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Author Topic:   GPS Receiver Position Solution Rate
jimh posted 09-12-2013 11:07 AM ET (US)   Profile for jimh   Send Email to jimh  
A GPS receiver computes a position fix solution at a certain rate or frequency. For quite a while, a GPS receiver that computed a position solution once per second or at a frequency of 1-Hz was considered to be a good, modern GPS receiver. Recently, newer models of GPS receiver have been produced which compute a position solution more frequently. Some receivers now compute the position solution five times per second or 5-Hz, and some of the newest compute the position solution ten times per second, or 10-Hz. As one might expect, the frequency of the position solution has become a metric for comparison, and the notion is that higher frequency means better results.

Let me also mention that a GPS receiver's real measurement is of its position. It deduces its position from timing intervals of signal arrivals from multiple satellites. A GPS receiver deduces its position from those signals. The GPS receiver can record a series of positions and time, creating a track of points (of position). From this track of points, a GPS receiver can also calculate the course over ground (COG) of the receiver by assuming that a straight line was followed from point to point in the track. And, because the time interval between these points of position is known with precision, a GPS receiver can also calculate the speed of movement between these points of position.

Accompanying the increase in frequency of position solution there have been two claims made. Most of the time these claims are made by consumers, not by the manufacturers of the GPS receivers, but the manufacturers seem to be suggesting these claims, too. The claims suggest that the higher the position solution frequency, the greater the accuracy of the calculated course over ground and the speed.

These claims have me confused. I do not understand how the position solution frequency increase would result in greater accuracy of the calculated COG and speed. The only method I can see where a greater position solution frequency might result in a more accurate COG and speed is through averaging.

If a large number of measurement are made of a particular value, and if those measurements are averaged, there should be a tendency for the average value to approach the true value, as long as the errors in the measurement are random. However, it is not clear to me, nor has it been made clear by the statements of the GPS receiver makers or the manufacturers of chart plotters and other devices that incorporate a high frequency GPS receiver, if any sort of averaging is being done. To the contrary, the usual presentation of the data is to just give the position solution frequency, and then to expect consumers to infer that because of the higher frequency, the accuracy of everything will be better. This introduces my question.

Is there some basis for expecting greater accuracy in the position solution and in the related values of COG and speed that are calculated from those position solution when the frequency of the position solution increases?

I anticipate there might be two general approaches to the answer to that question. In one case, the relationship between frequency and accuracy is very simple and it is something I just have not seen. In this case, perhaps a simple explanation might suffice. In the other case, the relationship between frequency and accuracy is much more complicated. In that case, perhaps a pointer to some scholarly paper on the topic might be helpful.

fno posted 09-12-2013 05:03 PM ET (US)     Profile for fno  Send Email to fno     
Jim, no pointers to scholarly info from me. It is no wonder that your heading information is lost when at a standstill. That is the information that is calculated by the successive GPS solutions. I am guessing that this is how the claims are made by virtue of more information-faster. Calculations such as this are subject to influences and inaccuracies of the position fixes when stationary. That is the reason that radar/MARPA and autopilots require a magnetic heading sensor in addition to the GPS. Until a manufacturer tells me I do not need the heading sensor I will be suspect of the COG values when floating about or tied up with no real movement of the boat. Also note your informative article about the Simrad/Lowrance GPS/heading sensor combo that was recently introduced. A disclaimer is made that because of the high position of a GPS sensor that the magnetic heading sensor information was not suitable for use with a radar/MARPA system or an autopilot. I am still on the fence with that GPS/heading sensor or a real magnetic heading sensor($500).
6992WHALER posted 09-12-2013 05:56 PM ET (US)     Profile for 6992WHALER  Send Email to 6992WHALER     
Garmin says the most accurate way to determination a fixed location is to have more time between position fixes and averaging this data.

But when you are moving more time between fixes might mean you out run the GPS receiver's ability to tell you your current location.

If you are getting fix information faster than you are actually moving or maybe faster than the accuracy of the unit, is the data you are receiving averaging?

http://garmin.blogs.com/softwareupdates/2009/04/waypoint-averaging. html#.UjIzGD_-t8E

6992WHALER posted 09-12-2013 06:09 PM ET (US)     Profile for 6992WHALER  Send Email to 6992WHALER     
25 MPH that equals 35 feet per second.

The GPS pings 5 times per second at 5-hz.
Lets say the accuracy is 10 feet.

