GPS

[meierlde]

I felt that I should make another post to hopefully dispel some confusions over GPS accuracy.

If you search the Web, you may stumble across some US Government official documents that describe the accuracy of even the military signal (called P/Y code, or PPS for Precise Positioning Service) as something like 6 m horizontal error, 95% probable. What that means is that over all conditions, all places on earth, and all time of day (remember that the satellites move and do not stand still), you can be sure that the horizontal error will be less than 20 ft, 19 out of 20 times.

That may appear crummy, and contradicts with the centimeter accuracy that is claimed by people who use GPS for surveying. So, what is the truth?

The answer is that both claims are correct. The difference is like trying to compare apples and oranges.

The surveyors use a method called differential GPS. And by using a technique called carrier phase tracking, they do get errors to less than 1". However, this accuracy is with respect to a reference GPS receiver set at a known reference location, and is achieved by logging data over a period, then doing some post-processing. It is not to be compared to the normal use of a stand-alone GPS like the normal use in a mobile application.

So, for surveying one can see that the absolute accuracy depends on the precision of location of the reference station. That reference location itself may not be known that well within the WGS-84 reference system, and may have to be adjusted. I guess that's what Ronstar said about the survey point coordinates being moved every so often.

I hope that clears up some questions readers may have about some apparent conflicting info.

But, can I raise another question, if anybody is really curious about all this GPS stuff?

Now, we know that the basic principle of operation of a GPS receiver is that of measuring the ranges to the satellites. The range to a satellite is measured by the propagation delay of the satellite signal to the receiver. Knowing the satellite positions and the ranges to them, we should be able to compute the receiver 3-D position using 3 satellites. However, because we do not have an atomic clock that is synchronized to the GPS system time, we need a 4th satellite to solve for that 4th unknown, meaning time. And how do we know the satellite positions? They tell us that by broadcasting their orbital parameters.

Here's the question. How do the satellites know their position?

As stated in this Wikipedia article there is a contingent of the airforce that tracks the GPS satellites and updates their clocks and onboard models of the orbit of the satellite. Global Positioning System - Wikipedia, the free encyclopedia

The European and Russian systems must have a similar tracking and update service as well.

 

[NW-Bound]

One of the great benefits of not working is only solving the problems I want to solve.

Well, it is not really that hard like actually solving the problems. I never did work on the so-called Space Segment of the GPS system.

It's more like asking about how things work, generally speaking of course, without using any math or equation. It's really something we are usually curious about, but often overlook or do not think of asking ourselves.

Here's a personal example. Though not a mechanic, I have worked on gasoline engines all my life, from small 2-cycle engines to big V-8s. But I have not been exposed to diesel engines. So it was only recently that it occurred to me that diesel engines do not have a throttle like gasoline engines. Yes, I knew how diesel fuel was injected, blah blah blah, but I did not make the connection to the missing butterfly throttle, and that diesel engines draw full air all the time.

 

[NW-Bound]

As stated in this Wikipedia article there is a contingent of the airforce that tracks the GPS satellites and updates their clocks and onboard models of the orbit of the satellite. Global Positioning System - Wikipedia, the free encyclopedia

The European and Russian systems must have a similar tracking and update service as well.

Ah yes! The satellites do not know their position and have to be told. Ground stations are used to track the satellites and upload their orbital parameters, which are then broadcast back to the GPS user receivers.

The ground stations compute the satellite positions by the inverse ranging, by knowing their own position and measuring the range to the satellites.

OK! Now, how do the ground tracking stations know their own positions?

 

[meierlde]

Ah yes! The satellites do not know their position and have to be told. Ground stations are used to track the satellites and upload their orbital parameters, which are then broadcast back to the GPS user receivers.

The ground stations compute the satellite positions by the inverse ranging, by knowing their own position and measuring the range to the satellites.

OK! Now, how do the ground tracking stations know their own positions?

As with all surveying you need to define a point as the origin. Then using todays technology of very long base baseline interferometry you can find out to inches how far it is to another point from the point of origin (this is how they track plate movements) do enough of these and assume a figure for the earth such as wgs 84 or newer and you have the location for the tracking stations. Here is Wikipedia on vlbi Very-long-baseline interferometry - Wikipedia, the free encyclopedia.

It was vlbi that discovered that surveying over an ocean had large errors in the distance between continents. VLBI then corrected it.

 

[Ronstar]

I felt that I should make another post to hopefully dispel some confusions over GPS accuracy.

If you search the Web, you may stumble across some US Government official documents that describe the accuracy of even the military signal (called P/Y code, or PPS for Precise Positioning Service) as something like 6 m horizontal error, 95% probable. What that means is that over all conditions, all places on earth, and all time of day (remember that the satellites move and do not stand still), you can be sure that the horizontal error will be less than 20 ft, 19 out of 20 times.

That may appear crummy, and contradicts with the centimeter accuracy that is claimed by people who use GPS for surveying. So, what is the truth?

The answer is that both claims are correct. The difference is like trying to compare apples and oranges.

