The algorithm used by the AutoCAD Civil 3D Survey Least Squares program uses a series of matrixes and formulas.
This algorithm is used to determine the probable position of points based on the least squares method.
The following matrix equation, based on a system of weighted observations, is solved iteratively:
where:
- X is a matrix that contains the difference between the current coordinates and the new coordinates of each unknown station, and that updates the current coordinates with each iteration (until X @ 0.0).
- A is a matrix that is created from the observations and coordinates of the points, based on a linearization by a Taylor series expansion of the specific observation type.
- P is a diagonal matrix with the standard deviations, or weights, of the observations.
- L is a matrix that contains the difference between measured observations and calculated observations.