APRS vs Handheld GPS: Discrepancies Explained

GPS precision: effect of number of decimal places

GPS precision: effect of number of decimal places. The more decimal places the GPS location has, the more precise. But precision and accuracy are two different things!

GPS precision is a function of the number of decimal places after the decimal point. Why is that important? Well, the APRS tracks that I’ve taken recently while riding my motorcycle do not agree with the track taken by my DeLorme PN-40SE GPS. My APRS tracker (see second photo in a previous post on APRS) uses a Byonics GPS-2 GPS receiver, a tiny little thing that’s pinned to the shoulder of my motorcycling vest. It’s connected via a cable to the APRS tracker, which in turn is connected to my 2-meter ham radio. That sends out a signal periodically which is picked up by local APRS repeaters and is also put onto the Internet. In riding around, I’ve given a lot of thought to GPS accuracy, and one thing that sticks out immediately is that there’s often a discrepancy between the simultaneous GPS-2 and PN-40SE readings. Why is that? Is one less accurate than the other?

The answer isn’t absolutely obvious at first glance. Looking at the figure below, which is really zoomed in on just a few hundred feet along a trail I’ve ridden several times this year, and you see that the GPS tracks don’t coincide. Well, given that they’re maybe accurate to ten meters at best, the fact that they repeat nicely is certainly an indication of the basic accuracy. And my Byonics GPS-2 is just as accurate. But…given it’s hooked to the world via APRS, it’s a lack of precision that makes for the difference. Look at the map below.

APRS vs handheld GPS: discrepancies

APRS vs handheld GPS: discrepancies. The red push pins (largely hidden under the distance labels) mark the APRS track points. The other linked track points are from my DeLorme PN-40SE. See text for letter "A"

First, look at the GPS tracks of various colors. In this map, the DeLorme PN-40SE is set up to record position every two seconds. DeLorme Topo North America interpolates between these points with a colored line—the different lines indicate trips on different days. Note that the “going and coming” discrepancies are very small atop the ridge (within a few feet) and get somewhat larger down at the bottom of a little canyon, which is to be expected. (Point “A” and its associated line represent approximately where I took the first photo in an earlier post.)

Let’s examine one point from the PN-40SE-generated .gpx file (yes, all this for one lousy point). It’s a bit abstract, but I’ll explain it.

<trkpt lat="38.595123" lon="-107.889624">

Okay, dig in. The latitude, 38.595123 (north), is given with eight significant digits of precision. Looking at the chart at the top of this article, adding a degree to this would add 366,667 feet. Adding a tenth of a degree adds a tenth of that, or 36,667 feet. Adding a hundredth gives 3,667 feet. A thousandth gives 367 feet. A ten thousandth gives 37 feet. A hundred-thousandth of a degree adds 3.7 feet. A millionth of a degree ads only 0.37 feet, or about 4 inches. That means the difference between 38.595123 degrees latitude and 38.595124 degrees latitude is 4 inches. Or, in other words, that many decimal places gives a precision of 4 inches. Precision means how finely-attuned the readout is. It has nothing to do with accuracy. (As an aside what you see above is called XML for eXtended Markup Language. The tags list the latitude and longitude, plus the elevation in meters, the date and time in UTC, the GPS’s report that the position is good in three dimensions, a speed in km/hour, and a heading in degrees from true north.)

To explain the difference, think of a digital bathroom scale. Your weight might be 201.4 lbs. Wow, you say! Accurate to a tenth of a pound! No…not so. It’s precise to a tenth of a pound. Most home bathroom scales are accurate perhaps plus or minus two or three percent. That’s four to six pounds! In this case the precision greatly exceeds the inherent accuracy.

In the case of the DeLorme GPS, it’s precise to four inches. But the accuracy can vary much more, usually plus or minus twenty to thirty feet. I judge how accurate a GPS track is by how repeatable it is. If I come along the same route later in the day, or on another day, the GPS satellites have changed positions and it’s a whole new set of computations going on inside the microprocessor. If repeated travel yields paths within a few feet of each other, then I’d say it’s pretty accurate. (Note: the GPS provides its own estimate of its accuracy. Don’t trust this, particularly in a canyon or between buildings.)

