Minimum number of sats?

[+Bill D (wwh)]

Does anyone know what the minimum number of nav satellites in earth orbit would have to be in order to ensure that anywhere on the earth's surface could receive three of them for 2D navigation, and the minimum number to ensure four everywhere for 3D nav?

 

I believe that there are actually twenty four in orbit, but presumably that's deliberate over-coverage to allow for malfunctions or whatever.

[+welch]

quote:

---

Originally posted by Bill D:

Does anyone know what the minimum number of nav satellites in earth orbit would have to be in order to ensure that anywhere on the earth's surface could receive three of them for 2D navigation, and the minimum number to ensure four everywhere for 3D nav?

 

I believe that there are actually twenty four in orbit, but presumably that's deliberate over-coverage to allow for malfunctions or whatever.

---

I think there are actually more than 24 in orbit. I want to say there are actually 28 but that might be wrong.

 

As for whats the min. number of Sats required for coverage? I have no idea.

 

[el10t]

Doesn't it all depend on the size of the satellites footprint?

 

Rich

mobilis in mobili

[dsandbro]

The sats are not geostationary. They are constantly moving relative to your position.

 

To have a truly global system you need enough in orbit and properly spaced so you have a minimum of four at any given second and any given location on earth, so as one passes out of view another is moving in. Various military posts around the world track the satellites and frequently 'correct' the satellite's orbit or upload its actual location. This is why the various planning software programs will not let you calculate coverage more than 30 days into the future (or gives you a warning).

[Kerry.]

To define things properly there's a fair range of variables to consider but in simple terms the standard specs are based on a 24 constellation and the worst case scenario is based on 22 satellites.

 

There's currently 26, down from the long time over populated 28 satellite constellation that has spoilt some users. Next GPS launch is scheduled for Jan 29, 2003 (GPS II-R8)

 

As one can imagine which 2 sats (there's 276 different possible permutations) will have a differing effect, which is part of the control system's responsibility in meeting the defined specs. In some cases removing 2 satellites can have zero effect where as in other cases even removing 1 satellite can be a problem. Even if one can see 4 satellites doesn't mean they are useful as the PDOP (and other things) might be totally off the scale and much more has to be taken into account then just the number of sats.

 

The systems spec's are based on parameters that some receivers might meet or exceed so just because the system provides a certain level of service the user might/might not be able to take full advantage of that service.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[Cape Cod Cacher]

triangulation is simple answer

[+OzzieSan]

3? Dont think that was the answer they were looking for? 3 min for 2D nav yes but not for complete nav coverage of the planet.

[+welch]

quote:

---

Originally posted by Kerry:

To define things properly there's a fair range of variables to consider but in simple terms the standard specs are based on a 24 constellation and the worst case scenario is based on 22 satellites.

---

 

If a "standard" system is based on 24, then why is the system the Europeans are setting up going to be based on like 30 birds? Will that system have lots of areas of "overlap"?

(simple answer please )

 

[Cape Cod Cacher]

Lat & Lon is my GPS want... 150 lobster traps, 200 days found. works on my end. do the math.

[+Scook]

3 points may work real well in an ideal world but the GPS receivers are designed to with 4 signals to eliminate clock errors.

See Trimble's GPS tutorial for an explanantion.

 

How GPS works - Getting perfect timing

 

The Trimble site requires a Shockwave Player to view the illustrations. The Tutorial starts here -

All about GPS

 

Hard work often pays off after time,

but laziness always pays off now!

[+MaxEntropy]

You really only need three satellites. Three spheres will intersect at two points. Only one of those points will be on the earth's surface so the GPS can assume that you are also and give a rough fix.

A fourth satellite's sphere will eliminate the second fix and give you altitude.

[+GEO*Trailblazer 1]

Well I do not know for shure,but when the Space Shuttle Endevor on its Earth Mapping Mission,Commander Kevin Kreigel stated that you only had to be locked on to 4 sats to triangulate precise measurements. 1,A,alpha 2,B,beta 3,C,gamma 4,D,delta = E,the Epsilon,the mathmatical equation,formula. thats what I can remember not a rocket scientist yet.

