Jump to content
Sign in to follow this  
Followers 3
GSHastings

GPS Accuracy

Recommended Posts

I guess that I had a nomenclature issue WRT altitude and elevation.  I used the "feet on the ground" discriminator.  For example, getting on an airplane at my local airport, SNA or JWA, I was 39 feet elevation.  https://forecast.weather.gov/MapClick.php?lat=33.6798&lon=-117.867#.XBPMp2jYrIU

After take off, we were gaining altitude.

 

Well, what do I know?  OTOH, as lead engineer of the Delta II Launch Vehicle, I participated in many of the current generation of GPS satellite launches.  All were successful, so I guess that no harm done using VAFB launch pad elevation for prelaunch calculations and vehicle altitude for trajectory calculations.

 

WHEW, how lucky was I?

  • Love 1

Share this post


Link to post
3 minutes ago, arisoft said:

 

Well...  The rocket has only failed a couple times, most spectacularly in 1997 when a Delta II carrying a GPS satellite exploded shortly after liftoff, prompting a launch director to say "Boys, this is bad," and dive under a computer console.

Well, I was on the team at that time and I can note that I was on the failure investigation team.  It was the casing of one of the solid motors that ruptured immediately after ignition.  We never did determine the exact cause of the casing failure.  However, we did not make the casing but we did review its product acceptance documents and accepted it.  

 

I didn't dive as I was not at the launch site; I was in a communications room in our home facility monitoring the prelaunch activities.

Share this post


Link to post
On 12/13/2018 at 8:26 AM, Red90 said:

My degree in mathematics says otherwise.  3 satellites provide a hoziontal (2D) location.  Four to give altitude (3D).  With 3 satellites, they assume altitude. 

 

Ignoring the Earth, just thinking in 3D space.  Distances from three points provides 2 intersections.  Now, being on the surface of the Earth, ... here I realize the confusion. Being a smartphone user, the phone can deduce which of the 2 locations is more likely based on other data, like service provider, cell towers, recent location, etc. Where a smartphone can 'talk' to another non-satellite source, a handheld GPSr may require the 4th satellite to make that distinction if it has no recent data from which to deduce.

However, once either device has its single location, to whatever accuracy (in 3D space), altitude and/or elevation can be determined. One way is by cross-referencing the elevation at the lat/lon calculated and citing the difference to the device's location in 3d space. Or having the algorithms for the curvature of the earth calculate the height over sea level for the calculated lat/lon.  Point being, with a single location determined from the intersections, the 'location' (+/- accuracy) is already in 3D space, thus elevation can be calculated relative to sea level (whether you're on the ground or flying in an airplane).  4 or more satellites (depending on device) strengthen the accuracy of the gps location. The more spheres intersect in the general vicinity (within meters or less), the closer the average will be to the actual location. (barring signal loss and bounce and other uncertainty factors)

 

ETA: As for time error, that's a matter of accuracy, really. It's a +/- give or take from the calculated location (one of 2 intersection points in 3-space having 3 spheres). The 4th (sphere) isn't required to determine a single intersection of the two unless no other reference data indicates which of the two points is most likely. But the 4th (sphere) will absolutely confirm and reduce intersection points from 2 to 1 if any device receives the 4th satellite signal (and helps to improve calculation accuracy)

Dislaimer: IANAM(athematician) - but I understand geometry ;P

Edited by thebruce0

Share this post


Link to post
9 hours ago, thebruce0 said:

Ignoring the Earth, just thinking in 3D space.  Distances from three points provides 2 intersections.

 

9 hours ago, thebruce0 said:

Dislaimer: IANAM(athematician) - but I understand geometry ;P

 

These 2 intersection points are very distant. They are on the opposite sides of the plane defined by the three reference points. One point is near the Earth and another far in the space because a receiver can receive only visible satellites over the horizont.

 

It seems that you still think that the timing problem is just a matter of precision. To get even a coarse estimation about your position with three satellites, you have to add more data to the equation. The easiest way is to guess that you are on the surface of the Earth. With this fourth distance from the center of the Earth, you can solve the equation, but only if you are on the surface of the Earth.

Edited by arisoft

Share this post


Link to post

We all know you need three signals to triangulate anything (thus 'triangulation'). Simple enough.

