GeezerHiker

January 13, 2015

GPS – Less is better

Filed under: GPS, Hiking, Inaccuracy, North Cascades — Tags: , , — geezerwriter @ 4:49 pm

In my previous posting on the issue of GPS track log accuracy, I made a case that the 500-600 points produced by recording every 6 meters (20 feet) or so should be plenty to give an accurate picture of the average 4 mile hike and that the additional 9000 or so points proffered by Garmin’s preferred (to put it mildly!) “1-second distance accumulation” method should not, assuming that the points are accurate, change the track length by any significant amount.

But we have the simple fact that my friends and I have gotten a substantial discrepancy on every single mountain hike we’ve taken with my new Garmin 62stc device, errors ranging from 10-40% – which I would call significant! So which one is right? Or, I should say, which is more accurate? Because nothing is perfect, after all. This is all about the accuracy.

Accuracy

I want to make it clear that I am not meaning to “dis” the accuracy of the GPS unit itself. The reason I didn’t take the thing back to REI after its first hike was that I could tell that it was handling the challenging conditions of hiking in the North Cascades quite well. It acquires a signal very quickly and holds it even under deep forest cover. It does a good job of tracking the switchbacks, reacting to a sudden direction change much faster than my other models. Each individual reading from the device is quite good, given the conditions.

But there will always be errors. Garmin only claims accuracy down to 2-3 meters (7-10 feet) in the very best conditions. If you are a few feet away from where you thought you were it is no big deal. The problems arise when you combine a whole bunch of slightly inaccurate readings:

  • Just how big are these errors?
  • Will they tend to cancel out?
  • Or will they tend to accumulate?

Looking at the last point first: if the errors were even as small as 3-4 inches, 9000 of them would accumulate to about a half mile! So this is not a trivial question.

Error analysis is difficult, by its very nature, especially when you have no independent means of verification. Nice straight lines just don’t exist in the forests on the sides of mountains. The trails tend to be hidden under the trees and thus not visible on aerial or satellite photos, and I don’t have a ball of twine long enough to stretch along the trail. So there will have to be a lot of guesswork and some hand-waving, but I will try to make the estimates very conservative and give the benefit of every doubt.

Assumptions

  • It is very, very conservative to say that you might expect any recorded point along the track to be off by a foot or so from the true path.
  • Because of the steepness and roughness of the trails, we are often traveling at only 1 or 2 feet per second; we hardly ever average better than 3 fps (2 mph).

So the  “1-second distance accumulation” method will be recording points only a couple of feet apart, about one for each step we take. (I ask you to meditate for a moment on the wisdom of recording points a foot apart when we only know the position of each point to within ten feet… Now back to the conservative assumptions.)

  • So it safe to assume that the errors in these points could easily be on the same order of magnitude as the distances being measured

Here come the numbers

Let me compare this to the situation you have when riding in a vehicle at, say, 20 mph (or 30 fps). In one second you travel about 30 feet and record a point that is off by, say 1 foot.

Sometimes the error in that point may be in the direction of travel, so the estimated distance might be as little as 29 feet or as much as 31 feet; but that sort of error will tend to cancel itself out – if this reading is a foot short, the next will likely be a foot long. This is not a problem since we are just interested in the total.

The sort of error that will NOT cancel is when the estimated point is off the true path to one side or the other. If this point is a foot off to the left, then the next might be off to the right, compounding the error rather than canceling. If the next point is off to the left also, then it might not add to the error, but there is no reason to expect that it would cancel it out. And when you go off the track you don’t have to go off to the other side on the next reading, but you do have to get back to the true path eventually if the track is to be worth anything.

What sort of error are we talking about here? The worst case would be where the estimated point is a foot to one side of the true path – I’m picturing a a right triangle with a 30 foot leg (the true distance) and a 1 foot leg (the error). The GPS will be measuring the straight line distance from the starting point to the estimated point, i.e., the hypotenuse of that triangle. Mr. Euclid assures us that the length of that hypotenuse is the square root of the sum of the squares of 30 and 1, that is, the square root of 901 or 30.0166. So the error is that 0.0166 foot or about 0.2 inch.

