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