Journal of Accident Investigation

A MATHEMATICAL CROSS-CORRELATION FOR TIME-ALIGNMENT OF COCKPIT VOICE RECORDER AND FLIGHT DATA RECORDER DATA
Figure 3. Example of running cross-correlation (bottom) of FDR on-key/off-key.
Cross-correlation results for a real-world case are illustrated
graphically in figures 4 – 8. The individual FDR and CVR
on-key/off-key data vectors are shown in figures 4 and
respectively. The x-axis in both figures represents elapsed
time into the respective recording. For the FDR data in
figure 4, this corresponds to the SRN. For the CVR data in
figure , this corresponds to elapsed time in seconds, since
the on-key/off-key data was re-sampled at 1 Sa/s to make it
compatible with the FDR on-key/off-key data. The y-axis in
both figures represents the Boolean variable for the microphone
on-key/off-key event, where a “1” indicates that the microphone
was keyed-on at the indicated sample time, and a “0” indicates
that the microphone was keyed-off. Figure 6 shows the result of a
discrete cross-correlation between these two vectors, indicating
that the best match occurred for n = 1763 lags. Figures 7 and
8 show the CVR data shifted by this amount and plotted atop
the FDR data to illustrate the goodness of the match. Note that
some on-key events are not simultaneously reflected in both data
vectors. This will often occur for extremely short transmissions,
where the microphone was keyed-on for less than 1 second.
In this case, the data are effectively undersampled at 1 Sa/s,
and so instances will occur where the FDR fails to register an
on-key/off-key event. Similarly, the algorithm gathering and
re-sampling the CVR data may misidentify the presence or
absence of an external transmission. These errors, unless
extreme in number, will not invalidate the cross-correlation.
Such mismatches will reduce the magnitude, and cause an
apparent broadening of, the correlation peak. To first order,
they will not change the number found for n. Once the number
of lags is known, the time shift in seconds required to transform
from FDR-time to CVR-time may be easily determined. This
will yield the constant, C, required for any transform between
elapsed time in each unit.
At this point, all we have done is to obtain the offset between
elapsed time in the CVR and elapsed time in the FDR. This
may or may not be sufficient to specify the required transform,
depending on the behavior of the time-base in each unit. The
exact form taken by this transform will fall into three broad
classes:
the time-base in each unit operates at the same
constant rate,
the time-base in each unit operates at a different
constant rate, or
the time-base operates at a different and variable
rate in one or both units.
For the first situation described above, the transform given
by Eq. (1) applies and a determination of C suffices to solve
the problem. For the second situation described above, the
transform given in Eq. (2) may be employed. This requires
the calculation of a slope, b, reflecting the difference in rate
between the two time-bases. For the third situation, which
may occur in the event of a malfunctioning tape based CVR
unit, the transform will take on a more complex, possibly
non-analytical, form.
NTSB JOURNAL OF ACCIDENT INVESTIGATION, SPRING 2006; VOLUME 2, ISSUE 1 47
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