The observation equations are given by the polynomial model (y = A x):
y contains the observed offsets in a certain direction.
denotes the location (line number) of the observed offsets in a certain direction.
denotes the location (pixel number) of the observed offsets in a certain direction.
denotes the unknown coefficients of the polynomial.
The data is rescaled (to the interval [-2, 2], see Annex D) so the normalmatrix is rescaled. otherwise there could occur very high values for, e.g., . The least squares parameter solution is given by:
is the (diagonal) covariance matrix of the observations. this matrix can be equal to identity or to the correlation values in version 1. (CPM_WEIGHT card).
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 ( ) that gives a hint on the stability of the solution.