 

Because the consumer grade GPSr internal clock is nowhere near accurate enough to measure the timing of those three signals in relation to each other;

 

The fourth signal is required simply to time the reception of the first three (using the atomic clock on the fourth satellite) to arrive at an accurate solution for current position.

 

This is as simple an explanation I believe possible.

Share this post


Link to post
16 hours ago, thebruce0 said:

ETA: As for time error, that's a matter of accuracy, really. It's a +/- give or take from the calculated location (one of 2 intersection points in 3-space having 3 spheres). The 4th (sphere) isn't required to determine a single intersection of the two unless no other reference data indicates which of the two points is most likely. But the 4th (sphere) will absolutely confirm and reduce intersection points from 2 to 1 if any device receives the 4th satellite signal (and helps to improve calculation accuracy)

Dislaimer: IANAM(athematician) - but I understand geometry ;P

Edited 16 hours ago by thebruce0

IM(not so)HO, I would not discuss both horizontal and vertical accuracy in a paragraph including both.  Characterizing the normally distributed random errors of both quantitatively by their standard deviations, I have a four times greater value for vertical than for horizontal.

 

Consequently, I prefer to discuss them individually and separately.  There is a calculational consideration regarding vertical errors that does not apply to horizontal.

 

DISCLAIMER:  I do not have a university degree in mathematics.

Share this post


Link to post

 

11 minutes ago, Team CowboyPapa said:

IM(not so)HO, I would not discuss both horizontal and vertical accuracy in a paragraph including both.  Characterizing the normally distributed random errors of both quantitatively by their standard deviations, I have a four times greater value for vertical than for horizontal.

 

Position is calculated in XYZ coordinates in Earth-centered, Earth-fixed (ECEF) frame. 

This cartesian three dimensional position is then converted to one the user have chosen, like WGS-84.

Reason why the height is less accurate comes from the fact that receiver can only see satellites above the ground, practically in one direction respect to height axis. To get a good dilution of precision you need signals from many directions.

Share this post


Link to post
24 minutes ago, arisoft said:

 

 

Position is calculated in XYZ coordinates in Earth-centered, Earth-fixed (ECEF) frame. 

This cartesian three dimensional position is then converted to one the user have chosen, like WGS-84.

Reason why the height is less accurate comes from the fact that receiver can only see satellites above the ground, practically in one direction respect to height axis. To get a good dilution of precision you need signals from many directions.

 

Nice attempt, but not what I will post in a while.

Share this post


Link to post

Vertical Error Analysis

 

I will firstly pose an analogy that all should find reasonable and the provide an example applicable to the elevation errors.

Newborn weighed shortly after birth at hospital delivery room as 10 lbs. Newborn, infant scale label specifies accuracy as ±1.00%. Consequently, baby could have a weight between 9.9 and 10.1 lbs, or an error of ±0.10 lb.

 

Next day, that scale is not available. However, quite accessible is an adult scale with the same ±1.00% accuracy, but it cannot display less that 150 lbs. Therefore, a custodian is asked to get on the scale and displayed weight is 200 lbs, or the actual weight could be between 198 and 202 lbs (±1.00%). Custodian is then handed the infant and the display is 210 lbs, or actual weight between 208 and 212 lbs (±1.00%). Subtracting, the possible range values (212 – 198 and 208 – 202) for the weight of the baby yields the possibility of between 6 and 14 lbs, or ±40%, approximately.

 

Now, applying the issue of accuracy to instances of subtracting one large value from another to obtain a small remainder to a GPS determined elevation, let's look at my backyard which the average 40 GPSr readings yields 7 feet. AMSL.

1. GPS satellite elevation of 12,550 miles, or 66,264,000 feet

2. GPSr calculates distance above my back yard of 7 feet less, or 66,263,993.

3. What % error would ensure an accuracy of ±13 feet, or elevation between -6 feet and 20 feet?

4. Or, does not that subtraction question apply to elevation determinations?

5. If it does apply to vertical distances, does it also apply to horizontal distance calculations?

 

DISCLAIMER: Do not ask me to prepare your income tax document.

Share this post


Link to post

I was about to attempt to draw the diagram but opted just to look for already-made versions that best depict what I'm talking about.