Garmin errorsWhich ain’t much. In terms of percentages an error of 0.2 inch in a measurement of 30 feet works out to about 0.057%. This is a very tiny error that explains why Garmin’s strategy works quite well when you use the device in a car, or even a bike.

But this all depends strongly on the fact that the thing being measured is thirty times larger than the error, more than an order of magnitude. If that ratio came down to 10 (one order of magnitude) the percentage error would still be small – about 0.5% – not enough to bother with.

Garmin errors 10Things go nuts, though, when the error is on the same order as the thing being measured. If the ratio comes down to 2, we get

Garmin errors 4And it gets quite silly when the ratio is 1:

Garmin errors 3

This is enough to bother a hiker – if you were training for a trip down into the Grand Canyon by making “10 mile” hikes that were in fact only 6 miles long, you could get a nasty surprise when you get to Arizona!

Now I’m not saying that you will always get 40% error on a real life hike. There are lots of reasons why you might do better than this. But back when I was using the default settings on the Garmin I did in fact record some errors of that size. And while the errors are not always that large, they are ALWAYS ON THE HIGH SIDE, just as this analysis would predict. (Again, if an error takes you off the track, you have to make another error to get back on it.)

(By the way, the same discussion applies to the odometer. Assuming that they are using the same method to stoke the odometer, it would explain why I long ago gave up on its consistently, and often laughably, high readings. On one hike the odometer gained a quarter mile while we were sitting down having lunch.)

Conclusion

I know that this does not prove anything. The thing I hope you take away is this: the small errors that are unavoidable in each point of a track will tend to accumulate, which means that sometimes less is better. And given our slow rate of travel and difficult sky conditions, it would be very reasonable to expect the “1-second distance accumulation” method to generate errors on the scale that I’ve observed on the trail.

Ironic Epilogue

The cruel irony is that Garmin’s decision to paste the one-per-second track length into the track log makes almost no difference in most situations, such as in a vehicle. Or when one is power-walking along an urban trail with a clear view of the sky in all directions. So it may not do harm in those situations, it never does any good! This is the easiest kind of cost-benefit analysis:

  • Substantial Cost.
  • No Benefit. Ever.

In my last note to Garmin, I also made an appeal to their sense of fairness:

If a user believes that the “1 second distance accumulation” is a good idea and gives her good results, then she can choose that option in the track log setup. But if she has a valid reason NOT to sample that many points and wants to make a track with the points spaced further out FOR WHATEVER REASON (but her reason, not yours), then there is currently no way for her to measure the length of that track in the field. You may not like her reason, you may snicker behind your hand that she would want to do something you think is foolish, but it is (pardon the expression) none of your freakin’ business!

 

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January 10, 2015

GPS – Just because you can doesn’t mean you should

Filed under: GPS, Hiking, Inaccuracy, North Cascades — Tags: , — geezerwriter @ 3:17 pm

After going back and forth since last June with the email support staff at Garmin Ltd I finally received a reply with some substance:

When the user uses anything but the one second track interval the track log is “missing” data.  We are putting a value for total distance in the GPX file in the track stats tag that gives BaseCamp the 1 second distance accumulation ( even if they are not setup for 1 second distance accumulation ).  So when the user removes the first point BaseCamp can no longer use our 1 second distance accumulation value and has to fall back on the old method of summing the delta between all of the points.  The problem is that all of the points are not there, because they are setup to record at a less than 1 second interval.  So when this happens they think they are just removing 1 point, while in reality they are removing possibly thousands of points along the entire track which is why the distance changes.

The substance is that they have finally acknowledged what I have been saying for the last six months and what I suggested in the last paragraph of my first posting on this issue back on June 10, 2014. That’s the good news; the bad news is that they clearly seem to think that substituting in  the “1 second distance accumulation” is a good idea! If it took six months to get them to even admit what they are doing, how long will it take to make them see that what they are doing is just plain wrong?

The Lily and Lizard Lake Trail, Skagit County, WA - 687 points provide a lot of detail.

The Lily and Lizard Lake Trail, Skagit County, WA – 687 points provide a lot of detail.

