Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27884 times)

DZ PLEASE · « **Reply #150 on:** September 28, 2017, 07:51:59 PM »

Quote from: Neil Obstat on September 28, 2017, 07:32:04 PM

It would make an interesting improvement to delete all their posts...

That would be a very useful block of training, in and of; how?

It seems to me, if no other, that offsite linking would introduce an element of positive control that is sorely lacking with the given system/platform; this would require something like permission, like raising a hand in kindergarten.

Back to kindergarten 'tactics' seem very strongly indicated nowadays. "Back to basic basics."

Neil Obstat · « **Reply #151 on:** September 28, 2017, 07:55:42 PM »

Unit 2. GNSS computational methods I - Coarse positioning »

2d. Determining the “pseudorange”

from the satellite using PRN synchronization

Knowing which satellite sent the signal is only a small part of the process. This provides us with the ability to locate each satellite. But in order to perform trilateration, we need to compute the distance from each satellite. Modern survey-grade GPS positioning systems use several methods to do this. We’ll start by looking at the most basic method, which is based on the delay between the time the signal is sent and when it is received.

The GPS receiver compares the PRN signal transmitted by the satellite to the copy of the PRN code in its library. This is done by reproducing the PRN code at the time the signal is expected to be emitted from the satellite and comparing it to the signal that arrives with a delay from the satellite. By comparing the two signals—the one received, with the one generated within the receiver—the receiver can compute the amount of time it took for the signal to travel between the satellite and the receiver. This elapsed time is used to estimate the distance between the satellite and the receiver. This process is illustrated in the following animation:

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[Video which did not copy belongs here. Click on the link below to see it live online.]
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The PRN code is broadcast as a repeating loop, repeated every millisecond. From the information contained in the almanac, the receiver knows when to expect the signal to leave the satellite. The receiver can therefore generate a duplicate code loop, as if it had started at the same time that the signal left the satellite (according to the receiver’s clock).

At some small time interval later, the GPS signal sent from the satellite arrives at the receiver. The receiver lines up the two codes and “slides” the replica code of the receiver along the received code until the two codes match. This sliding of the replica code is referred to as a “delay.” The amount of delay required to get the signals to match gives an estimate of the amount of time it took for the signal to reach the receiver. The distance between the satellite and the receiver can now be estimated by comparing the time delay between the two, and knowing that radio signals travel at the speed of light.
(distance = speed x time)

The basic calculation is done as follows:

Range = ∆T × c
      = (TR- TS) × c

∆T = elapsed time between when signal was sent and when it was received (in seconds)

c = speed of light, 299,792,458 m/s

TR= Time signal was received according to receiver

TS= Time signal was sent according to satellite

The distance between the satellite and the receiver (called the “range”) can be obtained by multiplying the interval of time it took for the GPS signal to reach the GPS receiver (∆T in the above example, measured in seconds) by the speed of light (299,792,458 meters per second).

Unfortunately, due to the error in the GPS receiver clock, this distance will only be approximate. For this reason, it is called a “pseudorange.”

Neil Obstat · « **Reply #152 on:** September 28, 2017, 10:08:37 PM »

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Maybe that mini-movie won't run for you but that's no big deal. It only lasts 15 seconds. What it shows is the two PRN tracks offset by some portion of a millisecond which the receiver matches with its data files to determine which satellite it is sending the code.
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The next section is really short. They must talk a lot about Pseudorange or else they wouldn't have given it its own name.

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2e. Pseudorange: Definition and limitations

Pseudorange is the approximate distance between a GPS satellite and the GPS receiver antenna, computed using approximate time elapsed between the moment the signal was emitted from the satellite, and the moment the signal was received at the GPS receiver antenna. The range is only approximate because the atomic clocks in the satellite and the quartz clock in the GPS receiver are not synchronized.

