Well, this sure took an interesting turn. I accumulated more than 12 hours of data from two GPS units sitting side-by side (one complete oribt of the GPS satellites), recording second-by-second. I then plotted their apparent-motion trajectories, individually, differentially, and as an average. Here are the plots (using the same relative scales for comparison):
The differential plot is clearly worse than the individual plots. But the big revelation is the average plot: it's much tighter than any of the others. This indicates that the errors between the two units are random rather than correlated. It also indicates that, if you have two GPS units, you will get tighter precision if you put them both on the roving platform and average their readings, rather than using one as a differential-reference base station.
In general, the standard deviation of the average of n independent observations is sqrt(1/n) of that of an individual observation. So, assuming the errors are random and independent across all 12 units (huge, unverified assumption), the standard deviation of their average would be about 29% of that from the individual readings. Notice that this says nothing of the accuracy -- only the precision.
I'm wondering if a better antenna setup might improve things - decent GPS antennas are careful to eliminate any reflected signal from the ground (the major cause of multipath reception in an open site). This sort of antenna for instance: http://en.wikipedia.org/wiki/Choke_ring_antenna
For the base station, you tell it its position in space and the distance to the satellite. The only variable is the quality of the signal, which the pseudorange tells you, and the base stations built in clock, which is usually sync'd with the mobile GPS to further increase accuracy.
You're looking at the cumulative errors on two similar units, the only correlation will be in the pseudorange data. The position data errors are most likely the two clocks being slightly out of sync. The DGPS base station can fix that problem, and if they were the same GPS, most likely show more of a correlation.
I'm wondering if a better antenna setup might improve things ...
It's possible. Not that things are bad, of course; the PMB-648 accuracy, by itself, is pretty darn good. But I'll give this guy (PMB-688 w/ external antenna) a run for its money tomorrow, and see how it compares:
I'm not sure if the antenna is of the choke ring variety, but the external shape suggests that it might be.
I must be missing something here. The GPS unit is placing it's position within a 1 meter circle. According to the FAA and Air Force data collections detailed on the gps.gov site, this is very good for high quality GPS units without using any augmentation services. The only way to get the cm accuracy is to tap into some of the augmented services.
With multiple units, isn't the best you could expect to see something like your averaged results. You still, at best are going to have numbers dancing around a 1 meter circle, aren't you?
It would be fun to set up this experimentation package in various locations around the country (or world) and see the results of the error circles.
Phil, you are right, better results averaging the readings.
Have to test it in open filed over a known coordinates point. A safe place in open filed will be the tricky part.
Massimo
re: DGPS came out after SA (selective availability) which was purposely induced errors to prevent GPS from being used against us, missile tracking, etc.
GPS Selective Availability signal degradation was discontinued May 1, 2000!
PRESS RELEASE FROM THE WHITE HOUSE
Office of the Press Secretary
For Immediate Release May 1, 2000
STATEMENT REGARDING THE UNITED STATES' DECISION TO STOP DEGRADING GLOBAL POSITIONING SYSTEM ACCURACY
Today, I am pleased to announce that the United States will stop the intentional degradation of the Global Positioning System (GPS) signals available to the public beginning at midnight tonight. We call this degradation feature Selective Availability (SA). This will mean that civilian users of GPS will be able to pinpoint locations up to ten times more accurately than they do now. GPS is a dual-use, satellite-based system that provides accurate location and timing data to users worldwide. My March 1996 Presidential Decision Directive included in the goals for GPS to: "encourage acceptance and integration of GPS into peaceful civil, commercial and scientific applications worldwide; and to encourage private sector investment in and use of U.S. GPS technologies and services." To meet these goals, I committed the U.S. to discontinuing the use of SA by 2006 with an annual assessment of its continued use beginning this year.
Even without selective availability, DGPS is still useful for applications such as surveying and automated farming, where centimeter accuracies are possible. But, AFAIK, DGPS is only available as a paid subscription or with expensive equipment. What I had hoped to accomplish in this thread (and sorta did, but rather obliquely) was a way to get some of the benefits of DGPS with bread-and-butter GPS modules, without the extraordinary expense.
With my work with the "Kansas City Space Pirates" we were looking at precision short range tracking methods.
One used a set of at least 3 laser beacons. Basically each rotating simultaneously in azimuth. A sensor on the vehicle times the reception of the pulses on the light sensor. The math wasn't to hard to extract the X-Y position with precision of an inch or better.
Only 2 laser beacons are required if a radio sync pulse is used.
The ultimate app I had in mind is robotic course-following, either land-based or aerial. Although I still believe it to be possible with inexpensive equipment, it has to be better than +/-10m. My objective is to bring that figure down to +/- 1m somehow. I have a Garmin Forerunner 405, whose GPS not only tracks my bike routes correctly, but puts me on the right side of the street most of the time when viewed in Google Earth. So I know that simple GPS units are capable of better accuracy than +/-10m.
'Just retrieved the PMB-688 from the garage roof. Here are the results, compared to the averages of the two PMB-648s:
The centroid is a little bit offset because the antenna was placed at a distance from the recording unit.
