Gpsr Format Accuracy?

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Can someone check my math and logic?

Being an analyst by profession I got to wondering if there was any difference in accuracy between my GPSr three data formats (DDD MM.MMM, DDD MM SS.S, DDD.DDDDD) especially when expressed as distance. I was curious about how far I could move before my GPSr would show a change in location, of course assuming a perfect accuracy.

The circumference of the earth, pole to pole, is approximately 39,948.49 kilometers. Therefore:

A. Each degree equals approximately 110.96803 kilometers (1/360 of circumference)

B. Each minute equals approximately 1.84947 kilometers (1/60 of “A”)

C. Each second equals approximately 0.03082 kilometers (1/60 of “B”)

So, for any given change in latitude:

For the format DDD MM.MMM the smallest measurable change is 0.001 minute. 0.001 times 1.84947 km (from B, above) is 0.00184947 km or 1.84947 meters.

For the format DDD MM SS.S the smallest measurable change is 0.1 second. 0.1 times 0.03082 km is 0.00308245 km (from C, above) or 3.08245 meters.

For the format DD.DDDDD the smallest measurable change is 0.00001 degree. 0.00001 times 110.96803 km (from A, above) is 0.00110968 km or 1.1096803 meters.

Looks like I’ll keep my GPSr set at DDD.DDDDD. Am I right?

- Fat Freddy

I believe that the DD.DDDDD format is a decimal point or two beyond what the expected range of error would be in any event. I also believe that with little effort, a format of DD.DDDDDD or perhaps even DD.DDDDDDDDDDDDDDDD could be programmed into your GPSr software, but this would not make your GPSr any more accurate.

I wouldn't rely on meaningless numbers that show up as digits to the right of the decimal point that are beyond the accuracy of my GPSr.

Edited by seneca

Shouldn't this be in the Mensa forums?

1) Your GPS isn't perfectly accurate. Hold 2 GPS units together and see how often the give you the exact same reading.

2) Any attempt to convert geocaching.com co-ordinates back and forth increases the risk of human error.

3) K.I.S.S.

Edited by bons

If I remember my college spherical geometry correctly, your number may be accurate for the equator but your numbers need to be modified as your latitude increases. I believe that there is a cos (math function) that needs to be remebered--so at the north/south pole you have a value of 0.

Ciao

RooBoy

Edited by rooboy
Looks like I’ll keep my GPSr set at DDD.DDDDD.  Am I right?

No, not really as precision is one thing and accuracy is quite different. Besides decimal degrees isn't really an often used format and those organisations that do use it (like weather forecasts etc) aren't really interested in being precise in the first place and probably only use 1 or 2 decimals. So really if one obtains a position in dDD MM.mmm then simply set the GPS to adopt this format direct as one can't increase the precision of a position by say changing the format from dDD MM.mmm to dDD.ddddd, it is what it is and can't be any better than the original. Going the other way, any difference is probaly more of academic interest than anything practical or really useful.

Any displayed (converted) format can only be as significant as the underlying GPS XYZ coordinate precision.

Also any "difference" in coordinate formats should take into account that positions are at least 2 dimensional.

Cheers, Kerry.

Edited by Kerry.

I don't know for sure but this seems logical to me.....

It is unlikely that the unit does the calculations in the output format that you select. That would require that three different sets of calcs be available. I would expect that the calcs are done in the best mode and that the display option is a simple conversion done afterwords as requested by the user.

Seems sensible to me anyhow, but as I said, I dunno!

However, your logic and assumptions are correct, although probably irrelevant in real world terms.

As has been said already, precision and accuracy are not the same thing - I will add resolution to that also.

I would expect that the calcs are done in the best mode and that the display option is a simple conversion done afterwords as requested by the user.

I agree. My thinking was that the best display I could request would be the one which would have the greatest precision.

However, your logic and assumptions are correct, although probably irrelevant in real world terms.

Again I agree. That's why my OP said "of course assuming a perfect accuracy." Best accuracy my GPSr has ever given me was 12 feet.

