Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27731 times)

Neil Obstat · « **Reply #210 on:** September 30, 2017, 10:05:15 PM »

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Multipath errors

Multipath errors (or simply “multipath”) occurs when a GPS signal bounces off a reflective surface before reaching the GPS antenna. This can occur if the GPS antenna is next to a building, a vehicle, or even a chain link fence. (Recall that the wavelength of the GPS signals are on the order of 20 cm so they cannot easily penetrate openings smaller than 20 cm.) The easiest way to avoid multipath is to position the GPS antenna away from buildings, vehicles, fences, or other reflective surfaces. But sometimes this is impractical.

Multipath can also be reduced by using a special antenna designed to avoid multipath, such as one with a ground plane or choke ring.

Although modern one-piece integrated GPS antenna-receivers are very practical, they tend to be more prone to multipath since they do not have large ground planes or choke rings. Therefore, care needs to be taken to place them away from reflective surfaces.

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Truth is Eternal · « **Reply #211 on:** September 30, 2017, 10:08:50 PM »

https://www.youtube.com/watch?v=sCAeshFGQIs#t=33.7457804

Truth is Eternal · « **Reply #212 on:** September 30, 2017, 10:12:09 PM »

Neil Obstat · « **Reply #213 on:** September 30, 2017, 10:13:20 PM »

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4c. Removing error via double differencing

Two GPS receivers relatively close to each other (e.g., within 100 km) will likely be seeing the same satellites at the same time. We can use this fact to remove some important sources of error such as receiver and satellite clock errors.

Since the two receivers are relatively close to each other, they will also share much of the same atmospheric biases when calculating their positions. Although each of their computed positions may be incorrect due to the accuмulation of the biases, their positions relative to each other should be much more accurate since they share similar biases. This relative position essentially amounts to subtracting one range from another in a process called “differencing.”

In addition to removing much of the atmospheric errors, differencing can also remove clock errors.

Measured pseudoranges are combinations of the true ranges with both satellite and receiver clock errors included.

Referring to the graphic above, two GPS receivers (Q and R) are observing the same satellite (A). By differencing the ranges from that one satellite to the two receivers, the satellite clock errors will cancel out since they are common to both.

Similarly, we know that if any one GPS receiver antenna is receiving signals from two different satellites, the GPS receiver clock errors will be common to both solutions. Therefore, by taking our earlier single difference (with respect to satellite A) and differencing it with another single difference from another satellite (satellite B in the figure), the common receiver clock errors will also cancel out. Therefore, by double-differencing, we remove both the satellite and the receiver clock errors.

Key Equations:

Single Difference (Satellite A):
Step 1: Substituting equations

Step 2: Arranging like terms

Step 3: Satellite A clock errors cancel

This is our first single difference, and we are left with receiver clock errors.

Single Difference (Satellite B):
Step 1: Substituting equations

Step 2: Arranging like terms

Step 3: Satellite B clock errors cancel

This is another single difference, and we are left again with receiver clock errors (satellite clock errors have canceled out).

Double Difference (Satellites A and B):

Step 1: Take the difference between the two single differences:

Step 2: Arrange Terms:

Step 3: Like terms cancel out:

Finally, if one of the GPS receiver antennas occupies a known position (known coordinates), we can use this knowledge to estimate the GPS error and apply it to the unknown position. In this manner, we can convert our differences (relative positions) back to actual coordinates. The GPS receiver antenna with the known position is typically termed the “base,” and the receiver antenna at the unknown location is called the “rover.”

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Neil Obstat · « **Reply #214 on:** September 30, 2017, 10:19:49 PM »

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What's really nice about these graphics and explanations is, someone who doesn't want to wade through the math doesn't have to, and can understand the gist of the message by only looking at the pictures and reading the text.
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Then, if it later on becomes worth going deeper into the techniques shown in the formulas, they can be read in more critical fashion once the math is worth applying in its own merits.
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These formulas in principle apply to other situations not related to satellites.
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St Ignatius · « **Reply #215 on:** September 30, 2017, 10:25:42 PM »

Quote from: Neil Obstat on September 30, 2017, 10:19:49 PM

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What's really nice about these graphics and explanations is, someone who doesn't want to wade through the math doesn't have to, and can understand the gist of the message by only looking at the pictures and reading the text.
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Then, if it later on becomes worth going deeper into the techniques shown in the formulas, they can be read in more critical fashion once the math is worth applying in its own merits.
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These formulas in principle apply to other situations not related to satellites.
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Only IF you can see the pictures...
Whatever the format is, I'm not able to view any of pictures, just a small picture icon (sometimes)...
:really-mad2:

Neil Obstat · « **Reply #216 on:** September 30, 2017, 10:36:17 PM »

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4d. The effect of length of observation on accuracy

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For all GNSS systems, the longer you observe, the more GNSS data you will collect, and the better your estimate will be of your receiver’s position. If a GNSS receiver is logging data for several hours, it will have tracked a number of satellites as they appear and disappear over the horizon. Each satellite provides an independent estimate for the receiver’s position.

In addition, over an extended observation period (e.g., more than 2 hours), each satellite will be in a different place in the sky, providing a number of different trilateration geometries. (It takes approximately six hours for a satellite to completely cross the sky.) Varied geometries increase the accuracy of a solution as they allow the solutions to average over a number of different error sources.

The longer the session duration, the lower the Root Mean Square Deviation (or RMSD) and the higher the degree of horizontal and vertical accuracy achieved.