Three satellites will give you two possible pinpoint locations, to some degree of accuracy in 3 dimensional space. A 4th with guarantee which point is the correct one as well as increase the accuracy of the acceptable region for the location.  On devices that have access to other resources, a 4th satellite isn't needed to achieve that general location (to whatever degree of accuracy), as one of those two points. On all devices, having 4 or more satellites provides a much higher accuracy, for latitude, longitude, and altitude.  But if the device can attain a latitude and longitude from 3 satellites, and has access to altitude data for that lat/lon, then sea-level altitude can be calculated by 3-space location in relation to said lat/lon data.

 

gps3-e1360160256111.jpg

image.png.29ae86a0532bb92e8e9ecd812374b753.png

image.png.e7b81bf3965574bc8b4aa2a1f96b97a7.png

Share this post


Link to post
38 minutes ago, thebruce0 said:

Three satellites will give you two possible pinpoint locations, to some degree of accuracy in 3 dimensional space. A 4th with guarantee which point is the correct one

 

In your first image one of the satellites seems to be inside or below the Earth. The last image is more realistic. Satelites are above the surface of the Earth and the second point is far in the space above the satellites as you can see in this image. There is no need to choose the correct point as far as you are not spaceborne.

 

image.png.e7b81bf3965574bc8b4aa2a1f96b97a7.png.7ac7f9000605426e1251d0d1dfdfa966.png

Share this post


Link to post

...obviously.

* the first image is showing the intersections of 3 spheres in 3D space

* the second image is showing the concept of accuracy of a location based on three distance readings

* the third image is emphasizing why only 3 are technically needed if you have access to another resource that removes that 2nd intersection point as an option (whether it's another satellite, a reliable nearest location, etc)

* not depicted: a 4th satellite that would also intersect at only one of the two locations

Edited by thebruce0

Share this post


Link to post

The GPS cant know the time accurately enough.  All that it looks at to determine location is the difference in time between the reception of the signals.  In essence, it knows that satellite A is x meters further away from itself than satellite B.  The radius of the spheres are unknown, but one is a known amount larger than the other.

 

From a calculation perspective it is simpler.  You have four unknowns x, y ,z and tc.  If you assume z to match the last altitude, then you can drop to three and use three equations.  ttps://www.courses.psu.edu/aersp/aersp055_r81/satellites/gps_details.html

 

The error in position location due to the use of the incorrect altitude is not great.  Too large for cache finding, but close enough for figuring out where you are located.

Share this post


Link to post
25 minutes ago, Red90 said:

From a calculation perspective it is simpler.  You have four unknowns x, y ,z and tc.  If you assume z to match the last altitude, then you can drop to three and use three equations.

 

Yes, if you know where you are, then  it is quite simple to determine the location. 😎

I see that you know the basics much better now when you have studied the problem.

 

Please note, height is not z, it is h or H depending on reference. See more

Edited by arisoft

Share this post


Link to post

Running launch vehicle preflight trajectory computer simulations, I can't recall that which I did use to represent height or altitude.  However, if I did use h or H, I was not terminated.

Share this post


Link to post

At VAFB the difference between h and H is only 118 feet. Whichever you used, the rocket navigation computer can handle such a small deviation.

Share this post


Link to post
2 hours ago, Team CowboyPapa said:

The pressure at the bottom of the liquid propellant tanks was p=ρgh

 

In this equation h means the height of the fuel inside the tank, not the height or elevation of the tank.

Share this post


Link to post
On 12/14/2018 at 10:45 AM, Thistler said:

The accuracy of a quartz oscillator can be far better than +- 20ppm. Inexpensive temperature compensated quartz crystal modules can be accurate to around +- 2 ppm when exposed to the typical ranges of temperature one would experience outdoors, and these consumer very little additional energy than a simple quartz crystal. To get even better accuracy from a quartz oscillator you can use a oven-ized quartz oscillator module, but these are larger and far more energy intensive.

 

A TCXO would be a power guzzler in a handheld. They shouldn’t be needed because the temperature coefficient of the crystal is known. 

You only need to monitor the temperature inside the unit (which Garmin handhelds do), and you can offset the drift fairly accurately.

