Proposed Mathematics of Atomic Time (UTC) measurement comparison calculations:
Assuming our clocks run at a uniform rate (some straight line of any slope) then:
Measure "r" as the difference between of Atomic time and individual Clock time = r1, r2, r3…. rN. at time period N. Assumes clocks are not set back to atomic time at the beginning of each time period. (+ = Clock reading faster than Atomic Time. - = Clock reading slower than Atomic time)
First derivative or slope in (sec/day) is then RN = r1/d1, (r2 - r1)/d2, (r3 - r2)/d3, . . . Where dN = Number of days (to at least several decimal places) between each measurement N.
Second derivative or acceleration of time (sec/day2) is then:
CN = (R2 - R1)/d2, (R3 - R2)/d3, . . . (RN - RN-1)/dN)
Next select the most reliable clocks using the resulting standard deviation as a reference. Average all Second derivative CN readings for selected clocks during each time period or ACN = (C2 + C3 + C4….+ CN)/(N-1) Where CN is second derivative for each of N-1 clocks.
First Integral of average ACN or FIN = AC1*d1, (AC1*d1+AC2*d2), (AC1*d1+AC2*d2+ AC3*d3), . . .
Integral of FIN or SIN= FI1*d1, (FI1*d1+FI2*d2), (FI1*d1+FI2*d2+ FI3*d3), . . .
This second integral then becomes the filtered constructed curve of the average comparison to atomic time.
Note that all straight-line trends of any constant slope in the original data are filtered out, as desired. Only the changing situation is plotted as the results.