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Test Accuracy of GPS


KayakGZ

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I'm using a Garmin Etrex 10. Lately, I've entered into "discussions" with CO's about the accuracy of their coordinates. Is there any way to test my GPS against an objective standard? Thanks.

 

In order to relate accuracy to geocaching, both the finders and hiders GPS has to be tested. You could have the best in the world, but if the hiders GPS is off by 50 feet, it won't help. On a similar note, it will talent onto the co-ords, not the cache. If the co-it's weren't taken exactly where the cache is, or the cache wasn't put back properly, again it won't matter how accurate your GPS is.

Edited by T.D.M.22
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I'm using a Garmin Etrex 10. Lately, I've entered into "discussions" with CO's about the accuracy of their coordinates. Is there any way to test my GPS against an objective standard? Thanks.

Yes, and the photo above of a couple of benchmarks isn't necessarily going to help you, either. Benchmarks are often as prone to location error as any other point on the ground - some significantly so if they haven't been updated for years.

 

There ARE a very few spots that have been so thoroughly checked with high precision commercial gear that they can be depended upon to provide accuracy at least as good as the 0.001 minute level of precision that you will be seeing for a published cache. Just as a point of reference, at your latitude, every 0.001 in the E/W direction amounts to roughly 4 feet. Every N/S 0.001 amounts to roughly 6 feet. So no matter what you're trying to accomplish, you can't figure on getting any closer than that with 0.001 minute precision on anything.

 

Whether there are any 'reference points' in your area of Connecticut that have been studied so thoroughly as to be known to be within a 0.001 level of accuracy - well, I'm in Colorado, so I have no idea. Ask your fellow cachers if they have run across any such sites. If there are any, there's also a fair chance that someone has placed a cache there to 'commemorate' it. There's one down somewhere in the metro Denver area that I wanted to point you to, but darned if I can find it at the moment.

 

Anyway - if you can find such a well studied reference point in your area, it's fun to see how your GPS responds. If you take the time (and at different days and times to shake up the satellite constellation configuration a bit) you will get a sense of two things: First, you will see how much your unit varies in its own report of the location when you're 'standing on' the reference point as you move away from it and back several times. Next, you'll see how, from day to day, the number moves around a bit, too. Another thing that can be interesting (and doesn't require a reference point) is to turn your device on, let it settle in for a few minutes, turn on a "Track" and sit it down and walk away for half an hour. Come back and stop the track and upload your track to some sort of mapping software. What you see is your device wandering a bit on the map, which is the drift in your unit's reporting of its location, even when it's sitting still. Gives you more idea of just how accurate things are or aren't out there in the real world.

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Find a USGS Benchmark whose official datasheet states that it's coordinates are "adjusted"....those coordinates are more accurate than your commercial grade GPS is capable of reporting. This is true for both horizontal and vertical (elevation).

The other standard type of coordinates is "scaled" which means they were measured or scaled on a map.....less accurate.

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Dunno, Grasscatcher. Some of those 'adjusted' ones were done an awfully long time ago, and probably aren't all as accurate as one would like for this kind of project.

 

As for 'scaled', wow -- you're right about that. Depending upon the map used and skill of the individual, they can be pretty close or quite a long way off. Not to be trusted for positional accuracy!

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Dunno, Grasscatcher. Some of those 'adjusted' ones were done an awfully long time ago, and probably aren't all as accurate as one would like for this kind of project.

 

As for 'scaled', wow -- you're right about that. Depending upon the map used and skill of the individual, they can be pretty close or quite a long way off. Not to be trusted for positional accuracy!

 

ECA,

Before you use opinion phrases like "Dunno Grasscatcher..." and "probably aren't....", you need to prove it to yourself just how accurate the "adjusted" coordinates from the specific BM's official datasheet are.

 

They are more accurate than any point that you can set, or accurately verify, with your commercial grade GPS.(or any of mine either)

 

Definitely a perfect place to check GPS accuracy.

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I say "probably" because it largely depends upon the date and/or a bit of luck on the part of the tech. Not all 'adjusted' benchmarks are equal. There's almost guaranteed to be a qualitative difference between the accuracy of a benchmark adjusted in 1992 from one adjusted in 2012. A sample follows, and the date shown at the very end (highlighted) should be considered relevant. While the CORS system provides obscene levels of accuracy, it had just started in the planning stages in 1992, the initial station build-out wasn't completed until 1997, and even then, recoveries that led to adjustments certainly didn't all use that system!

 

So yes, you have to be a little careful about assuming a particular level of precision on an 'adjusted' benchmark. May be great or may well not be a lick better than what your handheld will produce.

 

If I really wanted to nail something, I might head to one of the regional CORS sites! Access could be a bugger, though, unless you know somebody. I like Timpat's idea better.

Edit: Looking, and we still have two CORS sites in the neighborhood (Boulder and DIA). Would have guessed their might be one up north (Ft Collins?) but don't see one.

