Author Topic: Global Navigation Satellite Systems -- tutorial (Read 17361 times)

Neil Obstat · « **Reply #180 on:** September 29, 2017, 04:00:02 PM »

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The LORAN History site linked at the very end lists veterans who like to be remembered and share contact info.
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The http://www.loran-history.info/ site is copy protected. So if you want to see it you'll have to go there.
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As explained in the previous post, LORAN-A installations were lonely places where a small crew hung out for many months at a time living in quonset hut barracks and often surrounded by hostile wildlife such as viper snakes.
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Anyone who spent much time in one of these hot boxes will tell you they wanted nothing more to do with them once the War was over.
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Neil Obstat · « **Reply #181 on:** September 29, 2017, 04:22:49 PM »

Quote from: St Ignatius on September 29, 2017, 10:01:23 AM

Here's a suggestion, Neil...

Not sure what type of readership you have here on this tutorial, but I'm sure if there are any who are reading this and are new to the workings of GPS, they might be interested in other types of radionavigaton prior to GPS.

I have friends and family who are pilots, and the last I knew, private pilots who are certified to fly by IFR (instrument flight rules) can't rely on GPS exclusive of previous systems that supported radionavigation.

These types of navigation by radio are listed by type below...

*Bearing-measurement systems

*Beam systems

*Transponder systems

*Hyperbolic systems (this has been replaced now by the use of GPS)

What do you think?

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As for Transponder systems, around A.D. 2000 transponders started to become standard technology for automotive keys.
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The bow of the key (the top part that you hold) contains an IC chip which functions as a receiver/responder (thus the name transponder) which is activated by a radio signal generated and sent from the vehicle, from a sending unit located usually near the steering column. The radio signal stimulates the circuit in the key bow which in turn immediately broadcasts its own signature signal which the vehicle's unit receives. This communication between car and key identifies the key as being valid and allows the ignition system to operate normally. If the signal received from the key is incorrect the car won't start. When you have a key made for your car, the new key must be programmed to send the proper signal.
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There are many different systems for these keys. One funny story comes from a friend of mine who says he knows this guy who bought a used Ford, with only one key supplied by the dealer, and they told him he can easily get another key made. So he says, "Okay, fine," and drove away in his previously owned car. When he went to get duplicate keys, he was informed that would cost $3,000, because the car's computer module had to be replaced. You see, at this early stage Ford was using a system which has the module keeping track of how many keys are made, and the car was allotted a lifetime of 10 duplicate keys total. Well, this particular used car had already had 10 duplicate keys made, and therefore to make any more, a new module would have to be installed which has a factory setting of 10 more duplicate keys.
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Honda used a system 12 years ago which requires the owner to have ALL his keys present when he gets one new duplicate made, because they have to re-program all the keys together since the car deletes the old program and generates a new code whenever a new key is programmed.
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Neil Obstat · « **Reply #182 on:** September 29, 2017, 05:38:23 PM »

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There is an extension included for the previous section, giving a not-so-easily anticipated development, below.
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If you would like to challenge yourself, try to determine merely by looking at the diagram, what it is that makes this quasi-sine wave readable as the 1-0-1-... code written above it. Once you think you have the answer, THEN read the explanation that follows.
(Hint: the vertical dashed lines are not part of what a receiver reads but are only there to help in the illustration.)
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In depth: Detailed explanation of how carrier wave is modulated to encode PRN signal
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There are actually two types of Pseudorandom Noise signals imbedded in the carrier frequency: a short Coarse Acquisition code (C/A) and a much longer Precise code (P). The figure above shows that the P-code is binary series of 0’s and 1’s that is based on phase reversals in the underlying carrier wave (lines are shown as straight lines to save space). A typical sinusoidal wave alternates regularly between a peak and a trough (high point and low point). A phase reversal is like having a mirror inserted halfway between a peak and a trough, so the wave gets reflected back to the peak (or vice-versa). This results in two back-to-back peaks or troughs. When the wave is not reflected, the value of the code stays the same. When the phase is reversed, the code switches from a 0 to 1, or a 1 to 0. The sequence appears random, but it is actually deterministic and can be authentically reproduced inside the GPS receiver.

Truth is Eternal · « **Reply #183 on:** September 29, 2017, 05:42:11 PM »

Neil Obstat · « **Reply #184 on:** September 29, 2017, 05:45:09 PM »

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Oh, look, the troll is back. Why don't go play solitaire like you were doing a few minutes ago?
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3d. Estimating the range

We will use the carrier wave GPS signals as a giant “tape measure” between the receiver and the satellite.