A Quick Review

After a lot of experimentation, I have my Garmin GPSmap 62stc set up to record a track log point roughly every 20 feet (6 meters). Since we usually average only one or two feet per second when hiking uphill, Garmin’s “1 second distance accumulation” would mean recording a point every foot or so – ten or twenty times as much data. For example, on the first half of last Thursday’s hike I recorded 687 points in roughly 4 miles, at an average distance of about 30 feet, as shown in the picture; the elapsed time was about 2:37 so the 1 second method would have totaled up around 9,400 intervals of about 2 feet each. The total track length (by the 1 second method) was listed as 4.7 miles. When I deleted a single point and forced a recalculation (“losing” almost 9000 points) the length changed to 4.2 miles.

Why my points were 30 feet apart rather than the 20 I asked for is something only Garmin could answer, but it is not a big deal: 687 points is more than enough to make a very good picture of the trail we were on. The track agrees very closely both with my previous tracks (made with different Garmin devices) and with published information and maps of this very popular local trail. We had good weather, we were moving at a good, steady rate with few stops and the device showed an accuracy between 10 and 20 feet (about as good as it gets) every time I checked (which was often).

The Big Question

Pay attention here, as I am pretty sure this is the point where Garmin is going to counterattack (assuming I can get them to respond before I die.)

Even on these winding mountain trails it’s not like we are juking rapidly from side to side as we go along – with the exception of the occasional 179° switchback, you are usually traveling more or less in a straight line. I’ve been paying attention to that this summer – most of the time you can see straight ahead along the trail for 20 or 50 or even 100 feet, then there is a subtle change of direction and you go straight for another stretch. A lot of the trails, including large parts of this one, follow old logging roads and railroads (which are not prone to rapid direction changes) and have only a handful of sharp turns. I think if you joined us on a hike you would agree that if you could accurately record a point every 20 or 30 feet or so you would get a pretty darn good track, and it should contribute almost nothing (except for a whole lot of extra data) to the measured length of the trail to accurately record a few thousand intermediate points along the way.

So this is the first core of the issue – it is all about accuracy. How do we explain that half-mile discrepancy between the “1 second” method and the “20 feet” method? When I have done similar comparisons in town on a nice straight city street with a full, clear view of the sky (and where you can get a good independent verification of the distance) there was no such difference. Garmin is on record with its explanation: when I edit the track I am “removing possibly thousands of points along the entire track which is why the distance changes.”

And I agree completely! Where we differ is that Garmin seems to think that more is necessarily better, that those thousands of additional points must be an improvement. That is a common fallacy – more chocolate is better; more habanero pepper maybe not so much.

I think I made a pretty good argument that those thousands of extra points cannot increase the accuracy by more than few feet in a mere handful of sharp turns, nothing like a half a mile. My argument is that the 1 second method was adding in an additional 9000 tiny errors – that would be a positional error averaging only 3.5 inches per reading, and that on a device that is only claiming accuracy of 10-20 feet.

My Assignment

So my assignment (which I very much do choose to accept!) is to try convince a bunch of engineers who work and probably live in a place with very few hills, very few clouds and very few trees that there are situations where a lot of their precious data is more like pepper than chocolate and is ruining the result rather than flavoring it.

And more poignantly, that this particular kind of pepper never improves the dish – most of the time is does no harm but it can never help.

I intended to dig into the gritty geometric and arithmetic details that support this argument but this is more than enough for one day.

July 8, 2014

GPS – the adventure continues

Filed under: GPS, Hiking, Inaccuracy, North Cascades — geezerwriter @ 12:39 pm

Since my last post I have been locked in a death grip with Garmin’s “Help” desk about my new GPSmap 62stc handheld GPS unit. I write in, they respond with a condescending, patronizing reply that picks out one phrase to criticize and ignores the general thrust of my message. I then reply in detail (as I am sure you can believe) and it is picked up by a different “helper” who chooses a different irrelevancy to pick on, and offers a completely different “explanation” or “solution”.

This process started on June 16 and has gone through six or eight iterations. I was going to wait for a some sort of resolution before reporting back to this blog but it is becoming clear that they are so adept at ducking this issue that resolution is very unlikely. But in the meantime, I have accumulated enough evidence to be quite confident that I understand what is going on.

