We've all spoken to GPS users who've told us of their wonderful receiver which is accurate to a metre. I must admit I've seen receivers of my own giving a position to about 1 metre by 1 metre - but how often does that happen, and how much can we rely on that kind of performance?
The simple answer is not much; I'll endeavour to explain why below. Note that the numbers in brackets after various topics (such as 1.) refer to paragraphs where more detail is provided.
In simple terms, your receiver determines its position by being able to calculate its distance (called pseudorange, see 7. below) from several simultaneously observed satellites. It has to know where each satellite was when the measurement code signal was dispatched (from the broadcast ephemeris, see 1. below ) and it has to be able to match its own clock to GPS time to know the time difference between the instant the signal started and the instant it was received. If the satellites are not quite where they say they are; if the transmitted signals are delayed; if the timing corrections are faulty; if your receiver has excessive measurement noise; or if the available satellites are in a poor configuration, the position your receiver displays can be tens of metres off - even today without SA (see 8. below). Accurate positioning using DGPS, RTK, or phase measurements (see 9. below) remove most of these errors to produce sub-metre to millimetre level fixes - but no single receiver can match this.
If you want to determine your position on a highway, at sea, or on the side of a mountain, a single autonomous fix is probably going to be adequate. Don't expect an autonomous position to be better than + or - 15 metres and you're being realistic. Don't be surprised if fixes on different days are 30 metres apart. If you want to map your cultivated field, or features in a community, then you need to advance to the more accurate GPS methods described in 9. below. If you want to find your way into a harbour in a fog or land an aircraft in zero-zero (see 10. below) then you need all the GPS enhancements you can get.
The FAA monitors the performance of the GPS and Glonass (Russian) systems in order to gauge the accuracy and reliability for civil aviation use. In the quarter ended on Dec 31st 2000
they found the average accuracy from their monitor stations was from 5 to 6 metres. (At one station 7.4 metres.) The maximum horizontal errors measured at the nine stations ranged from 16.8 to 22.1 metres. Now these were in fixed locations, the antennas were not moving past obstacles or under trees, so they were ideal figures, not the realistic ones the average user may expect. However, they give the repeatability (two readings at the same place but different times) as being accurate to between 2.147 and 2.678 metres no more than 95% of the time - so much for buddy, whose receiver is always accurate to a metre.
1. Errors from the satellites:
The accuracy of the orbit information broadcast by the satellites is not perfect. The satellites are all monitored by the US Air Force ground stations and their orbit parameters are calculated by a kind of reverse GPS program which compares their pseudoranges to the known tracking station locations. From this information a prediction of each satellite's future orbit parameters is produced and this predicted information fed to each satellite up to a day ahead of its broadcast. While this is probably more exact than stock market predictions, at the time your GPS receiver is tracking it a satellite could be either ahead or behind in its orbital track and the orbit could be a few metres away from prediction. The more satellites you're tracking, the better each one's individual errors will cancel (you hope) rather than compound.
Timing errors are important because it's the measurement of time displacement of the code signals which the receiver uses to calculate the psuedoranges. The system uses highly accurate atomic clocks on the ground and in the satellites to produce a precise system time. When it begins to track, your receiver uses the broadcast clock data to correct its own electronic time circuits to this standard but there are, inevitably, errors. Even a nanosecond multiplied by the speed of light is about 0.3 metres.
It's estimated that putting these errors together can produce a User Equivalent Range Error (UERE) of about 5 metres.
2. Errors on the way:
The satellite signals travel through the ionosphere and troposphere on the way to your receiver and both affect the speed at which the signals travel. Since these instantaneous effects cannot be measured they give an unknown time error in the measurement of the psuedorange proportional to the length of path. Internally the receivers have a modelling program which allows a theoretical correction for the altitude of the satellite. Only dual frequency receivers, with the ability to compare the biases in both the transmitted satellite frequencies, allow the actual delays to be measured. No hand-held civilian GPS receiver can do this.
The ionospheric and tropospheric errors are least for satellites at zenith and greatest for satellites near the horizon - which is why good receivers allow the user to set elevation cut-off. The errors are especially bad near dawn and dusk when the ionospheric changes are greatest, and often receivers will report repeated loss of lock at these times. These errors can be as little as a metre or two, or up to 50 metres or more.
