How Does GPS Work?

[Dockhead]

Originally Posted by Wotname

And presumably this is spherical trilateration ( curved sides)???
Not trying to be smartypants, just wanting to get a more complete understanding; again maybe Dave or others who know can correct if required.

I will venture a guess that the answer is "no" -- spherical geometry is used for surfaces of spheres (or spheroids) -- like the surface of the earth. Since these triangles are in space, they must have straight sides.

[Ericson38]

Originally Posted by Wotname

And presumably this is spherical trilateration ( curved sides)???
Not trying to be smartypants, just wanting to get a more complete understanding; again maybe Dave or others who know can correct if required.

On the ranges between user and orbiting satellites, those rays aren't curved, except due to tropo and iono bending. These effects end up affecting the speed of light propagation, being 'C', nominally 2.9997 E8 m/s.

User coordinates are determined in ECEF frame since satellite ephemeris is in same earth fixed frame. Doppler measurement are made to develop the actual LOS vector rate of change of length. Equation for vector rate is :

V (LOS) = C x (1-Fr/Fo), where Fr is received L1 freg, and Fo is transmitted L1 freq.

Now we need a couple of these LOS vector rates to determine user movement in the ECEF frame. We use a direction cosine matrix to relate these vector rates to the user's rate on the earth.

[transmitterdan]

Originally Posted by Sailor Doug

Are all gps chip sets equal? Other than marine friendly interface does my phone perform as well as my garmin?


Sent from my iPad using Cruisers Sailing Forum

The main difference is in the antenna. Stronger signal plays a big part in the accuracy. Outdoors most GPS units give pretty much the same position and speed readings. Some units have better antennas so give better results when below decks or atmospheric conditions are poor. My experience is Garmin handhelds have amazingly good antennas. My iPhone isn't nearly as good. But when outside they both give same results. I have an Android tablet that is about as good as the Garmin.

Another difference may be the speed of the computer inside. Faster computers require more power. So to conserve battery power some units don't update as often as others.

But the accuracy of dedicated GPS units and phones is about that same when they have a clear view of the sky.

At least the iPhone 5 drains the battery fast when GPS is running. Probably others are similarly afflicted. Garmin does a great job in terms of battery life compared to my iPhone 5.

[wellin]

Dopppler shift could not be used to calc velocity from one sat unless the sat is travelling directly at or away from the receiver. Not possible.

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[Ericson38]

Originally Posted by wellin

Dopppler shift could not be used to calc velocity from one sat unless the sat is travelling directly at or away from the receiver. Not possible.

Sent from my SCH-I415 using Cruisers Sailing Forum mobile app

That's what the direction cosine (observation matrix) function is. Cos of 0 or 180 is 1, meaning full strength Dopper effect towards or away. Cos of 90 (satellite passing broadside to user), is 0, so no Doppler sensed.

The H matrix (Kalman Filter notation) for direction cosines is pre-computed based on satellite Az/El from user's perspective, at every time step. This in turn based on satellite locations and user location in the Earth Fixed Frame.

[wellin]

Originally Posted by Ericson38

That's what the direction cosine (observation matrix) function is. Cos of 0 or 180 is 1, meaning full strength Dopper effect towards or away. Cos of 90 (satellite passing broadside to user), is 0, so no Doppler sensed.

The H matrix (Kalman Filter notation) for direction cosines is pre-computed based on satellite Az/El from user's perspective, at every time step. This in turn based on satellite locations and user location in the Earth Fixed Frame.

So how does one get " a users perspective " without yet knowing ones position? I think your statement proves i am right.

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[Ericson38]

Originally Posted by wellin

So how does one get " a users perspective " without yet knowing ones position? I think your statement proves i am right.

Sent from my SCH-I415 using Cruisers Sailing Forum mobile app

This is a Doppler discussion which comes from from first knowing the intial user location, using pseudoranges. Kalman filter is not even running without an initial start location seed.

I have been involved in GPS receivers since 1996, but lately, not so much. Big push was in the early days, and Cincinnati Electronics, Trimble, Ashtech, Motorola, and Rockwell Collins were the vendors, then Novatel joined in our work.

[socaldmax]

Originally Posted by Ericson38

This is a Doppler discussion which comes from from first knowing the intial user location, using pseudoranges. Kalman filter is not even running without an initial start location seed.

I have been involved in GPS receivers since 1996, but lately, not so much. Big push was in the early days, and Cincinnati Electronics, Trimble, Ashtech, Motorola, and Rockwell Collins were the vendors, then Novatel joined in our work.

This seems to directly contradict those who claim that velocity is calculated via doppler shift or interferometry without the need for an initial position.