The practical application of all this was to be able to make a reasonable estimate of a position where I couldn't make a direct observation, say under a forest canopy or indoors. For example, if I were 16.5 meters due south of a desired location where I couldn't get an accurage fix, and my current position was indicating an accuracy of +-17 feet, I would know that if I added fifteen clicks (0.00015 degrees, or 0.00001 degree per 1.1 meters) I would know the latitude of the "shaded" position, obviously with the same accuracy of +-17 feet.

- Fat Freddy

I believe that the DD.DDDDD format is a decimal point or two beyond what the expected range of error would be in any event. I also believe that with little effort, a format of DD.DDDDDD or perhaps even DD.DDDDDDDDDDDDDDDD could be programmed into your GPSr software, but this would not make your GPSr any more accurate.

I wouldn't rely on meaningless numbers that show up as digits to the right of the decimal point that are beyond the accuracy of my GPSr.

But what about my *digital* tire pressure gauge I got for Christmas that shows results down to the hundredth?

Actually, my Dad got this. It displays the hundredth PSI in 5 hundredth increments. No telling how accurate it is.

Just go find stuff You can dive yourself nuts or you can go have fun

I got so many people complain about one of my caches and my coordinates I took four GPSr at the same time and got four reading that I posted with the cache, then they complained that they did not know which one to use.

http://www.geocaching.com/seek/cache_details.aspx?ID=50235

Some times you just have to say, Forget about it!!

The practical application of all this was to be able to make a reasonable estimate of a position where I couldn't make a direct observation, say under a forest canopy or indoors. For example, if I were 16.5 meters due south of a desired location where I couldn't get an accurage fix, and my current position was indicating an accuracy of +-17 feet, I would know that if I added fifteen clicks (0.00015 degrees, or 0.00001 degree per 1.1 meters) I would know the latitude of the "shaded" position, obviously with the same accuracy of +-17 feet.

This is a 'theory' thread. But, with that said, I don't want to go too deeply into the math of it all. If you (or anyone else) wants to take it a bit further then you need to start looking into the subjects of the error ellipse and predictive aiding. It is not quite as simple as your quote above would suggest that it might be.

Oh, (hee-hee) when I say 'take it further' I do NOT mean ask me! I am more than happy to get 'just about there' and search! In my professional life I have used GPS systems that can (consistently) achieve sub-metric accuracy. However, the 'weakest link' thing still applies. If the item that you are searching for was not placed with that degree of accuracy, then does it matter? No, not really. For work I will continue to use the latest super systems - for play, well, my basic yellow eTrex is just fine.

By the way, and slightly off topic, how is the cat these days?

By the way, and slightly off topic, how is the cat these days?

Cat up and died several years ago but I found a replacement. Like Freewheelin' Franklin said, "One orange cat is pretty much the same as any other."

.... and my current position was indicating an accuracy of +-17 feet, I would know that if I added fifteen clicks (0.00015 degrees, or 0.00001 degree per 1.1 meters) I would know the latitude of the "shaded" position, obviously with the same accuracy of +-17 feet.

A GPS does/can not indicate accuracy as it doesn't know where it is in the first place. Much of this isn't real practical and really has no guarantee of achieving a better end result.

Cheers, Kerry.

It is the same as asking if measuring distance in feet/inches is more accurate than measuring in meters.

Cat up and died several years ago but I found a replacement. Like Freewheelin' Franklin said, "One orange cat is pretty much the same as any other."

Franklin sure knows his stuff - I mean, Fat Freddy without a cat? Well, it's like a fish without a banjo, no, wait, I mean - uh, well, you know what I mean... dadgum, what was that stuff?

I've got a question very similar to that.

I've been playing around with the software and I'm trying to figure out what that therotical accuracy of this unit is.

Using the Deg/Min/Sec

I get watching the data stream 36 35' 30.50N and 082 21'31.30W

My question is the 30.50N or the 31.30W -- the last two digits normally don't show up on my display (what are they called -- milli seconds??) -- but if it did what approx inch or metric distance would that be.

