C. Cahillane

I have made a file in /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER8/H1/Scripts/compare_actcoeffs_ER8_craig_extrapolation.m
The purpose of this file is to find the frequency dependence of our uncertainty in A_pu and A_tst.  It takes our three measurements from August 26, 28, and 29 and finds their weighted means and weighted standard deviations at all frequencies.  (Thank you Jeff, Kiwamu, and Darkhan for the code infrastructure.)

I have used the Pcal measurements only for our uncertainty calculations since it is has the lowest uncertainty and is the main method of calibrating our actuators.  Free Swinging Mich and ALSDIFF are used to determine the accuracy of Pcal, and Pcal is relatively very precise.
Our measurements go from 3 Hz to 100 Hz, but I need uncertainty from 3 Hz to 5000 Hz, so I am currently using a Zeroth Order Extrapolation, which is basically where I take our final uncertainty value at 100 Hz and let that be our uncertainty value for all data points from 100 Hz to 5000 Hz.  
It is expected that the actuation term will fall off quickly after 100 Hz and this will be sufficient for our first-order result.  If actuation is the main contribution to uncertainty more intelligent steps must be taken to ensure we aren't underestimating our uncertainty.

I will do the same tomorrow with the sensing function residual C_r, probably using Zeroth Order Extrapolation down to low frequency in this case.

Plot 1, 2, and 3 represent our UIM, PUM, and TST actuation stages.  For now I will fold systematic error and statistical uncertainty together, i.e. if we have an |A_tst| std of 0.5 m/ct and a systematic residual of 3%, I will make our total uncertainty be 0.5^2 + ( 0.03 * |A_tst| )^2.