Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27720 times)

St Ignatius · « **Reply #60 on:** September 27, 2017, 08:40:58 PM »

Quote from: Neil Obstat on September 27, 2017, 07:02:25 PM

Cape Canaveral, Florida; Ascension; Diego Garcia; Kwajalein:

You mention these 4 places, are these the only locations which are allowed to be utilized by civilians?
I see that the DOD has a good number more around the globe... including some of the first stations that my father was stationed at during the 50's and 60's.

Neil Obstat · « **Reply #61 on:** September 27, 2017, 08:41:47 PM »

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NOW for those readers who are actually READING this thread and would like to check their answers, here is the key to the unit 1 Review questions 1-5:
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1e. Review questions

Question 1 of 5

The term GPS refers to all global navigation satellite systems. (Choose the best answer.)

a) True
b) False

GPS is specific to the US NAVSTAR Global Positioning System, one of several global navigational satellite systems (the answer is b. False).
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Question 2 of 5

Which of the following is NOT a component of GNSS positioning? (Choose all that apply.)

a) Satellite ground-based observing systems
b) International space station tracking system
c) Radio signal reception at the receiver
d) Radio signal transmission at the receiver
e) Radio signal transmission at the satellite
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The three basic components of GNSS positioning include: 1) the space component (GPS satellites orbiting Earth and transmitting positional signals); 2) the ground component (ground-based observing systems, including the Master Control Station); and 3) the user component (the GPS antenna and receiver). Note that the user component only receives signals; it does not transmit any signals to the satellites.
The international space station does not play a role in GNSS. (The answer is b. and d.)

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Question 3 of 5

What is the name given to the geometric/computational process used to derive a position based on GPS? (Choose the best answer.)

a) Trilateration
b) Triangulation
c) Interpolation
d) Parallax shift

Trilateration is the process of using distances to locate a position. Triangulation is the process of locating a position based on angles and known positions. Interpolation is the process of estimating values that lie between known or measured points. Parallax shift is used by astronomers to estimate the distance of some celestial bodies (e.g., stars) that are relatively close to Earth. (The answer is a.)
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Question 4 of 5

What is the minimum number of satellites required to determine a basic position, and why? (Choose the best answer.)

a) 1 – By calculating the distance from a radio signal and the direction the signal comes from, one can get a basic position but with less accuracy
b) 2 – With two satellites, one can calculate the position based on the intersection of the lines from the locations of the satellites
c) 3 – Using trilateration, we can determine the basic position based on distance from each satellite and the known location of each satellite

The minimum number of satellites required for trilateration is 3. It is based on the distance from each satellite and their known positions. GPS does not work by detecting the direction of the satellite transmissions. It must know the location of the satellite together with its distance. (The intersection of the "lines" generated from the locations of satellites would be a giant circle which only touches the surface of the earth in one place, however, depending on where the satellites are located, this "one place" might be ambiguously a very large area, perhaps thousands of square miles, or even an entire country, so a third satellite is necessary to determine even a "basic" position.)

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Question 5 of 5

A GPS receiver determines its position by _____. (Choose all that apply.)

a) Measuring the angles between its antenna and the satellites
b) Measuring the distances between the antenna and satellite
c) Measuring the distance between the antenna and the center of mass of Earth
d) Knowing the exact location of each satellite at a given time

GPS positioning relies on measuring distances between the GPS antenna and a GPS satellite, and knowing the exact location of each satellite in space. GPS positioning does not rely on angles, nor does it depend on the distance between the GPS antenna and the center of mass of Earth. The GPS satellite orbits, however, are sensitive to the center of mass of Earth, and their position in space (a piece of information required in GPS positioning) is a function of their orbits around the center of mass. (The answer is b. and d.)