Are you ready?

I my previous post I included this sentence:

 The best I can come up with would be an unlikely and deeply conspiratorial attempt to rig the results to agree with the odometer. But they probably wouldn’t do that.

Since that “4.2 mile” hike toward Excelsior Pass on June 5, we have gone to the Church Mountain Meadows on 6/12, the Goat Mountain Overlook on 6/19, a Middle Fork hike on 6/26 and back to Church Mountain yesterday, July 3. I have tried out all of the suggested settings proffered by Garmin and several of my own and gotten the same sort of results as the Excelsior hike every time. And at least twice, we have been joined by Carl sporting his Garmin 62st device, which seems to differ from mine only in that mine has a camera. He has gotten very similar results and has made a major contribution to my sanity (or what remains of it.)

The responses from Garmin have ranged from the merely patronizing to the positively ridiculous. In response to the fact that the device was generating spurious points when we stopped along the trail one respondent made this suggestion:

… try to stop as little as possible.

Another was quite insistent that accuracy could only be achieved by setting the device to record a track point every second – 3600 points every hour. Never mind that a track can only hold 10,000 points, limiting the device to a trip of about 2 hours and 45 minutes. Never mind that a track of that length causes their own BaseCamp software to bog down to the point of being unusable. And never mind that the “every second” track I made coming down on Goat Mountain is every bit as inaccurate as the one I made going up.

Most of my time with them has been spent dithering over these inaccuracies, where there is no outside authority to settle any dispute. There are hiking maps and websites, which are notorious for their casual inaccuracies –  it was my word against theirs. So I attempted to focus all the attention onto one verifiable, repeatable, incontrovertible inconsistency:

Why does their own device and their own computer software report different lengths for the same track under different circumstances?

It took a couple of exchanges to wrench their attention away from the accuracy question but last week I finally got someone to admit that there was something questionable going on when the removal of one redundant point from a log of over 500 points caused its length to changed from 4.2 miles to 3.6 miles and that he would have to look into it.

Then … silence.

The intervals between responses had been one or two days, mostly, but a full week elapsed before I saw a new email at about midnight before Thursday’s hike. I chose not to look at it before the hike since most of their responses had been simultaneously irrelevant and infuriating (or, in homage to Stephen Colbert, infurelevant) and I didn’t want to be in a bad mood in the morning.

On the hike to Church Mountain Meadows there were even more interesting results than before. I set the device to record a reasonable numbers of “bread crumb” points and kept a frequent watch on it along the way. I could see that it was doing a good job of following the shape of trail, catching even minor changes of direction and only rounding the switchbacks a tiny bit; I was confident that I had a very good track. I also was carrying my old Garmin 60CSx.

We stopped for lunch at a spot where all my previous experiences on Church told me the distance should be about 3 miles. I took the following readings from the devices:

  • 62stc Odometer: 3.55 mi
  • 62stc track: 3.4 mi
  • 60CSx Odometer: 2.9 mi
  • 60CSx track: 3.05 mi

I turned off the track logging on the new 62stc at this point, but didn’t save the track, yet. While I was sitting in the snow for the next half hour or so, I checked the 60stc now and then, watching the odometer go from 3.55 to 3.64 to 3.74 and by the time we got up to start hiking back, to 3.82. (That’s why I had turned the track logging off – so all that spurious junk wouldn’t be added to the track log.) All this time the device was sitting stock still on the top of my pack at 4950′ in an open meadow, showing excellent accuracy of about 2 meters (7 feet). Gaining an imaginary quarter mile in half an hour seems like pretty bad behavior, but long experience has driven my expectations for GPS odometers to be very, very low. But that’s another story.

As we prepared to start down the trail, I turned the tracking back on, saved the track (which still showed the 3.4 miles) and a minute later decided to use the “tracback” feature to show the distance back to the trailhead along that new track. Understand that I still thought it was an accurate track, just that its reported length was off  by almost half a mile.

And Lo! and Behold! The device now showed the distance to the trailhead as 3.0 miles!

