# accuracy thought

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I have been reading alot about accuracy. My question/statement:

Let us say you set a way point and your gps says accuracy within 20ft. Later you go back to find that way point and you gps again says accuracy within 20ft. At that point couldn't you be up to 40ft off your point, 20ft the first time + 20ft the second time = 40ft.?

What about geocaching. If the person placing the cache was within 20 feet of accuracy and you go to find it and you are within 20ft accuracy again couldn't you be up to 40ft off.

Averaging may help this but how accuarate can you really be?

Ross

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You've hit the nail exactly on the head. Usually my GPSR says accuracy of about 20 feet on a good day, 30-32 under not so good conditions. Those errors are compounded unless the hider has auto-averaging (seekers hate that feature, but that's another thread).

There are two schools of thought for GPSRs that don't auto-average. One common theory is that you can increase accuracy by taking multiple readings, with turning the unit on and off, walking away from the cache, etc., and then average the numbers (either throwing out highs/lows and numeric averaging or visually averaging via graph paper).

Another school of thought is that this is just averaging possibly bad data, and that to truly increase the accuracy, you should revisit the cache on a different day, during a different time of the day and include those coordinates in your averaging as well.

The best that we can do is hope that our coordinates are as accurate as possible, and that the same circumstances are there for the seekers.

But then, if everything was 99.999% accurate, where would be the fun of the hunt?

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quote:
Originally posted by Markwell:

But then, if everything was 99.999% accurate, where would be the fun of the hunt?

I just did the math - The earth is about 24,800 miles around at the equator. A GPS is accurate to, let's call it 20 feet.

That's 99.99998% accurate, and I still can't find a tupperware buried under leaves!

Another \$.02 in the pot.

Jerry.

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RLO, in theory it can work like that but like accuarcy specs the chance of it occuring is based on statitics. But it does have a name, Repeatable Accuracy.

Cheers, Kerry.

[This message has been edited by Kerry (edited 06 October 2001).]

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caching, accuracy is a red herring; it actually doesn't matter at all. What matters is the precision of the GPS fixes. (If everyone was 137.12 meters off, but everyone was off that very same distance in the very same direction, it wouldn't matter at all; however, if everyone is off 10 meters in a random direction, you could have up to a 20 meters of collective error due to that lack of precision*.)

*All you statisticians obviously know that there really isn't a "maximum positional error", but rather, there is a nice probability curve there that tapers off toward 0. The fixes *could* be off a whole lot more, but the probability of that happening is small enough to be irrelevant, especially with factors like sub-optimal reception thrown in.

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if the earth were compared to a haystack, and geocaches to needles, i'd say that gps recievers do a fantastic job most of the time!

the fact that anyone using one of these things can find anything just amazes me, if only there was a way to make this work with car keys, the person that figures that trick out will rule the world!

and if anyone uses my idea and does make it work, my cut should be at least 15%...lol

[This message has been edited by Elwood (edited 06 October 2001).]

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From the logs on every cache web page I have looked at, the number of smiley faces (founds) overwhelmingly outnumber the number of sad faces (not founds).

Sure there are other factors that go into successfully finding a cache, but what better way to gauge GPSR accuracy than these actual results?

If you were mapping or surveying, precision and accuracy would be more of an issue. But for geocaching, getting within 20 or 40 feet works just fine.

My opinion is like most others - be amazed at the accuracy of these small devices, and don't sweat about the last few feet.

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RLO writes:

Let us say you set a way point and your gps says accuracy within 20ft. Later you go back to find that way point and you gps again says accuracy within 20ft. At that point couldn't you be up to 40ft off your point, 20ft the first time + 20ft the second time = 40ft.?

