Finding GPS Center of Simulcast System

[Russell]

How do you find the geographic center of simulcast system? I know it's called waypoint averaging or GPS averaging, but I'm having trouble finding the answer.

In our DB, we have many simulcast sites/systems. The system center would actually be the center of all the simulcast towers. For the purposes of this, let's just assume all towers use same transmit power, same height and flat terrain.

So, what is the GPS center point for say Plano, Fort Worth, NE Tarrant, ETMC Tyler, Austin, etc. using the GPS coordinates of all the towers?

Russell

 

[Jay911]

I'd just put all the coords in an Excel sheet, average them out (one column for lat and one for long), and go with the averaged result.

But that may not work in all cases.

 

[soncorn]

I use the administrative boundaries to develop a system center.

So for example, the Tarrant County/Fort Worth system I just use the borders of the county + the city (it is part way into Denton and Prker Counties) to decide on a center and radius.

For a wide area system such as ETMC I use the tower locations plus a reasonable radius for system-wide talk groups and then use group locations for individual users like the City of Tyler. This is the same method I use for the Colorado Statewide DTRS.

I personally think that the true center of the simulcast towers is basically irrelevant to our uses.

 

[Russell]

I knew it was (forgotten) trig/calculus;

1. Convert latitude and longitude to Cartesian coordinates for each tower (1 to n)
   
   x1 = cos(lat1) * cos(long1)
   y1 = cos(lat1) * sin(long1)
   z1 = sin(lat1)
   ​
2. Average x, y and z coordinates; n = number of towers
   
   x = (x1 + x2 + ... xn) / n
   y = (y1 + y2 + ... yn) / n
   z = (z1 + z2 + ... yn) / n​
3. Convert averaged x, y, z coordinate to latitude and longitude.
   
   Center Longitude = atan2(y, x)
   h = sqrt(x * x + y * y)
   Center Latitude = atan2(z, h)​

Use the outermost towers only. Using towers inside the shape will actually 'average' the center away from the geographic center. I really don't want an average of all the points, I want to know what the center point is. So, averaging the outer locations yields the answer I'm looking for.

 

[texasemt13]

I knew it was (forgotten) trig/calculus

I'm currently in a Calc II class and had to stare at this a moment to process it. Good job, Russell- where'd you find this if you had forgotten?

 

[Thayne]

Question for the Peanut Gallery--

So I am wondering if you get as close to the spot as you can, and use an omni-directional antenna, wouldn't that be the worst spot to get the best reception??

What with timing issues, multipath, etc.

 

[Russell]

The geopgraphic center is not the same as equal distance to all towers. Think of a lopsided triangle. A simulcast system with a tower just east of downtown, one up in the far north central part of town, and one way out to the southwest. In this case the geographic center is just west of downtown. The closest tower, by far, is still the one just east of downtown.

Consider this Application for the City of Dallas P25 system. Click on the Locations tab. The geographic center turns out to be Childrens Medical Center just northwest of downtown.

 

[Russell]

Geographic Midpoint Calculator, find your Personal Center of Gravity

I don't get the age stuff, but it does a good job of finding the geographic center using GPS coordinates.