tcvr 5 b*tfdr + C

where b represents the timebase rate difference between the CVR and FDR (Gregor, 2006, p。 5)。 This problem is solved through a least squares regression。 The alignment optimi- zation problem can grow more complex when one considers variations in b, for example when the device timebase varies due to mechanical reasons, power fluctua- tions, or software anomalies。

Research Methodology

The general problem is the synchronization of one or more series of events, recorded at different sample rates, with different areas of emphasis and importance, with different tolerances, r, in the sampling timebase, and a different number of events in the timelines。 The problem is delimitated for this research to consider the synchroniza- tion of two series of events, recorded at different sampling rates, all of equal importance, where the timebase tolerance, r is assumed to be r 5 0。 The r 5 0 assumption means, for example, that 8,000 seconds in the CVR must be 8,000 seconds in the FDR: there is no allowance for different timebase rates within the series of events。 One timeline represents CVR microphone keyings recorded in relative time (i。e。, the start of the timeline is 0 seconds), and another timeline represents FDR microphone keyings, represented in clock time, or Greenwich Mean Time (GMT)。 CVR data will be expressed in elapsed seconds and FDR data expressed as seconds after midnight。 For simplicity, FDR sample data will be formed such that no GMT times cross midnight, i。e。, all times will be greater than zero。

A test-driven development (TDD) approach was used to develop the initial theoretical model。 Kent Beck, author of Extreme Programming Explained (2000), defines TDD as an approach to software development where tests are written before code。 With an appropriate number of purposively created test scenarios, when all the scenarios create the intended results, the coding effort is completed (Beck,  2000)。  Following  the  spirit  of  a  TDD approach,

many test cases were written before creating the final model and additional test cases were written to further exercise and explore the model as experience was gained from prior runs。

The alignment of the CVR and FDR recordings is accomplished in two steps: matching and optimization。 Matching involves aligning the CVR and FDR time series where a microphone keying on the CVR is matched with the identical microphone keying on the FDR。 Once microphone keying events have been matched, the exact alignment of each time series is optimized。 The second optimization step is necessary because, as will be shown, the matching step only tries a discrete number of trial offsets to align the two series of events; optimization is necessary to try a continuum of  offsets。

Step 1 – Matching

In step 1, two series of events are matched。 Specifically, the first series consists of start and stop times for CVR radio transmissions。 The second series consists of start and stop times from an FDR sampling based on microphone keyings。 It is assumed that both series are a sampling of the same set of events; however, each series has a different time reference and different sampling accuracy。 As shown in Figure 1, the intent is to shift the time frames until the patterns of events are in phase, i。e。,  aligned。

During the course of TDD, it was discovered that pre- treatment of the FDR start and end times was necessary to properly execute both step 1 and step  2  processing。 Figure 2 shows the nature of FDR sampling。 Since the FDR only samples once per second, the transmission represented in Figure 2 by samples 2 and 3, may have begun anywhere after sample 1 and ended anywhere before sample 4。 As such, the model allows for input of the FDR one second sampling rate and creates adjusted FDR start and end times。 The adjusted start time is created by subtracting 。999 seconds from the provided start time; the adjusted end time is created by adding 。999 seconds to the provided end time。 This constant is added or subtracted because the transmission could have occurred at any time within the one second。 As the transmission start or end occurred at some point within the recorded second, to determine the maximum range where the transmission occurred, the 。999 seconds expands the window to the most extreme possibility。 This creates two series for the FDR, represented as rFDR and aFDR, raw and adjusted, respectively, as shown in Figure 2。 These times provide