 

FQ0624******************************************************************

FQ0624 DESIGNATION - FRISCO

FQ0624 PID - FQ0624

FQ0624 STATE/COUNTY- AZ/COCONINO

FQ0624 USGS QUAD - HUMPHREYS PEAK (1983)

FQ0624

FQ0624 *CURRENT SURVEY CONTROL

FQ0624__________________________________________________________________

FQ0624* NAD 83(1992)- 35 20 46.83090(N) 111 40 40.60394(W) ADJUSTED

FQ0624* NAVD 88 - 3851.8 (meters) 12637. (feet)VERTCON

FQ0624__________________________________________________________________

FQ0624 LAPLACE CORR- -0.55 (seconds) DEFLEC96

FQ0624 GEOID HEIGHT- -22.51 (meters) GEOID96

FQ0624

FQ0624 HORZ ORDER - FIRST

FQ0624

FQ0624.The horizontal coordinates were established by classical geodetic methods

FQ0624.and adjusted by the National Geodetic Survey in August 1993.

Edited by ecanderson
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Probably...largely depends...bit of luck...almost guaranteed...

Words not displaying a high level of confidence in the subject being theorized on....

 

Theorize on this....ALL BM with adjusted coordinates have locations that are documented multiple times more accurately than your commercial grade GPS is capable of.

 

You don't use a spectrometer to measure a rope....

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It's not a question of confidence in the subject, it's a question of confidence / uncertainty in the measurement accuracy of any randomly selected 'adjusted' benchmark.

 

Benchmark "adjustments" have been being made over a considerable period of time, and the gear that has been available for that practice changed considerably over that same period of time, allowing for increasing accuracy as time went by. However, picking any adjusted benchmark at random, one cannot assume specific accuracy of the republished coordinates without knowledge of the method that was employed to take those particular measurements. There is no reason to assume that any particular adjusted benchmark from a pre-HARN and pre-CORS era will be any more accurate than what we see on a decent consumer grade unit now using best practices for measurement. It's likely, but it would be a bad assumption for any kind of testing purposes. I would agree that any new benchmark placed post-1987 using HARN would be good targets. On the whole, they're a lot easier to access and with a better view of the sky, too.

 

The whole thing went through several iterations of equipment build-out and increasing levels of accuracy. Here's a pretty decent description of the history. I don't know if you'll be able to review it directly without a login to the site, but it's free even if you do: https://www.academia.edu/1223247/Continuously_Operating_Reference_Station_CORS_history_applications_and_future_enhancements

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I think what amazes me is that over time, they were able to get down to accuracy for control stations down to some mm, and for vertical, they actually had to keep publishing new data for the reference sites that include subsidence of the structures where the antennae were located! Pretty impressive. The precision (digits after the decimal) used in the publishing of those data sets really does mean something! Gear that can accomplish that certainly would take all of the searching fun out of geocaching.

Edited by ecanderson
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One other item that gets forgotten at times when looking at benchmark pages ... NAD83 and WGS84 measurements keep drifting apart (long story there - one moves with continental drift and the other does not), and the benchmark data published as NAD83 will by nature vary somewhat from what is read on a receiver doing its work in WGS84. IIRC, that presently accounts for the better part of another 0.001 minute reading difference in the western half of the U.S. I've heard that in parts of California on the wrong side of some fault lines, they're drifting apart at about 2 inches per year. I never thought to ask, but surely the NGS NAD83 data isn't being continually adjusted for that, is it?

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I've heard that in parts of California on the wrong side of some fault lines, they're drifting apart at about 2 inches per year. I never thought to ask, but surely the NGS NAD83 data isn't being continually adjusted for that, is it?

 

It can't be. Those sorts of changes (land moving with respect to other land) cannot be fixed using a datum. That's why NAD83 has been turned into multiple datums depending on which continental plate you are on (one of the US, one for Hawaii, and one for Guam). The "main" NAD83 datum is fixed relative to the North American plate.

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In Montana we're lucky enough to have a fairly robust cadastral or plat system. Every private and public land parcel has been mapped (updated monthly) according to an aliquot part legal description describe in the warranty deed or certificate of survey. The plat grid is aligned to known points called Geodetic Control Points. These points have been precisely mapped using survey grade GPS recievers and are located in various densities across the state. There are several dozen within driving distance and I've visited a few with the same curiosity as others here: just how accurate can I expect Consumer grade GPS units (Garmin) to be? The results, with WAAS, GLONASS & GPS, using averaged waypoints, suprised me. I found myself within 2-3 meters (6-9 feet) of the pin/cap on the ground marking the control point in the majority of readings.

 

My own personal conclusions based on my results: If you give some consideration to how your GPS is positioned, are recieving 8 or more satellites with a good signal strength, allow a few minutes for the reciever to "settle", and average your position (waypoint averaging) you can achieve very good results. Waypoint averaging won't help you find a cache (would help to mark one) but as far as data collection goes it's a great tool. There are plenty of influencing factors that may negatively effect and reduce accuracy however, I'm not one to completely disregard consumer GPS uprecievers as inherently inaccurate. Give it a little thought and manage expectations based on site specific conditions.

 

I've loaded the Montana Geodetic Control Points into a POI database that can be downloaded from GPSfiledepot. If you live in Montana or plan to visit, it might be fun to locate a point near you and experiment for yourself. Or perhaps you can check with the agency that manages geo data in your state and find out if they have something similar.

 

Cheers!

Edited by yogazoo
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I'm using a Garmin Etrex 10. Lately, I've entered into "discussions" with CO's about the accuracy of their coordinates. Is there any way to test my GPS against an objective standard? Thanks.