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St Ignatius · « **Reply #62 on:** September 27, 2017, 08:45:39 PM »

Quote from: Neil Obstat on September 27, 2017, 08:35:40 PM

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All 4 places are locations where a GNSS Ground Antenna and an Air Force Monitoring Station are located, two out of 6 possible.
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There are no other places currently on planet earth where both of those facilities are found.
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Incidentally, the Diego Garcia location also has a AFSCN Remote Tracking Station.
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The other three facilities are Master Control Station, Alternate Master Control Station and NGA Monitoring Station
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Therefore, the answer is 4, but since Truth is Transitory doesn't read these posts, he'll never know that.
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Opps... seems you acknowledged my question while I was typing...

Neil Obstat · « **Reply #63 on:** September 27, 2017, 09:01:04 PM »

Quote from: St Ignatius on September 27, 2017, 08:40:58 PM

You mention these 4 places, are these the only locations which are allowed to be utilized by civilians?
I see that the DOD has a good number more around the globe... including some of the first stations that my father was stationed at during the 50's and 60's.

That's a good question. But as far as I know all the locations shown are accessible to civilians.
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Now, perhaps the actual facility mentioned is not so accessible, but "United Kingdom" and "South Korea" and "Guam" are places where civilians are not excluded.
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Or are you talking about using the GPS system located at those places?
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As far as I know, when a civilian uses GPS he does not get to select which station is to be used. His device automatically selects one or more.
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Now, I have a watch (made by Casio) with a radio control feature which can automatically select which signal to receive, but it has a manual override feature whereby you can exclude one or more signal(s) and only accept one. The Casio website has the user manual online, which depicts two radio control time signals broadcast in Japan, one in the north and one in the south. We only have one in the USA (weird) even though America is hundreds of times larger than Japan is. The place is Fort Collins, Colorado, if I recall correctly. There is one more place located in England and one in Germany. So if you're in South America or South Africa it might be a bit challenging to pick up a signal, that is, unless they've improved things since then.
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Incidentally, if the earth were "flat" all these transmission problems would be non-existent.
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St Ignatius · « **Reply #64 on:** September 27, 2017, 09:12:34 PM »

Quote from: Neil Obstat on September 27, 2017, 09:01:04 PM

That's a good question. But as far as I know all the locations shown are accessible to civilians.
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Now, perhaps the actual facility mentioned is not so accessible, but "United Kingdom" and "South Korea" and "Guam" are places where civilians are not excluded.
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Or are you talking about using the GPS system located at those places?
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As far as I know, when a civilian uses GPS he does not get to select which station is to be used. His device automatically selects one or more.
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Now, I have a watch (made by Casio) with a radio control feature which can automatically select which signal to receive, but it has a manual override feature whereby you can exclude one or more signal(s) and only accept one. The Casio website has the user manual online, which depicts two radio control time signals broadcast in Japan, one in the north and one in the south. We only have one in the USA (weird) even though America is hundreds of times larger than Japan is. The place is Fort Collins, Colorado, if I recall correctly. There is one more place located in England and one in Germany. So if you're in South America or South Africa it might be a bit challenging to pick up a signal, that is, unless they've improved things since then.
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Incidentally, if the earth were "flat" all these transmission problems would be non-existent.
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I've been using hand-held gps devices for probably nearly as long as they have been available for civilian use.
Accuracy was, and still is, limited to a certain range of accuracy. I was under the assumption that was due to availability of certain land mark stations. I could be totally wrong about this.

Tradplorable · « **Reply #65 on:** September 27, 2017, 09:52:43 PM »

Quote from: Neil Obstat on September 27, 2017, 09:01:04 PM

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Incidentally, if the earth were "flat" all these transmission problems would be non-existent.
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WHAT A TOTAL LIE!
The horizon controls transmission and the power of the signal.
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THE. END.

Tradplorable · « **Reply #66 on:** September 27, 2017, 09:58:09 PM »

Quote from: Truth is Eternal on September 27, 2017, 05:25:41 PM

Try me. Post a picture of a group of satellites in space.

