2 ms·

1) Technicaly, there are 2 possible locations that the same distance from each of 3 satilites, but the other point is far off in space. The 4th is vary useful

1) Technicaly, there are 2 possible locations that the same distance from each of 3 satilites, but the other point is far off in space. The 4th is vary useful for increased accruacy when you have a shitty ground clock, but it's not 'needed' it's it's loss simply results in lower accracy which can be compensated for by more readings over time. (Which can be vary useful when want accuracy and have a ground station that only get's to see a small chunk of the sky.) 2) They all have polar orbits that reach the same location 4 minutes earlyer each day. However, there horizontal ground speed relative to a stationary observer changes over the course of their orbit. (It's zero at the pole and maxes out at the equator.) And is also diffrent form the other satilites you are comparing it with. Which is why you get those S shaped paths: http://www.n2yo.com/satellites/?c=20 http://www.n2yo.com/satellites/?c=20 3)I agree but see 2. PS: Yea, that picture was fairly bad, I was looking for an easy to read article not a picture. The classic picture of a constilation with fixed polar obits is vary misleading once you take the earth's rotation into consideration. It's rare to find something that shows both the orbit's and their horisontal velocity fairly accuratly without making it look like they interweave. I once saw an animation showing the orbit of 4 satilites and the area they could cover area just those 4 satilites could give you coverage of but it's far harder with just a picture.

zb 15y ago
You need four because you must solve for 4 unknowns, the fourth being time. Note that getting the time is the whole point in this case. None of the satellites are in a polar orbit. The orbits are inclined at 55° to the equatorial plane.
- onemoreact 15y ago
  Suppose you have 3 points in 3d space. P1 = (1,0,0),P2 = (0,1,0), P3 = (0,0,1) You know point the distance from U to P1 is x, from U to P2 is x +1 and from U to P2 is x + 2) You know know U is on a 1d curve (c1) though 3d space. (Or as you say you don't know time aka distance.) Now suppose P1, P2, P3 velocity is more than 2x that of point U and you have you have new offsets from U to {P1,P2,P3} you are now going to have a new curve (c2) in 3d space, but you know U's vector must take it from c1 to c2. Now add another time cycle, and you know it's vector must take it from C1 to C2 to C3. As you keep adding C's you constrain both the valid vectors(direction and velocity) as well as positions. Now measurement accuracy as well as change in velocity limit the accuracy but GPS satellites are moving a lot faster than you are so you can get reasonably accurate information this way. Edit: Also you can basically ignore the sections of the curve that whose altitude is unreasonable so the solution space is fairly constrained to start with and for each subsequent curve. But you can also use an internal clock/oscillator, accelerometer, gyroscope to further constrain reasonable accelerations etc.

zb 15y ago

You need four because you must solve for 4 unknowns, the fourth being time. Note that getting the time is the whole point in this case. None of the satellites are in a polar orbit. The orbits are inclined at 55° to the equatorial plane.

onemoreact 15y ago
Suppose you have 3 points in 3d space. P1 = (1,0,0),P2 = (0,1,0), P3 = (0,0,1) You know point the distance from U to P1 is x, from U to P2 is x +1 and from U to P2 is x + 2) You know know U is on a 1d curve (c1) though 3d space. (Or as you say you don't know time aka distance.) Now suppose P1, P2, P3 velocity is more than 2x that of point U and you have you have new offsets from U to {P1,P2,P3} you are now going to have a new curve (c2) in 3d space, but you know U's vector must take it from c1 to c2. Now add another time cycle, and you know it's vector must take it from C1 to C2 to C3. As you keep adding C's you constrain both the valid vectors(direction and velocity) as well as positions. Now measurement accuracy as well as change in velocity limit the accuracy but GPS satellites are moving a lot faster than you are so you can get reasonably accurate information this way. Edit: Also you can basically ignore the sections of the curve that whose altitude is unreasonable so the solution space is fairly constrained to start with and for each subsequent curve. But you can also use an internal clock/oscillator, accelerometer, gyroscope to further constrain reasonable accelerations etc.