This method is described in [15]. It is a fast method that yields the radar coded heights. It is based on the idea to first compute the reference fase at a number of heights and then to compare the actual phase from the interferogram with these values to determine the height.

A problem is that the interferogram does not contain the reference phase anymore, so that has to be added to the estimated phi.

It uses a number of steps which are described below.

- Compute reference phase at a NL locations (line,pixel)
at NH (=3) heights (0, 2000 and 4000m).

for h=0, 2000, 4000:- ellips.a=wgs84.a+h, ellips.b=wgs84.b+h
- compute position of master satellite, corresponding point P on ellips and position of slave satellite, see annex D.
- store the values and locations and heights.

- Compute for each location a polynomial (1d degree 1dD (= NH-1))
to describe
the height as a function of reference phase at these points.

For each location it holds ( for height i):

(24) (25) (26)

So it is easy to solve (exact) for per location. - Compute (1dD+1=NH) polynomials to describe the coefficients of
the previous step as a function of location. (now, for a random
location, the coefficients of height as a function of the reference
phase can be computed.) For example for computed at NL
locations (l,p) a 2d polynomial can be used:

(27)

A linear system can be easily set up and solved (least squares) by cholesky factorization. A rescaling needs to be applied to avoid instability. The system can be solved simultaneously for all alphas, because the normal matrix (and factorization) remains the same, but somehow our cholesky routine introduced an error (which is probably caused by using fortran in c) so we just solve 3 seperate times with the same factored normalmatrix. - Evaluate for all points at (line,pixel) with ok unwrapped phase
the 2d polynomial to obtain the coefficients of the height(phi)
function.
Then evaluate the 1d polynomial to obtain the height.

For all (l,p) with ok unwrapped phase:- Compute the alphas.

For betas appropriate to alpha0:(28)

- For betas appropriate to alpha1:
(29)

- repeat computing alphas until you have them all (1dD+1).
- Compute the height.
(30)

- Compute the alphas.