Yes, and the photo above of a couple of benchmarks isn't necessarily going to help you, either. Benchmarks are often as prone to location error as any other point on the ground - some significantly so if they haven't been updated for years.

 

There ARE a very few spots that have been so thoroughly checked with high precision commercial gear that they can be depended upon to provide accuracy at least as good as the 0.001 minute level of precision that you will be seeing for a published cache. Just as a point of reference, at your latitude, every 0.001 in the E/W direction amounts to roughly 4 feet. Every N/S 0.001 amounts to roughly 6 feet. So no matter what you're trying to accomplish, you can't figure on getting any closer than that with 0.001 minute precision on anything.

 

Whether there are any 'reference points' in your area of Connecticut that have been studied so thoroughly as to be known to be within a 0.001 level of accuracy - well, I'm in Colorado, so I have no idea. Ask your fellow cachers if they have run across any such sites. If there are any, there's also a fair chance that someone has placed a cache there to 'commemorate' it. There's one down somewhere in the metro Denver area that I wanted to point you to, but darned if I can find it at the moment.

 

Anyway - if you can find such a well studied reference point in your area, it's fun to see how your GPS responds. If you take the time (and at different days and times to shake up the satellite constellation configuration a bit) you will get a sense of two things: First, you will see how much your unit varies in its own report of the location when you're 'standing on' the reference point as you move away from it and back several times. Next, you'll see how, from day to day, the number moves around a bit, too. Another thing that can be interesting (and doesn't require a reference point) is to turn your device on, let it settle in for a few minutes, turn on a "Track" and sit it down and walk away for half an hour. Come back and stop the track and upload your track to some sort of mapping software. What you see is your device wandering a bit on the map, which is the drift in your unit's reporting of its location, even when it's sitting still. Gives you more idea of just how accurate things are or aren't out there in the real world.

 

In Colorado between Denver and Cheyenne just to the west of the interstate there is a site...kind of up on a hill or rock as I remember it. I had about 4 Magellan Platinums and a 60 CSx in the truck and I tested them all and was really pleased with the results....2 of the Platinums were dead on....it was a nice location with a good view of the sky and horizon, I think there was a cache nearby which was my reason for stopping.

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Lots of great info in this thread. I've had a couple finds with the GPSMAP 64s where the unit literally put me right on top of the cache. Pretty amazing when you think about it; these are consumer-grade electronics that cost a few hundred bucks and rolled off an assembly line.

 

Heck, I can't find stuff within 9 ft. (3 m) accuracy in my own house. :lol:

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In Colorado between Denver and Cheyenne just to the west of the interstate there is a site...kind of up on a hill or rock as I remember it. I had about 4 Magellan Platinums and a 60 CSx in the truck and I tested them all and was really pleased with the results....2 of the Platinums were dead on....it was a nice location with a good view of the sky and horizon, I think there was a cache nearby which was my reason for stopping.

That's one I haven't visited, but is well within our 'map clearing' area. If you ever do recall the cache, let me know what it was and I'll try to locate the site you're referencing for a visit.
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Lots of great info in this thread. I've had a couple finds with the GPSMAP 64s where the unit literally put me right on top of the cache. Pretty amazing when you think about it; these are consumer-grade electronics that cost a few hundred bucks and rolled off an assembly line.

 

Heck, I can't find stuff within 9 ft. (3 m) accuracy in my own house. :lol:

There's days when I'd swear that there was some sort of HDOP Angel working on our behalf, too, but she comes and she goes. MOST of those really great days are when we're searching for a new collection of non-urban caches by one or more cachers who are very careful about how they take their measurements in the first place. In order to have a great 'Wow, these are close' day, you'll need:

 

1) COs who are exacting in their own method of placement. This is one game where it's definitely garbage in - garbage out. If the CO does a really good job, if you took all of the finders' errors, you should see a decently distributed circle around the COs coordinates.

2) A decent view of the sky, and one without too much multipath going on (these usually happen together). If you don't have that, neither you nor the CO are going to get a really great fix, and the error will large for both of you -- and caching karma being what it is, those errors will be in opposite directions on the day that you visit. Trees are pretty, but they are not your friends. Neither are 20 story buildings. Neither are canyon walls. There are places where even the best practices just aren't going to get you the kind of accuracy of a 'Wow' day. You'd better have a great hint, a good phone-a-friend network, or be prepared for a more thorough search.

3) A cooperative constellation. While the CO may have made multiple visits to try to decrease the impact of this variable, you probably won't. Get too many satellites too close to directly overhead, block a few really good ones out about 30 degrees above the horizon, and have another handful out practically AT the horizon, and it's going to be a tough day. Even though it's a determinate thing (good thing, or you'd be forever getting enough data to get a fix when you turn on your GPS), for caching purposes, the constellation might as well be random. Curious to know how good or bad it is on a given day in a given place? Here's a site that you can look back upon and stand on as an excuse for that little streak of DNFs:lol: http://satpredictor.navcomtech.com/ Of course, as I type that, it's presently down for the first time in all the times I've looked at it over the last couple of years. While a really crappy DOP day isn't very common, they do happen. That just means that for what usually only amounts to an hour or two, where they are in the sky will make it harder to get an accurate fix. In theory, addling GLONASS capability should help with this since it adds more birds to the sky, and increases the chances that enough of them will be in 'good' positions to help you lock your position down more tightly.