When I got home and uploaded the stuff to BaseCamp, I got the usual nonsense: the track length showed as 3.4 miles until I deleted one point, whereupon it also changed to 3.1 miles. I ran the track through my spreadsheet and it gave 3.06.

The Bottom Line

So the old 60CSx track was right on the money at 3.05, and the 3.0 on the “tracback” and the 3.1 in BaseCamp can be chalked up to roundoff error.

All the other numbers reported by the 60stc are sheer bullfeathers.

Back to the Garmin “Help” Desk

So then I was ready to read the response from Garmin that I had avoided. There was some more patronizing stuff, but the gist was contained in this paragraph:

I hope this helps to explain this isolated incident that you were experiencing. This is an extremely rare problem. Unfortunately, the only way to really explain this error is to contribute it to corrupt GPX data on your device.

So, ignoring the fact that this was a brand new device when this stuff started happening and that another person’s device was getting the same results, Kris had come up with an “reason” that conveniently would invalidate all the previous data that Carl and I had accumulated, and attribute it to my not knowing how to disconnect the device from my computer!

[ short pause while the lingering rage gradually subsides…]

At the risk of my declining sanity…

Kris had given instructions on how to purge the dread corruption from the device, but since it works quite well around town, I would have to wait to test the inanity of his/her directions. But I couldn’t wait so on Sunday morning I performed the purge and headed over to Stewart Mountain (a big foothill, actually) to check on the progress of the logging operation that is likely to obliterate some of the trails over there. The conditions there are not nearly so challenging for the GPS as our real mountain hikes, but it might be enough to generate some good (i.e., bad) data.

I stopped at a little knoll in an old clearcut when the new device’s odometer just happened to read exactly 2.00 miles; the track log said 2.0; the old GPS’s track was 1.9. I was expecting the “tracback” function to shave a little off that 2.0 mile track length and was disappointed when it didn’t. I headed home.

Back at the computer, however, the old bug reappeared: deleting one redundant point changed the length to 1.9 miles and my spreadsheet came up with 1.895.

I sent this information off to Garmin and finally got the first response that was neither patronizing nor inane:

This problem has been reported. We are still researching this to find out what is causing this and how to correct this. I have added your information/file to the case. We will contact you when we have more information.

Hmm. We shall see.

June 10, 2014

GPS – a cautionary tale

Filed under: GPS, Hiking, North Cascades, Snowpack — geezerwriter @ 7:59 pm

I was suckered into buying a new Garmin GPS handheld unit (GPSmap 62stc) by a half-price offer from REI – Garmin stuff never goes on sale and my old device (GPSmap 60-something) was getting a little long of tooth. I’ve always had problems with large errors that Garmin has never solved (or even fully acknowledged) so I’m not in love with the old one. And the newer model has some cool-sounding features – nothing earth shaking.

The long-standing errors are in the way the device reports distance traveled and elevation gained. For distance it has an odometer that tries to keep track of your total distance as you move, the same as in your car. But it also has a tracking feature (Track Log) that saves your location frequently, and is capable of going back over those saved points at the end of the trip and totaling up the distances between the points. These two measurements should be pretty close but they hardly ever are – differences of 20-40% are not uncommon. Years ago I examined it pretty closely and found that I could fool the odometer at will just by moving very slowly (which we often do when climbing steep trails). I once carried the device a quarter mile, according to the track log, and the odometer showed only 20 feet or so!

Elevation is just about as bad. My favorite example was a hike to Boundary Way where the trailhead is at 4300 feet and the high point of the hike at 5300, a nice round net gain of 1000 feet. There were some ups and downs along the way that added a bit to the total but the device showed a total gain of 750 feet.

I could never get either Garmin or REI excited about these software errors; I got as far as talking to a Garmin engineer who was puzzled and seemed convinced that there was a problem, but he never got back to me and I didn’t have the energy to start the whole process over. REI has replaced the device a couple of times but they didn’t seem to give a hoot, either.

