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3.6.14. Ranging Performance Vs Noise & Doppler
Ranging tones reception (and demodulation for the minor tones) is performed by a 2
programmable loop bandwidth (2Bn = 0.1 to 8 Hz for all tones) allows to cope with any mission requirements
(launch, transfer orbit or station keeping operations) or any type of spacecraft (LEO, GEO). Use the following
formulae to calculate the performances of the CORTEX CRT Quantum in the presence of noise and Doppler rate
(in radian):
And in case of PN Codes (in radian):
With:
2��
= ��
(�� +
��
��
��
: Standard deviation on the major tone
2��
: Bi-lateral loop bandwidth
��
��
: Doppler rate (in Hz/s)
��
: Damping factor (0.7)
��
: Loop pulsation (in radian/second)
��
��/��
: Signal-to-Noise ratio at RAU input (power ratio)
0
��
: In-phase correlation percentage (Major tone; PN sequence)
����
= 0.9544 for JPL, 0.9387 for T4B and 0.6274 for T2B
Example: ��/��
= 38 dB.Hz, R = 0.007 Hz/s on the major tone. The degradation of the measurement on the major
0
tone vs the loop bandwidth is:
L
B
OOP
ANDWIDTH
1 Hz
2 Hz
4 Hz
8 Hz
© Safran Data Systems
COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
1
)
4��
(2B
)
N
Table 31: Ranging Performances with Noise & Doppler Rate
This document is the property of
It cannot be duplicated or distributed without expressed written consent.
2����
��������
=
��������������
2
��
��
2��
��
��
= √
����������
��
2
��
0
1
2��
��
��
=
����������
√
��
��
����
2
��
0
Noise
0.51°
0.72°
1.01°
1.44°
Safran Data Systems
.
Ref.
DTU 100042
Is.Rev.
5.17
Date:
Dec.
03, 2021Sept. 30, 2021
nd
-order digital PLL. The
Bias
Doppler
2.80°
0.70°
0.18°
0.04°
Page 200
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