[Dockhead]

Originally Posted by socaldmax

This seems to directly contradict those who claim that velocity is calculated via doppler shift or interferometry without the need for an initial position.

Nobody said that an initial position is not used. What was said is that speed is not primarily calculated by differentiation of positions -- by taking a series of position fixes and calculating distance vs. time, as some have insisted.

Remember you need Doppler shift from several satellites for this to work. It's not done with a single satellite, any more than position can be calculated from a single satellite.

[Viking Sailor]

DH,

The old navy TRANSAT satellite navigation system is an example of a single satellite providing a position fix.

It used the "shape" of the Doppler shift of the satellite signal as the sole measurement needed to compute a vessels position. The shape of the Doppler shift is the measurement of the change in signal frequency, over equal time intervals, due to the geometry of the signal source and the observer.

The TRANSAT satellites were in polar orbits like GPS but fewer of them and at a lower altitude. The Doppler shape was used to determine when the latitude of the satellite and the vessel were the same, and to compute the difference in the longitude of the satellite ground track and the longitude of the vessel. What it could not determine was whether the vessel was east or west of the satellites ground track. For this the approximate vessel position was required.

[Viking Sailor]

The following is an example of how a GPS receiver could provided Doppler SOG. There are other possible implementations.

The time it takes to begin providing SOG depends mostly on the acquisition mode of the receiver.

GPS Doppler SOG can be provided once the receiver has acquired at least one satellite with a geometry that includes some minimum Doppler shift due to vessel motion. When the receiver has carrier frequency and code lock, determined the approximate satellite and vessel positions it can remove various Doppler effects from the carrier frequency until all that is left is the uncorrected Doppler shift due to the motion of the vessel. The vessel Doppler shift can then be corrected based on geometry of the receiver and the satellite. As more satellites are acquired this processes can be repeated and applied to a filter to improve the SOG accuracy.

[Wotname]

Originally Posted by Dockhead

I will venture a guess that the answer is "no" -- spherical geometry is used for surfaces of spheres (or spheroids) -- like the surface of the earth. Since these triangles are in space, they must have straight sides.

Originally Posted by Ericson38

On the ranges between user and orbiting satellites, those rays aren't curved, except due to tropo and iono bending. These effects end up affecting the speed of light propagation, being 'C', nominally 2.9997 E8 m/s.

User coordinates are determined in ECEF frame since satellite ephemeris is in same earth fixed frame. Doppler measurement are made to develop the actual LOS vector rate of change of length. Equation for vector rate is :

V (LOS) = C x (1-Fr/Fo), where Fr is received L1 freg, and Fo is transmitted L1 freq.

Now we need a couple of these LOS vector rates to determine user movement in the ECEF frame. We use a direction cosine matrix to relate these vector rates to the user's rate on the earth.

Thanks Gentlemen.

[El Pinguino]

Originally Posted by Viking Sailor

DH,

The old navy TRANSAT satellite navigation system is an example of a single satellite providing a position fix.

Ah... TRANSAT.... the people who gave us the 'Electronic DR'... I wonder how many yachts ( and ships) ended up on reefs because people thought 'Is electronic...is good...'

The 'electronic DR' could of course be 'improved' by applying a notional set and drift to it to get an 'Electronic EP' which would really bring you unstuck.

Deja vu all over again etc...

[Wotname]

OK, now we have some FITK (folk in the know) particating in the thread I wish to ask a perhaps unimportant question but one that has been bugging me for awhile .

Back in the early days (1990ish) of GPS receivers with single channel receivers or at the best, only a small number of channels, the aviation receivers were provided with an altitude input with the intent of creating a "pseudo satellite" that could be added to the number of "real" satellites for the resolution of position. In essence, if this pseudo satellite was considered to be directly overhead, all one needed was one's altitude in order for the pseudo satellite to be considered "real". Remember way back then, the number of satellites were somewhat less than today.

So I got to thinking (maybe a bad habit ) that in the maritime world, one's altitude is always at sea level so for all intents and purposes, one could use this pseudo satellite principle as a built in design feature of the GPS receiver.

Thus my question is: was this feature actually used in maritime GPS receivers in the early days and if so, does it still apply today now we have multi channel receivers and a full complement of satellites?

[El Pinguino]

Originally Posted by Wotname

Thanks Gentlemen.

Chill Bro!... ( I'm in Unzud just now trying to figure out how to survive the cricket results... either way... I'm toast )

Getting back to simple things a bog standard almanac for the sun and stars and stuff could be written in about four lines of 'basic'....

Get your head around Napier's Rules and all else will follow right along....