 

On 12/13/2018 at 8:21 AM, Cheminer Will said:

I see, so you think with a newer unit like the 66 series, there would be no reason to set it to GPS only, but just keep it on GPS + Glonass?

 

If power consumption is of no concern.

 

On 11/12/2018 at 7:33 AM, barefootjeff said:

Differential GPS can (according to Wikipedia) provide accuracies of up to 10cm, but it requires a close-by base station at a known location to cancel out some of the errors and distortions in the raw GPS data.

 

Not at all. New technology exists for fairly ordinary hardware to independently obtain accuracy down to sub meter accuracy with carrier phase recievers.

 

By the time the error was turned off in the early days so that civilians could access today’s kind of accuracy, it was already moot.

Farmers worked out that the error was uniform across all civilian units, so they only needed to put a GPS in a known location,

and send the offset for the true location to a second receiver (the unit that is actually moving), and then add the offset from the stationery unit to the reported coordinates

of the second unit, and then you have overcome any deliberate error that the Government introduced, and are only left to suffer inherent error from both GPS receivers.

 

 

 

Share this post


Link to post

Did I say sub meter accuracy? No, Let’s make that down to millimetres margin of error with relatively cheap hardware.

 

This is not some glimpse into the future. You can buy a stock mass market GPS module with centimetre level accuracy right now,

and it’s actually old news: https://www.u-blox.com/en/high-precision-positioning

 

 

 

Edited by _Art_

Share this post


Link to post
4 minutes ago, _Art_ said:

If power consumption is of no concern.

 

I have seen people say that power consumption would increase significantly with GLONASS on and others say that is no longer an issue.  I was having a chat session with Garmin support yesterday about a couple of things and I asked them about this.  The rep said that it was nothing to worry about and that I could also turn on WASS/EGNOS if I wanted to.  I then pointed out that one of the places I had seen it written that turning these on would increase power use was on one of their Garmin support pages.  The rep said that the page had old information.  He then hinted that many Garmin support pages had information that was dated. 

 

I have had both on for the past couple of days just to see what I thought.  I have several hours of use and the battery indicator is still on 3 out of 4 bars. 

 

On one short section of the hike that was out and back, I did it twice, on one loop turning off everything but GPS.  When I looked at the tracks in BaseCamp tonight they looked almost identical.  All sections pretty much overlapped each other, both the out and back within each setting and then also comparing the double track of the GPS only trip to the double track of the GPS+GLONASS with WASS/EGNOS on trip. 

Share this post


Link to post

I’m not lying when I say I don’t trust it enough to use it :D

But I’m going by their own user manual in "Satellite Settings”, and also people on GPS forums claim to have tested the difference.

 

So all that’s left is if one of the GPS module updates that have been released has improved the power performance for multiple service support.

I doubt it :D No identical sets of batteries here to test. Are you into wasting four new batteries to find out? I might be if they were already here.

 

 

 

Share this post


Link to post
6 minutes ago, _Art_ said:

But I’m going by their own user manual in "Satellite Settings”

It does indeed say that in the 66 manual:  "Using GPS and another satellite together can reduce battery life more quickly than using GPS only."  And given my comparison of a short section of today's hike, having them all on did not really seem to make any accuracy difference where I was in the woods.

Edited by Cheminer Will

Share this post


Link to post
1 hour ago, Cheminer Will said:

I have seen people say that power consumption would increase significantly with GLONASS on and others say that is no longer an issue.

I use a Garmin etrex30 with GLONASS on and never had a problem, even with it on all day, or longer even. With new batteries I could likely use it for several days before I needed to charge them. Besides, who would go caching without spare charged batteries?

Share this post


Link to post

GPSrChive published a detailed power consumption test with an Oregon 6x0 and found GLONASS increased power consumption by 15mA and WAAS/EGNOS showed no increased consumption.

 

The screen backlight is still the primary power drain. Keep it off if you can.

Share this post


Link to post
9 hours ago, _Art_ said:

A TCXO would be a power guzzler in a handheld. They shouldn’t be needed because the temperature coefficient of the crystal is known. 

You only need to monitor the temperature inside the unit (which Garmin handhelds do), and you can offset the drift fairly accurately.