To do this, we will need to know the signal’s wavelength, which is the distance required for a complete cycle of the signal to occur. The wavelength, in turn, can be derived from the frequency of the signal. Luckily, the specific frequencies of the carrier signals are known, and set by the GPS constellation.
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We need to look at how wavelengths are computed and what to do about partial wavelengths, accounted for by the "phase." First, we'll look at the basic approach to computing wavelengths and how we account for phases. Then we'll take a closer look at the issues involved in actually counting the wavelengths.
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DZ PLEASE · « **Reply #185 on:** September 29, 2017, 05:47:08 PM »

Quote from: Truth is Eternal on September 29, 2017, 05:42:11 PM

Do these people actually find some anonymous Art Bell reject convincing?

Also, I used to write quite a bit; I studied the craft, and this video 'reads' like complete, and completely bad, fiction.

Also, what's the ~altitude of these alleged faux satellites again?

Neil Obstat · « **Reply #186 on:** September 29, 2017, 05:53:09 PM »

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Quote from: DZ PLEASE on September 29, 2017, 05:47:08 PM

Do these people actually find some anonymous Art Bell reject convincing?

Also, I used to write quite a bit; I studied the craft, and this video 'reads' like complete, and completely bad, fiction.

Also, what's the ~altitude of these alleged faux satellites again?

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People? I'm convinced they're bots. Flat-earthers don't actually exist except as humanoid bots.
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Like C3p0.

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3e. Computation of GPS wavelengths

Sorry I didn't check the exponents first....
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Frequency is the number of wave crests that pass the same point per second. It is expressed in cycles per seconds denoted as Hz (1 Hz = 1 cycle per second).
The frequency of GPS L1 signal is 1575.42 MHz (1575.42 x 106 Hz) <----------"x 10⁶ Hz"
The frequency of GPS L2 signal is 1227.60 MHz (1227.60 x 106 Hz)
The wavelength of the two GPS signals can be computed using the following equation:
Wavelength = Speed of light ÷ Frequency of signal

L1 Wavelength = 299,792,458 m/s ÷ 1575.42 x 106 s-1≅ 0.190 m ≅ 19.0 cm
L2 Wavelength = 299,792,458 m/s ÷ 1227.60 x 106 s-1≅ 0.244 m ≅ 24.4 cm
NOTE: L2 has a lower frequency than L1 so its wavelength is longer
To use wavelength of the L1 band as our tape measure, we need to be able to count how many cycles lie between us and the satellite.

Figure shows a sine wave, representative of a GPS carrier signal. Although a cycle can start anywhere along the path of the wave, a full cycle is shown in the figure as spanning from the origin to the point (1,0) along the x-axis.

A full cycle is a complete sinusoidal curve, illustrated as the path from the origin to the point 1.0 along the x-axis. Counting wavelengths is essentially counting the number of cycles, and this is an integer count (1, 2, 3,... n).
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Question

Assume the satellite is 20,166,318.727 meters away from the GPS antenna. How many wavelengths of the L1 signal would make up this distance?
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These questions are worth looking forward to.
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DZ PLEASE · « **Reply #187 on:** September 29, 2017, 06:01:58 PM »

Quote from: Neil Obstat on September 29, 2017, 05:53:09 PM

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People? I'm convinced they're bots. Flat-earthers don't actually exist except as humanoid bots.
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Like C3p0.

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3e. Computation of GPS wavelengths
Frequency is the number of wave crests that pass the same point per second. It is expressed in cycles per seconds denoted as Hz (1 Hz = 1 cycle per second).
The frequency of GPS L1 signal is 1575.42 MHz (1575.42 x 106 Hz)
The frequency of GPS L2 signal is 1227.60 MHz (1227.60 x 106 Hz)
The wavelength of the two GPS signals can be computed using the following equation:
Wavelength = Speed of light ÷ Frequency of signal
L1 Wavelength = 299,792,458 m/s ÷ 1575.42 x 106 s-1≅ 0.190 m ≅ 19.0 cm
L2 Wavelength = 299,792,458 m/s ÷ 1227.60 x 106 s-1≅ 0.244 m ≅ 24.4 cm
NOTE: L2 has a lower frequency than L1 so its wavelength is longer
To use wavelength of the L1 band as our tape measure, we need to be able to count how many cycles lie between us and the satellite.
Figure shows a sine wave, representative of a GPS carrier signal. Although a cycle can start anywhere along the path of the wave, a full cycle is shown in the figure as spanning from the origin to the point (1,0) along the x-axis.
A full cycle is a complete sinusoidal curve, illustrated as the path from the origin to the point 1.0 along the x-axis. Counting wavelengths is essentially counting the number of cycles, and this is an integer count (1, 2, 3,... n).
Question
Assume the satellite is 20,166,318.727 meters away from the GPS antenna. How many wavelengths of the L1 signal would make up this distance?

