JOSEPH GREGOR Figure 1. Example <strong>of</strong> running cross-correlation (bottom) <strong>of</strong> FDR on-key/<strong>of</strong>f-key data vector (top) with CVR on-key/<strong>of</strong>f-key data vector (middle) for n = 0. Figure 2. Example <strong>of</strong> running cross-correlation (bottom) <strong>of</strong> FDR on-key/<strong>of</strong>f-key data vector (top) with CVR on-key/<strong>of</strong>f-key data vector (middle) for 0 ≤ n ≤ 530. 46 NTSB JOURNAL OF ACCIDENT INVESTIGATION, SPRING 2006; VOLUME 2, ISSUE 1
A MATHEMATICAL CROSS-CORRELATION FOR TIME-ALIGNMENT OF COCKPIT VOICE RECORDER AND FLIGHT DATA RECORDER DATA Figure 3. Example <strong>of</strong> running cross-correlation (bottom) <strong>of</strong> FDR on-key/<strong>of</strong>f-key. Cross-correlation results for a real-world case are illustrated graphically in figures 4 – 8. The individual FDR and CVR on-key/<strong>of</strong>f-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/<strong>of</strong>f-key data was re-sampled at 1 Sa/s to make it compatible with the FDR on-key/<strong>of</strong>f-key data. The y-axis in both figures represents the Boolean variable for the microphone on-key/<strong>of</strong>f-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-<strong>of</strong>f. Figure 6 shows the result <strong>of</strong> 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 <strong>of</strong> the match. Note that some on-key events are not simultaneously reflected in both data vectors. This will <strong>of</strong>ten 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/<strong>of</strong>f-key event. Similarly, the algorithm gathering and re-sampling the CVR data may misidentify the presence or absence <strong>of</strong> 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 <strong>of</strong>, the correlation peak. To first order, they will not change the number found for n. Once the number <strong>of</strong> 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 <strong>of</strong>fset 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 <strong>of</strong> 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 <strong>of</strong> 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 <strong>of</strong> a slope, b, reflecting the difference in rate between the two time-bases. For the third situation, which may occur in the event <strong>of</strong> 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 1. 2. 3.
- Page 1 and 2: National Transportation Safety Boar
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