# Use parameter estimates to estimate residual differential acceleration

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.

```

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);

```

Now this plist allows us call the method to get the acceleration noise

```
%% 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)

```

And compute the Amplitude Spectral Density (ASD) for the remaining time series.

```
%% 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)

```