# Waypoint Averaging Method

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My GPSr doesn't do waypoint averaging. So when I place a cache, I take about 8-12 readings by walking several feet away and returning to the cache. At first, I took an average of all the coordinates, but I realized that if there was one that was way off, it would distort the average. Instead lately, I've been using the coordinate that appears most often. For example if I get ...388, 386, 388, 387, 391, 388, 387, 382... I'd use the 388.

My question is, which method do you think is the most accurate. The actual average, or the most frequent occurring number?

In the example you used...

388, 386, 388, 387, 391, 388, 387, 382...

I would toss out the high and the low, 391 and 382, then average the rest. Which would produce 387.

Regards,

Tedoca

I save all the points, throw out ones that are way off from the others, and pick a visually weighted point in middle of all of them.

When possible, I also try to take readings at a different times of the day.

Last but not least... If I get a lot of comments that coordinates are off, I go back and take new readings.

I use the value that will result in the lowest sum of squares.

I get 387.125 ...

(388-387.125)^2=0.7656

(386-387.125)^2=1.2656

(388-387.125)^2=0.7656

(387-387.125)^2=0.0156

(391-387.125)^2=15.015

(388-387.125)^2=0.7656

(387-387.125)^2=0.0156

(382-387.125)^2=26.265

SUM=44.875

Any other value will result in a larger SUM. You can do this 2-dimensionally, too.

[This message was edited by DisQuoi on April 16, 2002 at 06:14 AM.]

What I have done lately is to not average at all....well...kind of...

When I set the first waypoint for a given location, I turn off the unit and walk away, usually about 500 feet. I turn the unit back on and walk back to the desired spot. When I get to the spot, I check the GPS to see where it is pointing. If I am within 20 feet, I take that reading and figure its good enough. If not, I make a note of where the GPS is pointing and how far, then manually increment the coordinates until it reads as close to zero as possible. At that point, I repeat the whole procedure...until I get a consistent reading under 20 feet. It takes only 5-10 minutes and I have gotten pretty good results with this method.

Change in 0.001 latitude: Near poles - half a foot, at equator, 6.07 feet

Change in 0.001 longitude: 6.08 feet

Since most GPSrs are only accurate to roughly 20 feet in the best of conditions, does it really matter if you've got the absolute best coordinates?

That being said, here's my thoughts on averaging.

Remember, the best possible solution would be to average your coordinates over a couple of different days.

Markwell

My Geocaching Page

You should read this current thread on waypoint averaging in the GPS Units forum.

I may be doing it wrong, but this is what I do. I take the first reading, wait a few minutes take another, then another, then another. I don't move, I just stay in the same spot the whole time, take as many as 20 different readings over a period of around ten minutes. Then I pick the mark that is pretty much in the middle of all the readings. Seems to work ok.

ummmm....not sure what to say here....so ummm, well errrr, uhhhh, well I guess that's it.

I like the least squares method. But are there any real mathematicians in this forum (e.g. John Nash)? Because the Garmin GPS will send an estimated position error for each transmission of position to a computer, and the NMEA GGA line sends (to a Magellan, etc) the number of satellites being tracked and the horizontal dilution of position. This data should be somehow factored-in (mathematically) with each reported position - and I sure would like to see a good formula for this!

quote:

I take the first reading, wait a few minutes take another, then another, then another. I don't move, I just stay in the same spot the whole time, take as many as 20 different readings over a period of around ten minutes.

Unfortunately, you may think you improving you accuracy this way, but in reality, you are doing nothing (except maybe trapping a gross error). Ten minutes of readings means 20 waypoints recorded with no consideration to the geometry of the satellites. To be of any value, the geometry must change. The birds move 30 degrees an hour, so waiting even half an hour is a big improvement.

All you may be doing is getting an average of bad data. It may be accurate but it is not precise. They may all be within 5m of each other, but they may also all be 100m out!

How you get the average is irrelevant. Whether by rigorous (least squares) or semi-rigorous methods does not make any difference, if the average you come up with is based on questionable readings.

RadDad, regarding not moving... moving is very important if it means moving to a location where the view of the sky is improved over the exact spot you have hidden or looking for the cache. Simply moving to the other side of a tree or more may improve you precision by several orders of magnitude.

Get to know your satellite screen. It is the best information your GPSr provides.

Again, you should read the concurrent thread in the GPS Units forum on this exact topic.

quote:
Originally posted by MrGigabyte:

All you may be doing is getting an average of bad data. It may be accurate but it is not precise. They may all be within 5m of each other, but they may also all be 100m out!

That's an example of precision without accuracy.

quote:
Originally posted by BrianSnat:

.... My question is, which method do you think is the most accurate. The actual average, or the most frequent occurring number?

