Satellite display on 66i

Thanks, Wombo24. 

The .pdf document you posted the link to contains a lot of information I am interested in.  I was also surprised by the clarity.  Not because Australians wrote it.  We all know they've been literate for many months now.  But rather because of the complexity of the subject. 

One takeaway from the document is that there are lots of ways to describe position accuracy, which is why it's hard to interpret what was meant by the third-hand report of a two standard deviation length measurement.

That I was worried about my GPS accuracy was a reasonable assumption given the context here on this forum.  I agree that no one is likely to get lost and starve for lack of a standard deviation.  However, my interest is academic.  I'd just like to know what x ft means.  Not for any practical reason.

Mathematicians are obsessive about publishing supported explanations of things no one cares about.  So it's possible the meaning of x feet on a Garmin GPS might be floating around somewhere.  Even if there's not a thorough explanation, I'd be pleased to learn just what independent variables are used to calculate the accuracy presented by the 66i.

Incidentally, some others here have spoken of a "true" measurement, which I believe, is an 19th Century concept that science relegated to metaphysics in the early 20th Century in favor of "mean" or "expected value."

I agree with skyeye.  Here is that which I use:  https://en.wikipedia.org/wiki/Standard_deviation.

I use the MS Office Excel app to caculate standard deviations.

also, I did have quick view on the above linked work .pdf

However exactly in this .pdf, we have the big difference between accuracy and precision. In that article, they describe measurements with aid of GPS but against fixed known terrestrial points. This can be then solved statistically and the result will be *accuracy*, as it describes error to a given and previously defined value.

Portable GPS receiver has no reference, it can only compare own result of unknown quality to its other own result of unknown quality. It has no predefined value, it has no idea where it is in space. It just notes down some measurements and uses then kind of averaging  of number of results over relatively short period of time.

Geometrical approximation build the potential dilution of position value, PDoP. This value is relevant, and was earlier main quality number displayed on all such receivers  20-30 years ago, my old Etrex displays it still.

As consumer did never bother to understand what this is al all, it was apparently dropped by the manufacturers and replaced by something called accuracy as this is the only word common folks seem to know, but do not care about what it is.

Free moving GPS Receiver, is not able to tell any difference between its measurements and something people like to call 'true position'.

Again, accuracy is like shooting one bullet at a target with a bullseye and measuring its distance from the center of the bullseye.  Precision is shooting a dozen or more and calculating the combined result.  So on the range, you don't compare the distance missed by one shot of one gun against the miss of another gun, its the combination of 12 of one versus 12 of another.

And that's exactly why manufacturers go a whole lot further than that and complete extensive tests over thousands of hours and millions of position observations to establish the device accuracy.

Here's a quick summary from one manufacturer, no single position test is less than 24 hours:

And an example summary plot of millions of positions tested to establish accuracy:

The full test is here, this document will give you some idea of the depth of the analysis that is required and the range of factors considered to arrive at an accuracy number or model used by the device to derive the accuracy estimate on the fly.

www.nstb.tc.faa.gov/.../2020_Q4_SPS_PAN_v2.0.pdf

In this case it's been completed the FAA but the principles are the same across the industry. Garmin will be no different but like most manufacturers it's clearly commercially confidential information so you are unlikely to find the details of the tests or resulting embedded accuracy estimation algorithms in the device.

I still think there are questions unanswered. 

I just set my 66i out in the front yard for a little over an hour and a half while set to record a track at 3-minute intervals.  Throughout that time the receiver reported an accuracy of 10 feet.  I cut and pasted the 32 position measurements into Mathematica to find the distance of each measurement from the mean.  Here are the results:

{20.073ft,14.2896ft,17.889ft,25.072ft,22.4507ft,13.6971ft,3.93678ft,7.20963ft,7.61889ft,7.20963ft,9.23887ft,15.0258ft,15.0258ft,10.4849ft,6.23916ft,3.23125ft,2.35564ft,6.84992ft,4.64403ft,3.40849ft,5.17587ft,14.7633ft,8.44471ft,21.8613ft,14.2053ft,14.2053ft,16.6628ft,14.2053ft,7.45044ft,8.44471ft,8.44471ft,9.93088ft}.  

In other words, 53 percent of the measurements were within 10 feet of the mean.  Keep in mind that according to posts on this thread the 10 ft report supposedly means 95 percent of measurements in a large enough sample will be within 10 feet of the population mean.  As I interpret that, it means the 10 feet is a maximum of error in any direction.  The errors in my list are each from a single point, meaning one direction.  So the distances in my test have to be less than or equal to the maximum deviation at that time and place. Moreover, all these measurements were within the same 1.6-hour period, which I think means they are probably more tightly clustered than would be measurements taken at intervals longer than three minutes.

Admittedly, 32 is a small sample size.  If I have time later, I may let the 66i run longer.  But I have no reason to think the result would change much.

You can run the same test on your device on as many measurements as you want using the function I published at https://www.wolframcloud.com/obj/jgourle2/Published/geodistance%20function.nb.  The only difficulty involved is getting the data from the device into numeric form with separate longitude and latitude.  It's not too hard using Excel find/replace.  The published function explains how to import the data from Excel.

Some people may read this and think I'm complaining about the accuracy of the 66i.  Actually, I'm satisfied with the accuracy in my test.  Some 95 percent of the measurements were within 7 meters, which meets my needs.  Even if I'm trudging up a steep mountain trail at my aged pace that 7 meters is less than 30 seconds.

My only point here is that I remain curious what the 66i means when it says the reported location is within x feet of the displayed coordinates.

First bear in mind the caveat for manufacturer estimated accuracy is "ideal" conditions.

However 7m still sounds excessive even for a small sample size from 66i and could indicate multipath. I've found mine is more susceptible than my other Garmin devices in forest conditions. Are you in a large clear, flattish area with no buildings or trees anywhere nearby?

The receiver can't see obstructions and assumes all signals are arriving on time even though they may have been reflected over longer paths.

The results can change with time. I would try and make the observations as long as possible close to 24hrs, the reason for this is to obtain complete orbit cycles to remove any biases from specific geometry and multipath from particular sources/angles.

And what datum are you using? Garmin's internal datum transformations by necessity are simplistic and can cause accuracy problems, if you haven't already it would be best to stick with native WGS84 to keep your base data consistent. And if you have a way to do the projection transformations more precisely on a PC application or online then collect the Lat Lon (not projected such as UTM).

this is quite the simple explanation, thanks!

Wombo24 said:

First bear in mind the caveat for manufacturer estimated accuracy is "ideal" conditions.

plase again: there is no accuracy for a GPS receiver, neither under ideal nor less ideal conditions, nor can be accuracy estimated

this is all independent of chart datum etc.