What is GPS "Accuracy", Anyway???
Ken in Regina
What is GPS "Accuracy", Anyway???

In every GPS forum on the internet, the question is often asked, "How accurate is the model XYZ-999 GPS?" There's no simple answer. Or, actually, there are multiple answers. .

What aspect of the GPS do you want to measure?

Absolute positional accuracy? I think this is the one most people sort of have in mind when they ask the question. When the GPS says I'm standing at a particular location on the face of the planet, how close is it - really - to where I am actually standing?

It turns out that it's not terribly accurate. Most manufacturers will claim between 10 meters and 5 meters. I have occasionally seen as good as 2.5 meters with WAAS enabled.

So, what does that mean, really? Well, if the GPS reports that it currently has an accuracy of 7 meters, if you draw a circle with a diameter of 7 meters centered on the coordinates being reported, odds are that you are somewhere in that 7 meter circle. That's plenty good enough to help you find Ikea in a strange city, find the nearest donut shop or to get you home or back to the campsite. But it's not likely to get a survey engineer very excited.

Speed? Most manufacturers will report something like 0.1 meters per second accuracy for the speed reading. That's right up there with the cop's radar gun. It's good enough to show you that your car's speedo is reading about 5% faster than you are really going. (Car manufacturers do this intentionally so you can't sue them when you get a speeding ticket.)

Relative Positional Accuracy? If you put a stick in the ground and take a reading, move somewhere else and take another reading, this is the distance between those two points. This would show up, for example, as the distance traveled on your trip meter and also as the direction you are traveling as you move from the first point to the second.

This is as accurate as speed. Has to be, if you think about it. Speed is calculated by taking two readings, marking the location and time at each reading, computing the distance between the two locations and the time it took to travel that distance, then dividing the distance by the time to get the speed. So to have very high accuracy for speed, you must have equally high accuracy for the distance travelled. And for the time.

Which brings us to the final measurement of GPS accuracy:

Time? The usual spec you will see will be "1 microsecond synchronized to GPS time".

As with the relative positional accuracy, this factor has to be very accurate to get the kind of speed accuracy claimed (and delivered). This is largely a function of the GPS satellites themselves, plus a little computation in the GPS receiver. Each GPS satellite has a cesium clock in it that is hugely accurate. Just one step short of the nuclear clocks like at Greenwich or Denver. It doesn't get much better than this. Definitely better than your average Timex (or Rolex, for that matter).

Y'er welcome.

Mandolin Guy
Good information. Thanks.
Hi. That's a pretty good answer to the question, but I want know if accuracy is detoriated if anyone of the orbiting satellite fails?
Only if you were in a low-reception situation to begin with. If you were receiving signal from 4 satellites, then you will lose a bit of accuracy if one of these 4 goes down. If you were getting 9 satellites, then dropping down to 8 has negligible effect.

On a systemwide level, there are more active GPS satellites than required to operate the system. In addition to this active redundancy, there are also inactive spares that can be brought up if necessary.

This question will soon (within the next 10 years) become moot because we will have 4 independent satellite navigation constellations in place -- GPS (US), GLONASS (Russia), Galileo (EU), and Compass (China) -- and each of these systems will also have internal redundancy. Of course, it may take longer for consumer multisystem receivers to become widespread.
Ken in Regina
Just to go a little farther with Tao's answer, there is more than one way to fail. Tao addressed a disastrous failure, as in the bird falls out of the sky or just goes dead. Another scenario is that one goes nuts and transmits garbage.

That scenario is also covered, multiple ways. Each satellite contains 3 cesium clocks. The timing signal that is transmitted is the result of a "majority rules" system. Simply, that means that if there is ever a discrepancy between the three clocks, the signal that at least two of the clocks agree on is the one that is transmitted. That triple redundancy in each satellite makes the system pretty reliable.

But if an entire satellite does go nuts and somehow starts to transmit junk, your GPS receiver will see a huge variance from that one signal compared to the others it's receiving and ignore it. No harm, no foul.