 

For one or two caches, you may have one of those 'stopped clock correct twice a day' experiences -- good old blind luck. You'll be standing at 0 feet and remarking at how great the coordinates are. Sometimes, the coordinates will actually stink, and your GPS, in the place, at that time, will be reproducing that stink faithfully, putting you right in the same spot. However, the odds of hitting a whole string of caches that way gets slimmer and slimmer. Chances of flipping 10 heads in a row and all that.

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You really can’t measure accuracy; you can only measure the precision of your GPSr. Accuracy is a human attribute and therefore cannot be quantified because it is a variable and a combination of skill plus luck. Precision is a machine attribute and can be measured because it is a built-in constant. For example, a pair of scissors (machine) makes a very clean and sharp cut (precision) but how well it cuts along a line (accuracy) depends on the user (human). An atomic clock (machine) is very precise time piece, but it will never tell the correct time (accuracy) if the user (human) doesn’t set it properly.

 

Likewise, a GPSr (machine) may display a very tight error circle (precision) but may still lead the user (human) far from the cache because neither the GPSr user or the cache owner (oh no, another human!) or both don’t know what they are doing or are just having a bad day or unlucky.

 

So how can you declare one GPSr (or clock, or pair of scissors) being more accurate than another when humans are involved? However, based on the information it receives, GPSr’s can calculate precision to a certain confidence level and displays it as an Estimated Position Error (EPE). There’s your measurement of precision. (Disclaimer: EPE calculations are proprietary and varies with manufacturers.)

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In Colorado between Denver and Cheyenne just to the west of the interstate there is a site...kind of up on a hill or rock as I remember it. I had about 4 Magellan Platinums and a 60 CSx in the truck and I tested them all and was really pleased with the results....2 of the Platinums were dead on....it was a nice location with a good view of the sky and horizon, I think there was a cache nearby which was my reason for stopping.

That's one I haven't visited, but is well within our 'map clearing' area. If you ever do recall the cache, let me know what it was and I'll try to locate the site you're referencing for a visit.

 

9 years does things.....its further north than I remembered, almost in Cheyenne.....interesting place.

Here is the link :

https://www.geocaching.com/seek/cache_details.aspx?wp=GC946E&title=cheyenne-gps-calibration&guid=78794e0a-d63b-4c8a-a3b7-30c4583a1fa7

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You really can't measure accuracy; you can only measure the precision of your GPSr.

Looked at one way, the precision of the GPSr is what it is, e.g., 0.001 minutes or 0.00001 degrees. etc. But I think you are considering it in its other form, which is what we'd call repeatability.

 

We are indeed discussing accuracy here. What one can attempt to measure are both accuracy and repeatability. We're trying to provide methods for seeing what kind of results occur for a particular unit by understanding as many of the variables as possible. Methods for testing each are different, and we've discussed them both. BOTH depend upon several different variables, most of which can't be controlled for, only understood and averaged out as best possible.

Edited by ecanderson
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In Colorado between Denver and Cheyenne just to the west of the interstate there is a site...kind of up on a hill or rock as I remember it. I had about 4 Magellan Platinums and a 60 CSx in the truck and I tested them all and was really pleased with the results....2 of the Platinums were dead on....it was a nice location with a good view of the sky and horizon, I think there was a cache nearby which was my reason for stopping.

That's one I haven't visited, but is well within our 'map clearing' area. If you ever do recall the cache, let me know what it was and I'll try to locate the site you're referencing for a visit.

 

9 years does things.....its further north than I remembered, almost in Cheyenne.....interesting place.

Here is the link :

https://www.geocachi...b7-30c4583a1fa7

Many thanks. We draw the 'map clearing' line at the border, and hadn't ever had a look at this one. One of these times, we'll go on up the rest of the way (not far!) and have a look at it.
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...What one can attempt to measure are both accuracy and repeatability. We're trying to provide methods for seeing what kind of results occur for a particular unit by understanding as many of the variables as possible. Methods for testing each are different, and we've discussed them both. BOTH depend upon several different variables, most of which can't be controlled for, only understood and averaged out as best possible.

 

I recently replaced an old electric clock mechanism with “Atomic Clock” movement. This clock uses a radio signal to auto-correct its time. It is very precise. However, I bent the minute hand during installation and now the clock is always two minutes fast. It is precise, it is repeatable, but it is not accurate.

 

Even if the hand wasn’t bent, being an analog clock, one must know the proper way to read the clock. If viewed from an angle the parallax effect would affect the accuracy of telling time. That is why old analog meters put a mirror behind the indicator to assure the reading is at ninety degrees thus mitigating human error.

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...What one can attempt to measure are both accuracy and repeatability. We're trying to provide methods for seeing what kind of results occur for a particular unit by understanding as many of the variables as possible. Methods for testing each are different, and we've discussed them both. BOTH depend upon several different variables, most of which can't be controlled for, only understood and averaged out as best possible.

 

That is why old analog meters put a mirror behind the indicator to assure the reading is at ninety degrees thus mitigating human error.

 

My favorite meter for trouble shooting is my old trusty Simpson 260 with the mirrored scale.....as you say its great when you're at odd angles to the display.