For every 35 feet I travel the GPS gets a location 5 times with the accuracy of 10 feet.

My logic might be wrong but it appears to me that the unit must be averaging the 5 pings at least on the display. My chart plotter is not updating 5 times per second.

If the unit is 10 feet off to the right on the first ping and then 10 to the left on the next ping and so on shouldn't my Chart plotter be jumping from fix to fix?

jimh posted 09-12-2013 06:40 PM ET (US)     Profile for jimh  Send Email to jimh     
John raises a corollary question: can your chart plotter use position fix data arriving at such a rapid rate as ten times per second. I know my chart plotter (an HDS-8 Gen-1) cannot.

The chart plotter is not supposed to be the sources of averaging of data. It is just supposed to report the data from the GPS receiver.

Beaux posted 09-12-2013 06:47 PM ET (US)     Profile for Beaux    
Jim-
I think you are correct if the older gps updating at 1hz is reporting the speed of a vessel that is traveling in a perfectly straight line and at constant speed.

During maneuvering and/or acceleration, a 10 hz gps is definitely more accurate for positional data and speed at any given moment of time. This translates to more accurate total distance traveled measurements as well. I must say I'm assuming this, but the GPS speed reported is an average of past positions with regard to current position over a given time period. The more accurate data points in regard to position at any given point in time by the 10hz should reveal a more accurate "average" speed.

I did find an article that compared a 10hz GPS to an older GPS 5hz. They were using much shorter distances as metrics (for athletics), so I'm not sure it's as significant at longer data intervals. They did,however, find more accuracy speed and position reliability with the 10hz updates.

http://vuir.vu.edu.au/21719/

As a side note:
I'm not aware of Garmin claiming more accurate "speed" calculations in their Advertisements. They do, however, accurately promote the more accurate relationship between the actual position of the vessel and the depth sounder returns while underway.. This can be used to better identify the exact position of structure/fish on the cartography.

Beaux posted 09-12-2013 08:04 PM ET (US)     Profile for Beaux    
As far as bring able to process updates of position data at 10hz..

Garmin advertising says 60% more processing power in 547xs than previous similar models. In my experience, I can't refute that information as this 547 is fast. It zooms without hesitation at high data shown settings. Moving the cursor causes instant movement with consistent map scrolling with very little if any delay or freeze frame. It's significantly better than any old Garmin unit I've used.

I have no reason to believe that a modern device will have difficulty displaying vessel position data at 10hz... That's simple math for the raw numbers and the map changes in such a small resolution screen shouldn't require that much processing power compared to 1hz updates.

Interested to hear opinions...

But I really don't care all that much . Haha

silentpardner posted 09-12-2013 09:40 PM ET (US)     Profile for silentpardner  Send Email to silentpardner     
quote:
Is there some basis for expecting greater accuracy in the position solution and in the related values of COG and speed that are calculated from those position solution when the frequency of the position solution increases?


Half of that question is NO, the other half is a qualified YES, but ONLY if the GPS Units in their entirety are equal.

quote:
Is there some basis for expecting greater accuracy in the position solution

The "frequency of the position solution", as you have described it here, if I understand your [question] above, is referring to the rate that a GPS unit samples the received signals from satellites. If that is not what you mean with this term, and, I must admit, your use of the English language does confuse me often, please disregard my answer completely.

[Editor's note' Here this author completely misunderstands what the 10-Hz figure means. A 10-Hz GPS receiver is one that produces a posiiton solution ten times per second. It has nothing to do with sampling of signals--jimh]

The rate or frequency, at which the GPS samples the received signal from the satellites does not change the ACCURACY of the signal from the satellite. The satellites that send the signals are still in the same geostationary position relative to earth that they are always in. This is how GPS works.

[Editor's note: Unfortunately this is completely wrong. The satellites that send GPS signals are not in geo-stationary orbit--jimh]

Every GPS unit, no matter what the sampling rate of that unit is, receives the same signals.

[Editor's note: unfortunately this is wrong. The sigals available to a GPS receiver depend on its location. The signals available vary with time and locaiton due to the orbits of the satellites.-jimh]

With that established, there are a couple of other factors involved in the overall accuracy of any GPS unit. [Long sidebar on clock speed frequency of the internal processor of a GPS receiver deleted. This has no bearing on the topic under discussion--jimh]

Your GPS screen also has a maximum refresh rate. This the rate at which the screen itself can actually display the "calculated position solution", as Jimh refers to it above.