 

When all else fails Geotry again.

[+writer]

quote:

---

Originally posted by MaxEntropy:

You really only need three satellites. Three spheres will intersect at two points. Only one of those points will be on the earth's surface so the GPS can assume that you are also and give a rough fix.

A fourth satellite's sphere will eliminate the second fix and give you altitude.

---

 

Actually, not quite. Two spheres intersect in a circle, unless they are tangential and meet at only one point. The third sphere will meet in a curved line. The line should meet the earth at the surface, but because the system can only estimate where that might be, it's less accurate than a four satellite lock.

 

The fourth satellite also adds time correction. Because the GPSr can, with the correction data sent by all the satellites, calculate the position of each, it can calculate where the fourth satellite *should* be, and, following, the distance from that satellite.

 

However, if the receiver's timing is a bit off (isn't that true of all of us?), all the distances to all the satellites will have been slightly miscalculated. When the receiver gets the fouth satellite's signal, it will likely show a distance different from the expected one. That tells the receiver that its timing is off. After working backwards from all the satellite signals, it can calculate the correct time, which improves the accuracy of everything.

[Kerry.]

Writer, actually not quite, either.

 

Timing is one of the main components of any fix, 2D or 3D.

 

3 satellites can solve for the 3 unknowns XY & Time (2d fix), 4 satellites can solve XYZ & Time (3d fix).

 

So in effect the 4th sat gives altitude as Timing is always part of the position solution. It's this altitude that improves the integrity of the position solution as the height has to be assumed (last height available or user input) in a 2D fix as part of the calcs.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[Kerry.]

quote:

---

Originally posted by welch:

If a "standard" system is based on 24, then why is the system the Europeans are setting up going to be based on like 30 birds? Will that system have lots of areas of "overlap"?

(simple answer please )

---

 

Galileo is a 27 satellite (plus 3 active spares) system in a 3 plane 14 hour orbit (10 satellites in each plane), is a simple system to launch, maintain and more suitable for high latitude areas. The aim is still to maintain a minimum 4 satellite world coverage.

 

GPS is designed as a 24 satellite (plus 3 spares) in a 6 plane, approx 12 hour orbit with a total capacity of 32 satellites.

 

Glonass is different again in design and best suits high latitudes (> 50 degrees).

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[+OzzieSan]

Anyone know how many it would take to totally block sunlight from reaching earth?

[+welch]

quote:

---

Originally posted by Team 5-oh!:

Anyone know how many it would take to totally block sunlight from reaching earth?

---

 

I think that would be related to how big the sat was, and its distance from the earth

 

[+GEO*Trailblazer 1]

It would only take 1 sattelite bigger than the earth.

On my earlier post that should be TRILATERATE not TRIANGULATE . (operator error),my one brain cell had a short circuit and the Elevation is the 3rd Dimension

When all else fails Geotry again.

 

[This message was edited by Trailblazer # 1 on December 22, 2002 at 08:22 PM.]

[+ron50eli]

Yep, all of those & the ones the government's don't tell. Top Secret? No really, I have no idea.

I just let my Garmin find what it can.

rocker51

[+mrp]

quote:

---

Originally posted by Team 5-oh!:

Anyone know how many it would take to totally block sunlight from reaching earth?

---

 

Well, Earth's first satellite occasionally blocks all sunlight from reaching a small part of the ground. Happened early this month in South Africa, the Indian ocean, and Australia.

 

-- Pneumatic

[+writer]

quote:

---

3 satellites can solve for the 3 unknowns XY & Time (2d fix), 4 satellites can solve XYZ & Time (3d fix).

---

 

Treceivers don't get a time fix from three receivers. Specically, it's the addition of the fourth satellite that allows the receiver to synchronize itself with the atomic clocks.

 

Here is a Web site that offers some explanation: http:

 

//www.mercat.com/QUEST/HowWorks.htm.

