Safran CORTEX CRT Quantum, User Manual

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COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
© Safran Data Systems
This document is the property of
Safran Data Systems
.
It cannot be duplicated or distributed without expressed written consent.
Page 154
3.6.3.2.
Ambiguity Solving & Quality Factor
Ambiguity solving is performed during minor tones (ESA, ESA-like, Hybrid Ranging and USB tone standards) or
PN codes (ESA code standard) transmission. For the INMARSAT and LMCO standards, only raw phase-shift
measurements are delivered.
In the ranging transaction response message returned to the Ranging Client, the status Quality Factor provides
a confidence indication on the ambiguity solving (a value of 100 denotes correct ambiguity solving).
3.6.3.2.1. ESA, ESA-like, Hybrid Ranging and USB Standards
For these ranging standards, ambiguity solving consists in finding the propagation delay that best matches the
phase measurements on the minor and major tones. For every tone, the relation between the propagation time
and the phase measurement is given by:
∆𝜃
𝑖𝑑𝑥_𝑡𝑜𝑛𝑒
= (𝐹
𝑖𝑑𝑥_𝑡𝑜𝑛𝑒
× 𝜏)
𝑚𝑜𝑑1
with:
∆𝜃
𝑖𝑑𝑥_𝑡𝑜𝑛𝑒
: phase-
shift value measured on “idx_tone” tone, expressed in cycles
𝐹
𝑖𝑑𝑥_𝑡𝑜𝑛𝑒
: frequency of “idx_tone” tone in Hz
𝜏
: propagation delay in second
These phase-shift measurements take into account the Board and Ground corrections and the Doppler
compensation.
Once estimated the delay
𝜏̂ =
(𝐶𝑁
𝑀𝑅𝑇
+ ∆𝜃
𝑀𝑅𝑇
)
𝐹
𝑀𝑅𝑇
⁄
, where
𝐹
𝑀𝑅𝑇
is the Major Tone frequency,
𝐶𝑁
𝑀𝑅𝑇
is the
number of cycles on the Major Tone computed by the ambiguity solving, we define the ambiguity solving
quadratic error
𝐴𝑅𝑞𝑒𝑟𝑟 as (where 𝑁
𝑀𝑖𝑛𝑇
is the number of Minor tones):
𝐴𝑅𝑞𝑒𝑟𝑟 =
1
1 + 𝑁
𝑀𝑖𝑛𝑇
∑ [(∆𝜃
𝑖
− 𝐹
𝑖
× 𝜏̂)
𝑚𝑜𝑑0.5
]
2
𝑁
𝑀𝑖𝑛𝑇
𝑖=1
In the computing of Arqerr, for each minor tone, an a posteriori estimation error is computed as the difference
between the phase measured on this tone and the phase obtained from the estimated propagation delay
𝜏̂
.
The Quality Factor Q is defined as:
𝑄 = 100 − 200 × √𝐴𝑅𝑞𝑒𝑟𝑟
This Quality Factor will mainly depend on the noise level (S/No at RAU input) and on the un-compensated
ground or on-board non-linearity (if any). It depends also on the ranging standard, number of used minor tones,
and integration time on each minor tone.