The surveyors use a method called differential GPS. And by using a technique called carrier phase tracking, they do get errors to less than 1". However, this accuracy is with respect to a reference GPS receiver set at a known reference location, and is achieved by logging data over a period, then doing some post-processing. It is not to be compared to the normal use of a stand-alone GPS like the normal use in a mobile application.

So, for surveying one can see that the absolute accuracy depends on the precision of location of the reference station. That reference location itself may not be known that well within the WGS-84 reference system, and may have to be adjusted. I guess that's what Ronstar said about the survey point coordinates being moved every so often.

I hope that clears up some questions readers may have about some apparent conflicting info.

But, can I raise another question, if anybody is really curious about all this GPS stuff?

Now, we know that the basic principle of operation of a GPS receiver is that of measuring the ranges to the satellites. The range to a satellite is measured by the propagation delay of the satellite signal to the receiver. Knowing the satellite positions and the ranges to them, we should be able to compute the receiver 3-D position using 3 satellites. However, because we do not have an atomic clock that is synchronized to the GPS system time, we need a 4th satellite to solve for that 4th unknown, meaning time. And how do we know the satellite positions? They tell us that by broadcasting their orbital parameters.

Here's the question. How do the satellites know their position?

Well said NW-Bound. Part of the reason for the coordinate change is improved accuracy made possible by an increased number of GPS baselines, and part is due to movement (1-2 mm per year) of the North American tectonic plate.

As to post processing - we no longer need it in the Chicago area. We subscribe to the regional Trimble VRS system that consists of several base stations whose data is transmitted to our receivers instantaneously. That coupled with observations on US and Glonass satellites (maybe 10-20 at a time) provide us with sub centimeter accuracy in a 1 or 2 second observation.
Trimble - Positioning Services - Trimble VRS Now

As to satellites knowing their position - I do not know the specifics, but after the launch, the government performs several weeks if not months of analysis on the orbit before it's ephemeris is derived.

In the old days of post processing data from few satellites, it was important to know the health of satellites. Toward the end of their life cycles, satellites would produce bad data for a while until the gov't turned off the satellite. During that time, the data had to be analyzed and faullty satellite data manually removed from the solution.

 

[ERD50]

But, can I raise another question, if anybody is really curious about all this GPS stuff?

...

Here's the question. How do the satellites know their position?

Yes, very interesting to some of us. I attended an in-house seminar at MegaCorp about 12 years ago that spent about half a day getting us familiar with GPS basics. I was really impressed with the technology, and the thought that went behind it.

Don't know the answer to your question, but I did remember why 4 satellites were the minimum required, and I recall that they picked up a repeating signal and just kept accumulating that signal until the sum (correlated) popped out of the noise (uncorrelated). And something about an 'almanac', that I think told the GPS unit where (or which?) to look for the satellites at that time.

So the summing explains how they can pick up such low level signals. What I don't understand is how this is resistant to being jammed by the enemy. Seems it would easy to mess with such a low level signal.

-ERD50

 

[NW-Bound]

As with all surveying you need to define a point as the origin. Then using todays technology of very long base baseline interferometry you can find out to inches how far it is to another point from the point of origin (this is how they track plate movements) do enough of these and assume a figure for the earth such as wgs 84 or newer and you have the location for the tracking stations. Here is Wikipedia on vlbi Very-long-baseline interferometry - Wikipedia.

It was vlbi that discovered that surveying over an ocean had large errors in the distance between continents. VLBI then corrected it.

VLBI indeed plays a part in modern geodesy, but there are other techniques that allow researchers to collect a lot more data and over more places on earth a lot quicker. See: Satellite geodesy - Wikipedia.

The reason for collecting a lot of data is to establish a global reference system, which is more involved than defining some origin points like done in the past. But what kind of data? Please read further.

Surveying used to be done with reference to some known landmarks, called geodetic datums (not data!). See: http://en.wikipedia.org/wiki/Datum_(geodesy).

Starting from the 1950s, the drive was towards a common and global reference system, hence the procession of World Geodetic System 60 (WGS60), WGS66, WGS72, and the current WGS84. See: World Geodetic System - Wikipedia.

WGS defines a reference ellipsoid that best matches the earth's mean sea level (MSL) surface. The problem is that the earth core is not homogenous, and its actual equipotential surface at MSL has significant deviation from the ideal ellipsoid. This is caused by gravity anomalies and deflections of the vertical. See: Gravity anomaly - Wikipedia and Vertical deflection - Wikipedia.

Hence, latitude and longitude of a point as defined in WGS84 may differ significantly from latitude and longitude of the same point, but obtained the old way by star sighting. See: Latitude - Wikipedia, the free encyclopedia and Longitude - Wikipedia.

The altitude as defined in WGS84 (or GPS altitude) also differs from the MSL altitude by a significant amount. The difference can be as high as a few hundred feet. Many GPS receivers now incorporate an altitude correction table, so that they can display MSL altitude. Many early GPS users were perplexed when they saw that their GPS receivers showed a big number (may be negative too) for altitude when they were right at the beach. They might not know what the old latitude and longitude was, but they surely expect an altitude of 0 right at the beach. No, GPS was not wrong; it was just different!

