Impact Of Phase Errors On Doppler Computing; Sampling Period Resolution; Error Due To Computing - Safran CORTEX Series User Manual

A typical second-order Doppler variation of 10 Hz.s
a phase error lower than (4.1610
-3
(41.6 + 6.2510 ) Hz for a sampling period Ts of 10 s.
3.3.10.8

Impact of Phase Errors on Doppler Computing

If 
is the error on the accumulated phase, the error on the computed Doppler is lower than
err

2
1
 err
, where Ts is the sampling period.
2 32 Ts
So, the maximum error on the Doppler computing due to the linear interpolation on the second-order
DR 
phase variation is 
Ts
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 10 s.
The relation between range rate and Doppler is:
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.
3.3.10.9

Sampling Period Resolution

3.3.10.9.1

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:
So the resolution on the period is
the phase increment computing (in this computing Ts
<<< incr).
Due to double-float format limitations, e = 2
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 = 10 s (worst case), the resolution is 6.810
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:
   
  
) ( t ( t Ts ) ) ( t ( t


Ts Ts
where f is the current IF frequency.
With a typical value of 720 MHz, the Doppler computing error will be 39 mHz with Ts = 0.125 s.
© Safran Data Systems – IMP000074 e14r1
HIGH DATA RATE RECEIVER
HDR-4G+ USER'S MANUAL
-3
+ 6.2510
 
2
T
.
2

  1
2 64 T
incr
14

Ts )
 
  
) ( t ( t Ts )

Ts ( Ts
-2
and third-order Doppler variation of 10
-9
) Hz for a sampling period Ts of 0.1 s, and lower than


f
2 v

r
, where f is the satellite carrier frequency, v
f c
2 64
 
Ts T where incr is the NCO phase increment.
eff
incr

 
2 64 T e Ts
 1   
e

incr e incr 2 2 64
is approximated by Ts, and e is consided as
eff
is higher than the possible error (11 bits come from the
-12
s.
 
 
 
) ( t ( t Ts )
 


) Ts Ts
This document is the property of
It cannot be duplicated or distributed without expressed written consent.
Ref. DTU 100782
Is.Rev 3.5
Date: June 1, 2021
-4
2
where e is the error made on

T
 

  
Ts
t f
,
2
Ts
Safran Data Systems
.
-3
Hz.s give
r
Page 117