 

Trimble's Web site offers additional good reference magterial:

 

http://www.trimble.com/gps/how.html

 

Also, from the Smithsonian Air and Space Museum:

 

http://www.nasm.edu/galleries/gps/spheres.html

 

The problem is that some of the popular descriptions of GPS are actually incorrect. Also, the explanatory diagrams are generally drawn in two dimensions. Yes, it's true that in a 2D situation (triangulating off land-based radio stations), three signals would be enough to adjust time. But GPS deals with a 3D space (as the satellites are above the "plane" of the earth, their positions force this). Three satellites only offer the 3D equivalent of the triangle of uncertainty you get using trianglulation with a compass and map.

 

It takes the fourth satellite to get the additional equation to solve the additional unknown of timing.

 

[This message was edited by writer on December 23, 2002 at 09:45 AM.]

[Kerry.]

quote:

---

Originally posted by writer:

It takes the fourth satellite to get the additional equation to solve the additional unknown of timing.

---

 

I believe you are trying to say timing is only available from the fourth but there are some extremely fundamental mathematical principles involved here and the over simplified explanations by some sites are obviously a little confusing.

 

The easiest way to come to grips with this is start with a 3 dimensional fix and most understand that 4 satellites are required to solve for the 4 unknowns. Those unknowns are XYZ & Time with "time" more to do with “timing” as opposed to pure "time".

 

That equation solution could also be solved if ONE of the “unknowns” was supplied/provided and that then requires only 3 values to be solved for and that requires a minimum of 3 equations (hence 3 satellites).

 

In the real world the only value that can really be provided is the Z and this can be provided by the user or the receiver (last occurrence in some instances) and this constitutes a GPS 2D fix in which the values to be solved are XY & Time (Z is provided).

 

To suggest a GPS receiver doesn’t solve for time in a 2D position fix situation (when only 3 satellites are visible) is really showing some misunderstanding in what actually occurs.

 

Just about every receiver made will enter into a 2D position fix with 3 satellites and the assumed value used in the computation is the Z. In the case where the receiver is moving/changing in the vertical (Z) then the position solution can be suspect (very). In this auto type 2D mode some receivers will allow a user defined altitude, where as other receivers can specifically be locked in a 2D mode (with a user provided altitude) and this was used in many marine receiver applications in the past (even the present).

 

These days a 2D fix is not a common occurrence (until specifically configured in receivers with this option) especially considering the state of the constellation. However the possibility certainly exists under differing conditions and receivers allow that 2D option and Time is one of the unknowns that is calculated in a 2D fix, that is for sure.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[DougMissyMickeyP]

I know the original question was about how big of a constallation would cover every part of the earth, but the question of how many satellites you need for a lock is interesting and needs to be considered to answer the constellation question.

 

The air and space museum's description is a pretty good description of how GPS works. Let me explain it in a different way... We have satellites (that know where they are because the ground control station tells them) and know a precise time (they have atomic clocks that are also updated by ground stations). We have a reciever with an unknown location and an innacurate clock. Your reciever goes through the following process to determine it's location (this description may be a little simplified because my brain works that way...)

 

- Reciever locks onto one satellite and recieves that satellite's message. The message contains the satellite's location and the time the message was transmitted. For the next few steps the reciever assume's its clock is accurate (not exactly the way it works, but it's the way my simplified brain works). The reciever compares the time the message was sent with the time in its clock, does the math (speed of light, etc.) to determine it's distance from the known location(Actually, since the clock's aren't perfectly synchronized this distance isn't perfect- it's called a "pseudo-range", but the reciever lives with it and continues the process). You could visualize your position as somewhere on a sphere at that distance from the satellite. (the GPSr doesn't make any earth surface assumptions yet.. if it did, you couldn't determine altitude from the signal)

 

- Reciever locks onto the second satellite and determines it's distance the same way as it did from the first. If you picture two sphere's intersecting, you'd see a circle. Now we know our position is somewhere along that circle.

 

- Reciever locks onto the third satellite and determines distance as above. Picture that circle we had from above and intersect that circle with a 3rd spere.. you're left with 2 points of intersection. Most of the time, one of these points can be thrown away (it's somewhere in space higher than the satellites themselves... There's where the earth surface assumption comes in)

 

If your reciever's clock were perfectly accurate, that's all you'd need, but your $100 GPSr doesn't have an atomic clock. The designers of GPS came up with a neat trick to solve that problem...

