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3.6.3.5. Doppler Rate Aid and Doppler Aid
3.6.3.5.1. Doppler Effects
The spacecraft radial motion relative to the ground station introduces a change on frequency, called Doppler
shift, both on the range tones and the radio frequency link carrier.
The two-way Doppler shift on the range tones is given by:
where:
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This formula indicates that, if the spacecraft velocity varies in time, the Doppler frequency shift is also time
varying. Its first-order variation is called Doppler Rate (radial satellite acceleration).
We can also define the two-way phase error ��
phase of the transmitted tone and the phase of the received one:
The spacecraft range is directly estimated from this quantity, as:
3.6.3.5.2. Carrier Doppler Shift in Coherent Mode
In the case of a coherent transponder, the Doppler shift affecting the carrier frequency is defined by:
This relation is obtained similarly as the ranging tone one, except that it is necessary to consider that the up-link
carrier differs from the down-link carrier. We can note that the major and minor tones undergo the same Doppler
effect as the carrier frequency. The ratio between the carrier Doppler shift and the tone Doppler shift is then:
where m and n are integers so that:
with:
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© Safran Data Systems
COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
( �� ) = ̂ ��
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Tone Doppler shift
Carrier Doppler shift
Major or minor tone transmitted frequency
Major or minor received frequency
Radial velocity
θ
tone
r ̂ ( t ) =
f
( t ) =
rx
ground station received frequency
ground station transmitted frequency
This document is the property of
It cannot be duplicated or distributed without expressed written consent.
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(��), that corresponds to the difference between the original
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2r(t)
(t) = ̂ − 2πf
tx_tone
c
−c
θ
(t)
tone
2πf
2
tx_tone
( t )
n
n
v
r
f
− 2
f
tx
tx
m
m
c
f
f
dop_tone
tx_tone
=
n
f
f
dop_carrier
tx
m
f
n
rx
=
f
m
tx
Safran Data Systems
.
Ref.
DTU 100042
Is.Rev.
5.17
Date:
Dec.
03, 2021Sept. 30, 2021
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Page 159
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