Kalman filtering to suppress spurious signals in Adaptive Optics control Page: 6 of 54
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
2. Incorporation of colored noise
In the standard formulation of the Kalman filter state space model, the measurement
noise is temporally white. This means that any specific instant of measurement noise
is temporally uncorrelated with all others. This is a reasonable assumption when
considering WFS noise due to standard CCD noise sources (i.e. photon noise and
read noise). However, noise due to another source may not be temporally white.
The AO state space model can be modified to deal with colored sources of noise. To
do so, we follow the procedure detailed in Candy,  (Section 5.8.2). We now present
a summary of these derivations.
The AO state space model is composed of two equations: one which describes the
temporal evolution of the state variables (AO phase to be corrected) and one which
describes the measurement process with white noise. In a very general form, the first
x[t + 1] = Ax[t] + Bw[t], (1)
where x is the state variables, A describes the temporal evolution, w[t] is temporally
white driving noise and B describes how that noise is used to generate the state. The
second equation is
y[t] = Cx[t] + Du[t] + v[t], (2)
where y[t] is the measurement (by the WFS) of the state, as described by C and v[t]
is temporally white measurement noise. The vector u[t] and matrix D are used to
Here’s what’s next.
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Poyneer, L & Veran, J P. Kalman filtering to suppress spurious signals in Adaptive Optics control, article, March 29, 2010; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc835045/m1/6/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.