[Editor's note. Unfortunately, this is wrong. The screen refresh rate has nothing to do with the rate at which the receiver can compute a new position solution. The screen might be refreshed 100-times with old data before any new data is plotted--jimh]

[Editor's note: Sidebar about internal communication speed of electronic devices deleted, This has no bearing on the topic under discussion--jimh]

quote:
As one might expect, the frequency of the position solution has become a metric for comparison, and the notion is that higher frequency means better results.

[Here followed a lot of mumbo-jumbo about] GPS antennas, connection cables and buses, and all the computational apparatus...data sampling of the signal received from the GPS antenna....less frequency or rate than the overall speed of processing of that data.... 7th-grade general math text...[followed by a tedious narrative of drawing points and circles on paper which failed to proved anything.--jimh]

jimh posted 09-13-2013 08:20 AM ET (US)     Profile for jimh  Send Email to jimh     
silentpartner writes:

quote:
The rate, or "frequency", at which the GPS samples the received signal from the satellites does not change the ACCURACY of the signal from the satellite.

Yes, that is my assumption, too. When you make a measurement of any kind, the measurement technique or method does not become more accurate just because you make more measurements. If I use a ruler with some inaccuracy in its markings, I don't get a more accurate measurement the more often I use the inaccurate ruler

quote:
The satellites that send the signals are still in the same geostationary position relative to earth that they are always in. This is how GPS works.

The satellites of the GPS system are not in a geo-stationary orbit. They are in orbits that cause them to move relative to a ground observer. The only signals in the GPS system that originate from geo-stationary satellites are the augmentation signals from WAAS. There are three WAAS signals. Two of the signals also send psuedo-range solution signals and can be used in a position fix solution, but all of the other satellites used in position fix solutions are moving in their orbits. That is how the GPS system works. But that has no bearing on my question about the claims of more accuracy by higher frequency of solution. We can ignore it. (But you should read a bit about GPS so that you understand the satellites are moving relative to a ground observer.)

Regarding your example of the accuracy increasing with more position solutions. I disagree completely. To use your analogy, let us suppose a boat moves from point A to point B in an actual direct line, the shortest possible distance, and it takes one minute. That is the actual track of the vessel. If a GPS computes the position of the boat every second, it is likely that there will be some error in the position calculated, so the GPS position will not be on the actual vessel's track. The vessel's track as shown by all the calculated positions is going to zig-zag back and forth across the actual track. The more position that the GPS calculates, the more zig-zagging of the track. If we add up all the distance in the track of many intermediate solutions between points A and B, we find the GPS solution thinks the vessel went a greater distance than it actually did. The result is that making more measurements means more errors.

The only way I can see that more measurements will produce less error is when the errors are random and the measurements are added together in a way that causes the errors to tend to cancel. Let me give you an example.

Two land surveyors start at sea level, and begin measuring inland and uphill. They use the traditional tools of the surveyor, and measure the increasing height of the land in six-foot increments. There is some error in every measurement they make. But the error is random in nature, that is, sometimes they err by measuring the height as greater than actual, and sometimes they err by measuring the height as less than actual. Now the two surveyors work themselves inland and uphill, until they get to the top of Mt. Everest. Now they are 26,000-feet higher than sea level. In getting there they have made a measurement of the height increase every six feet. Than means they have made over 4,300 measurements. Every one of those measurements had a random error, but, after 4,300 measurements, the errors have tended to cancel out. The result is the surveyors have made a very accurate measurement of the height of Mt. Everest. (This is a simplified version of the actual survey of the height of Mt. Everest, which was done c.1856 and produced a measurement that was accurate to within a few feet of recent measurements made with much more accurate instrumentation.)

If we put a GPS receiver in a fixed position and plot the position solutions over a long period of time, we will see that the deduced position of the GPS will create a series of points around the true position. If all of those points are averaged, the average of all the position solutions will become more accurate, and get closer to the true position.

As for the meaning of frequency of position solution, I don't quite understand the confusion. The signals from the GPS satellites are sent continuously. A GPS receiver receives those signals. It computes its position from the signals. The more often it computes its position is the rate of position solution or the frequency of position solution, and this is the parameter that people refer to when they say a particular GPS receiver has a 1-Hz rate or a 5-Hz rate or a 10-Hz rate.