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I agree with both ecanderson and Capt. Bob that accuracy and precision are two distinct quantities; consequently, they are neither synonymous nor interchangeable. Also:

http://en.wikipedia.org/wiki/Accuracy_and_precision

 

..........

 

So how can you declare one GPSr (or clock, or pair of scissors) being more accurate than another when humans are involved? However, based on the information it receives, GPSr’s can calculate precision to a certain confidence level and displays it as an Estimated Position Error (EPE). There’s your measurement of precision. (Disclaimer: EPE calculations are proprietary and varies with manufacturers.)

 

Regarding EPE, which is quite similar in context the ICBM measure of precision known as CEP (circular error of equal probability):

https://en.wikipedia.org/wiki/Circular_error_probable

The difference is that CEP has the defined value of 50% of the impacts being within the circle while the manufacturers will not, as noted above divulge the percentage of values within the EPE defined diameter.

 

However, one can acquire their own data to determine the EPE if their GPSr.

 

DISCLAIMER: Note that regarding posts of similar technical issues that I have been characterized as having posted in a psuedo (un)scientific manner:

http://forums.Groundspeak.com/GC/index.php?showtopic=318508&view=findpost&p=5337463

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I still hang onto of those mirrored 'analog meters' since even with the long needle, it is more responsive (faster visual 'update', if you will) than my digitals when there's no chance of using a scope on something. Not very accurate OR precise when bouncing around, but at least you know something is happening <g>.

 

However, the clock analogy doesn't hold too well here, since with ONE exception, I've never seen/heard of a GPSr with anything resembling a static offset in one direction. At least in open sky, with lots of readings over time, readings will always tend to describe a circle around a center point where 'reality' exists.

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I think a lot of new (and some old) users don't have a real appreciation for what "EPE" means, even when it's defined by the manufacturer - because it's never a clear definition. That's because the secret sauce used to create the EPE figure shown on the face of the unit is the result of an algorithm that will be unique to each manufacturer's development team - and is something that a given team might even tweak over time (see below). When a CPE is being calculated, the author of that number will at least always specifies the result in "x% of the time, within y distance of the 'target'", and will tell you what x and y are. With a GPSr, the distance shown as the probable level of accuracy isn't something you'll see defined in the spec sheets. It, too, will probably boil down to something that approximates an "x% of the time, within y of the 'target'" answer but without any spec for x and y. But the end users often see an EPE number on the face of the unit and assume that it's the result of some hard physics instead of hard physics plus a bit of metaphysics. It's all to do with statistical levels of confidence in the current fix, and it's up to the individual coders to sort out how they want to play with the statistics to put an EPE on the screen.

 

As an example (and it would be possible but a bit inconvenient to demonstrate if you could swap code loads fairly quickly) I'd swear that the EPE of each of my three Oregon 450s is less optimistic than it was during some of the earlier firmware releases. I think most of us have seen this in the field when caching with friends with different models of Garmin, or different brands altogether. One can see some pretty divergent values within the same general space.

 

Then there's misunderstanding the results. Standing at 0 feet with an EPE of 8 feet is certainly no assurance that you are within 8 feet of the theoretical coordinates (there's that x% of the time factor), much less within 8 feet of a cache, especially one whose owner did a haphazard job of getting the coordinates that were posted in the listing.

 

About all you can say about EPE is that generally, less is better, and that there is a very high likelihood of a major difference in the quality of the fix when you see an EPE of 60' vs. 10'. While these aren't 'hard' numbers, they usually do hold a real relative significance, and big differences are well worth paying attention to in the field.

Edited by ecanderson
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...

However, the clock analogy doesn't hold too well here, since with ONE exception, I've never seen/heard of a GPSr with anything resembling a static offset in one direction. At least in open sky, with lots of readings over time, readings will always tend to describe a circle around a center point where 'reality' exists.

 

The clock analogy was used to illustrate the machine versus human issue. The clock isn't accurate, it's the clock's fault. People tend to blame the machine first. Like the golfer who tosses his putter into the lake and can’t accept it’s not the tool it’s the user who missed the putt. The putter was precise, it was the golfer who wasn't accurate. The machine's precision doesn’t change if setup properly (human), operated properly (human) and maintained properly (human). The GPSr uses the same algorithm for all its calculations, it doesn’t change, but humans enter questionable data, operate it under poor conditions and tend to drop things or neglect things like drained batteries, for example.

 

As for less is better for EPE, I have to say it depends. Usually it represents a 95% confidence level but is that always true? The GPSr can only assess the error based on things it knows such as satellite orientation (DOP), receiver errors (noise) and signal bounce. Without a WAAS signal it is unaware of ephemeris corrections, satellite clock errors and atmospheric (ionosphere and troposphere) errors. With WAAS data the EPE circle may actually become larger, which is a good thing. It is a better, more realistic assessment of conditions.

 

I agree the EPE is influenced by the calculation algorithm and varies by manufacturer and their software versions (dare I say, even marketing?), but that’s why the first “E” in EPE is for “Estimated”.