Excelsior Pass

Upward Track

Upward Track – 4.2 miles

My first outing with the new device was a simple hike in Lake Padden Park and the results looked very good. The odometer and the track log were in pretty close agreement and the track agreed closely with tracks I’ve saved from other hikes there, and where they differed the new one looked better. So I was optimistic on our first high country hike of the season. Excelsior Pass Trail is a 4- to 4.5 mile hike that climbs about 3500 vertical feet through the forest from Mount Baker Highway at 1800′ to 5300′ at the pass. We were not going to make it all the way because of the remaining snow but we were aiming for a nice little spot with a view of the pass about 3 miles along the trail at about 4400′.

About that “3 miles”. I have traveled this trail many times (including 2 weeks ago) and saved a number of track logs that all look pretty similar. They range from 4.1 to 4.4 miles long, which I consider to be an acceptable tolerance range. This is a challenging environment for GPS: climbing out of a deep, steep-sided valley through heavy tree cover. Rain would make it worse, since water absorbs microwave signals, but this was a dry day. All in all, I have a lot of confidence in the 3 mile estimate.

I checked the device frequently (which was more difficult that with previous devices since Garmin has really screwed up their system for attaching the device to your person) and the accuracy was staying down in the 20-30 feet range and the new track (the red line on the map) was close to the old one. We had one stop that was a bit longer than usual while we waited for a hiker who wasn’t feeling well, but otherwise we plugged right along, getting to the aforementioned spot just before noon. We hit snow just above 4000 feet and lost sight of the trail near the middle of that east-west-ish traverse (at the word “Mount”).

The map also shows the old track from last fall in yellow – most of it is obscured by the new track, showing 1) we kept close the trail until just before we stopped and b) there was quite a good bit of trail left. The white arrow points to our longest stop, at the Excelsior Flume – more on that later.

The Upshot

And soon as we settled down into the snow for lunch I checked the new device and it showed an odometer reading of 4.2 miles, which was simply absurd. And puzzling – I expect huge errors in the odometer, but they are usually on the low side.

So as usual, I would resort to the track log – which also said 4.2 miles! It was most ironic that the first time these two measures had ever agreed they were both hugely wrong! Most of what I said and thought for the next few minutes is not suitable for a family publication.

I resisted the urge to pitch the thing into the nearby creek, saved the track and continued the track logging after lunch. When we got back to the trailhead the odometer and the track log both read about 7.9 miles, giving 4.2 miles on the way up and 3.7 on the way down, along the exact same trail – on the snow I was even stepping in own footprints. I’ve seen discrepancies like that before, too, and have written it off to the fact that we are traveling a bit faster on the way down (and the devices are known to have trouble with slow travel.) I was eager to upload these tracks to my computer and see if I could make sense of this before I started haranguing Garmin and REI. Again.

Upward half-track - 3.6 miles?

Upward half-track – 3.6 miles?

At the Computer

The first thing I tried only added to my puzzlement. I transferred the two tracks,

  • upward (4.2mi and 558 points) and
  • round trip (7.9mi and 1200 points),

to the Garmin BaseCamp program and, just for the heck of it, I made a copy of the round trip, located the place where I had saved the upward track and split the track in two, giving me another upward half-track and a downward one. Result:

  • upward (3.6 mi and 560 points)
  • downward (3.3 mi and 641 points)

The last I checked 3.6 + 3.3 is a little shy of 7.9. What the φθψκ is going on? The map on the left shows this upward half-track made of the same 560 (or so) points as the 4.2 mile track – can you see any difference? I can’t.

The point counts are close enough to make it pretty clear that both devices (the GPS and BaseCamp, too) are working with the same raw data and somehow deriving significantly different results in different contexts.

BaseCamp track details

BaseCamp track details

Getting Down and Dirty with the Data

I will be sending this data to Garmin, rest assured. You’d think a track that loses a mile, but not any points, when split in two would get an engineer’s attention. We shall see.

But I just couldn’t let this go. I wanted more ammunition before hacking my way through the telephone trees.

The first issue is “Where does that track length come from?” I’ve always assumed that the software is adding up the distances between each pair of successive points. In BaseCamp you see the display on the right, showing latitude and longitude for each point and the length (in feet) of each “leg”. There are way too many numbers to add up by hand and, moreover, are those distances accurate to begin with?

The latter question is a toughie, since it is not trivial to calculate the distance between two points given latitude and longitude – it involves spherical trigonometry, which I encountered for a couple of weeks in the spring of 1958. But it didn’t take root.