I guess the lesson here is that if you've got the money to spend on two PMB-648s and plan to average their readings to get better precision, buy one PMB-688 with an external antenna instead.
The Racelogic VBOX3i is claimed to be the fastest and highest accuracy GPS system commercially available. It uses real-time kinematics (RTK) techniques to achieve repeatable, stable results to within 2 cm and it can do this at a rate of 100 updates per second. By combining position accuracy with the ability to measure slip and pitch/roll angles at 100 Hz, the VBOX3i with dual antennas and RTK is an interesting solution for many vehicle-testing applications.
Featuring quick set-up and easy operation, it is flexible enough to be used for many kinds of tests, from brake testing to dynamic handling. The VB3iSL-RTK comes with an external VBOX Manager to give users control over the files they record. This device supports remote start/stop logging and assists users in setting slip angle data and antenna separation. A roof mounting pole is also available to ensure optimum
Position, direction and speed are calculated from a blend of doppler shift and position data with help of statistical and Kalman filtering methods in all GPS units and not from successive positions only.
The Racelogic VBOX3i is claimed to be the fastest and highest accuracy GPS system commercially available. It uses real-time kinematics (RTK) techniques to achieve repeatable, stable results to within 2 cm and it can do this at a rate of 100 updates per second. By combining position accuracy with the ability to measure slip and pitch/roll angles at 100 Hz, the VBOX3i with dual antennas and RTK is an interesting solution for many vehicle-
Featuring quick set-up and easy operation, it is flexible enough to be used for many kinds of tests, from brake testing to dynamic handling. The VB3iSL-RTK comes with an external VBOX Manager to give users control over the files they record. This device supports remote start/stop logging and assists users in setting slip angle data and antenna separation. A roof mounting pole is also available to ensure optimum
Wow, you guys are talking about what I'm trying to do. My idea is to have a GPS stationary module that a roving module can find with better than a foot accuracy. I was assuming that since most of the error comes from the signals travelling through the atmosphere, 2 modules in the same vicinity would produce the same position data even though it would contain some error in the absolute sense. However it is only relative data that would enable one module to find the other one. That is the theory anyway. When I actually had two modules a half a meter apart report positions, I was unpleasantly surprised to find that they did not correlate well. I now understand that the reason is there is no guarantee that they would use the same satellites, especially if one module travels in from a greater distance.
Talking with U-blox (the brand I am using) support, I found that there is not an interface option to force a module to use particular satellites. However I learned that most modules accept RTCM correction data and that some modules output a raw form of it. So the task at hand would be to take the raw data as outputted from the base module, put it into the correct RTCM format and send it to the roving module. Then the two modules should correlate very closely. Again, that's the theory.
Hi all, a question
your trying to create a static GPS beacon which is then used to improve a hand held GPS accuracy. Now you all seem very clever so this is a silly suggetion.
What you want is a fixed refrance point to use to create the correction data. Why not just use ordinance survey maps to find one..as I understand you can convert one to the other.....I realise this then only works from that location it's not portable. But when you then have a fixed point correctional data is far easier to generate. The actual beacon you have to create is far more simple. So in a way when you first reported results and it had the lock set.
with this you tell it it's location lock them in then use it as a refrance point to get your accuracy your after.
In a way all it needs to do is broadcast it's location on the correct signal and correctional data.
Your not trying to fix 2locations only one the handheld.
I may be missing something obvious so don't shoot me down in flames.
If the beacon was then programmable with a fix location GPS this then makes it portable as long as you work out this fixed location before hand.
Or in my case set up the beacon in the same location each time you can enjoy better tracking as the actual real world location is less important than been able to return to the same 1m2 area.
inaccuracies in the beacons location are irrelevant for a lot of applications if you want a lawn mower to know where it is say. As long as it knows where it is in relation to the static beacon.
It all comes down to how well you fix that beacon location. maps can be got at 1:200 scale online. With scanning and software you should get a good fix.
Comments
The differential plot is clearly worse than the individual plots. But the big revelation is the average plot: it's much tighter than any of the others. This indicates that the errors between the two units are random rather than correlated. It also indicates that, if you have two GPS units, you will get tighter precision if you put them both on the roving platform and average their readings, rather than using one as a differential-reference base station.
-Phil
In general, the standard deviation of the average of n independent observations is sqrt(1/n) of that of an individual observation. So, assuming the errors are random and independent across all 12 units (huge, unverified assumption), the standard deviation of their average would be about 29% of that from the individual readings. Notice that this says nothing of the accuracy -- only the precision.
-Phil
For the base station, you tell it its position in space and the distance to the satellite. The only variable is the quality of the signal, which the pseudorange tells you, and the base stations built in clock, which is usually sync'd with the mobile GPS to further increase accuracy.
You're looking at the cumulative errors on two similar units, the only correlation will be in the pseudorange data. The position data errors are most likely the two clocks being slightly out of sync. The DGPS base station can fix that problem, and if they were the same GPS, most likely show more of a correlation.
I'm not sure if the antenna is of the choke ring variety, but the external shape suggests that it might be.
-Phil
With multiple units, isn't the best you could expect to see something like your averaged results. You still, at best are going to have numbers dancing around a 1 meter circle, aren't you?
