Speed Through GPS Versus Old Fashioned Paddle Log

[Suijin]

Originally Posted by Sailor Doug

What commercial marine gps dose this. I know how Doppler shift works. Yes it will tell you a speed change from a satellite. It still needs more than one satellite. Next it needs to calculate change in position in 3D space to get position change rate (speed). No electronic device gives information in real time.

It only needs one satellite to make a first calculation, since the differential in frequency renders a velocity number. Additional satellites provide additional data which allows the unit to triangulate and measure a velocity vector in three dimensions. In other words, a boat travelling perpendicular to the satellite will have a velocity of zero because there is no doppler effect on the frequency.

So a GPS unit can accurately calculate velocity at one instant in time from multiple satellites.

[Training Wheels]

Try moving a hand held and watch the speed. Again, if we move our speed puck even a foot or two, the speed changes. That's why I don't believe Thea's speeds I here people brag about. The boat is yawing, pitching and rolling at the same time it moving forward, especially surfing down a wave. Depending on where the antenna is, this can be exaggerated. I like the max speed over a 10 second average on the speed puck. It factors out any spikes. Ours is 17.6 by the way, but we sail very conservatively.


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[lordgeoff]

Originally Posted by transmitterdan

You were taught incorrectly as were apparently many others so don't feel bad about it. From day 1 the GPS system was designed so that speed was as easy or easier to obtain than position. For many applications speed is more important than position. And speed needs to be known near instantaneously for lots of applications. So the GPS system designers planned for that feature and they made it easy and fast to calculate speed without knowing anything about position. A GPS receiver can compute its speed at a single moment in time thus position is not required (nor would it even help).

Here is how it works:

The GPS receiver measures the frequency of each satellite it receives (more accurately it measures the change in frequency). The frequency will always be a little bit off from the transmitted frequency. This is known as frequency or doppler shift. When the receiver is moving this frequency shift changes. If stationery the frequency doesn't change much (it does a tiny amount because the satellites are moving but not enough to matter). Einstein and another guy named Lorenz figured out the equations. It's how Einstein proved that the speed of light is constant in a vacuum. Anyway, if the receiver knows how much each satellite has shifted off frequency it can compute it's speed relative to each the satellite it can hear. No position data is required to do this calculation. It only needs the amount of frequency shift for each satellite and a lookup table of constant numbers that is sent down by the satellites. Because frequency shift can be measured at any moment in time speed can be computed nearly instantly using only one measurement (frequency shift).

The same technique is used by doppler radar to measure how fast the wind and rain is blowing and in what direction.

Transmitterdam. The basic calculation of any onboard GPS is position of your vessel on the surface of the earth at a point in time.
All other calculations from your GPS and display ( generally a plotter) such as AVERAGE SPEED between consecutive points, HEADING, SOG, VMG, ETA, TTG etc are just simple calculations and extrapolations based on the average speed between two consecutive GPS positions and GPS distance to your waypoint.
Because the GPS and PLOTTER make calculations about once each second SPEED, HEADING, SOG, VMG, ETA !TTG etc etc can be considered REAL TIME values.
The magic of GPS is in the detail. The GPS position is updated many times a minute and thousands of times an hour depending on the number of satellites in range and the quality of your onboard GPS.
As an example if your vessel is travelling at 6Kn and the satellites provide the data to calculate your position each second your GPS will be calculating your position 3,600 times in the hour it takes you to travel 6 Nautical Miles. This means your GPS UPDATES your position on the earth and hence your speed about every 10ft that your vessel travels in a second.
The other calculations provided by your plotter such as HEADING, SOG, VMG, ETA, TTG etc are also updated every 10ft or so.
You need to get your head around the speed and volume of the satellite signals and the GPS calculations. The GPS satellites are about 22,000Km above the earth and their signals travel at 186,000 Miles Per Second and your GPS may be receiving the signals from around 4-6 satellites simultaneously. The information received, calculations made and information provided per second, minute, hour by your GPS (and plotter calculations) is incredible compared to any information that can be provided by traditional navigation techniques.
Imagine Captain Cook getting his head around satellite and GPS/PLOTTER navigation and plotting his boats position on the earth accurately every second..........but that is another topic
Now returning to the speed camera in the C&D Canal. Assuming again that your vessel is at constant revs and your actual speed is a constant 6Kn (Actual) then the GPS would be calculating your position each second and calculating your AVERAGE SPEED every second. In each second at 6 Knots your vessel will travel just over 10 feet. If your vessel is 40 foot long then the GPS would calculate you average speed 4 times while your vessel passes a fixed point on the bank of the C&D Canal.........for example this point may be a fixed speed camera
If you were setting your throttle based on a paddle log the maintain within the speed limit then considering the inaccuracy of the Log and the variable tide currents in the Canal..... All I can say I'd good luck with your actual speed
Now the comment is that a vessels speed calculated by GPS is the AVERAGE speed between two points. CORRECT.
However the average speed between two points is done each second therefore for our purposes it is an INSTANT speed calculation...... Calculated maybe 3,600 times an hour.
When I departed from Galapagos heading to Hiva Oha, French Marquesas my GPS and PLOTTER did two different calculations. The GPS calculated my average speed for the first 10 feet of the passage as 6 Knots. The PLOTTER used this average speed information from the GPS to calculate my HEADING to the waypoint i.e.at Hiva Oha, my ETA, SOG, ETA, TTG. etc.......IF I maintained the current average speed of 6 Knots. The GPS and PLOTTER redid/updated these calculations more than 1,000,000 times during the 20 day passage .........automatically and accurately.
As I said previously the paddle log lets me know when my bottom needs a clean as it gets further and further away from showing my true speed.