The clocks on GPS satellites are extremely high precision atomic clocks. They are way too expensive to have in our relatively inexpensive GPS receivers (which have cheaper quartz clocks). So our GPS receiver clocks will be off by some amount. Because GPS signals travel essentially at the speed of light, being even a microsecond out of sync could cause positional errors on the scale of 300 meters. Luckily, by using principles of trilateration, our GPS receiver is able to estimate the clock offset between it and the satellite, which improves our ability to estimate the distances.
(See References for more resources on this topic.)

Pseudorange estimation is a fairly complicated process, but the principles are similar to the ones we saw in the two-dimensional case with the ship and lighthouses using sound.

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True or False:
A typical GPS satellite is equipped with an atomic clock.
Atomic clocks are affordable and widely used in all GPS components such as receivers.
When scaled down to 300 meters the distance from receiver to satellite needs no refinement.
The clock offset is eventually overcome using trilateration and needs no further precision.
The process of measuring approximate distance to a satellite is known as pseudorange estimation.
Quartz clocks used in GPS receivers are adequate for pseudorange once they're synchronized with an atomic clock.
The length of the receiver's antenna affects the length of time it takes to match up PRN data.
Atomic clocks cost a large number of dollars but the satellites somehow remain affordable.
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Tradplorable · « **Reply #153 on:** September 28, 2017, 10:25:43 PM »

Quote from: Neil Obstat on September 28, 2017, 03:06:08 PM

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Actually, it is true that "If the earth were 'flat' all these transmission problems would be non-existent."
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You have no proof of your "horizon" controlling transmission and the power of the signal.
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You're just making stuff up, as usual.
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Any ham radio operator knows he can perpetuate his signal even all around the world, showing that the earth is spherical, by his radio waves directed to bounce off the ground and off the ionosphere repeatedly, under the right conditions. This would not be the case with a "flat" earth because the waves would go off the "edge" of the so-called flat earth and be lost.
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There is no edge on the FE model and you know that. The Firmament encompasses all of Creation.

Neil Obstat · « **Reply #154 on:** September 28, 2017, 10:33:55 PM »

Quote from: Tradplorable on September 28, 2017, 10:25:43 PM

There is no edge on the FE model and you know that. The Firmament encompasses all of Creation.

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How nice of you to drop in and try to clog the thread up with your incorrect blatherings...... NOT
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But that's okay, go right ahead and make yourself look foolish.
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I'd ask you to prove "the Firmament encompasses all of Creation" but that would only further clog the thread and would never prove anything but for the above statement.
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Neil Obstat · « **Reply #155 on:** September 28, 2017, 10:34:23 PM »

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Last section in this part........
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2f. Estimating the position from pseudoranges

Because precise timing is absolutely critical to measuring distance using the speed of light, we need to account for the clock errors (clocks being out-of-sync) both at the satellite, which has much smaller errors, and the receiver, which has much larger errors. Therefore, the recorded times at which the GPS signals are sent by the satellite (TS) and received by the receiver (TR) can be expressed as the true times (tS and tR) plus the respective clock errors (δS and δR) [ δS and δR ]:

Note that the receiver clock error (or bias) is not necessarily constant and needs to be computed at each moment in time that the receiver is making the pseudorange calculation (every “epoch”).

The observed pseudorange (P) can therefore be expressed as the following, where c represents the speed of light:'

The first term in the above equation, (tR - tS)c, is the “true” range from the receiver (at receive time) to the satellite (at transmit time). This range can also be expressed as the straight-line distance in Cartesian coordinates, between the receiver and the satellite:

The position of the satellite (xS, yS, zS) is computed from the broadcast ephemeris message sent from each satellite. This, along with the time of transmission, are considered “known.”

A simplified observation equation for the pseudorange can therefore be written as:

Knowns	Unknowns
P - the measured pseudorange based on the time-distance computation (xS, yS, zS) - the position of the satellite at the time of signal transmission c - the speed of light δS - the satellite clock bias (stored in the broadcast ephemeris) [δS]	(xR, yR, zR) - the position of the GPS receiver δR - the receiver clock bias [δR]

We therefore have one equation and four unknowns.