Really neither as it's probably about 50/50. 50% chance of making it better and 50% chance of making it worse.

Cheers, Kerry.

I never get lost everybody keeps telling me where to go

quote:
Originally posted by BrianSnat:

.... My question is, which method do you think is the most accurate. The actual average, or the most frequent occurring number?

Really neither as it's probably about 50/50. 50% chance of making it better and 50% chance of making it worse.

Cheers, Kerry.

I never get lost everybody keeps telling me where to go

My GPSIII has a waypoint averaging funtion which continuously takes readings until I tell it to stop. Does this take anything else into consideration other than the individual lat/lons?

quote:
Originally posted by Markwell:

Change in 0.001 latitude: Near poles - half a foot, at equator, 6.07 feet

Change in 0.001 longitude: 6.08 feet

Just jumping in to correct a typo: you have latitude and longitude reversed. It is lines of longitude that converge near the poles, and lines of latitude that remain a constant distant apart.

quote:
Originally posted by denali:

My GPSIII has a waypoint averaging funtion which continuously takes readings until I tell it to stop. Does this take anything else into consideration other than the individual lat/lons?

Extremely difficult (basically impossible) to obtain the underlying principles behind Garmin's EPE, FOM etc but it would be a fair assumption the the computation of each set of coordinates has already taken into account geometry and other associated factors.

Similar with the averaging method it's difficult to "exactly" know what's going on in the background but I doubt it takes into account anything else but each set of coordinates?

Cheers, Kerry.

I never get lost everybody keeps telling me where to go

quote:
Originally posted by denali:

My GPSIII has a waypoint averaging funtion which continuously takes readings until I tell it to stop. Does this take anything else into consideration other than the individual lat/lons?

Extremely difficult (basically impossible) to obtain the underlying principles behind Garmin's EPE, FOM etc but it would be a fair assumption the the computation of each set of coordinates has already taken into account geometry and other associated factors.

Similar with the averaging method it's difficult to "exactly" know what's going on in the background but I doubt it takes into account anything else but each set of coordinates?

Cheers, Kerry.

I never get lost everybody keeps telling me where to go

quote:
Originally posted by DisQuoi:

I use the value that will result in the lowest sum of squares....

Could you explain this method to those of us that never studied statistics?

quote:
Originally posted by Moun10Bike:

quote:
Originally posted by Markwell:

Change in 0.001 latitude: Near poles - half a foot, at equator, 6.07 feet

Change in 0.001 longitude: 6.08 feet

Just jumping in to correct a typo: you have latitude and longitude reversed. It is lines of longitude that converge near the poles, and lines of latitude that remain a constant distant apart.

Ok let me get this straight....

When the longitude lines converge at the poles the distance between each approach zero. The greatest distance would be at the equator. Hence a varying value for longitude lines.

Distance between latitude lines, however, remains the constant.

Change in 0.001 longitude: Near poles - half a foot, at equator, 6.07 feet

Change in 0.001 latitude: 6.08 feet

[This message was edited by st_richardson on April 16, 2002 at 09:18 PM.]

Hmmm.

My physics teacher always taught me to example by extremes.

Hypothetical: I'm the Flash and can run at super-duper sonic speeds.

I start at Lat/Lon 0,0 in the middle of the Atlantic off the coast of Africa and I'm going to run north along 0° Longitude. As I tick off the Latitude lines in increasing value, the longitude lines of W001° and E001° are going to get closer and closer, but the latitude distance is uniform.

Same starting location, but now I run due east along the equator - and it would take me roughly 25K miles to finish the run while crossing latitudes at that longitude. Then I go to the pole and do the circumference in a fraction of the time because the longitudes are closer.

So a change in longitude is variable as you approach the poles.

I'm going to really shut up now. The original post is wrong, the correction is right. I think.

Markwell

My Geocaching Page

quote:
Originally posted by st_richardson:

Could you explain [least squares] to those of us that never studied statistics?

Sure. Not withstanding, I agree that data collected within a 10-minutes period will provide precise but not necessarily accurate coordinates. That said, the most common use of least squares is a simple way to derive a line through points (a "best fit" line). There's a great explanation and interactive window if you want to read about this. I only suggested it as one way of deriving a "best fit" coordinate when you have many points to use. You don’t need to be a mathematician to do it. I’d use a spreadsheet though. Simply put, you choose a coordinate such that you minimize the total (sum) of the distances squared.

I weight the individual readings based on the EPE (accuracy) level. I don't use readings with a high EPE at all. This usually eliminates the extreme readings. I have also found that it is a good idea to stand still at least a minute or two before taking any GPS position reading seriously, it seems that my GPS 76 needs to "settle down" after being on the move. I suspect that the GPSR uses a different algorith to determine position when it is moving, and it is not quite as accurate.

FWIW,

CharlieP

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