Kalman filtering to suppress spurious signals in Adaptive Optics control Page: 8 of 54
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To produce the new colored measurement noise state space model (of two equations)
we augment (3) and (4) with (5) and (6). The vectors become
x[t] = (x'[t], nT[t])T
w[t] = (w'[t], r[t])T.
The matrices for (1) and (2) are then:
A = ,
C = (C,
For use further on, we will also now define a
modified measurement matrix
modified measurement matrix where the
Cmod( C )
that picks out only the common-path phase and ignores the non-common-path phase.
We can solve for the Kalman filter, which will now correct the same aberrations as
before, and deal with the colored noise in an sensible fashion.
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Poyneer, L & Veran, J P. Kalman filtering to suppress spurious signals in Adaptive Optics control, article, March 29, 2010; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc835045/m1/8/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.