Now, let’s look at the APRS data, which is collected by the Byonics GPS-2 and reported via APRS. We now have the opposite problem. Here’s a raw record from the APRS file (not from the same location as the sample reading above):

KE0OG-5>APTT4,RBERRY*,WIDE2-1,qAR,FLATTP:@181717h3836.45N/10751.66W<339/006/TT4 involt 10.4V/A=006625

This takes some more work. Up until the @ sign, it provides a record of which stations handled the APRS position report. After that it notes it was recorded at 17 seconds past 1817 hours (UTC). The position was 38° 36.45' (north) and 107° 51.66 (west). The rest has to do with heading, speed, battery voltage, and altitude in feet. Note: the location is recorded only to the hundredth of a minute. In latitude, according to the chart at the top of this article, a change of one hundredth of a minute is equal to 61 feet and in longitude equal to 50 feet. The precision (for a GPS system) is terrible! The difference between 38° 36.45' and 38° 36.46' is 61 feet! It simply can't get any more precise because there aren't enough numbers after the decimal place! The accuracy is great, but the precision is poor. And that neatly explains the discrepancies between the highly-precise DeLorme readings and the rather coarse APRS readings.

Moral of the story? If you want to know precisely and accurately where you are, use a handheld GPS and make sure your going and coming tracks are very close to each other. If you want a relatively good location (plus or minus 60 feet in north-south direction and plus or minus 50 feet in east-west direction), APRS is fine. But...I carry the APRS so if something happens to me, people can find me. But the poor precision could mean trouble—if I go down in the woods, rescuers might really have to scour the place to find me!

(Note: there are other ways of setting up the APRS tracker to provide more precise measurements, but they involve some fancy coding that makes it too hard for me to extract the track to plot in DeLorme Topo North America. I'd write a piece of software to make the conversion, but my old standby GWBASIC doesn't work with Windows 7.)

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2 Responses to APRS vs Handheld GPS: Discrepancies Explained

  1. dave says:

    The GPS system relies on line-of-sight reception from the satellites, which can be severely limited in canyons. Further, the signals can be reflected off canyon walls, causing the signal from a given satellite to be heard twice, which confuses the receiver. I judge accuracy by how repeatable the reading is. The satellites are constantly moving. If my tracks going and coming are on top of each other, I think accuracy is probably pretty good. Often in deep canyons there’s a discrepancy, sometimes hundreds of feet. I’ve found that my handlebar mount for the DeLorme PN-40SE (see here) really helps accuracy because the receiver is out in the open rather than in my pocket. For example, last season I was unable to get a good track on Engineer Pass Road, but this season I have great out-and-back repeatability and made a good track. Many years ago I crawled through the GPS equations to see how the system really works (my undergraduate degree from BYU is in math). It’s highly dependent on the time difference of arrival of the signals from the satellites. If one of the signals is reflected rather than direct, it will affect the equations substantially and can create an error. The receiver may think it’s doing fine. (Mine told me today it was ±5 feet. Ha! No way!) The bottom line is that one needs to keep terrain in mind. Another thing to note is the “datum.” GPS uses WGS-84 (World Geodetic System 1984). Many of the USGS topo maps use NAD-27 (North American Datum 1927, yes, the year 1927—a long time ago!). In Colorado the north-south difference between the two systems is well over 100 feet (the earth is not, after all, nicely round).

  2. Bruce Duncan says:

    Found your comments while searching for info on GPS accuracy.
    Last week my DeLorme PN40 GPS was off by more than 1,500 ft.
    I was on the side of a mountain where there are cliffs in every direction.

    My guess is that the 2D accuracy is limited/determined by the horizon line. I suspect the accuracy comes from satellites near the horizon to be accurate (from geometry considerations). I haven’t seen any info on how accuracy is degraded by a limited horizon line. For example, what happens if you are in a canyon running E-W (full 180 degrees horizon running EW) where the sides of the canyon create a horizon line 30 degrees or 45 degrees above level. My guess is that the 95% accuracy zone will be oval or cigar-shaped, with the long axis of uncertainty running NS .
    This is the kind of information that DeLorme and the other manufacturers should be providing as a matter of good business practice.
    Please drop me an email if you have learned anything since May. Maybe I will know something by the time you write. I’ll book mark this but there is no guarantee I will return.
    Salt Lake City

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