Re: Coherent averaging

Thanks Andor for thinking out loud. We appreciated your suggestions,
but we are not able to use them. Even if often dealing with signal
processing, our background does not allow us to feel comfortable in
selecting the proper technique in this application.
We would appreciate if you could comment on a more detailed description
of the application, if you have time for it.

Our "measurements" are the trajectories of points of the surface of
the human body during movement. We are interested in estimating bone
movement. We are, thus, dealing with the estimation of the relative
movement between skin and bone.
Our "signal" is the trajectory of a skin point seen by an observer
fixed on the bone (Ob).
Our "realization" is the trajectory of a skin point seen by an
observer fixed on the skin (Os). Consequently, the realization is
composed by the signal PLUS the movement between observer Os and bone
(Ob).
In other words "noise" is the movement between observer Os and bone
(Ob).

Our signal and our noise are subject-specific, are not measurable, and
cannot be characterized. Moreover, the noise spectrum has a content
overlapped to that of the signal. (what a mess!).

We have many observers Os independent within each other (Os-i). The
relevant realizations (trajectories seen by the observers Os-i) are
independent within each other. However, we cannot infer that the noise
embedded in these realizations is normally distributed...

Using a sort of PCA analysis, we obtain a model of the signal. However,
we do not have any clue of the signal amplitude. We know HOW it
changes, but not HOW MUCH (this is what we meant by "signal
pattern").

We are now correlating the realizations observed by Os-i with this
model and, then, average these realizations after weighting them with
the correlation coefficient.

Is this approach theoretically correct, since we cannot assume that the
noise is normally distributed?
Can you suggest a different (and obviously better) approach to deal
with this data set?

Thanks a lot,
Valentina and Claudia

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