The process of observing a pseudorange is now repeated for each satellite in view. With four satellites in view at any given moment, we now have a system of four equations and four unknowns:

With only three satellites in view, theoretically the receiver should be able to figure out where it is in three dimensions (lat/long/height) on the surface of Earth. However, in practice, this is complicated by clock errors. With the addition of a fourth satellite, the receiver clock bias can also be estimated to provide a solution that is good to within at least a couple hundred meters. (Note that recent handheld high-end consumer GPS receivers can achieve accuracy to within 3-15 meters making use of additional augmentation satellites.)

Here is yet another nice picture of a group of satellites in space for Truth is Transitory!

But who would expect him to ever find it unless he reads these posts?

Measuring distance with a signal traveling at the speed of light is difficult indeed, and our solution is an approximation, due in part to the mathematics involved. Also, the PRN code is repeated at a frequency of about 1 MHz (one million times a second), so an error in computing the time delay using the PRN code (within a millionth of a second) could cause an error on the order of 300 m. Clearly, we cannot rely solely on this method of ranging for high accuracy surveying needs. Using the PRN code can definitely get us close though, and considering the distance separating the receiver from the satellite, even a few hundred meters is pretty good! As we’ll see in the next units, an additional method of ranging is used by survey-grade GPS receivers to refine the accuracy from a few hundred meters down to a few centimeters.

For a more detailed explanation of how the system of pseudorange equations are solved, please see APPENDIX 2: The mathematical solution of trilateration in three dimensions.

Neil Obstat · « **Reply #156 on:** September 28, 2017, 10:39:35 PM »

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The end.............
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2g. Summary

In this unit, we explored how the signals transmitted by GNSS satellites are used to obtain an approximate distance (pseudorange) from a point on Earth to each satellite. We looked at specifically how the pseudorange is estimated for the U.S. GPS constellation. We discussed the importance of the unique pseudorandom code (PRN) in not only identifying each satellite, but in allowing the receiver to estimate the time it took for each GPS satellite signal to travel from the satellite to the receiver. Since radio waves travel at the speed of light, we can estimate the pseudorange knowing the approximate elapsed time from signal transmission to signal reception.
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DZ PLEASE · « **Reply #157 on:** September 28, 2017, 10:41:35 PM »

1. Tell them what you're going to tell them.
2. Tell them.
3. Tell them what you told them.

:applause:

Neil Obstat · « **Reply #158 on:** September 28, 2017, 11:08:03 PM »

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And now the "questions"
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2h. Review questions

Question 1 of 7
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If the distance to your satellite is 20,135,196.834 meters, how long does it take the signal to reach you? (Speed of light = 299,792,458 m/s)
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Question 2 of 7
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What is the name given to the unique code assigned to each GPS satellite? (Choose the best answer.)
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a) Pseudorandom noise (PRN) code
b) Unique identity designation (UID) code
c) Identity confirmation code (ICC)
d) Digital satellite identity (DSI) code
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Question 3 of 7
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To estimate the travel time of a GPS signal from a satellite to your GPS receiver, a copy of the PRN code is generated by the | -- receiver / satellite / satellite tracking station |  and then compared to the code received from the | -- receiver / satellite / satellite tracking station |.
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Question 4 of 7
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To estimate the travel time of the signal from the satellite to the receiver, the code produced by the receiver is |   -- delayed / stopped / amplified | until the correlation between two signals jumps to its |   -- minimum / maximum / end point |.
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Question 5 of 7
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Pseudorange:
(Choose all that apply.)
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a) is an approximate distance between a GPS satellite and the GPS receiver
b) is contained in the ephemeris
c) may be accurate to within a few centimeters
d) is based on the travel time of the radio signal
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Question 6 of 7
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In its most fundamental form, what are the knowns and unknowns in the basic trilateration system of equations for computing a GPS satellite-based position?
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Satellite positions (xS,yS,zS) is |   -- known / unknown .
Satellite clock bias (TS) is |   -- known / unknown .
Receiver position (xR,yR,zR) is |   -- known / unknown .
Receiver clock bias (TR) is |   -- known / unknown .
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Question 7 of 7
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Why is the solution of a position approximate? (Choose the best answer.)
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a) We never really know where the satellites are in space
b) There are always more “unknowns” than “knowns” in our mathematical solutions
c) Measuring distance at the speed of light requires extremely precise timing, which is hard to achieve perfectly
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Neil Obstat · « **Reply #159 on:** September 28, 2017, 11:17:31 PM »

