navstar system question.

[georapper]

can anyone tell me how a gpsr can determine the distance from an orbiting satellite by only knowing the location of the satellite? the receivers clock is not known and is only a cheap crystal oscillator, so the clock has to be updated before a time difference can be determined.

 

the clock time of the satellite could be embedded in the signal but the receivers clock time could be off by a few nano or pico seconds and must be updated before being compared to the satellites time embedded in the signal. how does the receiver get an updated time equivalent to the atomic clocks on the gps satellites?

 

it shouldn't take 4 satellites because i can get a 2D fix with 3 satellites so a 4th should not be required to update the receivers cheap clock to atomic clock accuracy.

 

any ideas?

 

Creativity Within The Bounds Of Conformity

[+PDOP's]

Here are a couple of links for you

 

Trimble's How GPS Works

 

Dale Priest's How Does GPS Work

 

PDOP's GPS Pages

[+Stunod]

One more:

HowStuffWorks.com

 

"Just because I don't care doesn't mean I don't understand." - Homer Simpson

Eamus Catuli AC145895

[+EraSeek]

Yes, imbeded in the GPS sat signal is an almanac that is rebroadcast from the begining every 12.5 minutes. This almanac has loads of information including that atomic clock time on board the sat, and location of the gps satelite constellation. Your GPS is in effect an atomic clock(s) reciever, decoder, triangulator...

 

Here is a paragraph that may explain it better than I do:

" GPS satellites broadcast a timing signal (a tick of the clock) on a phase modulated L-band carrier along with information identifying the time for which the tick corresponds. The satellites broadcast a time code referenced to the clock on the satellite, but there is also information enabling the user to obtain an estimate of GPS system time as well as UTC(USNO). The user's receiver may then compare the arrival time of the GPS signal to the local clock with a Time Interval Counter (TIC). The major challenge here is to account for the propagation delay. The geometrical delay is obtained from the receiver’s location (which can be obtained from the GPS system) and from the broadcast satellite positions. Major sources of timing error are the geometrical delay, the effect of the ionosphere and troposphere on the propagation time, multipath, and hardware delays. Currently, the GPS system provides time to the general public with uncertainties measured in nanoseconds. With a well-designed receiver system the user can obtain the time to better than 100 ns in a few minutes, and to about +/- 10 ns with a 24 hour average (and a good local clock)."

 

 

"See the wonderous works of Providence! The uncertainty of human things!" Geo.Washington

[Kerry.]

quote:

---

Originally posted by georapper:

.... how does the receiver get an updated time equivalent to the atomic clocks on the gps satellites?

 

it shouldn't take 4 satellites because i can get a 2D fix with 3 satellites so a 4th should not be required to update the receivers cheap clock to atomic clock accuracy.

 

any ideas?

---

 

More than ideas as the "timing" mechanism involved with GPS is what makes it work as it all has to do with "timing" but not necessarily "time".

 

Effectively 4 satellites are required for a 3D fix and as you mentioned a 2D fix requires 3 satellites.

 

The 3 satellites required for a 2D fix is the minimum to solve for the 3 unknowns, XY & Time/ing. However height is still required and for a 2D fix this can be either provided by the user or assumed from the last fix. A 2D fix really isn't accurate if a reciever is constantly and continuously changing elevation.

 

4 satellites required to solve XYZ & Time and if any of the unknowns (except time in a practical sense) can/could be supplied then for each known value then 1 less satellite is required.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[+EraSeek]

And again:

"How does the gps know the travel time so that it can compute the distance?" The satellite sends the current time along with the message so the gps can subtract its knowledge of the current time from the satellite time in the message (which is the time that the signal started its descent) and use this to compute the difference. For this to work the time in your gps must be pretty accurate – to a precision of well under a microsecond. The satellite itself has an atomic clock to keep the time very precisely, but your unit is probably not big enough nor expensive enough to have an atomic clock built in, so your clock is likely to be in error! For this reason our assumptions about the distance calculation are likely to have considerable error and the fourth satellite fix will reveal this to us. However, if we assume the error is caused by an error in our clock then we can adjust our clock a little and recompute all 4 fixes, continuing to do this iteratively until the error disappears! We will then have a good position fix and as a side effect we will also have the correct time to about 200 nanoseconds or so. One of the applications of gps technology is to provide the correct time even when we don't care about our position"

[georapper]

i'm going to use this information to create a 3D cache that tries to draw an analogy to the navstar system by providing timing differences from 4 known points to an unknown point and providing a slight timing error so the cacher must first determine the distances based on timing then account for the timing error to obtain the corrected distances. once those distances are known, then solve for the unknown location in 3D. i've already created a cache using the intersection of spheres, next cache i create i will include the timing errors, propagation errors, as well as set up the constellation of satellites(known points) so that a 3D coordinates system translation is required to solve for the 3 quadratic equations in 3 unknowns. i may do this in two succeeding caches so as not to totally confuse everyone on the first of two caches.

 

Creativity Within The Bounds Of Conformity

[+EraSeek]

Navigation is distance and time! Each of the 24 satellites has 3 to 4 atomic clocks on board. One nanosecond of error (one billionth of a second) equals 1 foot of error in a GPS. GPS is at the present time the most competent system for time transfer, the distribution of Precise Time and Time Interval (PTTI). The system uses time of arrival (TOA) measurements for the determination of user position. A precisely timed clock is not essential for the user because time is obtained in addition to position by the measurement of TOA of FOUR satellites simultaneously in view. Your GPS display is accurate to about 1/10th of a second, but it’s inner workings are accurate to within a few nanoseconds

[+EraSeek]

I've been meaning to plant one for a long time now called "Cesium Pulse" (the tick of the Cesium atom) but have not found the 'just right' place for it yet. Your's sounds tougher. I'll be interested in seeing it.