You may be kidding but I'm not, at least not entirely.

The longer that I read their digital compost, the more it seems a hybrid of scripting, bots, cued intervention, and useful idiocy.

I suppose even simulated, i.e. 'artificial' intelligence is preferable to none at all.

In short, it's part of a Psyop.

I once suggested to someone how human interaction could be simulated using simple mining of actual convo's based on keyword correlation and correspondence.

The cued intervention of an actual intelligent/moral agent comes in based on disconnect responses to the faux intelligence/moral agent.

In crayon, that means just looking for same/similar web wide content and ripping off/averaging statistically standard responses tailored to the person's profile of similar usage of language.

Seems very similar.

Neil Obstat · « **Reply #188 on:** September 29, 2017, 06:16:22 PM »

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The tutorial supplies this answer to the question above. But they made one mistake, which then results in several errors.
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Can you find the errors or the one mistake? (Hint: They're off by more than "several centimeters.")
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20,135,196.834 m ÷ 0.19 m/wavelength = 105,974,720.179 wavelengths
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If we could count just the instantaneous number of cycles at this one epoch, we would have counted 105,974,720 wavelengths - the integer portion of the solution.
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Clearly, we’d be missing a fraction of the next cycle (shown as the extended part of the curve in the figure above). In the example, we’d be off by 0.179 cycles. At 0.19 m/wavelength, this error would be:
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0.179 m x 0.19 cm = 0.034 m = 3.4 cm.
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So we’d be off by several centimeters.

Neil Obstat · « **Reply #189 on:** September 29, 2017, 06:21:09 PM »

Quote from: DZ PLEASE on September 29, 2017, 06:01:58 PM

You may be kidding but I'm not, at least not entirely.

The longer that I read their digital compost, the more it seems a hybrid of scripting, bots, cued intervention, and useful idiocy.

I suppose even simulated, i.e. 'artificial' intelligence is preferable to none at all.

In short, it's part of a Psyop.

I once suggested to someone how human interaction could be simulated using simple mining of actual convo's based on keyword correlation and correspondence.

The cued intervention of an actual intelligent/moral agent comes in based on disconnect responses to the faux intelligence/moral agent.

In crayon, that means just looking for same/similar web wide content and ripping off/averaging statistically standard responses tailored to the person's profile of similar usage of language.

Seems very similar.

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Maybe we can have a new order of flame war online here:

"You're just a bot."
"No, I'm not a bot but YOU are!"

ETC.
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Neil Obstat · « **Reply #190 on:** September 29, 2017, 06:27:13 PM »

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I'll go over the error in the tutorial answer later.
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3f. Phase measurement

To resolve the remaining distance, we need to figure out exactly where along the waveform the signal is captured at the center of the GPS antenna at some particular instant. This is referred to as the phase measurement.

In GPS positioning, phase measurement is determining which location along the sinusoidal waveform is being received at any moment in time.

Phase measurement takes advantage of the sinusoidal characteristics of the signal. The amplitude of the wave (denoted as A0 in equation below) is nothing more than the maximum voltage sensed in the signal received. We can compute the fractional portion of the cycle (the fractional phase) by knowing the strength of the signal when we first measured it, the maximum voltage of the signal once we’ve received a whole wavelength, and the formula for a sine wave:

A(t) = A0 sin[2πφ(t)]

A(t) = the signal, expressed as the strength of the electric field given in the radio wave at a moment in time (t)

A0 = the amplitude of the signal

φ(t) = the fractional phase of the signal at time (t)

Knowing A(t) and A0, we can solve for φ(t), the phase of the signal.

The fractional phase measurement allows us to achieve accuracies of at least one percent of the wavelength, which in this case would be about two millimeters.

Therefore, using the characteristics of the carrier signal (L1 or L2), the GPS receiver can theoretically compute its distance from the satellite to within a few millimeters. However, in practice this is limited by:

Our ability to accurately count the full number of cycles
Phase biases/offsets at both the satellite and the receiver
Atmospheric effects, and
Other errors

DZ PLEASE · « **Reply #191 on:** September 29, 2017, 06:35:10 PM »

Quote from: Neil Obstat on September 29, 2017, 06:21:09 PM

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Maybe we can have a new order of flame war online here:

"You're just a bot."
"No, I'm not a bot but YOU are!"