I did.
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No pictures...hmmm...
Google: satellites
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comes up with illustrations....
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.but, no....photos. None.
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https://www.google.com/search?q=satellites&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj28fWa8MbWAhUhwVQKHf0XCAUQ_AUICygC&biw=1536&bih=759

Truth is Eternal · « **Reply #67 on:** September 27, 2017, 10:07:35 PM »

Quote from: Tradplorable on September 27, 2017, 09:58:09 PM

I did.
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No pictures...hmmm...
Google: satellites
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comes up with illustrations....
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.but, no....photos. None.
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https://www.google.com/search?q=satellites&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj28fWa8MbWAhUhwVQKHf0XCAUQ_AUICygC&biw=1536&bih=759

Maybe now that you couldn't find a picture of a group of satellites in space, Neil Obstat will feel so ashamed he will actually look for a photo of a group of satellites in space so he can find out satellites don't exist. I guess for Neil Obstat that one isn't getting off the ground. I guess that's what a lemming gets for blindly believing NASA without any proof for doing so.

DZ PLEASE · « **Reply #68 on:** September 27, 2017, 10:10:42 PM »

Quote from: Tradplorable on September 27, 2017, 09:52:43 PM

WHAT A TOTAL LIE!
The horizon controls transmission and the power of the signal.
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THE. END.

"THE. END."

What, the "Flat Earth Fairy" just waves her magic wand and poof, "Tis so!"?

"The horizon controls..." What, is it some kind of ancient pagan god or something?

The superstition and magical thinking of these people... crikey.

Tradplorable · « **Reply #69 on:** September 28, 2017, 07:18:48 AM »

Quote from: DZ PLEASE on September 27, 2017, 10:10:42 PM

"The horizon controls..."

Yes, it's called the LINE OF SIGHT, you idiot.
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All radio and microwaves travel in STRAIGHT LINES (no curve, DUH).
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Therefore, the reach of ANY radar system is limited BY THE HORIZON and THE POWER OF THE SIGNAL.
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The horizon is due to the law of perspective from the LINE OF SIGHT and POSITION of the source signal.
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You should have paid better attention when the Law of Perspective was being explained to you by the flat earthers.
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Cell towers, etc. actually have very limited reach: hence, the reason why there are SO MANY OF THEM. You have to send the signal from tower to tower.
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Why do you think RADIO towers are SO TALL and sit ATOP MOUNTAINS?
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SO they can get a longer line of sight on the horizon and transmit a greater distance.
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Tradplorable · « **Reply #70 on:** September 28, 2017, 07:34:57 AM »

Quote from: Truth is Eternal on September 27, 2017, 06:42:58 PM

NASA claim there are thousands of satellites orbiting the earth; it should be very easy for Neil Obstat to find a picture of a group of satellites in space.

Here's a good video of a satellite being sent into "space":
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Tradplorable · « **Reply #71 on:** September 28, 2017, 07:53:28 AM »

Also, Neil Obsitnate, did it ever occur to you how over-the-horizon radar bounces off what is above us??

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Because it is SOLID.

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"The ionosphere is really the Firmament, made of a Mirror-like Metal, which is why it behaves like it does."

kiwiboy · « **Reply #72 on:** September 28, 2017, 08:48:58 AM »

Quote from: Neil Obstat on September 27, 2017, 05:42:06 PM

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So there is no point in trying to make you happy. You are always going to be unhappy.
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You are an unhappy person, Truth is Transitory.
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You are unhappy, and that's the way you like it.
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You are miserable, cantankerous, discontented, spiteful, full of anxiety and calumnious.
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If you don't find a way to LIGHTEN UP you'll dig yourself an early grave.
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I just want everyone reading this to STOP RIGHT NOW, and read what I have just quoted. This is what Neil Obstat has posted. Emphasis are his.

