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First I introduce a set of important variables that will help us
build the desired filters.
- : the data vector; input to the problem.
- : the noise vector; assumed to be known.
- : the signal vector; output of the problem.
- : annihilation filter for the data; a Prediction
Error Filter (PEF).
- : annihilation filter for the noise; a PEF.
- : annihilation filter for the signal; a PEF.

The leading assumption is that the data vector is the sum of the signal
and noise vectors, i.e,
| |
(1) |

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Stanford Exploration Project

6/7/2002