Track details - UTM coordinates

Track details – UTM coordinates

I first found out that the Universal Transverse Mercator (UTM) coordinate system was invented to simplify this very problem. Instead of resorting to extremely skinny triangles based at the center of the earth it uses measurements in meters from standardized reference points. It is much more difficult to describe than Good Ol’ latitude and longitude. It turns out that BaseCamp is capable of displaying UTM, shown in the detail on the left, but it only exports the old style coordinates. I have a picture of that, too.

Track details as exported

Track details as exported

But a search on DuckDuckGo (like Google but without the spying and tracking) coughed up a detailed dissertation on the use of the Spherical Law of Cosines for just this purpose. So it was time to build a spreadsheet!

After importing all these points into Apple’s Numbers application and struggling with a bunch of sines and cosines and deltas and phis and lambdas and meters and feet and miles, I had a working spreadsheet that looked almost exactly like the first BaseCamp display above, with the “legs” of the track in feet. I didn’t check all 560ish points, but every one I did check was true to the nearest foot.

And the grand total of all those legs? I have picture of that, too:

Spreadsheet Results

Spreadsheet Results

5720 meters or 3.554 miles. So this is consistent with the upward half of the split track, even though the data is from the saved 4.2 mile upward track. Where did that 4.2 come from? I have no mathematical answer for that. The best I can come up with would be an unlikely and deeply conspiratorial attempt to rig the results to agree with the odometer. But they probably wouldn’t do that.

Closeup of the Bulge at the Flume

Closeup of the Bulge at the Flume

Had enough yet?

Now 560 points is more than one needs to draw a pretty good picture of a 3 mile trail. Given that all the GPS coordinates have some error (or jitter) in them, having more data might give worse results. So I modified the spreadsheet to skip every other point and this dropped the track to 3.28 miles. Stripping it down to every third point brings it down to 3.00, and every fourth point gives 2.92. At some point just throwing data away willy-nilly like this is going to chuck out some good stuff (for example, it could seriously round off the switchbacks). To do this well one would have to detect places where the track has a serious change of direction and make sure those points are kept, while tossing out points when you are loping along a straightaway.

Another way that those inherent errors can exaggerate the track length is that the device doesn’t do a very good job of handling times when you are stopped. (To be fair, this is a difficult problem for a mere machine: How can you tell if you are moving or not when all you know is your position, and that is almost certainly in error?) What happens when you stop is that the GPS sees these inherent errors as legitimate movements (We’re here. No, now we’re over here! No! Over here!…). Going back to that white arrow on the first map, above, you can see a little bulge in the track at that right turn by the Flume, where we paused for 5 or 10 minutes. (Sometimes I remember to manually turn off the track logging when stopped, but not this time.) The map on the left is a closeup of that spot – there are actually 25 spurious points in that little bulge! In this case I culled almost a mile out of the 4.2 mile track just by deleting obviously extraneous points like these.

There are some settings in the GPS device that might serve to control the numbers of excess and spurious points without losing too much detail, and I will experiment with that. But consider that this is a $500 device which seems to be generally regarded as the best consumer-grade GPS available for hikers, that I was using the default settings and that 99 and 44/100 percent of users are using those defaults.

So the next time someone authoritatively announces what the cheap little GPS in their phone says, I hope you take it with enough grains of salt to gag a buffalo.

Appendix – Later that night…

Just a quick note – it occurred to me that the one difference between the 4.2 mile up-track and the 3.6 mile half-track: the former had been uploaded directly from the device and the latter had been created on the computer. I went back and made a duplicate of the original track; it still showed the 4.2 mile length. But when I deleted the last point, which should have changed the length by 18 feet, that length instead changed instantly to 3.6 miles. As soon as I forced the computer to recalculate the length it got the “correct” length, that is, the length based on the actual point data. So I conclude that the 4.2 number really had nothing to do with the actual track points but had somehow been attached to the track while it was in the GPS device. The conspiracy theory just got a bit more plausible – somehow the track length has been fudged, perhaps to make it agree with the odometer.

I can’t wait to hear Garmin’s explanation…stay tuned.

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