Neil Obstat · « **Reply #73 on:** September 28, 2017, 01:08:55 PM »

Quote from: Truth is Eternal on September 27, 2017, 10:07:35 PM

Maybe now that you couldn't find a picture of a group of satellites in space, Neil Obstat will feel so ashamed he will actually look for a photo of a group of satellites in space so he can find out satellites don't exist. I guess for Neil Obstat that one isn't getting off the ground. I guess that's what a lemming gets for blindly believing NASA without any proof for doing so.

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There's only so much time to go around, Truth is Transitory. I'm sure your searching for a picture of a group of satellites (congratulations for finally dropping the plural possessive apostrophe) in space is time spent in abundance sufficient to make up for several others who are not searching. BTW a group of satellites in space is known in the industry as "a constellation," which you would know by now if you had been reading the posted material. That is, you would know it if you were willing to learn about the industry.
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Speaking of "proof" perhaps you would be interested in the Appendix 1 page, below, which ought to be perfectly agreeable to you since it assumes a two-dimensional working surface otherwise known as a Cartesian plane.
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Flat-earthers and Cartesian planes ought to be bosom buddies -- we'll have to see if you can substantiate that expectation with your ready and appropriate comments. Or perhaps your two side-kicks kiwiwimpy and Tardplorable might be capable of lending you a hand. But I doubt it.
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APPENDIX 1:

The mathematical solution of

trilateration in two dimensions

In our example of the boat off the coast receiving the audible signal from two lighthouses (from the introduction on trilateration), we wanted to know the latitude and longitude corresponding to the position of the boat. In mathematical terms, the latitude and longitude can be expressed in the two-dimensional Cartesian Coordinates X and Y. These are the two variables we wish to solve for. Note that the positions of the lighthouses can be plotted in the same plane:

To solve for the unknown position of our boat, we use the Pythagorean Theorem to express the distances we computed from the signals into geometric relationships with respect to the light houses. The Pythagorean Theorem expresses the relationship between two sides of a right triangle and the hypotenuse (note, this is the same method which can be used to estimate the distance to the sun based on an assumed distance to the moon, and observing the angle between the sun and moon in the sky at the moment of the first or last quarter moon):

Equation 1:

Equation 2:

For Lighthouse 1, we would have the following geometric relationship:

Equation 3:

Similarly, for lighthouse 2:

Equation 4:

So we have our two equations and two unknowns.

Known:
Coordinates of Lighthouse 1 (5,11)
Coordinates of Lighthouse 2 (13,19)
Computed:
Computed distance between ship and Lighthouse 1 (based on the signal heard, 13 units)
Computed distance between ship and Lighthouse 2 (based on the signal heard, 5 units)
Unknowns:
Coordinates (XS, YS) of ship
Solution:
Step 1: Define the two equations with two unknowns. We will eventually solve for the unknown position of ship (XS, YS).
Equation 5:

Equation 6:

Step 2: We now have a system of equations: two equations with two unknowns. If the equations were linear (e.g., y = mx + b), this would be an easy solution. However, the equations are decidedly non-linear, so the solution is a lot more complex. One way of solving this is to linearize the non-linear equations using a Taylor Series Expansion of the square root function. Taylor Series are an infinite series, so we will only use the first (and most important) terms.
Apply a Taylor Series expansion to each distance equation (we need to linearize the nonlinear equation):
Equation 7:

Equation 8:

Equation 9:

Equation 10:

Note that the terms D1(xS, yS) and D2(xS, yS) refer to the observed distances (obtained by using the fog horn blasts from the two lighthouses). The computed distances refer to an initial estimate of the position based on where we think we are (called the “a priori” position estimate in GPS lingo).
Step 3: Take the partial derivatives of D1 and D2 with respect to x and then y:
Equation 11:

Equation 12:

Equation 13:

Equation 13b:

Substituting the Equations 5 and 6 into these partial derivatives (Equations 11-13) allows us to simplify these expressions:
Equation 14:

Equation 15:

Equation 16:

Equation 17:

