Aerospace and Electronic Systems Magazine February 2018 - 26
MH370 Burst Frequency Offset Analysis
over the satellite is via bursts, which are scheduled to arrive at the
GES at a specified time and a given frequency. As explained in [1]
and [2], communications from multiple users are coordinated by
the allocation of different time and frequency slots to each user.
This is done without knowledge of individual AES locations or
precise knowledge of the satellite location. Therefore, messages
from a given AES might not arrive at the GES at exactly the expected time and generally would arrive slightly later. The difference between the expected time of arrival (based on a nominal
assumed position for the satellite and the AES) and the actual time
of arrival is called the burst timing offset (BTO). The BTO is a
measure of how far the aircraft is from the subsatellite position.2
The relative velocity between the satellite and the AES, as well
as between the satellite and the GES, leads to a Doppler frequency
offset on the signals received at the GES. Coupled with small frequency offsets inherent in the reference frequency oscillators in
the AES, satellite, and GES, this results in a net difference between
the expected and the actual frequencies of the signal presented to
the modem in the GES for a given user. Frequency compensations
applied onboard the aircraft (aircraft-induced Doppler precompensation) and at the ground station (enhanced automatic frequency
correction, which uses the reference signal transmitted from a
reference station in Burum, the Netherlands), [1] and [2] serve to
reduce the possible difference between the expected and the actual
frequencies of the messages received from the aircraft. The residual difference between the expected frequency of each communications burst and the actual received frequency is called the BFO.
Figure 2.
Histogram of BFO errors for 20 flights of 9M-MRO before MH370
(reproduced from Figure 5.5 of [2]). The mean and standard deviation
for the distribution are 0.18 and 4.3 Hz, respectively [2].
BFO noise. The noiseless component of the BFO is defined in [2]
as the sum
hkBFO ( x k , s k ) = ΔFkup ( x k , s k ) + ΔFkdown ( s k )
+ δ f kcomp ( x k ) + δ f ksat ( s k )
+δ f
AFC
k
(1)
( sk ) + δ f ( xk , sk ) ,
bias
k
where
REVIEW OF BFO STATISTICS
Based on 20 previous flights of 9M-MRO in the week leading up
to the accident flight (see [2] for further details), a histogram was
produced for the difference between the predicted BFO (based on
known details of the plane and the satellite's position and velocity)
and the measured BFO (based on Inmarsat ground-station logs). This
difference (i.e., predicted minus measured) is called the BFO error.
The histogram of the BFO error is shown in Figure 2, along with a
Gaussian distribution fit line. It can be seen that the distribution is
somewhat Gaussian. The standard deviation of the BFO error was
found in [2] to be 4.3 Hz. While it is reasonable to apply bounds on
the possible BFO error based on ±3 standard deviations, as was done
for the approximate analysis described in [6], for the purpose of the
descent analysis presented later in this article, it is assumed the BFO
error is strictly bounded on the larger interval [−28, +18] Hz, which
corresponds to the bounds of all 2,501 observed valid3 in-flight BFO
error values available from the preceding 20 flights of 9M-MRO.
EFFECTS OF AIRCRAFT POSITION AND VELOCITY ON THE BFO
MATHEMATICAL DESCRIPTION OF THE BFO
In [2], the BFO is defined mathematically at time step k as the sum
of a noiseless component hkBFO and a scalar wkBFO that represents the
2
3
26
The subsatellite position is the point on Earth directly below the
satellite.
One outlier was removed, as explained later in this article.
C
xk denotes the state vector of the aircraft;
C
sk denotes the state vector of the satellite;
C
ΔFkup ( x k , s k ) is the uplink (aircraft to satellite) Doppler shift;
C
C
ΔFkdown ( s k ) is the downlink (satellite to ground station) Doppler shift;
δ f kcomp ( x k ) is the frequency compensation applied by the
aircraft;
C
δ f ksat ( s k ) is the variation in satellite translation frequency;
C
δ f kAFC ( s k ) is the frequency compensation applied by the
ground-station receive chain; and
C
δ f kbias ( x k , s k ) is a slowly varying bias because of errors in the
aircraft and satellite oscillators and processing in the SDU.
By treating the bias δ f kbias ( x k , s k ) as a constant determined at
the source tarmac for any particular flight, as was done in [2] for
MH370, any small time-varying component of the bias during a
particular flight can be considered part of the BFO noise (this was
done when compiling the results used to obtain the BFO error histogram shown in Figure 2). Details regarding the terms δ f ksat ( s k )
and δ f kAFC ( s k ) are provided in [1]. Tabulated values of the sum of
these two terms were provided by Inmarsat to the MH370 Flight
Path Reconstruction Group to use in estimating the likely trajectory
flown. These two terms depend on the satellite state sk only, not on
the aircraft state xk. Moreover, the downlink Doppler ΔFkdown ( s k )
does not depend on the location or velocity of the aircraft and can
IEEE A&E SYSTEMS MAGAZINE
FEBRUARY 2018
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