Wouldn't that be down to somewhere in the cm or inch range and not the meter range.

I'm just a kid trying to understand the theory, I know it will never be accurate to that level.

Please don't flame me -- I'm just trying to learn.

Thanks

therotical accuracy Ok therotical accuracy is well defined in the system specifications and what you probably mean is "therotical precision".

Theoretically 1 second is around 31 metres (~ 101 feet), 0.1" is then roughly 3 metres and 0.01" around 0.3 metres but is there any recreational GPS that displays to 0.01"?

Many recreational GPS units these days will output via NMEA to 0.0001', as in minutes as NMEA doesn't support Deg/min/Sec output anyway. Theoretically that (0.0001') is around 0.2 metres but considering GPS SPS accuracy is nowhere even near that capable then yes it's really only theoretical.

Cheers, Kerry.

Edited by Kerry.
Can someone check my math and logic?

Being an analyst by profession I got to wondering if there was any difference in accuracy between my GPSr three data formats (DDD MM.MMM, DDD MM SS.S, DDD.DDDDD) especially when expressed as distance. I was curious about how far I could move before my GPSr would show a change in location, of course assuming a perfect accuracy.

The circumference of the earth, pole to pole, is approximately 39,948.49 kilometers. Therefore:

A. Each degree equals approximately 110.96803 kilometers (1/360 of circumference)

B. Each minute equals approximately 1.84947 kilometers (1/60 of “A”)

C. Each second equals approximately 0.03082 kilometers (1/60 of “B”)

So, for any given change in latitude:

For the format DDD MM.MMM the smallest measurable change is 0.001 minute. 0.001 times 1.84947 km (from B, above) is 0.00184947 km or 1.84947 meters.

For the format DDD MM SS.S the smallest measurable change is 0.1 second. 0.1 times 0.03082 km is 0.00308245 km (from C, above) or 3.08245 meters.

For the format DD.DDDDD the smallest measurable change is 0.00001 degree. 0.00001 times 110.96803 km (from A, above) is 0.00110968 km or 1.1096803 meters.

Looks like I’ll keep my GPSr set at DDD.DDDDD. Am I right?

- Fat Freddy

You made the process of calculation much harder than it needs to be.

DDD MM.MMM = smallest increment is 1/60,000 of a degree

DDD.DDDDD = 1/100,000 of a degree

1/60,000 > 1/100,000

Can someone check my math and logic?

Being an analyst by profession I got to wondering if there was any difference in accuracy between my GPSr three data formats (DDD MM.MMM, DDD MM SS.S, DDD.DDDDD) especially when expressed as distance. I was curious about how far I could move before my GPSr would show a change in location, of course assuming a perfect accuracy.

The circumference of the earth, pole to pole, is approximately 39,948.49 kilometers. Therefore:

A. Each degree equals approximately 110.96803 kilometers (1/360 of circumference)

B. Each minute equals approximately 1.84947 kilometers (1/60 of “A”)

C. Each second equals approximately 0.03082 kilometers (1/60 of “B”)

So, for any given change in latitude:

For the format DDD MM.MMM the smallest measurable change is 0.001 minute. 0.001 times 1.84947 km (from B, above) is 0.00184947 km or 1.84947 meters.

For the format DDD MM SS.S the smallest measurable change is 0.1 second. 0.1 times 0.03082 km is 0.00308245 km (from C, above) or 3.08245 meters.

For the format DD.DDDDD the smallest measurable change is 0.00001 degree. 0.00001 times 110.96803 km (from A, above) is 0.00110968 km or 1.1096803 meters.

Looks like I’ll keep my GPSr set at DDD.DDDDD. Am I right?

- Fat Freddy

That would be true for longitude, but not latitude. The closer you get to the poles, the circles of latitude get smaller and smaller thus the distance between degrees of latitude also get smaller.....I think

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