8-8
T(t) = T0 +
R(t)dt + e(t) = T0 + (R0t +
1/2At2 + …) + Ei(t)dt +e(t)
Where,
T(t) = time difference between two clocks at time t after synchronization
T0 = synchronization error
at t = 0
R(t) = the rate (i.e., fractional frequency) difference between the two
clocks
under comparison; R(t) = R0 + At + …Ei(t)
e(t) = error due to random fluctuations = tsy(t)
R0 = R(t) at t = 0
A = aging term (higher order terms are included if the aging is not
linear)
Ei(t) = rate difference due to environmental effects
(temperature, etc.)
- - - - - - - - - - - - - -
Example:
If a watch is set to within 0.5 seconds of a time tone (T0 = 0.5 s), and the
watch initially gains 2 s/week (R0 = 2 s/week), and the watch rate ages -0.1 s
per
week2, (A = -0.1 s/week2),
then after 10 weeks (and assuming Ei(t) = 0):
T (10 weeks) = 0.5 (2 x 10) + 1/2(-0.1 x (10)2) =
15.5 seconds.
Clock Errors