Apply PCI to simulated data

Here we apply PCI to data simulated via the LISA Simulation Suite, following the simulation scripts described in Simulate LISA data: noise and signal.

The simulated datasets are 3 days long. PCI is applied to 12 hours of data, with 4 hours of skipped data at the beginning of the simulation.

We need the following simulated datasets:

full simulation noise dataset (including laser noise and secondary noises), with filename ending in _measurements_4Hz.h5
secondary noises dataset, with filename ending in _noise_sec_4Hz.h5

1. Build data vector of the six LISA single-link channels

To build the data vector of the six LISA single-link channels \(\vec{y} = \left[y_{ij}\right]\), with \(i,j=1,2,3\) and \(i\neq j\) we resort to the intermediary TDI variables \(\eta\), implemented within pytdi as ETA_SET.

Note

Eleonora: how can we justify being independent from TDI if we use the intermediary TDI variables \(\eta\) to build the \(y\) s?

We build the single link \(\vec{y}\) data vector for the full noise simulation and for the secondary noises, ending up with two single link vectors:

full simulation single link vector \(\vec{y}^{\text{full}}\)
secondary noises single link vector \(\vec{y}^{\text{sec}}\)

2. Apply PCI to the data

We now resort to PCIFilter to evaluate PCI from \(\vec{y}\).

An instance of PCIFilter has two required inputs:

ydata: matrix with the single link LISA temporal phase data streams \(\vec{y}\).
fs: sampling rate of the data streams (Hz).

The optional parameters are

nhalf: filter stencil halfwidth in samples. The default is 45.
order: order of PCI. The default is 1.
maxcompts: PCA results will be truncated to this length after initial processing. The default is 10.
Tscale: if dt is None, then dt defaults to Tscale/ns

The input channels \(\vec{y}\) are stretches of data, usually of length ns+2*nhalf, but sometimes varying. The variations are: : (full length of matrix) 0:ns_fixed 0:ns+2nhalf skip:skip+ns+2nhalf In every case the window is trivial np.ones([data lenght])

The PCIFilter class applies the following methods

self.build_data_matrix(ydata, zero_mean=zero_mean,detrend=detrend)
self.apply_pca(datamatrix, maxcompts)
self.set_stencil(self.maxcompts)
self.channels = self.components.dot(datamatrix.T).astype(np.float64)

3. Run channel analysis on the PCI output

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4. Reconstruct single-link channels

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5. Estimate sensitivity

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