Quote from: Tradplorable on September 28, 2017, 10:25:43 PM

There is no edge on the FE model and you know that. The Firmament encompasses all of Creation.

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Even if they're afraid to admit it, flat-earthers deny the existence of satellites (even while they use GPS technology to find their way to the bowling alley or trailer park) because satellites orbiting the spherical earth at 20 million meters makes their fabled "solid" firmament quite impossible.
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So they have, let's say, an a priori and vested interest in preventing the recognition of satellites, even while like I said, they use them to get to the bowling alley or the trailer park.
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DZ PLEASE · « **Reply #160 on:** September 28, 2017, 11:21:36 PM »

Quote from: Neil Obstat on September 28, 2017, 11:17:31 PM

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Even if they're afraid to admit it, flat-earthers deny the existence of satellites (even while they use GPS technology to find their way to the bowling alley or trailer park) because satellites orbiting the spherical earth at 20 million meters makes their fabled "solid" firmament quite impossible.
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So they have, let's say, an a priori and vested interest in preventing the recognition of satellites, even while like I said, they use them to get to the bowling alley or the trailer park.
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Well, I'm thinking "put up, or shut up."

After all, sounds to me like if what they're saying is true, there's some really choice real estate just waiting to be developed at the ends of the earth.

Just think of it, it's like some kinda wonky Dyson (Hemi) Sphere with loads of firmament to build on.

You could deep-sea fish right off your porch, not to mention cliff dive.

Truth is Eternal · « **Reply #161 on:** September 28, 2017, 11:27:16 PM »

Quote from: Neil Obstat on September 28, 2017, 11:17:31 PM

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Even if they're afraid to admit it, flat-earthers deny the existence of satellites (even while they use GPS technology to find their way to the bowling alley or trailer park) because satellites orbiting the spherical earth at 20 million meters makes their fabled "solid" firmament quite impossible.
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So they have, let's say, an a priori and vested interest in preventing the recognition of satellites, even while like I said, they use them to get to the bowling alley or the trailer park.
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I use GPS. Satellites don't exist.

Truth is Eternal · « **Reply #162 on:** September 28, 2017, 11:28:15 PM »

Truth is Eternal · « **Reply #163 on:** September 28, 2017, 11:30:57 PM »

Neil Obstat · « **Reply #164 on:** September 28, 2017, 11:46:25 PM »

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So we could have flat-earthers providing Scripture verses to "prove" their so-called solid firmament (even though no such thing is found in Scripture) and they could quote chapter and verse to profess their faith in a "flat" earth (even though the Bible says no such thing) but then on an equal footing, we can ask flat-earthers to show us in Scripture where to find GNSS systems, ephemerides, atomic clocks, pseudorange, predicted orbital parameters, PRN synchronization, ground-based observing stations and Global Positioning Systems.
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There isn't any point in asking them to show us where to find satellites in Scripture because they're more than happy to announce they're not to be found there and that "proves" that satellites are not real.
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Don't forget to turn off your GPS because

you don't believe in the satellites it relies on to operate.

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Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27884 times)

DZ PLEASE

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Neil Obstat

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Neil Obstat

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Tradplorable

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Neil Obstat

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Neil Obstat

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Neil Obstat

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DZ PLEASE

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Neil Obstat

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Neil Obstat

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DZ PLEASE

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Truth is Eternal

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Truth is Eternal

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Truth is Eternal

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Neil Obstat

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