3.3.4.3. Interpolation Process
In some cases, when the sampling rate and the generation rate are asynchronous, a linear interpolation is
applied to provide the accumulated phases at the required sampling frequency.
Such an interpolation generates an error. Let's call
10-ms period and
the time between 0 and T when the phase is interpolated.
The Taylor expression of the phase at
where D(t) is the input Doppler and R2(t) the rest such that (Lagrange overestimation):
So
For instance, a Doppler rate of 1000 Hz/s with a second-order Doppler variation of 10 Hz.s
lower than (0.0125 + 3.33x10
In most cases, user would not use cranky values for the sampling rate. Thus, no interpolation would be applied,
because accumulated phase is generated synchronously with the sampling rate dates.
© Safran Data Systems
COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
( + ) = ( ) +
+
is :
( + ) = ( ) + [ + () ] × + '() ×
‖
( + ) ‖ ≤
( + ) =
( + ) − ( + ) =
'
( )
=
× ( − ) +
‖
( + )‖ ≤
-6
) cycle.
This document is the property of
It cannot be duplicated or distributed without expressed written consent.
the interpolated phase,
[ ( + ) − ( )]
×
‖ ''() ‖
!
∈],+[
[ ( + ) − ( )] − [ ( + ) − ( )]
×
( + ) −
'
‖
( )‖ +
×
×
∈],+[
∈],+[
Safran Data Systems
.
Ref.
DTU 100042
Is.Rev.
Date:
Dec.
03, 2021Sept. 30, 2021
the phase error, T the
( + )
( + )
‖ ''() ‖
-2
gives a phase error
5.17
Page 49