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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 ��
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 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 ����
So
A typical Doppler rate of 1000 Hz/s and a typical second order Doppler variation of 10 Hz.s
error lower than 6.1x10
© Safran Data Systems
COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
��
( �� + �� ) = �� ( �� ) + �� [ ��
����������
�� ( �� + �� ) = �� ( �� ) + [ ��
����
‖ ��
(�� + ��) ‖ ≤
2
��
(�� + ��) = ��
������
��
����
'
��
( �� ) =
��
����
��
����
(��) is:
������
����
2
1
��
‖ ����
( �� + �� )‖ ≤
[
������
��
2
����
-13
s, very lower than 1 ns.
This document is the property of
It cannot be duplicated or distributed without expressed written consent.
the interpolated phase, ��
����������
(��) − ��
����
����
the emitted one.
����
] × �� + ��
(��) − ��
'(��) ×
����
����
3
��
× sup
‖ ��''(��) ‖
3!
��∈]��,��+��[
2
��
'(��) ×
��
(�� + ��)
����
2
2
��
����
'
''
( �� )
��
( �� ) =
����
��
����
��
(��)
������
( �� ) =
������
��
����
3
��
'
‖ ��
( �� )‖ +
× sup
× sup
6
��∈]��,��+��[
Safran Data Systems
.
Ref.
DTU 100042
Is.Rev.
5.17
Date:
Dec.
03, 2021Sept. 30, 2021
the phase error, T the
������
]
2
��
��
(�� + ��)
2
2
��''(��)
‖ ��''(��) ‖ ]
��∈]��,��+��[
-2
give a range delay
Page 164
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