I have a certain problem in surveying in which I'm trying to do some error analysis. I'll layout the problem first.
- My current goal is to evaluate the variance-covariance matrix for the position of a point T on the ground.
- Now to first calculate the position of T, I observe this point from 4 other points (S1, S2, S3, S4).
- The observation is done in terms of (Ri,θi,φi) and is converted to (xi,yi,zi) position of T.
- Now using simple least square adjustment I calculate the adjusted position of (X,Y,Z).
- I need to find out the net variance-covariance matrix of (X,Y,Z) provided I know the following information
- Var-Covar matrix of the positions of S1, S2, S3, S4.
- Var-Covar matrix of the observations (Ri,θi,φi) that is converted into the matrix for (xi,yi,zi)
- Var-Covar matrix of (X,Y,Z) obtained through the co-factor matrix in least square adjustment procedure - this matrix is only a by-product of the adjustment - it assumes no uncertainty in S1, S2, S3, S4.
I need to know how can I propagate the errors in the positions of S1, S2, S3, S4 into the errors of point T.