Although GPS positioning is resolved in three dimensions, the horizontal dimensions (latitude and longitude) are less noisy than the vertical. This is due to the wide separation between the satellites at any moment in time (θ1,θ2, θ3 in figure above), and the fact that any given satellite will change its horizontal position over the course of a long observation session.

The vertical dimension, however, lies very close to the orientation between the satellite and the receiver (θa,θb, θc in figure above) so it ends up being harder to determine precisely. For these reasons, horizontal errors are smaller than vertical errors.

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DZ PLEASE · « **Reply #217 on:** September 30, 2017, 10:40:33 PM »

Quote

NEIL OBSTAT, YOU HAVE A PROBLEM.

Several, yet they troll on like a drunk in a john-boat.

Neil Obstat · « **Reply #218 on:** September 30, 2017, 10:40:45 PM »

Quote from: St Ignatius on September 30, 2017, 10:25:42 PM

Only IF you can see the pictures...
Whatever the format is, I'm not able to view any of pictures, just a small picture icon (sometimes)...
:really-mad2:

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Let me know if this picture is visible now. It's the Double Differencing .jpg from the previous page, 4c. Removing error via double-differencing.
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I'm getting 800 x 450 pixels and I don't know how to adjust it. The original I saved is over 1,000.
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St Ignatius · « **Reply #219 on:** September 30, 2017, 10:43:36 PM »

Quote from: Neil Obstat on September 30, 2017, 10:40:45 PM

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Let me know if this picture is visible now. It's the Double Differencing .jpg from the previous page, 4c. Removing error via double-differencing.
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I'm getting 800 x 450 pixels and I don't know how to adjust it. The original I saved is over 1,000.
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Yes, I see! I see!

St Ignatius · « **Reply #220 on:** September 30, 2017, 10:45:01 PM »

Although, the text is blurry...

Neil Obstat · « **Reply #221 on:** September 30, 2017, 10:47:02 PM »

Quote from: St Ignatius on September 30, 2017, 10:43:36 PM

Yes, I see! I see!

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That one is pretty interesting because it shows what they're saying about canceling out errors from clocks using two receivers and two satellites, since they both are dealing with close to the same interference in the atmosphere.
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Neil Obstat · « **Reply #222 on:** September 30, 2017, 10:53:09 PM »

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Now this is the last page before the unit summary. Maybe I'll try uploading some of the images if that helps.
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4e. Post-processing GPS data using the CORS network

Remember we said that if we do double differencing with two locations, and one of the locations is known to be very accurate, we can therefore know the other location with great accuracy? The very accurate location is known as a base station. So how does one go about finding a base? Luckily, there are networks of GPS base stations, such as the United States’ Continuously Operating Reference Stations (CORS).

Networks like this operate 24/7/365 and accuмulate a large quantity of data over a long period of time. The positions of these GPS stations are therefore very well known and can be used as base stations for double differencing. The large number of CORS within the United States means that there is a good chance that there will be one or more nearby, receiving signals from the same satellites at the same time as your GPS receiver.

You can access the closest CORS through the National Geodetic Survey’s CORS website (http://www.ngs.noaa.gov/CORS_Map/). The differently colored icons correspond to different data acquisition rates and active vs. inactive CORS.

Typically, the double-differencing using the CORS is computed in post-processing. Post-processing products, such as the National Geodetic Survey’s Online Position User Service (OPUS, http://www.ngs.noaa.gov/OPUS/), draw from a large number of available CORS operating at the same time you were observing GPS satellites. OPUS chooses the three stations from the network with the best characteristics to compute a highly accurate three-dimensional position based on your data.

The ability to correct for a large number of atmospheric and other influences (including ocean tidal loading, and Earth tides) greatly improves the accuracy of the coordinates you are able to compute from your GPS data. In addition, these post-processing programs can use “precise” satellite orbits that are made available to the public a few weeks after you have taken your data.

Although a post-processing program such as OPUS is restricted to GPS and the CORS, many other post-processing engines exist. Some even simultaneously use the Russian GLONASS satellites to help provide additional data. A number of different techniques are available to estimate the integer ambiguity described earlier. Different methods also exist to model the troposphere component of satellite signal delay. Techniques may also rely uniquely on the satellite orbits and time correctors (instead of also using CORS) to provide a precise position (Precise Point Positioning). But all of these methods involve post-processing the GPS data.

For more information please see the video: Best Practices for Minimizing Errors during GNSS Data Collection.
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That last picture is a repeat from an earlier page and it has some good stuff in it, so I'll upload a copy here.
Processing with OPUS .jpg
Does that help?
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Neil Obstat · « **Reply #223 on:** September 30, 2017, 11:02:40 PM »

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That CORS map shows a lot of Continuously Operating Reference Stations.
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Maybe someone ought to let them know they're wasting their time collecting data from satellites because Truth is Transitory and Eric Dumbay are convinced that satellites don't exist.
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If you think it's "fake" or whatever you can go to the linked site and see it's being continuously updated.

http://www.ngs.noaa.gov/CORS_Map/
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St Ignatius · « **Reply #224 on:** September 30, 2017, 11:04:48 PM »

Yes, the opus-jig thing worked... your going to have understand, my composition is bad, computer savy is even worse...

Author Topic: Global Navigation Satellite Systems -- tutorial (Read 27731 times)

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

Truth is Eternal

Re: Global Navigation Satellite Systems -- tutorial

Truth is Eternal

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

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DZ PLEASE

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

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Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

Neil Obstat

Re: Global Navigation Satellite Systems -- tutorial

St Ignatius

Re: Global Navigation Satellite Systems -- tutorial