Tuesday, January 5, 2016

Things We Do Not Know We Don't Know

"There are things we do not know we don't know. So when we do the best we can and we pull all this information together, and we then say well that's basically what we see as the situation, that is really only the known knowns and the known unknowns."

- Donald Rumsfeld

I am not now, nor have I ever been, a fan of Rumsfeld. However, even a blind squirrel finds an acorn once in awhile (my standard admonition to my direct reports on those occasions when they actually did something useful). So it goes, I believe, with the Rumsfeld observation above. Subsequent commentators, while agreeing with Rumsfeld, have described the language used as "tortured". I certainly agree with that as well.

Problem solving often resembles a random walk. As new information becomes available and old information is reviewed from a different perspective, we gradually home in on the truth. An appropriate metaphor is driving down the road to Solutionville while bouncing off the guard rails. As Jeff Wise implied recently, and I feel it also, we (independent investigators) are converging on the realization that we were perhaps more confident about our conclusions relative to an MH370 terminus than the information we had at hand warranted. 

Consider a trivial example - flying from the 19:40 arc crossing to the Cocos. Of course, the location of the 19:40 arc crossing is subject to debate, and I have it further North than most everyone else (red line in Google Earth graphic below)





































The spreadsheet describing two different ISAT solutions is presented below. As is my custom, the upper part is the calculation of a priori Doppler residuals - those elements such as satellite to Perth Doppler and BFO bias that do not change with flight path. Below that are shown two solutions for aircraft related Doppler. The middle part is for a constant heading, but variable speed solution (speed is selected to minimize Doppler residual at the arc crossings). The lower part is for constant heading and constant speed (the constant speed was once again selected to minimize residuals using a least squares metric).




The speed varying solution approaches perfection with respect to BFO residuals. The constant speed solution has residuals well below my own estimated bound of +/- 5Hz and the Inmarsat suggested bound of +/- 7Hz. In both cases the BTO errors are within the ATSB calculated two sigma limit. 

The point here is NOT to suggest that the plane flew in a straight line (or any other path) to the Cocos, but it could have if one relaxes the ISAT data constraints or abandons the notion of fixed speed and heading or both. The purpose of this exercise is to raise the following questions:

1> Are we over-constraining our ISAT calculations?

2> What are reasonable bounds on residual BFO errors?

3> What are reasonable bounds on residual BTO errors?

4> Does a straight line and constant speed path deserve greater respect than a curved path with varying speeds?

I don't have any answers, but the questions seem legitimate to me in the context of trying to probe the unknown unknowns. It would be useful (to me, at least) if we had some degree of convergence on the answers to these questions. 

Was the PIC heading to the Cocos before having a change of heart and diverting Eastward?  Stay tuned for another ramble using a flight path to waypoint ketiv (a sort of crossroads in that region) before heading directly to CI (another waypoint). This latter exercise to address Jeff's "pesterings" on waypoint navigation. 

Ah, nope. Could not make ketiv work. Also could not make a path from the Cocos back toward CI work out to my satisfaction, and I have a pretty low bar relative to most other ISAT data twiddlers.