 

Manufacturers do everything they can to make the oscillator as accurate as it is possible. 1 ppm means 300m drift per second. 0.01ppm means 3 meters per second. So - you can not use the internal clock to get fix with 3 satellites but you will find them much faster when the unit is powered back on.

Share this post


Link to post
9 hours ago, Cheminer Will said:

It does indeed say that in the 66 manual:  "Using GPS and another satellite together can reduce battery life more quickly than using GPS only."  And given my comparison of a short section of today's hike, having them all on did not really seem to make any accuracy difference where I was in the woods.

Another instance of the "Law of Diminishing Returns".  Or, has it been repealed by the DoD or NASA?

Share this post


Link to post

The extra satellite system(s) do not improve normal accuracy.  What they do is provide more satellites to see.  In some situations, with marginal coverage, this can improve accuracy.

Share this post


Link to post
7 minutes ago, Red90 said:

The extra satellite system(s) do not improve normal accuracy.  What they do is provide more satellites to see.  In some situations, with marginal coverage, this can improve accuracy.

 

In my receiver the number of satellites seems to have effect on the reported accuracy. Your receiver may be broken if you have no effect at all. Check this

Maybe there is a limit where more satellites do not make it any better.

Edited by arisoft

Share this post


Link to post

Just collected a waypoint with my handheld GPSr.  10 US GPS satellites acquired with EPE ±6 feet.

 

If one additional US GPS acquired, how much would the EPE be decremented?

One additional GLONASS?

One additional Galileo?

 

Waypoint collected near geocahe GC3N62E.

 

 

Share this post


Link to post

10 satellites is fine.  It is when you are in the mountains on the side of steep slope in heavy tree cover.  You get down to four satellites with a ton of multipath and your accuracy goes out the window.  When you can then see another four Glonass birds, it makes a huge difference.

Share this post


Link to post
5 hours ago, Red90 said:

The extra satellite system(s) do not improve normal accuracy.  What they do is provide more satellites to see.  In some situations, with marginal coverage, this can improve accuracy.

 

Exactly.

 

The only advantage of having GLONASS and/or GALILEO access is when there are to few GPS satellites in view of the receiver (in deep narrow canyons, etc.), thus providing the GPSr a better chance of having 4 satellites from any combination of systems to make the best triangulation possible.

 

My experience is that, when 4 or more GPS satellites are in view of my GPSr, I get the best positioning accuracy with GLONASS/GALILEO turned off. Enabling either of those systems when I already have an excellent GPS signal only dilutes the precision of the GPSr.

 

WAAS/EGNOS is a different story. These always improve your positional accuracy.

Share this post


Link to post
On 12/19/2018 at 11:28 PM, _Art_ said:

 

A TCXO would be a power guzzler in a handheld. They shouldn’t be needed because the temperature coefficient of the crystal is known. 

You only need to monitor the temperature inside the unit (which Garmin handhelds do), and you can offset the drift fairly accurately.

 

 

A TCXO module can use as little as 2 mA. Of course, what you are describing is essentially a TCXO in software instead of dedicated circuitry. I would be curious to know how the engineers actually go about it with a handheld GPS.

The power guzzler would be a OCXO.

Share this post


Link to post
23 hours ago, Team CowboyPapa said:

Just collected a waypoint with my handheld GPSr.  10 US GPS satellites acquired with EPE ±6 feet.

 

And +/- 6 feet from a Garmin GPSr is absolutely no guarantee. I've been taking serial daily readings from a fixed point with the GPSMAP 66ST with the unit indicating 8 foot accuracy, and frequently get positions much more than 8 feet away from the post-processed GPS position using RTKPOST (integrates nearby base station data and refined ephemeris data). There are nearby tall hills that are no doubt adding multipath error, but the GPS doesn't seem to recognize that despite having a good number of GPS and GLONASS satellites to work with.

Share this post


Link to post
15 minutes ago, Thistler said:

 

A TCXO module can use as little as 2 mA. Of course, what you are describing is essentially a TCXO in software instead of dedicated circuitry. I would be curious to know how the engineers actually go about it with a handheld GPS.

The power guzzler would be a OCXO.

 

When it is about timekeeping you can let the TCXO running and just adjust the frequency constant in the software depending on temperature to measure time more precise while the receiver is powered off. This has nothing to do with the accuracy of the coordinates but it helps a lot when powering the device again.

