By altering the position of a grid as well as the coarseness of a grid, additional information can be introduced to the problem of PEF estimation. This information can be used for both stationary and non-stationary PEFs in any number of dimensions. As the dimensionality of a problem increases, the number of possible grid positions increases exponentially, whereas the number of scales of data is unaffected by the dimensionality of the problem. The benefits of this method increase with dimension, as shown in the differences between the 2D and 3D examples. The method also shows greater effectiveness around larger gaps in the data. However, the cost of regridding the data many times as well as the associated bookkeeping is problematic.

This method can be used to glean more information from the data using existing techniques. The question of how to best regrid the data remains, as does the question of whether it is best to manipulate the filter or the data when attempting to estimate a PEF on sparse data. Overall, this method provides one more means of manipulating the data to better constrain the PEF, and shows improvement over existing methods.

10/14/2003