COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
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It cannot be duplicated or distributed without expressed written consent.
3.6.3.6. Range Measurements Sampling
As the sampling rates 250 ms or 100 ms and the generation rate are asynchronous, a linear interpolation is
applied to provide the range measurements.
The Major Tone PLL is updated every (13.1072 / 8) = 1.6384 ms.
Such an interpolation generates an error. Let’s call
the interpolated phase,
the phase error, T the
1.6384 ms period and the time between 0 and T when the phase is interpolated.
where
is the received Major Tone frequency, and
the emitted one.
The Taylor expression of the phase at is:
where R2(t) the rest such that (Lagrange overestimation):
The Major Tone Doppler and second order variation are deduced from the IF input frequency f(t) and the RF
beacon frequency FRF following:
The range delay error
is:
So
A typical Doppler rate of 1000 Hz/s and a typical second order Doppler variation of 10 Hz.s
-2
give a range delay
error lower than 6.1x10
-13
s, very lower than 1 ns.
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