Converting Southing/Easting GPS coordinates to Latitude/Longitude

Question

I am developing a web application using JQuery Framework and am using Geolocation to determine the locations of our hardware stations to display on Google Maps.

In our database the locations of the sites are stored in Southing/Easting format.

I need a way to convert Southing/Easting coordinates to Latitude/Longitude that Google Maps can understand.

Can anyone please tell me the formula or the best way to approach this problem?

I have done searches on Southing/Easting however nothing came up, more like northing/westing etc and even then, not much info..

The programming part I don't really need much assistance just the actual concepts on how the conversion between these two formats can be performed.

Thanks!

Answer 1

There's not enough information in your question to answer it -- but you may be able to figure out the information on your own. Here's how I would go about it.

Southing and easting (and northing and westing) are simply measuring a distance from a certain "zero-point". It makes it much easier if you know what the zero-point is, and what the units are -- but it's not impossible to convert if you don't.

For example, the city of Atlanta was founded exactly 5 miles west of Decatur, Georgia (I'm assuming due west for this example, although it was actually 5 miles west-by-southwest). And Emory University is 1.5 miles north and 1.5 miles west of Decatur (this is an approximation, but for our purpose, let's assume it's exactly right).

Now let's assume a few things:

1. We have been told that Atlanta is north-0 and west-8800.
2. We have been told that Emory University is north-2640 and west-2640.
3. No one remembers that Decatur is the origin of the grid.
4. No one remembers what unit is represented by the distances (it's yards, by the way).

If we go to Google Maps and drop a latitude marker (may have to be enabled in Google Maps labs) on the zero-mile post in Atlanta, we find it is at 33.75116, -84.38740.

And if we do the same for Emory University, we find that it is at 33.7909, -84.3248.

Then we can do the following math to find the ratio of longitude to the unknown westing units:

abs( -84.38740 - -84.3248 ) = ( abs ( 8000 - 2640 ) ) * x
0.0626 = 5360 * x
x = 0.0626 / 5360
x = 0.000011679

And from there we can find the longitude of our theoretically-unknown zero-point by multiplying Atlanta's westing value by this factor and then adding it (because Atlanta is west of the prime meridian, and thus has negative longitude numbers) to Atlanta's known longitude:

zero-longitude = -84.38740 + ( 8000 * 0.000011679 )
zero-longitude = -84.293968

Applying the same logic to latitude, we could find a factor based on the unknown northing units:

abs( 33.75116 - 33.7909 ) = ( abs ( 2640 - 0 ) ) * y
0.03974 = 2640 * y
y = 0.03974 / 2640
y = 0.000015053

And we find the zero-latitude point the same way (which is obvious in this example because Atlanta was at north-0 -- but it's good to go through the motions anyway):

zero-latitude = 33.75116 + ( 0 * 0.000015053 )
zero-latitude = 33.75116

So our calculated zero-point is 33.75116, -84.293968. Google Maps confirms that this latitude falls where expected in relation to known points.

So then I could find any other of the northing and westing points by using this derived zero-point and the derived ratios. For example, if we were told something was north-3000 west-500, we'd get it's latitude and longitude as follows:

latitude = 33.75116 + ( 3000 * 0.000015053 )
(adding because we're moving north)
latitude = 33.796319

longitude = -84.293968 - ( 500 * 0.000011679 )
(subtracting because we're moving west)
longitude = -84.2998075

Thus, north-3000 west-500 = 33.796319, -84.2998075

If your zero-point and your units of measure haven't been lost to history, you've got a major head start. If they have, you can use this technique to deduce them -- but you may have to fine-tune it with multiple correlations until you have values that feel reliable.