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The observation equations are given by the zero-degree polynomial model (y = A x):

$\displaystyle \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots \\ y_N \\ \end{array...
...array} \right] \left[ \begin{array}{c} \alpha_{l=0, p=0} \\ \end{array} \right]$ (R1)

y contains the observed offsets in a certain direction.
$ \alpha_{lp}$ denotes the unknown coefficients of the polynomial.

The least squares parameter solution is given by:

$\displaystyle A^T Q_y^{-1} y = A^T Q_y^{-1} A x = N x$ (R2)

$ Q_y^{-1}$ is the (diagonal) covariance matrix of the observations.

The coefficients are estimated by factorization of the matrix N.

The inverse of matrix N is also computed to check the solution (stability) and to compute some statistics.

A check number is given ( $ {\rm\max(abs(}N N^{-1} - I))$) that gives a hint on the stability of the solution.

Leijen 2009-04-14