None of this has anything to do with how fast the circuitry inside the receiver runs. I don't care if the receiver has a 3-GHz clock or a 100-MHz clock. It has no effect on anything. The GPS receiver is continuously receiving signals from the GPS satellites, and every so often it spits out a position solution. If it gives a position solution once per second, we say it has a 1-Hz frequency. I think this is clear, and I don't think any further elucidation is needed.

So at this point, I am still awaiting an explanation of how a 10-Hz GPS is going to be more accurate than a 1-Hz GPS in calculating the speed and COG.


jimh posted 09-13-2013 09:02 AM ET (US)     Profile for jimh  Send Email to jimh     
Beaux--Many thanks for the pointer to that scholarly research paper. We can only see the summary, not the actual paper. The summary says:

quote:
Ten Hz GPS devices were 2-3 times more accurate than 5 Hz when compared to a criterion value for instantaneous speed during tasks completed at a range of speeds (coefficient of variation; 3.1 - 11.3%). Similarly, 10 Hz GPS were up to 6-fold more reliable for measuring instantaneous speed than 5 Hz units (coefficient of variation; 1.9 - 6%).

I am willing to accept the conclusion of this scholarly research, but I would like to better understand the mechanism that makes the 10-Hz more accurate.

Cf.: http://vuir.vu.edu.au/21719/

jimh posted 09-13-2013 02:20 PM ET (US)     Profile for jimh  Send Email to jimh     
When Lowrance came out with the POINT-1 they said it would provide position solution updates at 10-Hz. I asked if this was compatible with my HDS Gen1 chart plotter. The answer from Lowrance was "no." The POINT-1 would sense the older model chart plotter and reduce its update rate to 5-Hz, which is all the HDS Gen1 could handle. From that information it seems reasonable to infer that an older chart plotter is not going to automatically be able to make use of position data at a higher rate from a new GPS receiver like the POINT-1.
jimh posted 09-13-2013 02:31 PM ET (US)     Profile for jimh  Send Email to jimh     
A bashful correspondent sent me an email with his view, which presented this scenario:

A boat sails from point A to point B by following a curved course line, say an arc line from A to B. In this argument it is proposed that a low-frequency GPS receiver only provides a position fix solution at point A and then later again at point B. In that situation the GPS assumes that the vessel must have sailed a straight course to B from A, so it makes an error in the calculation of speed and COG.

That argument is valid if the time between calculation of positions A and B is quite long, say 10 minutes. However, in the situation with the GPS we are talking about the difference in position solution calculation for an interval of 1-second compared to an interval of 0.1-second. If the vessel were moving at 500-MPH, I think there is more chance for an error. But in the case of a vessel moving slowly there is not much chance for error.

Let us assume a vessel moves at 6.82-MPH. That happens to be 10-feet-per-second. In the case of a GPS with 1-Hz rate, the position solutions should be only 10-feet apart. I don't see how you are going to get an improvement in accuracy by increasing the rate to 10-Hz. This suggests each position solution will be only 1-foot apart. Just exactly how much deviation from a straight line course can occur in an interval of 10-feet?

K Albus posted 09-13-2013 02:59 PM ET (US)     Profile for K Albus  Send Email to K Albus     
So you're asking about practical accuracy as opposed to actual accuracy?

(By the way, I'm the "bashful" correspondent.)

silentpardner posted 09-13-2013 11:26 PM ET (US)     Profile for silentpardner  Send Email to silentpardner     
Do you have any evidence of any GPS system that makes random errors in position points each second it makes a calculation? I gather from what I read above, but I could have misinterpreted your writing, that this is your assumption. Is it possible that a GPS system could always make the SAME, or very SIMILAR, error within the specified limits of it's accuracy in EVERY calculation that system makes?
Are the manufacturers specified accuracy of position fixes based on differences between their machines fixes and paper charts, or actual physical locations that were previously marked on the same machine? If the GPS systems were making (+- 15 feet) errors in calculations every second, would this not result in a VASTLY GREATER error in the actual marking of the end waypoint, say 100 miles or so from the start waypoint? I don't see how they would be able to market a machine like that as a navigation tool with any credibility, do you? I don't think your Lowrance unit or my Garmin units make the kind of errors you are suggesting here at all. I seem to get back to the same place that fix as my end waypoint every time I use my modern machines within 5 ft or so, are you saying in your thread that you DON'T?