The actual MSL surface of the earth is called the geoid which undulates above and under the reference ellipsoid. As the geoid surface is defined by the earth gravity with all its local variations from the ideal values, the two are tightly related. Spherical harmonics is the most convenient way to express the earth gravity model, using field measurements that were collected. As more and more data is incorporated, the degree and order of the spherical harmonics keep increasing. See: Geoid - Wikipedia.

I was surprised to learn that they now have up to degree 2160 and order 2160. Moreover, the entire model with over 4 million coefficients is now available to the public. Fifteen years ago, it used to be that even much smaller models were classified data, as they would be useful for ICBM trajectory calculations among other things. Amazing!

 

[NW-Bound]

As to post processing - we no longer need it in the Chicago area. We subscribe to the regional Trimble VRS system that consists of several base stations whose data is transmitted to our receivers instantaneously. That coupled with observations on US and Glonass satellites (maybe 10-20 at a time) provide us with sub centimeter accuracy in a 1 or 2 second observation.
Trimble - Positioning Services - Trimble VRS Now

Very cool! As I know, Trimble has been into higher-end products for specialized applications, and this service they provide would be much appreciated by people like yourself.

Back in the early 90s, I was involved in a civilian GPS application. As S/A degradation was on during that time, the GPS position would have jitters as high as a few hundred feet, which made it not usable for what we wanted to do. We did not need precision to the inch, only a couple of feet. The way to do it then was to establish our own reference station, and use a dedicated radio link to transmit the correction data. That was the way everybody was doing it then. The problem is the hassle of getting FCC frequency clearance.

And then, in the late 90s, there was a company that sold subscription to their differential correction, which was broadcast on the SCA subcarrier of some FM radio stations around the country. We bought their data receiver and incorporated it in our product. Then, the S/A was turned off and the business model of this company vanished overnight! I do not even remember the name of this company, but just realized I may still have one or two of their differential data receivers in my attic or garage. Gosh, I still keep a lot of junk!

Further more, there was WAAS that the FAA started working on in the mid 90s, and what everybody could use. See: Wide Area Augmentation System - Wikipedia

As to satellites knowing their position - I do not know the specifics, but after the launch, the government performs several weeks if not months of analysis on the orbit before its ephemeris is derived.

Even once in operation, each GPS satellite ephemeris must be uploaded by the ground tracking station every few hours. Yes, the satellite actual orbit deviates from the ideal orbital calculation that quickly. In fact, one of the drivers of the error budget of GPS is called AOD (age of data).

This frequent update of the satellite ephemeris causes another problem. The discontinuity in satellite position when the satellite starts broadcasting a new ephemeris means a corresponding jump in the GPS ground user position! That may cause problems in some critical applications.

 

[NW-Bound]

I recall that they picked up a repeating signal and just kept accumulating that signal until the sum (correlated) popped out of the noise (uncorrelated). And something about an 'almanac', that I think told the GPS unit where (or which?) to look for the satellites at that time.

So the summing explains how they can pick up such low level signals. What I don't understand is how this is resistant to being jammed by the enemy. Seems it would easy to mess with such a low level signal.

-ERD50

The "payload" of the GPS C/A signal is a very low 50 bits/sec data rate, mainly to broadcast the satellite ephemeris and various status bits. As any radio amateur would know, this low data rate could be transmitted in an extremely narrow bandwidth signal. However, GPS uses "spread spectrum", whereas the signal is further modulated by a repeating pseudo-random code of a higher bit rate. That spreads out the bandwidth of the signal to a few megahertz. Each GPS satellite uses a different code, although they all transmit on the same frequency.

To tune into a particular satellite, the receiver uses correlation to match the intended signal. The correlator then rejects the unmatched or undesired codes.

This spread spectrum technique is quite common, and used by some US cell phone carriers (IS-95 standard by Qualcomm).

About jamming, one can see that if the code is known for the public to receive, anybody can transmit the same for jamming. On the other hand, since the military code is secret, one needs a much higher level signal to overcome the correlator for a P(Y) code, which is designed to tune in to only the wanted signal (and known only to the GPS satellites and intended receivers).

PS. Worse than jamming is "spoofing", where one can pretend to be a GPS satellite and transmit false data to drive the receivers to the wrong position. Very, very bad! Some receivers do have logic to protect themselves against this. See Receiver autonomous integrity monitoring - Wikipedia.

 

[NW-Bound]

You asked about the "almanac". This is an abbreviated version of the orbital parameters. It does not allow the receiver to compute a satellite position to the level of accuracy good enough for navigation, but only so that the receiver would know what satellites are above the horizon. Else, the receiver software would keep looking (with its correlators) for signals that are not there.

Because the almanac is only used for acquiring the signals, it does not have to be accurate or fresh. Six months or a year old would still be good. Once the receiver has locked onto a signal with its correlator, it then decodes the 50 bps data stream to get the ephemeris, then the ranging computation to the satellite can begin.

Note that if the receiver does not know roughly where it is, nor a rough time, then it is the same as not having the almanac. It would have to do a cold search, and it would take longer to obtain a position fix.