It would be fun to set up this experimentation package in various locations around the country (or world) and see the results of the error circles.
-Phil
30ft will cause robot mower to miss the garden gate by a bit!
Have to test it in open filed over a known coordinates point. A safe place in open filed will be the tricky part.
Massimo
A valid observation as ANY receiving antennae acts as a transmitting antennae by its design.
GPS Selective Availability signal degradation was discontinued May 1, 2000!
PRESS RELEASE FROM THE WHITE HOUSE
Office of the Press Secretary
For Immediate Release May 1, 2000
STATEMENT REGARDING THE UNITED STATES' DECISION TO STOP DEGRADING GLOBAL POSITIONING SYSTEM ACCURACY
Today, I am pleased to announce that the United States will stop the intentional degradation of the Global Positioning System (GPS) signals available to the public beginning at midnight tonight. We call this degradation feature Selective Availability (SA). This will mean that civilian users of GPS will be able to pinpoint locations up to ten times more accurately than they do now. GPS is a dual-use, satellite-based system that provides accurate location and timing data to users worldwide. My March 1996 Presidential Decision Directive included in the goals for GPS to: "encourage acceptance and integration of GPS into peaceful civil, commercial and scientific applications worldwide; and to encourage private sector investment in and use of U.S. GPS technologies and services." To meet these goals, I committed the U.S. to discontinuing the use of SA by 2006 with an annual assessment of its continued use beginning this year.
http://www.gps.gov/systems/gps/modernization/sa/data/
[h=2]GPS Accuracy Before and After SA Removal (Graph in the link)[/h]
http://www.gps.gov/systems/gps/modernization/sa/data/
Even without selective availability, DGPS is still useful for applications such as surveying and automated farming, where centimeter accuracies are possible. But, AFAIK, DGPS is only available as a paid subscription or with expensive equipment. What I had hoped to accomplish in this thread (and sorta did, but rather obliquely) was a way to get some of the benefits of DGPS with bread-and-butter GPS modules, without the extraordinary expense.
-Phil
Do you have an application for this?
With my work with the "Kansas City Space Pirates" we were looking at precision short range tracking methods.
One used a set of at least 3 laser beacons. Basically each rotating simultaneously in azimuth. A sensor on the vehicle times the reception of the pulses on the light sensor. The math wasn't to hard to extract the X-Y position with precision of an inch or better.
Only 2 laser beacons are required if a radio sync pulse is used.
Duane J
The ultimate app I had in mind is robotic course-following, either land-based or aerial. Although I still believe it to be possible with inexpensive equipment, it has to be better than +/-10m. My objective is to bring that figure down to +/- 1m somehow. I have a Garmin Forerunner 405, whose GPS not only tracks my bike routes correctly, but puts me on the right side of the street most of the time when viewed in Google Earth. So I know that simple GPS units are capable of better accuracy than +/-10m.
-Phil
The centroid is a little bit offset because the antenna was placed at a distance from the recording unit.
I guess the lesson here is that if you've got the money to spend on two PMB-648s and plan to average their readings to get better precision, buy one PMB-688 with an external antenna instead.
-Phil
Featuring quick set-up and easy operation, it is flexible enough to be used for many kinds of tests, from brake testing to dynamic handling. The VB3iSL-RTK comes with an external VBOX Manager to give users control over the files they record. This device supports remote start/stop logging and assists users in setting slip angle data and antenna separation. A roof mounting pole is also available to ensure optimum
http://www.velocitybox.co.uk/
Jim
Talking with U-blox (the brand I am using) support, I found that there is not an interface option to force a module to use particular satellites. However I learned that most modules accept RTCM correction data and that some modules output a raw form of it. So the task at hand would be to take the raw data as outputted from the base module, put it into the correct RTCM format and send it to the roving module. Then the two modules should correlate very closely. Again, that's the theory.
http://www.rt66.com/~shera/index_su.htm
Rick
your trying to create a static GPS beacon which is then used to improve a hand held GPS accuracy. Now you all seem very clever so this is a silly suggetion.
What you want is a fixed refrance point to use to create the correction data. Why not just use ordinance survey maps to find one..as I understand you can convert one to the other.....I realise this then only works from that location it's not portable. But when you then have a fixed point correctional data is far easier to generate. The actual beacon you have to create is far more simple. So in a way when you first reported results and it had the lock set.
with this you tell it it's location lock them in then use it as a refrance point to get your accuracy your after.
In a way all it needs to do is broadcast it's location on the correct signal and correctional data.
Your not trying to fix 2locations only one the handheld.
I may be missing something obvious so don't shoot me down in flames.
If the beacon was then programmable with a fix location GPS this then makes it portable as long as you work out this fixed location before hand.
Or in my case set up the beacon in the same location each time you can enjoy better tracking as the actual real world location is less important than been able to return to the same 1m2 area.
inaccuracies in the beacons location are irrelevant for a lot of applications if you want a lawn mower to know where it is say. As long as it knows where it is in relation to the static beacon.
It all comes down to how well you fix that beacon location. maps can be got at 1:200 scale online. With scanning and software you should get a good fix.