Are you thinking that that the specified overall accuracy of modern GPS machines that you see on a spec sheet are actually the error margins, in feet and inches, for EACH 1 second calculation the machine makes for a position point to plot? Does that really make any sense, considering that you have already stated in other threads your Lowrance machine actually positioned you at the slip you were in inside a harbor?

[Long sidebar about LORAN deleted--jimh]

Personally, I just believe the engineers on this topic, since I know more calculations of position always results in greater accuracy for me when I had to navigate using paper charts and a compass, before all these fancy machines became so affordable.

Of course, it seems, the more satellite signals being triangulated [Editor's note. There is not triangulation in GPS. This is about the fifth or six fundamental misunderstanding displayed in these replies--jimh] within the calculation, the more accurate each point would be also. The Garmin GPS units I use are able to fix a position with less than the maximum number of individual satellite signals the unit is capable of using to make a position fix.

For now, let's just agree to disagree [This is fine with me, but I had deleted most of your misunformation from the thread. I am not interesting in promulgating misinformation, so you will have to excuse me for deleting so much of your replies--jimh]

jimh posted 09-14-2013 11:59 AM ET (US)     Profile for jimh  Send Email to jimh     
As far as I know from my reading about GPS receivers, I believe that each position solution is derived from the present data, and does not take into account any prior solution.

One significant error that occurs in a GPS receiver in its position solution is caused by variation in the speed of propagation of the signals through the ionosphere. The augmentation from the WAAS satellite signal is intended to provide a correction for this variation, and a GPS receiver that can use WAAS signals can provide an enhanced position fix, that is, a position fix with more precision because it uses the WAAS information to improve its ranging calculations.

The ionospheric variations are typically not something that changes from one second to the next, so it is reasonable to think that if a GPS receiver is computing a position fix with WAAS it computes an enhanced or more precise fix each time it computes a position solution. This means that each position fix it computes is just as prone to being in error as the previous position fix. The fixes do not become more accurate the more often they are calculated. The only way the position fix could become more accurate is by using some sort of averaging algorithm, and distilling many fixes into an average that was more accurate. As far as I know, however, these GPS receivers with 10-hz output are just sending more position fix solutions; they are not sending some sort of averaged position fix solution.

I am, again, at a loss to understand how a GPS that calculates more position fix solutions per second is going to produce a more accurate solution for speed and course over ground.

jimh posted 09-14-2013 12:08 PM ET (US)     Profile for jimh  Send Email to jimh     
My understanding of the sources of error in GPS measurements comes from reading articles like this one:

http://www.kowoma.de/en/gps/errors.htm

The article describes many influences which can result in an error in the position solution. In mentions "Atmospheric effects" as one source of error. This is the error the WAAS signal tries to provide a correction for.

The article has a table that lists the error sources and amount of error they introduce. The ionospheric effects cause the greatest error.

The article concludes that with WAAS signals present a GPS receiver error should be reduced to a range of plus-or-minus three to five meters.

In a boat that is moving at 6.82-MPH, or 10-feet-per-second, a GPS receiver that computes a position solution ten times per second (or 10-Hz) will be computing a solution for every one foot of motion of the boat. So we have a position solution that is computed in one-foot increments but is only accurate to about plus-or-minus 10 to 15-feet.

saumon posted 09-14-2013 12:46 PM ET (US)     Profile for saumon  Send Email to saumon     
Maybe I view it from a too simplistic approach but, as I can understand it, 10hz receivers aren't more accurate for their individual positions readings, they simply have a higher refresh rate, thus being able to acquire ten times more position fix than a 1hz receiver.

But, as shown in the (childish) drawing I made, this translate into a more accurate distance reading. From 0 to 2 seconds, the 1hz receiver will calculate the distance along the blue line while the 10hz receiver will calculate it following the yellow dots, along the black line, and that distance will be greater than the one calculated by the 1hz receiver.

http://www.myfishingpictures.com/data/500/medium/gps_track.png

On the other hand, I'm definately not enough technically savvy to know if the added precision gain is enough to overcome the cumulated acquisition errors.

saumon posted 09-14-2013 03:13 PM ET (US)     Profile for saumon  Send Email to saumon     
It would be interresting to see if there's a practical difference in the "real world" application between a 1hz and a 10hz GPS receiver.