Tao also makes a good point about the number of satellites you are receiving from. There are situations where your accuracy will be much better with a good constellation of only three or four satellites than with a bad lineup of eight or nine. Your GPS receiver is trying to determine your location by triangulation. So the accuracy will be better if you have signals from a few satellites that are spread widely apart than from a bunch that are all in a neat line with each other.

Accuracy cannot be expressed as a hard number value so it's defined in statistical terms.

Why? For GPS the parameters that go into a fix a constantly changing:

1) Satellites are moving from fix to fix affecting the geometry of crossing lines of position. Additionally, the multipath environment is changing as the signals arrive from time varying directions. Reflected signals confuse the range to satellite calculation.

2) There is a basic satellite error caused by the the very small, but extremely significant, drift of its atomic frequency standard. That error combines with errors in the orbital parameters the receiver requires to calculate the satellite position and subsequent range. Each satellite has its own basic error that must be monitored by a network of ground stations and then corrected by the system operators on a daily basis.

3) Signal time transit through the ionosphere depends on 'space weather'.

4) Satellites are routinely are removed from service for maintenance or repositioning. Accuracy statistics can depend more upon which satellite is not available than the actual number available.

5) There is also a receiver implementation error. Some high quality sets are significantly better at rejecting multipath signals.

The attached scatter plot shows about twelve hours of fixes collected at my coffee table using a BU-353 without WAAS. Twenty nine satellites were set usable during the test. The constellation closely repeats itself over the earth every twelve hours.

You might see an error of over a hundred feet if you were unlucky enough to turn on the receiver during one of those excursions away from center zero but, in general for this particular sampling, one half of your fixes will be within ten feet of center zero.

--- CHAS

Ken in Regina
Hey Chas,

Some high quality sets are significantly better at rejecting multipath signals.
Some of the newer GPS receivers have algorithms that actually use the multipath if the prime signal is bad enough. I think that's why I can get a fix in my basement office with my eTrex Legend HCx when my other receivers mostly won't. There can't possibly be anything but multipath down here.

The main advantage of WAAS is that if your receiver can see one of the WAAS satellites it can download adjustment factors for those problems you mentioned. (I know you know that. I'm just adding it for those who read these threads to learn stuff.)

Ken in Regina
What application did you use for the plot. That's pretty interesting.

Man, a ski hill out your back door and what looks like a pretty nice golf course about five minutes away. Life is tough!

Originally Posted by Ken in Regina
What application did you use for the plot. That's pretty interesting.

Man, a ski hill out your back door and what looks like a pretty nice golf course about five minutes away. Life is tough!

It's a another GPS program I wrote for my own use as an attempt to average fixes to determine true position.

The strategy is:

a) Use the first fix as a reference

b) Determine the scale of feet vs degree (WGS84 ellipsoid) at the reference fix

c) Plot successive fixes and calculate the mean center of the scatter plot; indicated by the + mark. As fixes are averaged that + approaches the true position.

d) Normalize the entire plot centering the + in the range circles; adjust the reference Lat and Lon by the amount of the plot centering shift to remove the bias.

I'm not sure how my methodology stands up to statistical rigor, but observations with Google Earth have consistently shown excellent congruence.

The histogram depicts range error counts at five foot intervals. You can intuitively judge how the process is progressing by its appearance. By the way, that's a Rayleigh Distribution.

The software reads NMEA GPRMC at 4800 baud. It's attached if anyone who would like to try it with no guarantees of performance.

--- CHAS
Attached Files
File Type: zip StatsGPS.zip (334.8 KB)
Ken in Regina
Thanks, Chas. I'll try to give it a whirl in the next few days. What I want to do is hook up my eTrex Legend HCx to the laptop. My Legend has an averaging function so I want to run them simultaneously. With the Legend as the GPS receiver I can compare the result of its averaging and your program's averaging from the same data stream. I'll let you know.

I keep hearing about RTK-based dual GPS/GLONASS hardware that combined with DGPS, aspires to accuracy of less than 1 meter. Perhaps as good as 10 cm. Good enough to allow autonomous navigation of vehicles. Is that accurate information?
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