3. Errors in your hand:
We all understand the term receiver noise when it's applied to a communications radio - it gives us the crackles and pops which make it hard to make out what's being said. In a GPS receiver the noise translates into errors in range measurement. Not all receivers are equal, some are noisier than others. Manufacturer's published data are not going to give you a number on this, but experience with different units will let you know which receiver might be reading within 5 metres of true while another is 20 metres off.
What's going on inside the receiver can affect displayed accuracy as well. When Selective Availability (SA, see 8. below) ended, I took a hand-held receiver to a known point and was pleased to see a reading within a metre or so in the WGS84 datum. When I switched to the NAD27 datum this same receiver was now about 15 metres out - purely as a result of a poor internal conversion. Not only that, but when I tried each of the different varieties of NAD27 offered (for Canada East, and West, and Alaska etc) they all gave the same number - which didn't give me a good feeling about the manufacturer. This same receiver also displays time two seconds slow and their tech support says it cannot be corrected.
4. Errors on the horizon:
Since the position reported by the GPS receiver comes from measurements from a number of satellites, the configuration of these can result in either a strong or a weak position solution. This is called DOP, Dilution of Precision - HDOP for horizontal, VDOP for vertical, PDOP for position, and so on. If the satellites being received are well spaced around the horizon and complemented by one overhead, the PDOP could be less than 2, and the position given will be accurate to twice the compounded UERE mentioned above. If there are only four or five satellites visible, and they are grouped in one segment of sky the PDOP can be in the tens or even hundreds, and the position reported totally unreliable. In mapping we generally discard positions produced with a PDOP higher than 7, depending on the mapping accuracy required. Hand-held GPS receivers tend not to report PDOP, as the manufacturers would rather use their own reassuring numbering system for quality. Just take a look at the satellite positions reported on the appropriate screen and decide for yourself whether they're spread out enough to give a good fix.
5. Errors overhead:
It's easy to compare the reliability of a GPS receiver in the open with the same receiver under tree canopy. All sorts of things happen to the signals under tree canopy. Satellite signals can come and go, not only as the receiver and its antenna move but as the satellites move their positions in the sky. Since the accuracy of position depends upon the configuration of the satellite constellation, the loss of a satellite creating good geometry can mean a jump in reported position of many metres. GPS receivers, no matter how brainy in computation, are dumb in judgement. They cannot compare one position report with another and decide from the discrepancy that something is amiss - in fact there is no "carry-over" from one fix to the next, so there may be no relationship between them. It's this that has lead the aviation community to require a system of integrity monitoring before GPS can be used in critical navigation situations, such as instrument landing. It's also the reason why a map produced with an autonomous GPS receiver can have large distortions - unless the area mapped is very large in comparison to the probable errors.
I have a pair of old hand-helds which allow position averaging, and can smooth the errors to some degree. I can also download data to a computer and weed out fixes that look suspicious, but it's not as productive as going to differential positioning (9. below) would be.
6. Multiplying errors:
Multipath, where the signals are split into two or more paths by reflection or refraction, can complicate the receiver resolving a good psuedorange. Signals can reflect off a metal building, a tree, or almost anything, and as well as causing a measurement error it can also cause something I've never seen described in the literature but which could be called bamboozling.
The positions reported by the early Magellan differential GPS I used would, when the receiver passed under some trees, suddenly zoom off into the sky at flying saucer speeds. For some reason the software had stopped taking the movement of the satellites into account and assumed the receiver was keeping pace at nearly 10,000 mph. Magellan were able to fix this when the information I sent back to them helped pin down the problem, but I once saw something like it in data from my older single frequency Ashtechs as well. I've also seen the plot screen of another receiver show a one city-block jump in mapping position part way into a small town. I suspect this was a result of the poorly matched external antenna that the manufacturer sold.
7. Pseudorange and satellite fixes:
A GPS receiver measures the time shift in the code signals by comparing the code at transmitted time with the code at receive time. Before this can be done the receiver needs to have been tracking four or more satellites long enough to have computed a time correction. This time shift is multiplied by the speed of light to derive an approximate distance (without accounting for possible transmission errors) called pseudorange from that satellite. Knowing the pseudorange from three or more satellites allows it to resolve a point on the earth's surface where these ranges intersect.
8. Selective Availability:
Although SA is gone, the issue of military security hasn't, and the Pentagon is developing methods whereby accurate GPS measurements can be denied to enemies in time of conflict. These would likely be in the form of service interference in conflict areas. What SA did was dither the satellite clock corrections to introduce an error of up to 100 metres horizontal (and 156m vertical) to the Standard Positioning Service (SPS) fixes. Several SA methods were tried in the early to mid Nineties, some of which produced errors as much as 500 metres at times, and others which were less than random and would average out nicely if data was collected for long enough. Ironically, whenever the US military was engaged in conflict during the Nineties (the Gulf War and Grenada for example) the SA was actually switched off, because the US and its allies were making a greater use of the civil GPS service than was the enemy.