Response:

Yes you could, or even more, depending on the meaning of the accuracy number, or Estimated Position Error, as it is called. Averaging can help significantly, either by using the averaging built into the GPS, or by taking several independent position readings at least 10 minutes apart (30 minutes or more is even better). The error is reduced by dividing by the square root of the number of independent readings. Averaging 4 independent readings would cut the error in half, 16 would cut it to 1/4. But when I average readings I also try to use only readings which have a low EPE. The EPE will vary primarily with the number and position of the satellites *received* by your GPS. This is why a good antenna and receiver make things easier. Also, the EPE means different things for different GPS units, there is no standard way of computing this. For some units it may mean average error, others may use 95% confidence interval, and some older units, programmed before SA was turned off, may overstate the error by a large factor. For practical purposes, with good satellite geometry and reception of 6 or more sats, the *minimum* error level is about 15 feet on a 95% confidence interval.

RLO writes:

What about geocaching. If the person placing the cache was within 20 feet of accuracy and you go to find it and you are within 20ft accuracy again couldn't you be up to 40ft off.

Response:

Yes, this is the same as the example above.

FWIW,

CharlieP

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So far, with each of the 7 caches found to date, our Garmin eTrex Legend has brought us within 7 feet of each cache. And a few have been right under my feet! I think the system is working just fine!

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I know this has been discussed in the past, but add my vote for changing the coordinates to decimal degrees shown on the geocaching pages.

Decimal Degrees (ddd.ddddd) have a 3ft precision circle, where the current method of Degrees and decimal Minutes (ddd mm.mmm)have a 6ft precision circle.

This would at least make the coordinates more accurate!

Thomas

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quote:
Originally posted by tcchap:

I know this has been discussed in the past, but add my vote for changing the coordinates to decimal degrees shown on the geocaching pages. This would at least make the coordinates more accurate!

Thomas

Provided the person hiding the cache had precise coordinates. With a REPORTED error of 20 feet most of the time, what difference does an additional 3 feet make.

And, that is only true if you go out to a far enough decimal point. N43.5° is the same as N 43° 31.485. Which of those is more accurate?

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I know! How about we all go and read the accuracy vs. precision explanation on http://www.bartleby.com/64/C004/003.html . I can say that my cache is at 31.010023045782108934892471357 N, 90.892235471976231583132598623 W, but it doesn't matter a plug nickel; since the receiver only has so much precision, all those extra numbers are 100% fictitious.

It doesn't matter how many digits you show if you don't have the precision. The whole dd.ddddd/dd mm.mmm/whatever debate is pointless. It may make you feel like you're using better numbers, but it's not. EOT.

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quote:
Originally posted by ClayJar:

Repeatable Accuracy? We science and engineering people have a word for basically that: precision.

Yes! To finally hear someone state it correctly! You should hear the debates we get into in the air rifle forums on precision and accuracy.

My question is can something have high accuracy and low precision? I do not think the accuracy can be state as any better than half the highest precision. So if your GPSR only reads out in whole degrees, it could never be stated to be more accurate than +/- 0.5 degrees. It could actually be more accurate in a single measurement but you would not be able to tell because you would not have the degree (ahem) of confidence without the precision

Lou

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quote:
Originally posted by ClayJar:

Repeatable Accuracy? We science and engineering people have a word for basically that: precision.

Yes! To finally hear someone state it correctly! You should hear the debates we get into in the air rifle forums on precision and accuracy.

My question is can something have high accuracy and low precision? I do not think the accuracy can be state as any better than half the highest precision. So if your GPSR only reads out in whole degrees, it could never be stated to be more accurate than +/- 0.5 degrees. It could actually be more accurate in a single measurement but you would not be able to tell because you would not have the degree (ahem) of confidence without the precision

Lou

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quote:
Originally posted by ClayJar:

Repeatable Accuracy? We science and engineering people have a word for basically that: precision.

Then for GPS people who should have an interest in Positioning Accuracy which for most here includes mostly Repeatable Accuracy but the others such as Predictable (somtimes referred to as absolute) and to a lesser extent Relative.

In the context of this discussion the clear distinction between "Repeatable Accuracy" and "Precision" is that precision is the measure of how close a single position is to other measures of the "same" quantity and normally done using the same device at the same time, same input conditions, same methods etc. Significant digits also have a bearing on the "preciseness" as a position can have high accuracy but low precision which is a reflection of how GPS "Positioning Accuracy" is defined and in particular Predictable Accuracy which is how close a position solution is to the truth.