I currently have a Garmin GPSMAP 740s, a 1hz receiver, on my boat but may also install a echoMAP 50s, a 10hz receiver, to use mainly as a sonar and to keep the 740 for chartplotting only. If I ever do so, I'll certainly simultaneously record tracks on both units, at 1 sec interval on the 1hz receiver and at 0.1 sec on the 10hz receiver, and superpose them the see if there's any noticeable difference.

jimh posted 09-15-2013 11:52 PM ET (US)     Profile for jimh  Send Email to jimh     
Another aspect of the 10-Hz position solution rate that I do not understand: when the boat moves at 10-feet per second, each position solution is calculated at one foot of movement. I don't see how leeway or other effects on the course could introduce much change from a straight line motion. Just how far off from a straight line course will the boat get in 1-foot of forward motion? Even if the instantaneously reversed course 180-degrees it would only be off the expected track by two-feet. And the error in the position fix is still 15-feet. On a typical course the deviation from straight line that might occur in one foot for forward motion would only be a few inches. Now we are talking about measuring to a resolution of a few inches with a system that is only accurate to about 15-feet. It is this sort of conflict that prevents me from understanding how the faster position solution rate is going to mean a more accurate speed and COG.

Now if you told me that we were only calculating position solutions once an hour and you could offer me a position solution ten times more often, say every six minutes, I would agree that such a track would give more accuracy, would represent the actual COG and speed more precisely. But I just can't see these one-foot increments adding anything to the precision.

jimh posted 09-16-2013 01:13 AM ET (US)     Profile for jimh  Send Email to jimh     
I am not aware of any mechanism in the GPS system or in receivers that causes the accuracy of a position fix solution to become greater the longer a GPS receiver is in a particular position, other than due to influences from the position of the satellites being used in the position solution.

Let me give an example so this is clear, as some readers seems to have trouble understanding me and tend to invent something I have not said. A GPS receiver is positioned in a certain place, with a good view of the sky, and turned on. After a few minutes the receiver has acquired enough satellite signals to obtain a position solution. Now we wait a few more minutes until the receiver has obtained signals for six or more satellites, which should be typical for any location with a good clear view of the sky. At this point we start to measure the accuracy of the position solutions (because we know with precision where the receiver actually is located).

It is my understanding that there is no mechanism in the GPS system or in a GPS receiver that is going to allow the position solution to become more accurate the more often it is computed. The position solution that is computed will always tend to have the same errors in its calculation.

To see what causes errors in the position solution, see the article I linked to earlier regarding the source of errors.

The next concern is what is the typical rate of change in these sources that cause errors. If all of the sources of error were completely stable, then one might expect that the error would become a consistent error, that is, the variation of the deduced position from the real position would tend to always be in the same range and direction. I do not belive that is true.

First of all, the signals used to compute the position solution are from moving satellites, and the range, azimuth, and elevation to these satellites is constantly changing. Other than than two WAAS satellites that transmit a psuedo-range solution signal, all the ranging signals are in motion. So even if a fixed receiver location were to be used, the position of all the range solutions would be changing all the time. As a result, the errors created by those signals are changing.

As evidence of this, I have seen scatter plots of GPS receiver solutions plotting the deduced position relative to the actual, and these plots are usually random collections of points in a circular arrangement around the true position.

As the satellites move around, the lines of position to their range solutions become different, and this introduces more or less error into the solution. This uncertainty is described by the dilution of precision metric. The horizontal dilution of precision or HDOP can vary over quite a range, depending on how the satellite orbits happen to align over any particular receiver location at any particular time.

If you want to see evidence of this random error, just turn on the track function of your GPS receiver and chart plotter, then let the GPS record the track while the receiver is stationary. You will find your own scatter plot of position solutions.

It seems clear that with present day marine GPS receivers using WAAS and having favorable HDOP metric that one can get a position fix that is accurate to about 15-feet . That is to say, if you take the GPS deduced position, you can be reasonable certain that your actual position was within 15-feet of that point about 95-percent of the time.