Step 4: We can express the difference between the observed distance (the one we obtained using the sound blast and the speed of sound) and the computed distance in x and y (our unknowns):
Equation 18:

for i = 1, 2
Step 5: Since Appendix 1 Equations 7 and 9 are of the form

we can see that ΔD reduces easily to the form

Note that the differences (ΔD’s) are approximate from the Taylor Series’ expansions. The exact solution therefore specifies an error term, v:
Equation 19:

Substituting the simplified Equations 14-17 into Equation 19 yields the following expressions:
Equation 20:

Equation 21:

The reader can see that we have retained our two equations and two unknowns.
Step 6: This system of linearized equations can now be expressed in matrix form:
Equation 22:

This can also be written in the matrix form:
b = Ax + v
Where:
b is a matrix that contains the differences between the observed and computed distances
Ax is the cross product of the matrices that contain the unknown correction parameters for the positions.
The positional solution is contained in the matrix x, since these are the differences between the a priori estimates of the boat’s position and the unknown (true) position of the boat. Least squares approximation techniques are used to minimize the error matrix v, and the solution can be expressed as:
x = (ATA)-1 ATb
One can also solve the equations iteratively by hand, as is shown in the example below:
Back to our boat example: assuming we guessed that our initial starting coordinates were (15,15); we have the following “knowns:”

[th]Variable[/th] [th]Value (km)[/th]
XLighthouse 1	5
YLighthouse 1	11
XLighthouse 2	13
YLighthouse 2	19
XBoat-estimated	15
YBoat-estimated	15
D1	13
D2	5

D1 (observed) is 13 km. D1 (computed) is obtained from the Pythagorean Theorem:
Equation 23:

Equation 24:

Taking the difference between the observed distances minus the computed distances, we arrive at:
Equation 25:

… and
Equation 26:

We can plug numbers into the system of equations (matrices described above) and come up with a set of two equations relating the differences between observed and computed distances (we omit the error term, as we will solve the system of equations iteratively):
Equation 27:

or
Equation 28:

and
Equation 29:

or
Equation 30:

We solve the first equation for Δx:
Equation 31:

and plug this into the second equation for Δy:
Equation 32:

or
Equation 33:

Plugging this value for Δy back into the first equation for Δx yields:
Equation 34:

We can now use these differences to get a better estimate of our position. Substituting these new values into the original system of equations will yield a second set of Δx and Δy, and thereby a third estimate of our position. Usually only a couple iterations are needed to obtain a convergent solution, XS ≅ 17, YS ≅ 16.
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In case it's not obvious, this is a very simple example using only two dimensions and therefore presuming a flat working surface. The trilateration used in GNSS has to cope with three dimensions as well as 4 moving satellites, which ought to be far more complex and as such the additional computations accordingly far more extensive. Not only are they more complex calculations, they must be performed continuously as the satellites keep moving. If you have any experience using GPS you no doubt have noticed how it updates constantly even while you're moving in an automobile at even very high speeds. You may not be surprised then to find out there has yet to be anyone in a land bound vehicle whose movement has been impossible for GPS to keep updated continuously. After all, the satellites are orbiting the earth much faster than vehicles being tracked on earth are moving over the undulating surface of the spherical earth. Additionally, or at least so far, the GPS systems have not required the user to give his assent to the existence of the satellites upon which his use of the system depends.
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Truth is Eternal · « **Reply #74 on:** September 28, 2017, 01:49:20 PM »

NASA claim there are thousands of satellites orbiting the earth; it should be very easy for Neil Obstat to find a picture of a group of satellites in space.

Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27720 times)

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial

Tradplorable

Re: Global Navigation Satellite Systems -- tutorial

Tradplorable

Re: Global Navigation Satellite Systems -- tutorial

Truth is Eternal

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DZ PLEASE

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Tradplorable

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Tradplorable

Re: Global Navigation Satellite Systems -- tutorial

Tradplorable

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kiwiboy

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

Truth is Eternal

Re: Global Navigation Satellite Systems -- tutorial