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As for less is better for EPE, I have to say it depends.
Which is why I said "generally, less is better"
Usually it represents a 95% confidence level but is that always true?
I have no information from ANY handheld consumer GPSr manufacturer that the 95% actually applies to their particular algorithm on a particular model or even firmware level. That's the problem. Two teams can take exactly the same information and depending upon their own preferences and experience and 'suggestions' from the marketing department, arrive at a different set of numbers. So it remains a somewhat useful relative measure and that's about all. I would imagine that some 'estimates' are better than others. As to "signal bounce", there are claims by some chip manufacturers that they manage multipath issues better than the competition, but it would be nice to see a white paper that defends those claims by drawing hard comparisons between the performance of different chips using some of the different algorithms (I've seen at least half a dozen different approaches explained). We'd be smarter for it, I think. Probably out there somewhere in someone's desk drawer.
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As the manufacturer will not divulge the the true meaning of the value of the EPE displayed, I was inspired to determine that for my GPSr as follows:

1. I selected a spot in front of my house with decent, typical view of the sky,

2. To have the EPE not be determined by a uniform set of satellites in almost the same positions, I did not gather a set of waypoint data one second apart. Instead, I obtained one a day ensuring that various combinations of satellites in various positions were observed.

3. For each reading, I waited a few minutes at the position, allowing the readings to stabilize and then recorded a waypoint consisting of an average 20 determinations.

4. In addition to recording the latitude and longitude at each reading, the displayed EPE waa also recorded.

5. To be on the conservative side, I gathered 20 points on 20 almost consecutive days.

6. The latitudes were summed and divided by 20 to determine the average; similarly for the longitudes.

7. With these averages characterizing the average of the calculated positions, the N-S and E-W distances of each location from the average were then calculated. Then, the radial distance for each point from the average was calculated. Lastly, the average of the 20 values of the EPE were averaged.

8. Comparison of the number of radial distances less than the average EPE, divided by 20, provided the characterization of the percentage of readings within the displayed EPE value.

 

I later gathered another 20 points and recalculated with all 40; however, the additional 20 provided an inconsequential variation.

 

DISCLAIMER: That noted in my previous post may still apply in the context that I might still engaging in pseudoscience.

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......

 

However, the clock analogy doesn't hold too well here, since with ONE exception, I've never seen/heard of a GPSr with anything resembling a static offset in one direction. At least in open sky, with lots of readings over time, readings will always tend to describe a circle around a center point where 'reality' exists.

OK, I would term the static offset in one direction as a bias in the collected data. (This would be like always reading the volume of liquid in a graduated cylinder in a downward direction.)

 

Consequently, it the bias in a set of observed data was zero, then the average of that observed data (of a statistically significant quantity of data) would be coincident actual location of the GPSr.

 

Recall, that accuracy is the difference between one observed value and an accepted, known, good, reference value. Here the single observed value is the average of the set of observed values and the accuracy will be 100% perfect if the bias is zero.

 

Regarding precision, the quantitative value characterizing repeatability, it is independent of the value of accuracy. Regardless of the inherent accuracy of the instrument, the precision is only 100% if all the readings collected are identical.

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And? The envelope please? How did the EPE on the unit correlate with the actual errors, on average? How close to the 95% benchmark did you achieve? Which unit were you using at the time? Inquiring minds want to know.

Again bad question, errors relate to accuracy. EPE relates to precision or repeatability. As noted above in my prior post linking the Wikimediaearticld, accuracy (actual errors) and precision are two different quantities. Now, accepting your speculation on zero static offset, all devices calculate location from received data in an error free mode. Consequently, any lack of precision, as quantified in the EPE, is due to the random errors in the transmitted data as opposed to inconsistencies in the devices algorithms.

 

OK, late tonight, back tomorrow. (I need to locate the standard deviation resulting from my repeatability data, EPEs.)

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Perhaps badly worded? Your displayed EPE provides an expected worst case error radius around a theoretical position (yes, some % of the time). If you looked at all of the actual darts on the board and their standard deviation, how did it look when compared to the displayed EPE values?

 

Not sure I'd go so far as to say '..due to the random errors in the transmitted data.'. The clocks on those birds are pretty good and errors corrected. OTOH, there are plenty of opportunities for errors in the received data -- propagation errors due to [fill in blank with several possibilities of geometry, reflections and S/N ratio].

 

Over time, any deviation from actual coordinates should be random, not fixed in any particular direction. So without such 'bias', the circle eventually described by a great many data points should eventually place the 'true' coordinates at the center. The EPE will ideally describe the probable radius of that circle at the current moment. That's where I got wrapped around the axle with the use of the word 'precision' in this case. For other cases, one can legitimately discuss precision that is represented by the spread of points that are offset from an ideal point (a shot group the size of a quarter, but low and to the left by 4" would be precise, but not very good for scoring), or as in this special case, one can discuss the precision of points that by rights should remain spread around the 'true' centerpoint. EPE in this instance then implies a centerpoint. To beat the prior analogy to death, this is a case where the centroid of the shot group is right on the bullseye, with the EPE telling us how far out into the scoring rings we're likely to be. To me, that's a somewhat different discussion than simple precision, because precision doesn't imply the proximity to some true center point, just that the data points are in some proximity to each other.

 

Wow - reading that back, it's a mess to follow. I'm a real fan of white boards.

