

It's not fair to suggest someone said something they didn't really say, and then argue against it.

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.
See, that's the thing. If you think that the hider's error is probably within 20 feet and your own error also also probably within 20 feet, then the conclusion shouldn't be that the total error is probably within 40 feet, and you also shouldn't be telling that to anyone else because it's not right, but they'd believe it anyway because it sounds so logical. You should be telling them that the total error is probably within 28 feet.

Here's another thing. He never said the two errors were "probably within 20 feet". When I read it I thought he was talking about some random situation where the 40 foot statement was true, and the point was that he didn't feel comfortable with the mathematical explanation enough to get into that conversation with someone else.

It's not fair to suggest someone said something they didn't really say, and then argue against it.

Maybe check out the word I have bolded...

3) If I tell a new cacher "The cache might not be where your gps says it is, but is probably within 40 feet" I should also tell them that I can't defend that statement mathematically.
See, that's the thing. If you think that the hider's error is probably within 20 feet and your own error also also probably within 20 feet, then the conclusion shouldn't be that the total error is probably within 40 feet, and you also shouldn't be telling that to anyone else because it's not right, but they'd believe it anyway because it sounds so logical. You should be telling them that the total error is probably within 28 feet.
Here's another thing. He never said the two errors were "probably within 20 feet". When I read it I thought he was talking about some random situation where the 40 foot statement was true, and the point was that he didn't feel comfortable with the mathematical explanation enough to get into that conversation with someone else.

It's not fair to suggest someone said something they didn't really say, and then argue against it.

Maybe check out the word I have bolded...

I don't understand why you'd bring up something that nobody is saying and then argue against it.

And also IF you think that the GPSr is going to bring you straight to within one foot of the cache every time, you'd be wrong, and you also shouldn't be telling people that or posting on the forums that it does. You should be telling them that it will only get them within 30 feet on a good day.

I don't understand why you'd bring up something that nobody is saying and then argue against it.

Nobody's arguing against anything (other than you). No idea what you're talking about.

Edited by dfx

I am afraid I am beginning to see the issue - it appears there may be more than one. But it seems the largest issue revolves around whether the proposed formulas measure the error between two random points generated from the same target or from two points where the second is generated from the position error of the first. Those are two different problems, but it is certain that the second condition is the one that applies to geocaching. So dfx, when you generated your table, did you use the same target point for each of the two test columns. I think the answer is no - and therefore you have tested the second condition - the one applicable to geocaching.

Edited by CharlieP