There is certainly more precision available from GPS if more than one carrier signal is used and if a local differential reference is used. With those augmentations the accuracy can increase to just a few inches of error. But such receivers are not typical in recreational boats, and certainly not typical in the latest round of 10-Hz GPS receivers being discussed here.

jimh posted 09-16-2013 01:21 AM ET (US)     Profile for jimh  Send Email to jimh     
The error that introduces the most uncertainty in a position solution is the atmospheric propagation error. This can be corrected for, in part, with the WAAS signal. It is my understanding that the rate of change of the propagation error is not second-to-second, so that a measurement made at a certain time and a second measurement made one second later are both likely to be affected by the propagation error in the same way. This means that this error might be considered something of a steady state error, at least over a span of a minute or so. The WAAS signal provides some correction for this error, but it does not completely eliminate the error because the correction information is gathered over a wide area and is intended for the general area, not just for the specific spot a particular GPS receiver happens to be sitting. But in using the WAAS signal, we have already eliminated the propagation error from our estimate of precision. Thus the fact that it is a steady-state error over a short time is of no effect.
jimh posted 09-16-2013 01:31 AM ET (US)     Profile for jimh  Send Email to jimh     
Here is a great analogy that demonstrates my position:

A lathe operator is given a lathe in which there is a loose connection of one of the tools to the rest of the structure. This loose connection causes the parts made on this lathe to vary in dimension as the loose connection wobbles around during operation of the lathe. The lathe operator makes parts using this lathe, but because of the loose connection, the dimensions of the parts vary. Initially the operator makes parts on the lathe with the wobbly tool at a rate of 1 part per minute. Then, he speeds up his work flow, and makes parts on the wobbly lathe at the rate of ten parts per minute.

On what basis could we possibly expect that the parts made on the lathe at a faster rate are going to be more accurate in their dimensions than the parts made at the slow rate?

I believe this is exactly the situation we have with the GPS receiver making a position measurement at 1-Hz compared to 10-Hz.

K Albus posted 09-16-2013 10:09 AM ET (US)     Profile for K Albus  Send Email to K Albus     
I don't think there's any argument that each position fix in a 10-Hz system would any more accurate than each position fix in a 1-Hz system. However, when it comes to distance traveled, course-over-ground, and speed, the system with more fixes will always be more accurate anytime you're not traveling in a straight line.

In your example with the boat traveling at 6.82 mph, the difference in accuracy may be negligible. A boat traveling at 50 mph, however, is moving almost 75 feet per second. With a 1-Hz system, the distance traveled could be under-reported by a couple of feet each second. Although the system will give you an accurate report of your position at the end of that one second, it will not give an accurate report of the distance traveled to get to that point, or the speed you traveled to get there. Over the course of a day or a week or month, those inaccuracies can add up to a significant number. Again, with a 1-Hz system, after a month, you will still know where you are, but you will have a less accurate picture of how you got there than if you had a 10-Hz system.

If your contention is that a 10-Hz system is no more accurate than a 1-Hz system in telling you where you are at any given moment, I totally agree with you. However, your initial inquiry was about COG and speed. With regard to those, the more data points you have, the more accurate your calculations will be. At 6.82 mph, the difference may not be significant. At 50 mph, I believe it would.

K Albus posted 09-16-2013 10:11 AM ET (US)     Profile for K Albus  Send Email to K Albus     
For clarification, the first sentence in my immediately preceding post should read: I'm not making the argument that any given position fix in a 10-Hz system would be any more accurate than any given position fix in a 1-Hz system.
jimh posted 09-17-2013 01:19 AM ET (US)     Profile for jimh  Send Email to jimh     
The fundamental problem in the proofs presented that the speed and COG of a 10-Hz receiver is more accurate than an 1-Hz receiver is that the amount of error in the position fix is about 15-feet while the distance between position solutions in the 10-Hz receiver is about one foot (at 6.82-MPH). So there is an uncertainty of the position that is 15-times greater than the distance between position solutions.

It is easy to understand how a 10-Hz receiver will be more accurate at COG and speed if the ratio were reversed, that is, if the distance between position solutions was 15-time greater than the uncertainty of the position. But that is not the case for most speeds at which a small boat travels.

padrefigure posted 09-20-2013 12:55 PM ET (US)     Profile for padrefigure  Send Email to padrefigure     
I think that the advantage of a faster sampling rate will be greater position accuracy over time rather than better accuracy at a point in time. I have a Garmin GPSMAP 540S and will see changes in location and particularly heading even when I am still or adrift. If you take Jim's example to a more practical speed of, say 30MPH, then at 1HZ, the unit would calculate position every 44 feet. Simple math suggests that at 10Hz, the position would be calculaed every 4.4 feet. Intuitively, this seems like a more accurate reading.

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