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Five or six years ago I found two sources list 10-12? factors affecting gps accuracy. Today I found this on the Trimble web site http://www.trimble.com/gps_tutorial/howgps-error2.aspx

 

Summary of GPS Error Sources

Typical Error in Meters

(per satellites) Standard GPS, Differential GPS

Satellite Clocks 1.5, 0

Orbit Errors 2.5, 0

Ionosphere 5.0, 0.4

Troposphere 0.5, 0.2

Receiver Noise 0.3, 0.3

Multipath 0.6, 0.6

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Five or six years ago I found two sources list 10-12? factors affecting gps accuracy. Today I found this on the Trimble web site http://www.trimble.com/gps_tutorial/howgps-error2.aspx

 

Summary of GPS Error Sources

Typical Error in Meters

(per satellites) Standard GPS, Differential GPS

Satellite Clocks 1.5, 0

Orbit Errors 2.5, 0

Ionosphere 5.0, 0.4

Troposphere 0.5, 0.2

Receiver Noise 0.3, 0.3

Multipath 0.6, 0.6

Quite interesting. Many years ago I was taught to perform cause and effect analyses by using the two basket methodology. Using this approach, I put all similarly defined variables in one basket and all others, in the second basket.

 

Applying that here, I assume two baskets, one of error sources internal to a subject GPSr, and the second basket contains all others (in this case this would be error sources external to a GPSr. Specifically:

Basket of Internal Sources: I assume that the source of the Receiver Noise error is internal to the GPSr, and

Basket of External Sources: I consequently assume that the other error sources listed are external the the GPSr.

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Dope slap to self.

 

In a nutshell, this is a special case where over the long term, the data should group around a fixed center point (assuming no weird bias), so it is a case where level of precision also implies level of accuracy.

Yes, I agree, well, not with the slap.

 

However, it is an interesting conjecture to use the result (average center point) of a number of readings that determine precision to characterize the accuracy. In so doing, it seems that the definition of accuracy is being ignored as it states accuracy as the result of subtracting one experimental data point from a known good, reference value. For example, in target shooting the difference between a single bullet hole and the center of the bulls eye constitutes the accuracy. In contrast with multiple shots, the minimum circle which includes all the shots is called the group and is the quantification of repeatability. Note, that it may be rare but not impossible that rifle A may have a group of 5" in diameter the center of which is 3" from the center of the bulls eye while rifle B has a group of 3" in diameter but whose center is 5" distant from the center of the bulls eye. Consequently, how could one not state that rifle A is more accurate while rifle B is more precise using the definitions stated in Wikipedia referenced above?

 

On the other hand, while using the definition of accuracy rigorously, I do feel it reasonable to state that the average location of a statistically significant number of readings (devoid of non-random errors as indicated by the absence of bias) does indicate true location of the GPSr although there is no standard reference point that may be used to determine true accuracy in front of my house.

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And? The envelope please? How did the EPE on the unit correlate with the actual errors, on average? How close to the 95% benchmark did you achieve? Which unit were you using at the time? Inquiring minds want to know.

Ahhhh...what goes around comes around. I this thread, post #26, you previously asked for quantitative data:

http://forums.Groundspeak.com/GC/index.php?showtopic=318508&view=findpost&p=5336703

However, I was the only one in the thread to post quantitative data:

http://forums.Groundspeak.com/GC/index.php?showtopic=318508&view=findpost&p=5337093

and also in posts #35, #38 and #45 of that thread I presented quantitative data.

 

Nevertheless, in post #41 of that thread I was accused of practicing pseudo-science in my endeavors to obtain quantitative data to characterize the functional performance of my GPSr. Well, once burned - twice shy, I have learned my lesson and will no longer post quantitative data that I have created. I am afraid that a similar posting on my part may provoke another similar castigation of my work as pseudo-scientific data development.

 

Please note that I am not afraid of such on a personal basis; however, I want to obviate someone from humiliating themselves in the eyes of others for embarking on such mistaken denigration of my outstanding work performed following the true Grand Method of Science:

https://en.wikipedia.org/wiki/Philosophy_of_science

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Ah yes, I remember that exercise from the old thread. Nothing like presenting hard evidence to back up a point and having it called "dribble" (not even the intended word, I don't think). Actually, if you're linking to Wiki, this one might be even more apropos >> https://en.wikipedia.org/wiki/Foundations_of_statistics

 

Would still be interesting to know how your particular unit fared vs. the displayed EPEs. I never do find enough time to perform all of the experiments that I'd like to perform. At present, I'm involved in two precision/accuracy projects not unlike what we've been discussing in our analogies.

 

Picked up an old Finnish Mosin where the 'precision' goes all to crap after about 5~10 rounds until it cools off. Someone had 'sportsterized' it and obviously knew squat all about proper bedding. Got it dirt cheap, though (<$100), so I guess I can't gripe. It's fixable. The other project is a steel match timer that includes count/timing for each round right up to the stop plate time. Our 10 x 100yd indoor range is available only to LEO qual and training during the week, but we open to the public on weekends, and figured we make up a fun mini Steel Challenge for them. I'm having some clock issues that need to be resolved. Once in a while, there's a stutter that throws things off by +0.01s. Not close enough since this stuff is normally timed to the nearest 0.01s. In the aggregate, it would probably never matter in 100 years, but it'd be just my luck... I'd be the only one who knew, but I don't think the participants will care if we call it precision or accuracy, they'll want it 'right'!

