enter image description hereI'm studying about algorithms for GPS or several surveying problems. I want to know is it possible to solve the problem below.
We know
- Global coordinates of two points.
- Bearings, azimuths and distances of the two points above from certain unknown point X. (It is such a local coordinate system.)
and the goal is
- Find the global coordinate of the unknown point
So, I tried to find the transformation matrix from the global coordinate system to the local coordinate system which has a origin at X. But, than I have to find the rotation matrix with 3 angles. So, I want to know is it possible to find that 3 angles with the given conditions.
I appreciate any of your help. Please understand me if there are strange sentences because I'm not good at English.
I hope this image helps you to understand this problem.
If you know azimuth and distance from a single known point to an unknown point you can determine its coordinates. Knowing its distance from a second known point and its azimuth as seen at that known point is unnecessary. The two points and the north pole are vertices of a spherical triangle. You know the length of the side from the known point to the pole (90 degrees minus the known point's latitude), you also know the length of the side from point to point, and you know the included angle between those sides (the azimuth of the unknown point as seen at the known point). Using the law of cosines for spherical triangles you can find the length of the third side (from the pole to the unknown point) and subtracting that length from 90 degrees gives you the unknown's latitude. Then using the law of sines for spherical triangles find the angle at the pole which gives the difference in longitude between known and unknown.