I'm working on a project where I have a GPS and two receivers to create a triangle with a transmitter. The problem I'm trying to figure out right now is how can I get the position of the two receivers?

I know it can be done, but I'm blanking on the math and Google hasn't been too helpful, maybe I'm not searching it correctly.

Here's my circumstance: GPS is reading lat: 42.331429 and lng: -83.045753. My device is sitting perfectly level and pointing due north. My two receivers are 30 inches to the left and 30 inches to the right. Can anyone help me figure out the equation to get their positions? I know these are going to be very small differences, but that's as far as I've gotten so far.

Also, if things were more complex, how would that be solved? Such as pointing North/West, and 5 degrees rotated on each axis, x, y, and z? I realize that's kind of a crazy scenario, but I like to potentially prepare for every scenario. These are based on being in fixed positions from the GPS and the plane that the GPS is on.


Someone can please correct me if I'm wrong, but:

  1. The distance left/right in degrees of longitude depends on the latitude you are at. Calculating longitude length in miles? explains how that works. Basically 30 inches is not a set number of degrees. So you should be able to figure it out using this. But...
  2. If your GPS is reading to 6 decimal places I think that's a precision of about 4 inches, so your result is going to be no better than that. What precision were you hoping for?
  3. You mention your GPS is pointing north. I don't think it matters where your GPS is pointing. It only returns the coordinates it sits at. Most GPS that I know of only give direction when they are moving or if they have an inbuilt compass.

I can't help feeling that you're trying to create a very precise measurement using quite a blunt instrument.

  • I'm taking a look at the link you provided. You are correct in that my GPS doesn't care about the direction, I just used the north direction for the sake of simplifying traversing the x-axis, in this case it runs exactly on a latitude. As for the degrees of accuracy... I'm currently counting down to 9 decimal places. I don't have a specific target in mind for the accuracy, but I'd like to keep things as accurate as possible. – John Sly Jun 23 '16 at 17:18

Trigonometry and algebra? A triangle has three side lengths and three internal angles. If you know any three of those six measurements you can solve for the rest using the Law of Sines or the Law of Cosines. A little bit of skill converting between Cartesian and polar coordinates should solve your problem. Keep in mind that Mark is correct-your current measurements are probably less than the accuracy of your GNSS unit.

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