LTPDA Toolbox™ contents Non-linear least squares fitting of time series   LTPDA Training Session 2

IFO/Temperature Example - signal subtraction

During this exercise we will:

  1. Load the AOs with the IFO and Temperature data
  2. Load the transfer function of the data
  3. Split the TF to select the meaningful region only
  4. Fit the TF with zDomainFit
  5. Subtract the temperature contribution from the IFO signal

Let us load the test data and split out the 'good' part as we did in Topic 3: 

    ifo = ao(plist('filename', 'ifo_temp_example/ifo_fixed.xml'));
    ifo.setName();
    T = ao(plist('filename', 'ifo_temp_example/temp_fixed.xml'));
    T.setName();

    % Split out the good part of the data
    pl_split = plist('split_type', 'interval', ...
                'start_time', ifo.t0 + 40800, ...
                'end_time', ifo.t0 + 193500);

    ifo_red = split(ifo, pl_split);
    T_red = split(T, pl_split);

These data are already preprocessed with ao/consolidate in order to set the sampling frequency to 1Hz.
We could look at the data... 

    iplot(ifo_red, T_red, plist('arrangement', 'subplots'))

Let us load the transfer function estimate we calculated in Topic 3. 

  tf = ao('ifo_temp_example/T_ifo_tf.xml');

The meaningful frequency region is in the range 2e-5 Hz - 1e-3 Hz. Therefore we split the transfer function to extract only meaningful data. 

    tfsp = split(tf, plist('frequencies', [2e-5 1e-3]));
    iplot(tf, tfsp)

The plot compares full range TF with splitted TF:

Once we have the proper transfer function, we could start the fitting process. A rapid look to the TF data should convince us that we need a very simple object to fit our data so we could try a fitting session "by hand". In other words, it is more convenient to skip the automathic functionality of zDomainFit. Moreover, we force zDomainFit to fit a stable model to data because we want to output a stable filter. 

    plfit = plist(...
        'AutoSearch', 'off', ...
        'StartPolesOpt', 'clog', ...
        'maxiter', 5, ...
        'minorder', 3, ...
        'maxorder', 3, ...
        'weightparam', 'abs', ...
        'Plot', 'on', ...
        'ForceStability', 'on', ...
        'CheckProgress', 'off');

    fobj = zDomainFit(tfsp, plfit);
    fobj.filters.setIunits('K');
    fobj.filters.setOunits('m');

It is time to filter temperature data with the fit output in order to extract temperature contribution to interferometer output. Detrend after the filtering is performed to subtract mean to data (bias subtraction). 

    ifoT = filter(T, fobj, plist('bank','parallel'));
    ifoT = split(ifoT, pl_split);
    ifoT.detrend(plist('order', 0));
    ifoT.simplifyYunits;
    ifoT.setName();

Then we subtract temperature contribution from measured interferometer data 

  ifonT = ifo_red - ifoT;
  ifonT.setName();

The figure reports measured interferometer data, temperature contribution to interferometer output and interferometer output without thermal drifts. 

  iplot(ifo_red, ifoT, ifonT)

If you now compare spectra of the original IFO signal and the one with the temperature contribution removed, you should see something like the figure below: 

  ifoxx = ifo_red.lpsd;
  ifonTxx = ifonT.lpsd;
  iplot(ifoxx, ifonTxx)


Non-linear least squares fitting of time series  Non-linear least squares fitting of time series   LTPDA Training Session 2 LTPDA Training Session 2

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