"Repeatable Accuracy" is the difference of a position when compared to a "previous independent" determination of that position. Repeatable accuracy is the most common form of accuracy involved when dealing with simple waypoints. In other words the accuracy that Geocaching basically relies upon.

Repeatable Accuracy is therefore basically comparing 2 different time frames where as Precision is over a single period of time relative to the "mean of the positions" within that same period of time. The precision solution spread can be wide while the accuracy can be close to truth (slightly different to a gun fellows).

Prior to SA being terminated GPS Repeatable Acucracy was specificed as 141 metres @ 95%. The new spec (with SA terminated) should not be that far from being released.

Cheers, Kerry.

[This message has been edited by Kerry (edited 06 October 2001).]

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Interesting, Kerry. So let me see if I understand this. "Repeatable accuracy" is basically the overall precision of the entire Global Positioning System (taking into consideration various receivers at various times under various possible conditions), while "precision" would generally be applied to a single GPS receiver taking multiple measurements of a certain location?

(As for Lou C's question about high accuracy and low precision, when science types talk about accuracy, they are generally talking about averages. For an example of low precision but high accuracy, there's the joke about a scientist practicing his archery: His first shot just hit the top of the target. He corrected for his second shot, but it hit right of the bull's eye, and his third hit on the left. He pulled back and let the fourth arrow fly, and as it just hit the bottom of the target, he jumped in the air and ecstatically shouted, "Wow! A Bull's eye!")

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Myself, I would like to know how much the time of day has to do with either accuracy or

precision. In all things being equal, the same style of GPSR with the same style of

batteries, etc etc, two different people on both ends of the cache game.

Look at it this way. I plant a cache at 8:00 am with say, nine birds on the screen. You come along several days later at 6:00 P.M. and have nine birds showing. You have a tough time and e-mail me and say my cords are off by say somewhere around fifty feet. I, being the nice guy that I am, go back out the next day at 8:00 am again and find my cords are just the same as before.

I e-mail you that I was right on with my stats and that you might want to try it again. You, being the nice person that you are, wonder where things might have been off, go back after work and find that your numbers are right. My thought is that we

are both right, but with the nature of the beast being we are using eighteen different birds, things will be off. Close enough for a cruise missile, but not enough for a Tupperware.

Anyway, that is my opinion on it, for what it is worth. Try it on a close cache at different times of the day and see where your numbers plot out at. TTFN, logscaler

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quote:
Originally posted by ClayJar:

... when science types talk about accuracy, they are generally talking about averages.

Well, only if they state it as the average accuracy. Accuracy is really how close something is to the actual thing (coordinate, voltage, or bulls eye). In the case of the archer ClayJar mentioned, his average accuracy might mathematically add up to zero but his shooting is terrible. (This is another example where averages really are not all that good). The root-mean-square of the accuracy would really be a better measurement of the archer's shooting.

As for logscaler asking about measurements at different times, I would think the satellite positions would be rather random at the same time of any day. So a measurement at 8 AM one day might use a different mix of satellites than a measurement at 8 AM another day.

Lou C

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ossible conditions), while "precision" would generally be applied to a single GPS receiver taking multiple measurements of a certain location?

Clayjar, based on the pure definitions of Accuracy & Precision (but not all precision definitions) I understand the analogy of the target scenario.

Maybe the following definitions straight from the GPS Standard Positioning Survice Specification Signal Specification would be a better starting point. This document (1998)is currently in the process of being re-written mainly to take into account (I understand) termination of Selective Availability. I could e-mail it (quite large) if you would like to review it.

Standard Positioning Service Performance Characteristics ? Annex B (in part only)

Given that coverage is provided, the service is available and all satellites are performing within reliability tolerances, GPS position solution accuracy represents how consistently the receiver's output conforms to an expected solution. Users view accuracy in many different ways, depending on their application. To accommodate the majority of users' needs, GPS positioning accuracy is defined in the Signal Specification from four different perspectives:

* Predictable Accuracy,

* Repeatable Accuracy,

* Relative Accuracy, and

* Time Transfer Accuracy.