9. Differential and beyond:
With real-time DGPS and RTK (Real Time Kinematic) an operator with GPS can obtain an accurate fix within the working area in a matter of seconds. I was working this past winter with a company using RTK to map culture and mark survey line positions. I was delighted to find, when setting survey lines on the edges of some frozen lakes, that using the data to set a theodolite between any two of these points I could swing the instrument to any other fix hundreds of metres across the lake and find the survey stake square in the cross-hairs. The mapping operator would write the fix coordinates on the lath for our use and generally alter his day's schedule to come and run us some new points whenever we ran out. It was truly the realisation of a survey dream generations old.
Two methods of differential corrections are used - the simplest determines the present error at a known point and applies that correction to other roving receivers. The other method uses the measured satellite data to calculate not a position fix but a vector. Software compares the differences in measurements between antennas at two different sites to compute a distance and direction between them. When one location is known precisely the other can be fixed accurately provided they are close enough that the satellite signals are travelling through similar ionosphere and troposphere. When the measurement is carried out with the GPS SPS code data the level of accuracy is to a metre or so - or sub-metre with close-correlator type receivers. When using the carrier phase data the measurements are carried out on the high frequency carrier wave and can be as precise as a few millimetres, although good surveying techniques from the operators, and longer data collecting sessions are called for to attain this. Actually, the Navstar GPS system was never designed for these purposes, but the development people recognised the possibility early and wrote software to resolve a factor called Ambiguity in order to realise it.
The code measurements in GPS are resolved from a signal wavelength of 293 metres - the carrier measurements on a wavelength of 19cm. giving 1500 times the resolution. The problem was that - unlike the coded signals - the carrier carried no way of reading the number of whole wavelengths between the satellite and receiver. The solution of this unknown factor comes from a huge number of statistical estimates of ranges that only a computer can carry out in less than months of human effort - until a number is attained that answers to all the varying ranges in the survey session. Many surveyors, trained in the old school where one always verified one's surveys by cross-checking and calculation, are still too suspicious of this mathematical sleight of hand to use GPS.
Differential GPS can be conducted in real time or post processed, the first depending on the reliability of radio communications and - sometimes - one's patience with the kind of UHF two-step that cell phone users hate. Most hand-held GPS receivers will accept differential corrections by radio. Some services are offered world-wide from communications satellites, some area-wide by FM radio stations, and some can be set up by the users - the only variables are accuracy and cost. Two concerns are that the base (or virtual base) from which the corrections are derived should be no more than 10kms away for RTK and no more than 800 km for code differential, and also that the correction rate should allow the roving receiver to get a new correction packet every few seconds.
10. Integrity monitoring and On-the-Fly DGPS:
Where lives depend on the reliability of the GPS fix the system requires two enhancements. One is to upgrade the fix accuracy by one of the differential methods described in 9. above. Even the early experiments showed the excellent potential of On-the-Fly by fixing the track of a test aircraft to centimetre accuracy while it was on its final approach. The other enhancement must show the user monitoring information which assures him or her that the fixes are not degraded. Accurate surveying is always carried out between three or more points at once - two of them known. If the baseline between the known points goes off, then the unknown point fix is likely suspect. This procedure is used in various proposed blind landing systems to ensure the instantaneous corrections relayed to the aircraft are good. The system also monitors continuity between successive fixes for a smooth and believable track, which no simple GPS receiver can do. To see this problem demonstrated, watch a track plot as you travel under tree canopy and see the big jumps in your track every time the constellation changes due to trees blocking satellites.
I've used - as well as personal experience - several references to check numbers used in this article. "Guide to GPS Positioning" by Canadian GPS Associates, "GPS Positioning Guide" from the Geodetic Survey of Canada, the FAA quarterly report for October-December 2000, an article in GPS World "The GPS Error Budget" March 1997 by Prof. Richard Langley, and a paper by Gourevitch, Qin, and Kuhl presented at ION 1992 called "Very Precise Differential GPS". If there are still errors, they're all mine - I'm an oil-patch surveyor, not an electronics tech or a mathematician.
(published June 18, 2001)