[transmitterdan]

Originally Posted by lordgeoff

Now the comment is that a vessels speed calculated by GPS is the AVERAGE speed between two points. CORRECT

No, it is not correct. GPS speed is not based on position in most GPS receivers. A boat traveling at 4 knots is only moving 2 meters per second. There is no way to accurately calculate speed from distances that are only 2 meters apart.

Originally Posted by lordgeoff

Let us agree on that at least.

[transmitterdan]

Originally Posted by Sailor Doug

Transmitterdan you need your money back

For what?

[lordgeoff]

Originally Posted by transmitterdan

No, it is not correct. GPS speed is not based on position in most GPS receivers. A boat traveling at 4 knots is only moving 2 meters per second. There is no way to accurately calculate speed from distances that are only 2 meters apart.



Let us agree on that at least.

Sorry trans. Re read my comments again.

[Ex-Calif]

So in ight winds and outgoing current when the little boat icon turns around and starts heading out of the channel you won't turn the boat around... like my buddy did...




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[Sailor Doug]

Anybody know how a paddle wheel works?


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[transmitterdan]

I hear it's all done with magnets...but that can't be right

[valhalla360]

Originally Posted by transmitterdan

So far as I know all GPS chipsets do this. It does not have to calculate change in position. It only has to know the frequency shift to determine speed. Position is no where in the formula for Doppler speed measurement. It is possible to measure frequency shift in real time. Frequency shift is an analog real time value. You can measure it as often and as fast as you like even a billion times per second. And only one measurement of frequency shift is needed to calculate speed.

Here is another example. The police radar used to measure speeding cars doesn't know anything about the position of the speeding car. It uses the same formulas and frequency shift measurement. It works in real time to capture the maximum speed of its victim.

I understand doppler would give the speed that the satilite and the reciever are traveling towards or away from each other but that will only provide speed of the boat if the boat is traveling on a straight line between the satilite and boat (not the case with an overhead satilite).

It's similar to VMG. VMG can never exceed SOG and the further you are from straight towards your destination the lower VMG gets.

Police radar is dependent on a shot that is close to in line with the direciton of travel. I used to have a handheld unit for work and had the oppurtunity to play with it. If you stand 100' off the road and take a reading just as a car passes, the speed will read near zero. The further you are from a straight on shot, the lower the speed it will report. This is OK for purposes of issuing speeding tickets as it never over estimates the speed but almost always results in a low estimate.

Once you have a position for the boat, the satilite and the shape of the earths surface, it's simple trig to adjust the doppler speed for direction.

How would it account for the difference in angle if it doesn't know the position? The only way I can see this working is if they system uses a crude early estimate of position before it gets a final lock (I understand trig so just saying complex trig doesn't answer the question).

[transmitterdan]

Originally Posted by valhalla360

How would it account for the difference in angle if it doesn't know the position? The only way I can see this working is if they system uses a crude early estimate of position before it gets a final lock (I understand trig so just saying complex trig doesn't answer the question).

The mathematics are complicated and I don't pretend to know the formulas. But the GPS constellation at any point in time is "fixed" relative to the earth and the GPS receiver knows about that based on tables downloaded from the satellites. By measuring the doppler frequency of a few satellites the speed of the receiver relative to the entire constellation can be computed. Once that is know all that is required is to remove the speed of the constellation relative to the earth (the receiver knows this value for every satellite) and then the speed of the receiver relative to earth is the result. Note that GPS instantaneous speed is a 3D number because the receiver can't tell what direction it is moving based on doppler shift alone. So if you throw the receiver up in the air it will read out the speed at which it rises and falls.

I have no idea why people on this thread are so worried about this. But it is a fact that GPS system designers did a lot of thinking before they spent several billion $ launching space craft. They knew that speed was an important parameter and they could not afford (nor would the US DOD allow them to) provide sufficient positional accuracy to derive speed from position. Maybe everyone is forgetting about the old days when we had Selective Availability (SA). But in those days GPS speed indication was very accurate within +/- a few tenths of kM per hour the same as today when we don't have SA. That's because GPS never needed to know an accurate position to derive speed.

[transmitterdan]

Since nobody seems to be able to Google any more I took 3 minutes away from my lunch break today and searched a little. I found this paper:

http://nujournal.net/HighAccuracySpeed.pdf

A quote from the article:

Proof of speed is possible even though we
may not be able to prove an exact location
where that speed was achieved.