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As for less is better for EPE, I have to say it depends.
Which is why I said "generally, less is better"
Usually it represents a 95% confidence level but is that always true?
I have no information from ANY handheld consumer GPSr manufacturer that the 95% actually applies to their particular algorithm on a particular model or even firmware level. That's the problem. Two teams can take exactly the same information and depending upon their own preferences and experience and 'suggestions' from the marketing department, arrive at a different set of numbers. So it remains a somewhat useful relative measure and that's about all. I would imagine that some 'estimates' are better than others. As to "signal bounce", there are claims by some chip manufacturers that they manage multipath issues better than the competition, but it would be nice to see a white paper that defends those claims by drawing hard comparisons between the performance of different chips using some of the different algorithms (I've seen at least half a dozen different approaches explained). We'd be smarter for it, I think. Probably out there somewhere in someone's desk drawer.

 

You are correct, I don’t know if a 95% confidence level is used by all manufacturers and who knows what evil lurks in the heart of marketing personnel (assuming they have a heart). However a 2-Sigma span gives a good representative sample of the dataset. A normally distributed curve depends on the data set from which a standard deviation unit can be derived. A 1-sigma (68% or one standard deviation) sample would produce a very small error circle because of the narrow span near the top of the curve. Also, a 3-sigma (99.7%) would make a huge error circle and it would include outliers that really should be filtered out. Therefore, 2-Sigma (95%) seems appropriate.

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Five or six years ago I found two sources list 10-12? factors affecting gps accuracy. Today I found this on the Trimble web site http://www.trimble.com/gps_tutorial/howgps-error2.aspx

 

Summary of GPS Error Sources

Typical Error in Meters

(per satellites) Standard GPS, Differential GPS

Satellite Clocks 1.5, 0

Orbit Errors 2.5, 0

Ionosphere 5.0, 0.4

Troposphere 0.5, 0.2

Receiver Noise 0.3, 0.3

Multipath 0.6, 0.6

Quite interesting. Many years ago I was taught to perform cause and effect analyses by using the two basket methodology. Using this approach, I put all similarly defined variables in one basket and all others, in the second basket.

 

Applying that here, I assume two baskets, one of error sources internal to a subject GPSr, and the second basket contains all others (in this case this would be error sources external to a GPSr. Specifically:

Basket of Internal Sources: I assume that the source of the Receiver Noise error is internal to the GPSr, and

Basket of External Sources: I consequently assume that the other error sources listed are external the the GPSr.

 

After reading your post I had a thought. Because I feel it is impossible to quantify accuracy (because of the user variable), perhaps a comparison is the only reasonable method. A test that negates as many uncontrollable variables as possible would test just the units themselves.

If two different GPSrs that have been correctly setup, are placed on the ground, with open access to the sky and oriented to maximize their antenna radiation patterns, i.e. helical-vertical and patch-horizontal, most uncontrollable variables would cancel out including with the biggest potential variable HDOP. It would measure only how well they deal with multi-paths receptions and effects of the receiver.

If left to run for fifteen minutes at a sample rate of five seconds, 180 track lines would be displayed. The “birds nest” of lines and EPE would visually indicate the precision of each unit under similar conditions. A more detailed analysis would require the data to be downloaded to a spread sheet, the mean determined (RMS), standard deviation, and the variance from the mean at the 2-sigma (95%) level for each data set. The results would indicate which unit performed best. Just a thought, I can’t afford two GPSrs.

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Not by coincidence, four(4)Drok inline USB V/A/P/C testers arrived in my mailbox yesterday. I had considered making at least two of them stocking stuffers for others, but am now getting greedy.

 

So while some folks are only tinkering with personal knowledge of statistics lore (plus Wikipedia), I am staring at blue and red LCD displays of USB electrical values and coordinate point tracking while simultaneously disabling USB power to GPS devices and causing them to show zero(0V) power draw while still sending an nmea string to my mapping software display which will turn all red if I let the tracking run long enough.

 

Bottom line: I suspect that those who live in glass houses on mountaintops at an elevation above the tree line may not have nearly as much fun as those located in a valley of trees.

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....... Just a thought, I can’t afford two GPSrs.

Capt. Bob, at first glance, I agree with all but one consideration in your post. I can afford a second GPSr. However, my granddaughter reminded me that such a purchase would result in a decrement in her inheritance, so a side-by-side is off the table.

 

Addressing the issue of determining accuracy without access to a known, good, acceptable, reference point, I have done this:

1. I have collected 40 data points, after waiting for sufficient stabilization, at my home (having reasonably open view of the sky).

2. Documenting the data on a spreadsheet and plotting them on an x-y (or NS-EW) plot, I see no strong directional bias (essentially, the number in each of the four quadrants is not all that unequal).

3. Consequently, I assess all the differences in location to be the result of random errors.

4. They do resemble a normal distribution in that the density of the points is higher at the center of the family of point and such density decrease with distance from the center.

5. Therefore, I conclude that in the absence of bias and the dominance of random effects that the center of the family is very representative of a bona fide reference point, if there was one.

6. I further conclude that the random errors are the result of conditions external to the GPSr. That is, the internal characteristics of the GPSr, do not propagate errors, neither biased nor random.

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