3 GPS Satellites & Receiver Clock Synchronization

[rajeshmarndi]

Please help me in removing my mistake, since i see 3 satellite required to locate an place on Earth and synchronization of receiver clock with gps satellite.

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I have assumed at any moment a place on Earth will see certain satellite at a certain distance from it in the sky. That is a location can be known, if it can compute the distances of visible gps satellite.

Information transmitted by each satellite include time of transmission and satellite identity
]


If the receiver side clock is not synchronized with the atomic clock of the satellites, the distances from 3 satellite will not point to a single location on the surface of the earth. So the receiver clock adjust its time, so that the distances from the satellite fall on one location on earth, which is the exact location of the receiver and as well, the receiver clock get synchronized.

So why do we require 4th satellite for.

What am i missing?

Thanks in advance for your help.

 

[johnbbahm]

I think the simple answer is more data is better.
The not so simple answer is what kind of errors do you encounter
in measuring a di-phase signal from 24000 miles?
The satellite wobbles in it's orbit.
The Optical path length has a funny increase in the atmosphere. (Index from 1 to 100023)
Receivers most likely do not do phase info, so are limited to integer clock counts.
It's like that Nyquist theory. 2 data points are all that is necessary to find frequency,
true, but 10 data points let's you see the signal shape.

 

[Michael C]

It's true that if you could be sure that the clock in the GPS receiver was perfectly synchronised with the clocks in the satellites, three satellites would suffice to fix a point. In fact the distances calculated from three satellites will normally indicate two points, but in most cases one of these points will be very far from the surface of the Earth and can therefore be ignored.

However we cannot be sure that the receiver clock (usually a simple quartz clock) is perfectly synchronised with the super-precise atomic clocks in the satellites. If it is not perfectly synchronised, the supposed distances from the three satellites will still indicate two points but neither of them will be the correct one. If the clocks are nearly synchronised, one of the points should indeed be near to the surface of the Earth, but that doesn't give us enough information to synchronise the clocks. For this we need a fourth satellite. If the point as calculated using satellites 1, 2 and 3 coincides with the point as calculated using the satellites 1, 2 and 4 (or any other selection of three satellites) we know that the clocks are already synchronised. If it doesn't, the gps corrects its clock so that the points do coincide.

Data from additional satellites will provide better accuracy, but four satellites are the necessary minimum to fix a point.

 

[rajeshmarndi]

However we cannot be sure that the receiver clock (usually a simple quartz clock) is perfectly synchronized with the super-precise atomic clocks in the satellites.

If the receiver clock is not synchronized with the atomic clock, the receiver cannot get a common point on Earth from the three satellite distances it measured and from their specified location in their orbit.

Bcoz from the received position of the satellites on their orbits at the specified time when they were transmitted, it can only intersect at one location on the surface of the earth, which the receiver get it by adjusting its clock and thereby as well get synchronized with the atomic clock of the satellite.


In other words, every location on Earth at a certain time should receive signal from certain satellite at a certain position on their orbit.

Only problem i see is that if the signal got delayed due to atmosphere, then the receiver cannot find an common intersection on Earth from the distance that it will measure, then.

 

[Michael C]

If the receiver clock is not synchronized with the atomic clock, the receiver cannot get a common point on Earth from the three satellite distances it measured and from their specified location in their orbit.

The distance data will still intersect at a common point somewhere near the surface of the Earth (unless the receiver clock is badly out of sync). The receiver doesn't know its altitude, so it cannot know if the calculated point is too high or too low.

 

[rajeshmarndi]

The distance data will still intersect at a common point somewhere near the surface of the Earth (unless the receiver clock is badly out of sync). The receiver doesn't know its altitude, so it cannot know if the calculated point is too high or too low.

I want to know, just with one satellite, let's assume the clock of the receiver is synchronized, is it possible to know the possibility of the receiver position on earth. Am i right to say the possibility of the receiver lies on a circle on Earth that will be intersected by the satellite spherical range on the surface of earth. The position of the circle on Earth is also predicted.

 

[Michael C]

I want to know, just with one satellite, let's assume the clock of the receiver is synchronized, is it possible to know the possibility of the receiver position on earth. Am i right to say the possibility of the receiver lies on a circle on Earth that will be intersected by the satellite spherical range on the surface of earth. The position of the circle on Earth is also predicted.

Even if we know the altitude of the receiver and we know that the clocks are synchronised, one satellite is not enough. Here's why:

- If we know the distance d between ourselves and a certain point p, this tells us that we are somewhere on the surface of a sphere with radius d with its centre at p.

- If we also know the distance e between ourselves and a second point q, we know that we are somewhere on the intersection of the two spheres with respective radii d and e and centres at p and q. Two spheres intersect in a circle, so we can now say that we are somewhere on the circle where the two spheres intersect.

- If we also know the distance f between ourselves and a third point, we know that we are somewhere where a sphere of radius f centred on this point intersects with the circle already calculated. A sphere and a circle normally intersect at two points: we now know that we are at one of these two points.

Back to the case you describe; If we know our altitude, we know that we are somewhere on the surface of a sphere with its centre at the centre of the Earth. Knowing our distance from one satellite tells us that we are also somewhere on the surface of a sphere centred on the satellite. All we can tell from this is that we are somewhere on the circle where these two spheres intersect.

 

[rajeshmarndi]

Knowing our distance from one satellite tells us that we are also somewhere on the surface of a sphere centred on the satellite. All we can tell from this is that we are somewhere on the circle where these two spheres intersect.

Yes, the difference between my and your case is that in my case we get the possibility of the receiver on Earth on the circle i.e formed by the intersection of the first satellite sphere.

But in your case the possibility of the receiver on the circle is formed by intersection of two sphere(satellite) i.e in space and not on earth, since you are not at all considering the earth. So you get a single point intersection only with four satellite.

Can't we take Earth in the first place and narrowed down the possibility of the receiver on the circle, on Earth that is formed by the intersection with the first satellite on Earth surface. So in this way we can get one location on Earth by just three satellite.

 

[Michael C]

Can't we take Earth in the first place and narrowed down the possibility of the receiver on the circle, on Earth that is formed by the intersection with the first satellite on Earth surface. So in this way we can get one location on Earth by just three satellite.

Yes, if we know our altitude on Earth. Indeed it's probable that the combination of three satellites with exact elevation information will give a more accurate fix than four satellites without this information. This could be the case if we are navigating a boat on the sea, or on a lake with known elevation.

In general, however, the GPS receiver does not know its altitude: it could be lower than sea level or it could be much higher, up a mountain or in a plane. So there are four unknowns: latitude, longitude, elevation and clock synchronisation error. To solve for these four unknowns we need the data from four satellites.

 

[rajeshmarndi]

Ok.

I was taking Earth as a uniform radius around it and therefore eliminated the elevation of a place which obviously differ at many place around the globe.

i was taking altitude factor only for aeroplane in flight which would definitely need four satellite and for, on the Earth surface mistakenly three satellite.

Thanks for assisting me.

 

[rajeshmarndi]

Would like to also know, does normal gps that are used in cars also shows the elevation of that place too?

I thought only gps used by airplane give you the altitude.

 

[Michael C]

As far as I know a car GPS unit will calculate altitude even if it doesn't display it. The unit can only be sure that the horizontal coordinates are correct if it also knows the altitude: an error in altitude will cause an error in horizontal coordinates.

It's possible that the GPS already calculates a position after getting a fix on 3 satellites, by assuming that the altitude has not changed since the last reading ("2D fix"). Here's a short article about 2D and 3D fixes.

 

[rajeshmarndi]

@Michael C, thanks a lot.