ETC.
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More like performance "art".

It would be kind of funny, two non-persons seemingly arguing about which is the person.

It wouldn't surprise me if this or like hasn't already been done, at least as someone's doctoral thesis, with actual people getting sucked in pro and con.

The more you think about it though, the more it seems to be another instance of art imitating life, and then co-opting it.

"A bot I am, lest a bot I become."

How well do you script?

Neil Obstat · « **Reply #192 on:** September 29, 2017, 06:40:44 PM »

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Hey, I'm just the messenger here. That last part about being accurate "theoretically" to within a few centimeters might be something found on the Review Questions later, but you don't have to believe it. They have entirely ignored the topic of significant figures in this tutorial, and I suspect there is a large portion of the readers who have used it that have noticed this glaring omission.
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Physics professors at colleges and universities don't cut much slack for students who repeatedly ignore estimation of error by way of not paying attention to significant figures.
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Quote

How well do you script?

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So far, I haven't attempted to script. You? Most scripts get the deep-6.
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DZ PLEASE · « **Reply #193 on:** September 29, 2017, 06:44:06 PM »

Quote from: Neil Obstat on September 29, 2017, 06:40:44 PM

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Hey, I'm just the messenger here. That last part about being accurate "theoretically" to within a few centimeters might be something found on the Review Questions later, but you don't have to believe it. They have entirely ignored the topic of significant figures in this tutorial, and I suspect there is a large portion of the readers who have used it that have noticed this glaring omission.
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Physics professors at colleges and universities don't cut much slack for students who repeatedly ignore estimation of error by way of not paying attention to significant figures.
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So far, I haven't attempted to script. You? Most scripts get the deep-6.
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In a manner of speaking, back in the days of Hex, binary, and assembly language.

I think it better to do it myself, otherwise I'm just automating something that I found unworthy of doing myself.

"TANSTAAFL"

Neil Obstat · « **Reply #194 on:** September 29, 2017, 06:56:01 PM »

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3g. Counting the number of signal cycles

[There is a very nice short video here which I have no idea how to embed since it's not YouTube
so you'll have to go to the website and register in order to view it. It consists of a receiver station
on the ground with a satellite moving in a curve overhead and a description of the method they
use to calculate the continually changing distance to the satellite, beginning here with "integer
count." Keep in mind the system has been developed to interface the different orbital movements
of 4 satellites all at the same time in order to get a fix on the receiver location.]

[Well, duuuh, somehow the video now is visible here. Hmmmm.]
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Unfortunately, there is no direct way of counting how many cycles have occurred between the satellite and the receiver at the time the signal is first received. The counting of cycles can only start after the signal reaches the receiver. Resolving the ambiguity of the original number of cycles (shown as “N” in the figure above and also called the “integer ambiguity”) is addressed using high-level, iterative approximation algorithms. These algorithms use the pseudorange estimation as a starting point, and take into account the counted number of cycles as the receiver is locked onto the satellite.

As the satellite proceeds along its orbit around Earth, its distance away from the GPS receiver changes (N, N+∆Φ1, N+∆Φ2, etc.). This means that at each epoch, there will be a different fractional phase measurement, and a different number of cycles between the GPS satellite and the receiver’s antenna.

However, there is a direct relationship between the change in distance, the initial ambiguity, and the counted number of cycles at the receiver at each epoch. For this reason, as long as the receiver is locked onto the satellite, it continues to count cycles—and both the original integer ambiguity (N) and all subsequent range measurements (based on the cycles counted) will become more accurate.

Estimation of initial distance N becomes more accurate over time; as more epochs are recorded, the confidence in our estimate of N increases.

There are a number of different mathematical procedures available to do this, each with their strengths and weaknesses. Some methods provide very fast estimates and are ideal for situations in which you cannot observe your point for very long. If you can stay on your (unknown) location for say 24-48 hours, slower but very robust algorithms will provide a very good solution.

Over the course of a long observation session, a GPS receiver may lose lock on a satellite as the satellite may be momentarily occluded by a tree, building, or telephone pole, etc. Unfortunately, this means that when the satellite reappears, a new lock will be made together with a new ambiguity that will have to be resolved. For this reason, there are always more ambiguities to resolve (called “fixing”) than the number of satellites viewed over the course of a GPS observation session.

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In depth: The doppler effect .............. - to be covered later.
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Author Topic: Global Navigation Satellite Systems -- tutorial (Read 17361 times)

Neil Obstat

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Neil Obstat

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Neil Obstat

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Truth is Eternal

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DZ PLEASE

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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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DZ PLEASE

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Neil Obstat

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