Edited by arisoft

Share this post


Link to post
On 12/20/2018 at 3:37 PM, _Art_ said:

Did I say sub meter accuracy? No, Let’s make that down to millimetres margin of error with relatively cheap hardware.

 

This is not some glimpse into the future. You can buy a stock mass market GPS module with centimetre level accuracy right now,

and it’s actually old news: https://www.u-blox.com/en/high-precision-positioning

 

 

Did you actually look at this link? It's still a form of differential GPS requiring a nearby base station at a known location to provide corrections for atmospheric distortions, etc. You won't get your centimetre or millimetre accuracy from just a single isolated handheld device. This screenshot is taken from their presentation on how their system works:

 

GPSCorrection.jpg.50f7239f5ade14adbbda7a5073a29c48.jpg

Edited by barefootjeff
  • Upvote 1

Share this post


Link to post
On 12/19/2018 at 11:37 PM, _Art_ said:

Did I say sub meter accuracy? No, Let’s make that down to millimetres margin of error with relatively cheap hardware.

 

I have a post here with a plot using a GPSMAP66ST and post-processing with RTKPOST and RTKPLOT. The base station was 27 km away, which may account for only getting about 1 meter precision. To get better accuracy, I think you would have to have a much closer base station, and perhaps hardware whose reception characteristics were well defined.

 

Share this post


Link to post
On 12/16/2018 at 11:44 AM, Team CowboyPapa said:

Characterizing the normally distributed random errors of both quantitatively by their standard deviations, I have a four times greater value for vertical than for horizontal.

 

Consequently, I prefer to discuss them individually and separately. 

+1.  VDOP represents a far larger error than HDOP.  Fortunately, that doesn't figure into a typical geocache find, but certainly does provide some additional error when calculating current position AGL ... above the runway.    As I recall, cleaning that up a bit that was the reason for the first SBAS system (WAAS), not for finding geocaches   :P

Share this post


Link to post
On 12/20/2018 at 11:38 AM, Team CowboyPapa said:

Just collected a waypoint with my handheld GPSr.  10 US GPS satellites acquired with EPE ±6 feet.

 

If one additional US GPS acquired, how much would the EPE be decremented?

One additional GLONASS?

One additional Galileo?

 

Waypoint collected near geocahe GC3N62E.

 

 

I know that YOU know that any particular value for EPE under any specific set of conditions is a function of the guy writing the firmware, with the exact algorithm held as closely as Col. Sanders' mix of 21 herbs and spices.  Further, I know that YOU know that the angle of incidence (good as anything else to call it, I guess) of any satellite being added to the current mix vs. the angles of the ones already being received is more than half the battle.  Spread 'em wide to get the best triangulation.

 

That said, it WOULD be fun to be get hold of some firmware that would allow selection of which satellites in a current constellation are being used just to see the impact on the code writer's EPE results.

Share this post


Link to post
On 12/22/2018 at 6:16 AM, barefootjeff said:

 

Did you actually look at this link? It's still a form of differential GPS ..

 

 

Obviously not! :D

On 12/22/2018 at 4:23 AM, Thistler said:

 

A TCXO module can use as little as 2 mA. Of course, what you are describing is essentially a TCXO in software instead of dedicated circuitry.

Kind of, but a resistor would be turned on to heat the crystal oven to make the freq stable, rather than adjust a DDS to compensate.

UBlox have a page about oscillators, and the same manufacturer produces GPS modules with TXXO and without.

I guess the handhelds do have them, or they wouldn’t be able to even maintain the appearance of keeping up.

Share this post


Link to post

To end the argument on 3 versus 4, I pulled out my GPS38.  It takes five minutes to lock, so you have time to see what is happened.  With three locked, it reports "2D" with an EPE of 38 meters. Compared to the 64S, the coordinates are 0.004' and 0.005' different, with elevation 207 feet different.  Close enough for most uses and much less than 38 meters.  When it gets the fourth satellite, it shows "3D" and the EPE drops to 25 meters shortly after this photo.

IMG_0553.JPG

IMG_0554.JPG

IMG_0555.JPG

Edited by Red90

Share this post


Link to post

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
Sign in to follow this  
Followers 3

×
×
  • Create New...