C. Cahillane

I have generated the latest uncertainty results for LHO.  I have characterized the uncertainty in the actuation function by quadratically summing the statistical and systematic errors.  There are more elegant ways to combine systematics and statistical errors, but for now we will see if this is sufficient.
Plot 1 and 2 are the Mag and Phase components of σ_h^2, and Plots 3 and 4 are the Mag and Phase of σ_h itself.
We have greater than 10% and 10 degree uncertainty just below 100 Hz with our current analysis, but this is just an update with inflated flat uncertainties in the kappas and f_c.

Note that the linear sum of our PUM and UIM stage uncertainties into our A_pu uncertainty is not correct, but only an estimate used for calculations in the meantime.  I have performed the correct calculations in Mathematica and will implement them given time.
The following are the sigma values I have used:

σ_|A_tst| = A_coeff_sigma_mag_A_tst .* abs(A_tst);  
σ_|A_pu| = A_coeff_sigma_mag_A_pum .* abs(A_pum) + A_coeff_sigma_mag_A_uim .* abs(A_uim);
σ_|C_r| = 1.0 .* abs(C_r);
σ_|kappa_tst| =  5;
σ_|kappa_pu| = 5;
σ_φ_A_tst = A_coeff_sigma_phase_A_tst;
σ_φ_A_pu = A_coeff_sigma_phase_A_pum + A_coeff_sigma_phase_A_uim;
σ_φ_C_r = 5;
σ_φ_kappa_tst = 5;
σ_φ_kappa_pu = 5;
σ_kappa_C = 5;
σ_f_c = 23.4731;

I have inflated the errors in the kappas and f_c to 5% and 5 degrees based on our systematics seen from the calibration group calculations.  We hope that we can deflate these errors when the calibration group discovers the systematics responsible for our kappa deviations from 1.
The next step is to propagate uncertainty for the sensing function, after which I will have finished analysing the uncertainty of measurements at LHO.  Then I may move onto LLO.

Steps:
1) Get sensing function uncertainties at LHO
2) Implement correct A_pu uncertainty propagation
3) Check sanity
4) Move on to LLO uncertainty measurements
(?) Correct for kappas and f_c uncertainties as better calculations are made available.  For now, apply flat 5% and 5 degrees.