 

- Reciever locks onto a 4th satellite and determines distance as above.. but.. the 4th sphere doesn't go through the point determined after the 3rd lock! (because the clock in the reciever is not perfectly synchroized with the transmitters. That's why the proper terms for the distances above is "pseudo-range") What your reciever does is adjust it's internal clock (and re-calculates each of the 4 pseudo-ranges) until all 4 spheres intersect at a single point in space. (this point could be on the earth's surface, or up in the air at 35,000 ft where the jetliners are). That becomes your GPS fix.

 

2d and 3d fixes have nothing to do with the number of satellites being tracked... You NEED 4 to get a fix because of the clock/pseudo-range problems mentioned above. 2d or 3d (and your GPS's Estimated Position Error (EPE) or Figure Of Merit (FOM)) are determied by the geometry of the satellites (where are they in the sky). For example, if 2 satellites are very close together, the angle between them is very small and the resulting fix is therefore not very accurate.

 

Sorry if I'm just repeating the obvious, but like I said I like to over-simplify things because that's the way my brain works.

[Kerry.]

quote:

---

Originally posted by Doug Missy Mickey P:

.... 2d and 3d fixes have nothing to do with the number of satellites being tracked... You NEED 4 to get a fix because of the clock/pseudo-range problems mentioned above. 2d or 3d (and your GPS's Estimated Position Error (EPE) or Figure Of Merit (FOM)) are determied by the geometry of the satellites (where are they in the sky). For example, if 2 satellites are very close together, the angle between them is very small and the resulting fix is therefore not very accurate.

---

 

But accuracy has nothing really to do with the PRINCIPLE of a 2D or 3D fix.

 

You have all the pseudo-range just about right but when the height, altitude, Z can not be determined (not enough sats) it is supplied (as in a 2D fix) then there's only 3 pseudo-ranges allowing 3 unknowns to solve, which are Position (XY) & Time.

 

A 2 dimensional fix has no height as part of the calc (it is assumed) where as a 3D fix has, that's why there can be a 2D and a 3D fix, however these days the 3D fix is generally the norm.

 

2D or 3D isn't really an issue these days but back during the Gulf war there were only 16 satellites in orbit which provided between 19 to 20 hours of "two-dimensional" (latitude and Longitude) coverage with "three" satellites in view and 15 hours in all of "three dimensional" (including altitude) coverage with four satellites in view. Outside that 2D 3 satellite coverage (~ 4 hours per day) there was simply no GPS capability.

 

2D and 3D has everything to do with the number of satellites being tracked. Except with a receiver that can manually be locked in 2D mode, which then can in fact be even more accurate than a 3D fix especially if the altiude provided is accurately known.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[+GOT GPS?]

3 Sats for your position

4 Sats for your position and elevation.

5 or more sats are needed for geocaching,

because of trees.

 

Overhead satellites are the most important, when you are out in the woods. If you have mainly low to the horizon satellites, you will get better results out in a boat, or anywhere you have a clear view of the sky.

 

------------------------

My home page about GPS units and information

[crr003]

Experiment - I turn on my GPS receiver (Garmin 3+).

Before it locks onto sats, I switch to a view that shows the time (with seconds) and the lat/ long (Position page for Garmin).

Now I watch the seconds - as they count up watch what happens when the lat/long fields go from blanks to a real position - the seconds will jump. (I think the longer the unit has been turned off the bigger the jump - internal clock drift).

This coincides with the receiver switching from the acquiring sats mode to the 2D or 3D Navigation mode.

For this discussion it is important to note the time changes with a 2D lock (I can confirm by going back to the Sat page and seeing 3 sats locked/2D Nav declared - I block half the sky with a building).

 

So, if the time is being corrected with a 2D lock, isn't Kerry's description more correct, i.e. you do get time information from 3 sats?

 

Nil Satis Nisi Optimum

[Kerry.]

I realize many here view GPS as simply a positioning system but the full name NAVSTAR GPS (NAVigation Satellite Timing And Ranging Global Positioning System) does a lot more than what is generally regarded as primarily a positioning system.

