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News report to date that FOUR different soundings (pinning) of the airplane's black box have been heard by search teams. Since common sense says that only three directional lines are needed to locate a point in space (via the triangulation method). The public may wonder as to why we still have not pinpointed the location of the plane crash. This is a reasonable question andperhaps a good occasion for a lesson in estimation (or more narrowly as to why the famed Kalman filter deserve the equivalent of a Nobel prize in Engineering–the Draper Prize - in 2008 http://blog.sciencenet.cn/blog-1565-14253.html). Here are my“explanations”:
1. Since my ability to draw three dimensional pictures in two dimension is limited, I shall try to do my explanation in two dimensions and assume we have only three soundings to workwith.
2. Sound waves do not travel in straight lines in ocean water depending on current and temperature. This introduces uncertainty in the directional angle).
3. Detection of distance via the strength of the sound in an ocean is not precise. There are all kind of noises from animate and inanimate objects to distort the sound in an ocean.
4. Because the pinning sounds do not travel far in ocean water, most of the sounds heard are near a small area which makes the directions of the sounds detected nearly the same.
5. Finally there is the issue of the authenticity of the sounds heard. But let us assume for the moment thatthey are all genuine.
Combining the above points #2-#5, we can visualize the following in two dimensions as illustrated in the below Figure.
The intersection area shaded by the black lines indicate the resultant area of search which is smaller than the vast ocean but can be still uncertain and relatively large (.Adding a third nearly parallel line will not help much. Extending this view to three dimensions, the intersection will be in the shape of a ball complicatingthe situation further. ).
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