.
Note the 4 satellites are numbered 2 through 5.
We then applied a cross-correlation to the unsmoothed data.
For example, when we cross correlated the event on satellite 2
The software used is documented here.
Here is a plot of the event:
.
Note the 4 satellites are numbered 2 through 5.
We then applied a cross-correlation to the unsmoothed data.
For example, when we cross correlated the event on satellite 2
against the data from satellites 2, 3, 4, and 5 we found this:
Please note that the cross correlations are normalized so that the values must lie in the interval [-1,1]. (1 is a perfect match, and -1 is one function is the negative of the other.) The CrossCorrelation is documented here.
We next took the data, and removed the mean, and then applied a Butterworth Filter. (The theory of the Butterworth filter we used is here.)
After the filtering, the data looked like this:
We then extracted the events for each of the satellites:
| Satellite | Event Range |
|---|---|
| 2 | Sample 1500-2500 |
| 3 | Sample 1500-2500 |
| 4 | Sample 1250-2250 |
| 5 | Sample 1500-2500 |
(The results will confirm this eye-ball estimate. The event occurs earlier on Satellite 4.)
Drum Role Please
The results are in the next four figures. Each plot is event x=2,3,4,or 5 cross correlated with the filtered data from satellites 2, 3, 4, and 5. So for instance, if we are using event 3 against data 2, 3, 4, and 5, we would expect the highest cross correlation to occur on data 3. That is indeed the case. Here are the plots.
In each case the peak occurs when the event is measured against itself. Also the quality of the events can be assessed:
The unfiltered data has a peak of .25 versus a much better .55 for the filtered data.
Finally when we ran the cross correlation, we recorded the sample number of the peak. Thus we have this table:
| Event | Data 2 | Data 3 | Data 4 | Data 5 |
|---|---|---|---|---|
| 2 | 0 | 0 | 0 | 0 |
| 3 | -43 | 76 | -47 | -58 |
| 4 | 51 | 115 | 52 | 35 |
| 5 | -135 | -50 | -129 | -152 |
As you can see, the data (with the exception of Event 3 versus Data 3) are consistent.
In addition we see the lag of event 4 is evident. This confirms our eyeball estimate.
Of course, this then leads to the puzzle of how the satellites are configured. But with this information and with the location of the satellites we should be able to find out the direction of the incoming wave.