Tuesday, September 27, 2016

Oscillator Comments Holding Area

A family of random walks is shown below - as would be obtained by "integrating" coin flips e.g. a head you move up, a tail you move down. Graph shows progress after 100 flips. The walk was repeated eight times to create the graphic below.































A "blizzard" of trials below illustrate a zero ensemble mean and a variance that grows with time.

































From DSTG "Bayesian Methods..." book.

















Statistical estimates from manual (and tedious) data extraction from the above figure:

mean ~ -6.5 Hz  standard deviation ~ 5.3 Hz

It is important to note that the flight time from Mumbai to Kuala Lumpur is a bit over five hours, so that figure 5.4 above represents essentially all of the BFO data from that particular flight. It is also important to note that statistics from all the flights of 9M-MRO looked at by the DSTG (some 20 flights in all) and summarized in Table 5.1 have an in-flight standard deviation of 5.5 Hz when outliers are included. See table 5.1 below. So, what makes figure 5.4 unique is not the standard deviation, but the mean of -6.5 Hz relative to an ensemble mean much closer to zero.

In fact, the DSTG comments relative to Figure 5.4 have more to do with the deviation from a mean close to zero and a structured bias. No comment was made relative to the standard deviation which leads one to the same conclusion above - that it was not considered abnormal.

"The bias used for the plot was obtained by analysing BFO measurements while the aircraft was on the tarmac. The residual error is clearly not zero-mean, and the mean varies with time."  




In fact, if one were to generate representative statistics for the BFO error for 20 flights the data might very well resemble the data below.





























The figure above strongly suggests that most previous analytics with highly constrained BFO errors may be suspect relative to terminal accuracy, and that the DSTG is probably correct in modeling flight paths with an emphasis on ground speed, track constraints, and BTO residuals.

The recent work of Iannello and Godfrey is among the first produced by "mainstream" analysts to relax the notion of a highly constrained BFO.

Iannello and Godfrey

See also the link below which supports the DSTG use of a nominal BFO sigma of 5Hz when computing the range of speeds and tracks at 19:40.

Midflight Speed

Afterthought

None of the above presents a challenge relative to the notion of the plane tracking South after the FMT or the hypotheses of a rapid rate of descent at 00:19. What it does challenge is the notion of accurately predicting where the plane actually went, and where the rapid descent took place.