


 Multidimensional autoregression  

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Here we see how the interpolation beyond aliasing was done.
The first ``statement of wishes'' is that the observational data
should result from a linear interpolation
of the uniformly sampled
model space
; that is,
.
Expressing this as a change
gives the fitting goal
in terms of the model change,
.
The second wish is really an assertion
that a good way to find missing parts of a function
(the model space)
is to solve for the function and its PEF at the same time.
We are merging the fitting goal
() for irregularly sampled data with the fitting goal
(44) for finding the predictionerror filter.
Writing this out in full for 3 data points
and 6 model values on a uniform mesh
and a PEF of 3 terms,
we have

(52) 
where
is the convolution of the filter
and the model
,
where
is the data misfit
,
and where
was defined in equation (11).
Before you begin to use this nonlinear fitting goal,
you need some starting guesses for
and
.
The guess
is satisfactory (as explained later).
For the first guess of the filter, I suggest you load it up with
as I did for the examples here.



 Multidimensional autoregression  

Next: Seabeam: theory to practice
Up: LEVELED INVERSE INTERPOLATION
Previous: Test results for leveled
20130726