[georapper]

reading on "how stuff works.com" site, it showed an analogy of the clocking error. 2 circles will always intersect no matter what the timing error is, but a third circle will not intersect if there is timing error. it didn't say how the receiver figured out the timing error then adjusted for it.

 

after looking at the geometry of the 3 circles that have timing error, it looks like finding the exact center of the triangle formed by the 3 known satellites will result in the corrected distances, thereby providing the timing error to update the receiver clock.

 

in 3 dimensions, the 4 known satellites would create a tetrahedron, finding the center of the tetrahedron,or finding the center of mass assuming a uniform mass distribution would provide the timing error and be used to correct the distances thereby providing the corrrected timing. this is all assuming that the distances between the satellites is known. all i have to do know is find the equation for finding the center of mass of a tetrahedron and i've figured out what i am going to do to introduce a timing error into my 3d triangulation cache.

 

ahhh, yes, i just found it. the center of mass of a solid volume is the triple integral of the density function over the volume. it's been so long since i've been out of school, i'd forgotten about integrating the density function over the volume. now i can solve for the clock timing error in 3 dimensions. oh, this next cache is going to be funnnnn, with a capital FUN>... of course i will give plenty of app notes and references to aid in solving the problem, hey people it's just solid geometry, some integral calculus and a bit of 3dimension axial rotation but whose cares?

 

geocaching can be very educational. my kid is soaking all of this up like a sponge. it's great.

 

Creativity Within The Bounds Of Conformity

 

[This message was edited by georapper on September 09, 2003 at 10:05 PM.]

[+EraSeek]

Oh Great! My kid (secret weapon) just departed for school back east! Now what am I going to do? ("some integral calculus and a bit of 3dimension axial rotation"??? what the heck...?)

[Kerry.]

quote:

---

Originally posted by georapper:

 

.... i will include the timing errors, propagation errors ....

 

---

 

make believe propagation errors yeah right.

 

Cheers, Kerry.

 

I never get lost everybody keeps telling me where to go

[georapper]

it's just an exercise. i'm sure when students are learning about the navstar system, there are exercises to be done that simulate the real system. i'm sure you know more about the navstar system than anyone else on the planet, maybe even more than god himself, but it's not going to stop other people from learning about it, no matter how much you think you know.

 

Creativity Within The Bounds Of Conformity

[+EraSeek]

While you guys are arguing about who's smarter (I don't even pretent to compete), let me just say, we have a really smart local guy, who set up a simluar cache (intersection of proximity of varied waypoints), and he (as well as I) was impressed with the variety of methods used to come up with the cache. Point being, you need not be traditional smart, nor have a knowledge of math systems to figure out math problems. Usually the big hinderence is simply understanding a system's esoteric terminology.

 

 

"See the wonderous works of Providence! The uncertainty of human things!" Geo.Washington

[+Doc-Dean]

Well if Time tech is so advanced, then explain to me why I am always running late??

 

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

Free your mind and the rest will follow

[georapper]

yes, you can solve these types of problems graphically without any mathematics at all. besides solving them analytically or graphically what other methods have people come up with? although when you are talking about time differentials based on phase shift of psudo random signals, you do need some math to subtract out the clock error and determine the distances based on time.

 

in the cache i was thinking of doing, i would provide 4 psuedo random siganls, and show a phase shift of the 4 signals from a gps receiver clock, then have the cacher determine the clock error from the given received signals compared to the gspr clock. once the clock error is determined, then the cache can be solved graphically or using a system of equations, either one.

 

Creativity Within The Bounds Of Conformity

[+EraSeek]

To DOC-DEAN, Well, as a matter of fact, I have the answer to that! Check out one of my caches here: MOM-TIME

[+EraSeek]

quote:

---

Originally posted by georapper:

yes, you can solve these types of problems graphically without any mathematics at all. besides solving them analytically or graphically what other methods have people come up with? although when you are talking about time differentials based on phase shift of psudo random signals, you do need some math to subtract out the clock error and determine the distances based on time.

 

in the cache i was thinking of doing, i would provide 4 psuedo random siganls, and show a phase shift of the 4 signals from a gps receiver clock, then have the cacher determine the clock error from the given received signals compared to the gspr clock. once the clock error is determined, then the cache can be solved graphically or using a system of equations, either one.

 

Creativity Within The Bounds Of Conformity

---

 

Yeah smart guy? I usually use a ball and a length of string! When that fails, I ask my kid!

No, there are plenty of things beyond me, I'm just saying there are often other methods other then the intended one if you can get by the terminology. For instance, on one of these trickier math type caches, I simply used my GPS's tools to find the cache. It is amazing that others didn't know how to use the proximity tool in the gps to find that cache without a bunch of complex math (all math is complex to me). But there are also simplifing methods. Take a big complex thing and break it down into smaller simpler pieces that you can understand. I believe this is the Fermi Solution if I recall, isn't it? Who was it, when they dropped the first atom bomb, standing in the block house someone tore up piece of paper and dropped it as the shockwave hit. From that simplified method he had a pretty good idea of the megaton output of the blast because of the displacement of the scraps of paper as they drifted to the ground.

Another problem involved figuring out the relative distance of different size spheres where one represents the Earth and the other the Moon. Well, the Earth is about 24000 miles around, the moon about 240,000 miles away, yeah, wrap a string around the Earth 10 times, measure it, there you go. The problem can be made to sound more complex then the solution calls for.