Figure 2。 FDR sampling example, where ‘‘Key’’ indicates the microphone is transmitting。

necessary degrees of freedom in the mathematical model that were discovered during the TDD development process。 The method used to perform the alignment is as follows。 Given a series of CVR radio  transmissions, (CVRs, CVRe)i  m and FDR Microphone keyings, (aFDRs, aFDRe)j n, where s and e indicate start and end times, the two   series   are   cross   joined   to   create   m   x   n   trial

displacements, [Si m,j  n], according  to

2 aFDR1 3

          6 aFDR2 7

The result of the mixed binary, linear program is an offset, S, which is the one S out of all the m x n S9s that maximizes the total area of overlap of the two series of transmissions。 This result is then used in a dynamic programming loop to create the aligned transmissions in a format suitable for the Step 2-Optimization。 The pseudo- code for the loop is shown in Listing  1。

Listing 1

For (each CVR transmission)

。CVR1 CVR2 。。。 CVRi 。6 7

6 。 7

ð1Þ

For (each FDR transmission)

If (CVR transmission length 。 aFDR

4 5

aFDRJ

where CVR and aFDR represent the midpoint of the transmission, s + (e2s)/2。0 and the mathematical operation performed on each cross join is simply,    aFDR2CVR。

The array of trial displacements are used in a mixed binary, linear programming model, consisting of m x n binary decision variables, SMatchij (where (i,j) m,n) with one constraint such that one and only one SMatchij  can  be

1。 The objective function is designed to maximize the overlap of the CVR and FDR transmissions and is expressed as

Max

transmission length)

If (aFDR midpoint is contained within (S + CVRs) and (S + CVRe))

{Output Line Match}

If (aFDR transmission length 。 CVR transmission length)

If ((S + CVR) midpoint is contained within aFDRs and aFDRe)

{Output Line Match} End FDR For

End CVR For

Each output line of the matching step consists of six

numbers, as shown in Listing 2。 The CVR times in Listing 2 are the CVR times provided as input to the step 1 model。 The

FDR outputs are both the adjusted FDR times and the raw FDR times (the FDR times provided as input to the model)。

m SMatchi,j

where the farea is a custom function to calculate the pseudo- area of overlap for each of the conditions expressed in Figure 3。 For example, the pseudo-area of overlap for case 4 from Figure 3 is defined  by

Listing 2

CVRs  CVRe  aFDRs  aFDRe  rFDRs  rFDRe

The dynamic programming step also lists those points that did not find a matching CVR or FDR point。 This   can

。 。 。。2

sðlÞ i,j eðkÞ 

happen   if  the   CVR   analyst   did  not  hear   or  code   a