Hi If you already *have* data over a year (or multiple years) the fit is fairly easy. If you try to do this with data from a few days or less, the whole fit process is a bit crazy. You also have *multiple* time constants involved on most OCXO’s. The result is that an earlier fit will have a shorter time constant (and will ultimately die out). You may not be able to separate the 25 year curve from the 3 month curve with only 3 months of data.
Bob > On Nov 13, 2016, at 10:59 PM, Scott Stobbe <scott.j.sto...@gmail.com> wrote: > > On Mon, Nov 7, 2016 at 10:34 AM, Scott Stobbe <scott.j.sto...@gmail.com> > wrote: > >> Here is a sample data point taken from http://tycho.usno.navy.mil/ptt >> i/1987papers/Vol%2019_16.pdf; the first that showed up on a google search. >> >> Year Aging [PPB] dF/dt [PPT/Day] >> 1 180.51 63.884 >> 2 196.65 31.93 >> 5 218 12.769 >> 9 231.69 7.0934 >> 10 234.15 6.384 >> 25 255.5 2.5535 >> >> If you have a set of coefficients you believe to be representative of your >> OCXO, we can give those a go. >> >> > I thought I would come back to this sample data point and see what the > impact of using a 1st order estimate for the log function would entail. > > The coefficients supplied in the paper are the following: > A1 = 0.0233; > A2 = 4.4583; > A3 = 0.0082; > > F = A1*ln( A2*x +1 ) + A3; where x is time in days > > Fdot = (A1*A2)/(A2*x +1) > > Fdotdot = -(A1*A2^2)/(A2*x +1)^2 > > When x is large, the derivatives are approximately: > > Fdot ~= A1/x > > Fdotdot ~= -A1/x^2 > > It's worth noting that, just as it is visually apparent from the graph, the > aging becomes more linear as time progresses, the second, third, ..., > derivatives drop off faster than the first. > > A first order taylor series of the aging would be, > > T1(x, xo) = A3 + A1*ln(A2*xo + 1) + (A1*A2)(x - xo)/(A2*xo +1) + O( > (x-xo)^2 ) > > The remainder (error) term for a 1st order taylor series of F would be: > R(x) = Fdotdot(c) * ((x-xo)^2)/(2!); where c is some value between x > and xo. > > So, take for example, forward projecting the drift one day after the 365th > day using a first order model, > xo = 365 > > Fdot(365) = 63.796 PPT/day, alternatively the approximate derivative > is: 63.836 PPT/day > > |R(366)| = 0.087339 PPT (more than likely, this is no where near 1 > DAC LSB on the EFC line) > > More than likely you wouldn't try to project 7 days out, but considering > only the generalized effects of aging, the error would be: > > |R(372)| = 4.282 PPT (So on the 7th day, a 1st order model starts to > degrade into a few DAC LSB) > > In the case of forward projecting aging for one day, using a 1st order > model versus the full logarithmic model, would likely be a discrepancy of > less than one dac LSB. > _______________________________________________ > time-nuts mailing list -- time-nuts@febo.com > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.