COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
This document is the property of Safran Data Systems.
It cannot be duplicated or distributed without expressed written consent.
3.3.4.5. Impact of Phase Errors on Doppler Computing
If
is the error on the accumulated phase, the error on the computed Doppler is lower than
, where Ts is the sampling period.
So, the maximum error on the Doppler computing due to the linear interpolation on the second-order phase
variation is
.
For example, with a Doppler rate of 1000 Hz/s, the maximum error will be 0.43 Hz for a sampling period of 0.1 s
and 0.0043 Hz for a sampling period of 10s.
The relation between range rate and Doppler is:
, where f is the satellite carrier frequency, v
r
the radial velocity (range rate) and c the light celerity.
For a 2.2-GHz beacon, the corresponding range rate error will be 2.93 cm/s for a sampling period of 0.1 s
and 0.293 mm/s for a sampling period of 10s.
3.3.4.6. Sampling Period Resolution
3.3.4.6.1. Error Due to Computing
The accumulated phase and Doppler sampling is processed owing to an internal 64 bits - NCO running at T = 10
ms. The effective sampling period is:
where is the NCO phase increment. So the resolution on the period is
where is the error made on the phase increment computing (in this computing
is approximated by , and
is considered as ).
Due to double-float format limitations, e = 2
14
is higher than the possible error (11 bits come from the difference
between the 64 bits and the 53 bits mantissa of the double-float representation, on which up to 3 bits may be lost
in the computing process).
When Ts = 10s (worst case), the resolution is 6.8x10
-12
s.
This resolution is effective when the programmed sampling period is a value for which the floating representation
does not generate any error (examples: 10 s, 1 s or 0.125 s).
An error made on the sampling period generates an error on the Doppler estimation:
where f is the current IF frequency.
With a typical value of 70 MHz, the Doppler computing error will be 3.8 mHz with Ts = 0.125s.
To Next Page
Loading...