Commit 93fd1820 authored by hannahm's avatar hannahm
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intro and method edits

parent 2e0731e3
......@@ -4,29 +4,34 @@
\begin{document}
Gravitational wave (GW) observatories are sensitive devices which can be affected by noise from their environments.
The data from observatories such as Advanced LIGO and Advanced Virgo contain persistent spectral noise lines.
Gravitational wave (GW) observatories such as Advanced LIGO~\cite{AasiEtAlAdLIGO:2015} and Advanced Virgo~\cite{AcerneseEtAlAdVirgo:2015} require high sensitivity to make GW detections.
To achieved this precision, GW observatories employ a variety of techniques to isolated them from environmental noise.
However they cannot be fully isolated and detector data contains short (glitches~\cite{}) and long (narrow spectral~\cite{CovasEtAl:2018}) duration noise artifacts.
Mitigation and removal of these lines is an area of active study.
Much effort has been made to identify the source of lines and, where ever possible, to mitigate them.
For example, in Ref.~\cite{CovasEtAl:2018}, noise lines are identified from blinking LEDs ..... and the effect eliminated by ,......
However it is not always possible to prevent the process causing these lines and in many cases the cause remains unidentified.
Mitigation and removal of nosie spectral lines is an area of active study.
GW detectors have a wealth of physical environmental monitors (PEM) which record environmental effects on the instrument and are used to assess the quality of the data at any one time~\cite{DetCharGW150914:2016,MarinShoemakerWeissPEM:1997}.
Much effort has been made to identify the source of lines and, wherever possible, to remove the source of the noise.
For example, in Ref.~\cite{CovasEtAl:2018}, a comb artifact (with $1\,{\rm Hz}$ spacing and $0.5\,{\rm Hz}$ offset) is identified in Oberving Run 1 data to originate from blinking LEDs in the timing system for the observatory.
The effect whas reduced by preventing the LEDs from flashing.
Another approach is to remove the effect of the line after data aquisition.
GW detectors typically have a wealth of physical environmental monitors (PEM) which record environmental effects on the instrument and are used to assess the quality of the data at any one time.
This information is also useful removing noise from the GW channel.
Recent work ....
Preventing the process causing noise lines is not alway posible and in many cases the cause remains unidentified.
It can, however, be possible to remove the effect of a noise line after data aquisition.
Information from PEMs provides a useful resouce for removing noise from the GW data if there is a correlation between the PEM channel and the noise in the GW channel.
Recent work has used PEM channels to remove noise spectral lines with machine learning techniques~\cite{} Nonsens, Deep Clean
Noise lines pose a particular difficulty to seraches for continuous gravitaitonal waves (CWs); persistent, periodic gravitational wave signals which are expected to be emitted by rotating neutron stars.
Searches target millisecond pulsars[], low mass x-ray binaries [], supernova remnants, and post-merger remants[].
The noise lines are often loud and can obscure a CW signal in the affected frequency bins.
CW candidates in proximity to noise line are typically vetoed ~\cite{} (Hmm papers)
Efforts have been made to ensure CW searches are robust against instrumental artifacts (Keital paper)
In this study we investigate the prospects of adaptive noise cancellation~\cite{WidrowEtal:1975} (ANC) for line removal in GW data.
Similar to ...., we focus on the removal of the $60\,{\rm Hz}$ noise line, which is caused by interference of the United States power grid.
ANC can be applied to situations where a reference signal provides an independent measurement of the noise interference.
We focus on the removal of the $60\,{\rm Hz}$ noise line, which is due to interference from the United States power grid.
ANC can be applied to situations where a reference signal provides an independent measurement of the noise interference, similar to the methods applied in Refs.~\cite{}.
The PEM data recorded at each observatory provides an excellent opportunity to test this method in GW data.
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\begin{document}
Adaptive noise cancellation provides a means of estimating a signal which has been corrupted by some interference or noise.
The method can be applied in the situation where there is a primary signal and a reference signal.
Adaptive noise cancellation provides an eatimate of a signal which has been corrupted by some interference or noise.
The method can be applied in the situation where there is a dataset of interest, the \emph{primary} signal and a witness to the interference; the \emph{reference} signal.
The primary signal contains the information of interest, plus some additional unwanted interference.
The reference signal contains a measurement of the interference which is correlated in some unknown way to the noise in the primary signal.
The ANC computes an estimate of the noise as it appears in the primary and subtracts it.
......@@ -16,7 +16,7 @@ The primary may also contain a signal of interest $h_i$, as well as additional n
\begin{equation}
d_i = h_i + c_i + n_i\,.
\end{equation}
Our objective is to remove $c_i$ with the aid of a reference measurement $r_i$, leaving $h_i$ intact.
The objective is to remove $c_i$ with the aid of a reference measurement $r_i$, leaving $h_i$ intact.
It is likely that the relationship between $r_i$ and $c_i$ is unknown; the coupling of the mains interference into the interferometer maybe extremely complex.
We use $r_i$ to construct an estimate $y_i$ of $c_i$ and remove it in the time domain.
The filtered timeseries is
......@@ -36,7 +36,10 @@ We now wish to compute $\mathbf{w}$ at each timestep.
\subsection{Adaptive Recursive Least Squares Method}
In this work we use the adaptive recursive least squares (ARLS) method to compute the estimated signal.
There are two input parameters, the order $M$ and $\lambda$, the meaning of which is discussed below.
The method is described in Chapter 9 of Ref.~\cite{HaykinAdaptiveFT:2002}.
\han{block diagram of method?}
ARLS requires two input parameters, the order $M$ and $\lambda$, the meaning of which is discussed below.
Here we describe the algorithm as pseudo code.
\begin{enumerate}
\item Initialise zero value $M$-by-$1$ vectors $\mathbf{u(n=0)}$ and $\mathbf{w(n=0)}$ for the tap-input and tap-weights respectively for timestep $n=0$. .
......
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