On the other hand, with spatial filtering applications a local PEF is more appropriate. In my book GEE, I explain how to build a time-variable PEF. It seems an alternative could be based on a training data set that varies locally. I see this as perhaps theoretically superior. In the GEE example, the filter itself is stated to vary smoothly. Now I would be proposing that the training data set be varying smoothly. In general, PEFs tend to ``look bad'' because their frequency content is inverse to that of the signal. This could mean that smoothing a PEF is not nearly such a good idea as using a training data set.
Imagine we seek a new PEF upon the arrival of each new trace, or perhaps even upon the arrival of each new data point. Naturally, the Wilson-Burg spectral factorization method might be helpful. Generally however, I am not sure how to proceed.