[lordgeoff]

Originally Posted by transmitterdan

The mathematics are complicated and I don't pretend to know the formulas. But the GPS constellation at any point in time is "fixed" relative to the earth and the GPS receiver knows about that based on tables downloaded from the satellites. By measuring the doppler frequency of a few satellites the speed of the receiver relative to the entire constellation can be computed. Once that is know all that is required is to remove the speed of the constellation relative to the earth (the receiver knows this value for every satellite) and then the speed of the receiver relative to earth is the result. Note that GPS instantaneous speed is a 3D number because the receiver can't tell what direction it is moving based on doppler shift alone. So if you throw the receiver up in the air it will read out the speed at which it rises and falls.

I have no idea why people on this thread are so worried about this. But it is a fact that GPS system designers did a lot of thinking before they spent several billion $ launching space craft. They knew that speed was an important parameter and they could not afford (nor would the US DOD allow them to) provide sufficient positional accuracy to derive speed from position. Maybe everyone is forgetting about the old days when we had Selective Availability (SA). But in those days GPS speed indication was very accurate within +/- a few tenths of kM per hour the same as today when we don't have SA. That's because GPS never needed to know an accurate position to derive speed.

I'll try one more time......
GPS is designed to locate your vessel's Position (Lat and Long) on the Globe. That is why they call it Global Positioning System.
The GPS calculates the vessels position (Lat and Long) based on packets of data from the GPS Satellite Network. The vessels Position is established frequently and relentlessly. All calculations of Speed, SOG, VMG, ETA, TTG etc etc are calculated by comparing consecutive positions of the vessel continually and relentlessly. By comparing two consecutive positions very simple mathematical calculations can be made. Determining a heading between two points is Navigation 101. Calculating Speed is simply DISTANCE/TIME. The satellite time stamps position data.
Distance between two points is a simple calculation.
ETA, VMG, SOG are just very simple manipulation, by the receiver/plotter of the data on hand.
These calculations are all based on the very simple strings of data sent from the satellites in NMEA format.
The speed of transmission of the data makes GPS results extremely accurate. This is why you can get the accurate speed of a vessel travelling at 0.5 Kn or a car travelling at 100 kph or a Formula 1 travelling at 300kph.

[goboatingnow]

Originally Posted by lordgeoff

I'll try one more time......

GPS is designed to locate your vessel's Position (Lat and Long) on the Globe. That is why they call it Global Positioning System.

The GPS calculates the vessels position (Lat and Long) based on packets of data from the GPS Satellite Network. The vessels Position is established frequently and relentlessly. All calculations of Speed, SOG, VMG, ETA, TTG etc etc are calculated by comparing consecutive positions of the vessel continually and relentlessly. By comparing two consecutive positions very simple mathematical calculations can be made. Determining a heading between two points is Navigation 101. Calculating Speed is simply DISTANCE/TIME. The satellite time stamps position data.

Distance between two points is a simple calculation.

ETA, VMG, SOG are just very simple manipulation, by the receiver/plotter of the data on hand.

These calculations are all based on the very simple strings of data sent from the satellites in NMEA format.

The speed of transmission of the data makes GPS results extremely accurate. This is why you can get the accurate speed of a vessel travelling at 0.5 Kn or a car travelling at 100 kph or a Formula 1 travelling at 300kph.

I'm afraid you are wrong here lordgeoff. TransmitterDan is correct gps speed is calculated in relation to Doppler shift of the carrier. Position does not have to be computed. I personally stand corrected myself because I always taught this method was only implemented in high end GPS systems. But in fact today it seems to be persuasive throughout most chip sets. In fact with the extensive use of phase locked loops in GPS chip sets. Doppler shift computation is very easy.


The fundamental reason for doing this, is that computing instantaneous speed from a position change over time on GPS simply isn't accurate enough. ( due to the distribution of positional errors. )
Dave


Furthermore , while ephemeris and sat health data is overlaid on the C/A code to enable the GPS receiver to cold start , there is otherwise no actual data transmitted from the satellite. What is transmitted is in fact pseudo random noise. The GPS receiver merely used clock correlation mechanisms to determine the range of the satellite. After that it's somewhat similar to a three point fix ( for 2D) determination or 4 fixes for 3D.

In assisted gps for example this data can be fed to the GPS receiver by any data transmission method( wifi gsm etc ) . It does not have to come from the satellite per se

Of course many downstream systems often compute overall speed from waypoints etc. but this isn't what we are talking about here.

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[goboatingnow]

Here's an even simpler explanation of speed and it's errors

http://gpsinformation.net/main/gpsspeed.htm

O.2m/s accuracy is possible using the precise positioning service which is available since SA was turned off

Note that DOP , multi path etc all affect Doppler derived speed as did SA when it existed. This is because SA in effect caused additional clock wobble and hence affected the accuracy of the Doppler shift as well as the derived range ( hence positional ) accuracy


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