Use parameter estimates to estimate residual differential acceleration (LTPDA Toolbox)

Our last step once we have recovered the correct parameters for our system is to translate the interferometer displacement noise to accelerometer noise, as previously shown. We will need first to load the objects that we have previously created. In this exercise, we will take the initial noise segment and translate into acceleration noise.

  
  
        %% Load objects
        
        noise  = matrix('noise.mat');
        mdl    = ssm('fitting_model.mat');
        Fcmd   = matrix('cmdForces.mat');
        params = pest('fit_mcmc.mat');

Since our objects contain two experiments, we will focus on one of them, the second experiment to do this analysis.

  
          
        %% Focus on noise for 2nd experiment
        
        [o1_0002, o12_0002]   = unpack(noise(2));
        [Fsc_0002, Ftm2_0002] = unpack(Fcmd(2));

As shown in Topic 3, the <>ltp_ifo2acc<> method requires a mapping of parameters because a change of notation.

  
          
        %% Parameters mapping
        
        % Define new variables with the name of the parameters used in ltp_ifo2acc
        Gdf  = params.find('FEEPS_XX');
        Gsus = params.find('CAPACT_TM2_XX');
        SD1  = params.find('IFO_X12X1');
        w1   = -1*params.find('EOM_TM1_STIFF_XX'); % use a different convention from ssm so the -1
        w2   = -1*params.find('EOM_TM2_STIFF_XX'); % use a different convention from ssm so the -1
        
        %% Conversion to acceleration
        
        % set the input plist for conversion to acceleration
        pli2a = plist(...
              'Gdf', Gdf, ...
              'Gsus', Gsus, ...
              'SD1', SD1, ...
              'w1', w1, ...
              'w2', w2, ...
              'Hdf', Fsc_0002, ...  
              'Hsus', Ftm2_0002);

  
  
        %% Convert to acceleration
                
        % ifo2acc with commanded forces
        [a1, a12] = ltp_ifo2acc(o1_0002, o12_0002, pli2a);

We will remove some samples from the last part of the acceleration noise time series to avoid a transient that appears in the x1 channel.

  
          
        %% set paremeters for lpsd
        plpsd = plist('times', [-inf -2010]);
        
        a1s  = split(a1, plpsd);
        a12s = split(a12, plpsd);
        
        iplot(a1, a1s)

  
          
        %% Calculate Amplitude Spectral Density
        
        % set paremeters for lpsd
        plpsd = plist(...
              'order', 1, ...
              'SCALE', 'ASD');
        
        a1xx  = lpsd(a1s, plpsd);
        a12xx = lpsd(a12s, plpsd);

Which leads to our final result: the perfomance of the instrument in acceleration noise.

  
  
        %% Plot results
        plplot = plist(...
                    'Linecolors', {'k', 'r'}, ...
                    'LineStyles', {'-', '--'}, ...
                    'LineWidths', {3, 3}, ...
                    'XLABELS', {'All', 'Frequency'}, ...
                    'YLABELS', {'All', 'Spectral Density'});

        % Plot results
        a1xx.setName('accel(DELAY_IFO.x1)')
        a12xx.setName('accel(DELAY_IFO.x12)')
        
        iplot(a1xx, a12xx, plplot)