Each of these aspects of GPS accuracy are described in more detail below. Figure 1-2 compares and contrasts the four different ways of viewing GPS accuracy as it is defined in the Signal Specification.

Predictable accuracy represents how well the position solution conforms to "truth". Truth is defined to be any specified user location where the position is surveyed with respect to an accepted coordinate system, such as the World Geodetic System 1984 (WGS-84) Earth-Centered, Earth-Fixed (ECEF) Coordinate System. GPS was implemented to specifications that are stated in terms of predictable accuracy. Predictable accuracy is a measure used by those who are concerned with how well they can position themselves relative to a known, surveyed location. Factors which affect predictable accuracy include geometry variations unique to a given user location, and the sample interval over which measurements are taken.

Repeatable accuracy is a measure of position solution consistency relative to a user's previous position solution. Users who are interested in returning to points where they previously used GPS to determine their position will rely upon GPS repeatable accuracy performance. Repeatable accuracy varies primarily as a function of time between measurements.

Also the following link is one attempt I had at trying to practically outline the effects of Repeatable Accuracy using real data. Please note it is based on data prior to May 2, 2000 (pre SA) but the "principle" still applies.

Cheers, Kerry.

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quote:
Originally posted by Lou C:

As for logscaler asking about measurements at different times, I would think the satellite positions would be rather random at the same time of any day. So a measurement at 8 AM one day might use a different mix of satellites than a measurement at 8 AM another day.

Lou C

LouC, all things being equal the same satellites will be in the same positions at "about" the same time each day if the approximate 4 minute progression in orbit time is taken into account.

In reply to Logscaler's original query Logscaler's thought is correct, you are both right if those measurable quantities fall within the defined and outlined GPS accuracy specifications remembering GPS is a global utility and hence there are specific minimum conditions to meet. The system is dynamic and conditions which occurred today at say 8am may or may not occur tomorrow at 8am actually may never occur again but time of day can matter (see hastily compiled link) http://www.cqnet.com.au/~user/mattk/gps/gps_plan.htm . The statistical nature and type of the accuracy specifications allows a user to measure and quantify different types of accuracy outcomes against these standards. I being a third person could possibly come along (similar GPSR and all) when there were only 5 satellites visible and get a different result again (still within specifications). The thing is, that result could be a ?stronger? result than either yours or your mates but at this point nobody knows which is ?more right? than the others.

You and your mate as you outlined are working within Repeatable Accuracy specifications. Now if some nice person came along with the gear that could locate your cache to say sub centimeter level (basically absolute type world wide position) then you and your mate (and I) could compare co-ords in terms of Predictable Accuracy (to a position of ?truth?). General GPS specifications are quoted in Predictable Accuracy terms and Repeatable Accuracy will always be ?less accurate? (rarely equal too and certainly never better) than Predictable Accuracy.

Cheers, Kerry.

[This message has been edited by Kerry (edited 07 October 2001).]

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quote:
Originally posted by Kerry:

Maybe the following definitions straight from the GPS Standard Positioning Survice Specification Signal Specification would be a better starting point. This document (1998)is currently in the process of being re-written mainly to take into account (I understand) termination of Selective Availability. I could e-mail it (quite large) if you would like to review it.

Oooh! I love reading technical things! (Actually, I tend to read just about anything, but I prefer technical things and sci-fi.) If you wouldn't mind sending it my way, I would be very appreciative. (The excerpt you posted was quite informative.)

My e-mail address (for GPS-related topics) is "GPS@mygeocachingnickname.com". Of course, as you well know, my geocaching nickname is ClayJar (which is the same name I use just about everywhere else, including on my license plate).

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quote:
Originally posted by ClayJar:

Oooh! I love reading technical things! (Actually, I tend to read just about anything, but I prefer technical things and sci-fi.) If you wouldn't mind sending it my way, I would be very appreciative.

Has been done. Sorry can't help with the sci-fi but I think you'll find it interesting even if not being all that technical.

Yell if it doesn't find you and we'll "repeat" the process.

Cheers, Kerry.

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