Progress on Finding a Pinger Location

  I made a little progress yesterday on finding a pinger's location based on the ping intensity data in the simplified problem previously mentioned. The first result is that the pinger's depth for an assumed position, z₀, can be determined from the intensity data, a.

A grid size of 4 km with 3 points on each side was assumed. The second result is that the gradient of the intensity data can be found using a linear fit and that gives a direction for the source.

The matrix M just contains information on the relative positions for the data points. The gradient for 1/a was found since its function is a little simpler. There is a total of 9 data points in the grid used. The computed direction was off by about 1.6 degrees. Doing a quadratic fit allows one to get a better estimate of the direction relative to the corner used as the reference point.

So in theory it is possible to locate a pinger using just the intensity data. The reference point and direction gives one line of position for the location the source of the pings. A second set of data for an area some distance away would be needed for another line of position and their intersection would be an estimate of the pinger's location. In the real world the data is corrupted by errors but using a large number of data points can improve results. If enough ping data was collected it still may be possible to determine location of the black boxes of Flight 370.