 

However the pure "Timing" function of the system might explain some of the concepts of 2D and 3D positional fixes.

 

Many of the pure "Timing" boards "generally" require a minimum of 4 satellites to calc the four unknowns (Position XYZ & Time) and of course in the real world more is better for redundancy.

 

These pure Timing boards have one purpose and that is to provide an accurate time, which in some respects is ONE single unknown, which can be provided from

 

4 (or more Sats) to solve Position (XYZ) & Time

3 Sats to solve 2D position (XY) & Time

2 Sats to solve for EITHER X or Y or Z & Time IF any 2 precise values of the 3 values XYZ are provided

1 Sat to solve Time IF precise values are provided for X and Y and Z

 

Generally the antenna's of these timing boards are permanently fixed so precise XYZ positioning can be provided if that mode of operation is required. This is generally not the best type of solution (based on a single Sat) but the option is provided as a function of many of these timing devices.

 

All this gets back to the number of unknowns and minimum number of equations to solve for these unknowns. For every known value provided then one less obervation is basically not required (without taking redunancy into account).

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[DougMissyMickeyP]

Kerry,

 

Okay.. I'm following you now. I was thinking pure GPS theory and hadn't thought of the 2d trick. I guess what the reciever is doing is essentially what I said above, only assuming it is on the surface of the earth (or at an entered altitiude) and using the earth itself as the "third sphere" for determining position. 2 satellites give a circle of position, the earth's surface "sphere" interesected with that circle would give 2 possible points (both of which would be on the earth's surface, and one could be thrown away based on last known fix or user entered info) and the 3rd satellite could be used to synchronize clocks . What the reciever is doing is basically adding an imaginary satellite, at the center of the earth. I've had aviation recievers in mind and was thinking in three dimensions.

 

Geez, those GPSr programmers are pretty crafty people eh?

[Kerry.]

quote:

---

Originally posted by crr003:

.... Before it locks onto sats, I switch to a view that shows the time (with seconds) and the lat/ long (Position page for Garmin).

Now I watch the seconds - as they count up watch what happens when the lat/long fields go from blanks to a real position - the seconds will jump. (I think the longer the unit has been turned off the bigger the jump - internal clock drift).

This coincides with the receiver switching from the acquiring sats mode to the 2D or 3D Navigation mode.

For this discussion it is important to note the time changes with a 2D lock (I can confirm by going back to the Sat page and seeing 3 sats locked/2D Nav declared - I block half the sky with a building).

 

So, if the time is being corrected with a 2D lock, isn't Kerry's description more correct, i.e. you do get time information from 3 sats?

---

 

Probably what you are seeing here is GPS time, corrected for leap seconds both of which are part of and updated direct from the actual broadcast Nav message. This current UTC type time is then further changed by the user defined zone offset to give simple local clock time. Receiver display "time" is different to "timing" and "time offsetting", with the latter being part and parcel of each and every position solution.

 

On recreational receivers the LCD time display is basically for convienience and since this has an extremely low order of priority when compared to the highest priority given to processing position etc.

 

Generally the LCD time on most handhelds is late by between 0.5 to 2 seconds.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[Kerry.]

quote:

---

Originally posted by Doug Missy Mickey P:

Geez, those GPSr programmers are pretty crafty people eh?

---

 

Yeah, it's very cleverly (and simply) done and eliminates the need (and prohibitive expense) for precise clocks in the receivers.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[Kerry.]

quote:

---

Originally posted by welch:

.... why is the system the Europeans are setting up going to be based on like 30 birds? Will that system have lots of areas of "overlap"?

(simple answer please )

---

 

Another simple answer to Galileo is that there just might not be any satellites to worry about anyway.

 

The Galileo program (at the moment) has appeared to have collapsed due to the unresolved differences of several of the partner countries.

 

This issue was always one of the underlying unknowns as to how all countries were going to agree on the fine details required. One thing that really doesn't affect GPS (NAVSTAR).

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[+apersson850]

Isn't it so that the current GPS system guarantees a certain number of satellites (four or five) visible at a reasonable angle above the horizon (maybe 5º) all the time?

Or is that something I have from a dream?

 

Anders