My first pass reaction is similar to the reaction I had to the “Bayesian Methods…” book that preceded it. References below refer to the paper.
When you create a graphic such as figure 2 – “Histogram of BFO Errors…” you are stepping onto a slippery slope. You are subconsciously (perhaps even consciously) making the assumption that the ensemble mean and variance (from the data collected from the 20 previous flights) would yield the same statistics as if you were to collect the same data from a single flight 20 times as long.
Without stating it as such, Holland makes the implied assumption that the oscillator behavior is stationary and ergodic. Stationary in this context means that the mean and variance do not change over time. A process is said to be ergodic if its statistical properties can be deduced from a single, sufficiently long, random sample of the process. The reasoning is that any collection of random samples from a process must represent the average statistical properties of the entire process.
Unfortunately oscillators do not behave in this manner. If an oscillator is turned on and drifts off 5Hz over some time interval, it does not imply that the oscillator is more likely to drift back to zero than it is to keep drifting in the same direction that produced the 5Hz error. Figure 5.4 of the “Bayesian Methods…” book is a good example of the behavior I am referring to taken from a previous flight of the accident aircraft. A link to Figure 5.4 is provided below.
It is clear that the data in Figure 5.4 does not have a zero mean nor does it appear likely that the data will regress to a zero mean if the flight were to continue. I made no attempt to estimate the true mean and variance of the data points in Figure 5.4. It would have been very helpful if Holland included the raw data from the 20 previous flights as an appendix to his paper. My guess is that the 20 previous flights would look very much like the flight shown in figure 5.4 with smaller excursions on both sides of zero error (the ensemble mean in Holland’s figure 2 is near zero).
We are aware that the oscillator behaviour is strictly speaking, not stationary and ergodic. Fig. 5.4 from the DST Group book indeed indicates this. The first paragraph below that figure states “The mean bias is different between flights and even within a single flight there is evidence of structured variation.” The next paragraph in the book explains that the structured bias variations happen over a timescale of minutes rather than hours, but for MH370 the values are only available approximately hourly, and that is why we did not use a coloured BFO noise model in our trajectory analysis.
What is this data telling us? In my view it is telling us that the plane sure enough flew South, but the ground track angle is not reliably deducible from the BFO values.
Figure 4 from the article provides an indication of the degree of variation the BFO implies with respect to the track angle at different times during the flight. Particularly towards the end-of-flight, the BFO is seen to be a less effective discriminator of ground-track angle. However, as noted, the DST Group Book takes that into account. Please refer to last two sentences of the second last paragraph on page 4 of the article and the referenced figure in the book.
I was a bit disappointed that Holland did not spend more time on the 18:25 reboot. The curious thing, if we believe the ground speed derived using the cell phone connect and the radar data (the radar data also providing a good estimate of location and ground track at 18:25) is why the BFO is virtually error free. If power had been removed from the AES oscillator prior to this reboot, one would expect a significant residual error. Luck perhaps? Certainly not impossible, but I am suspicious.
This was indeed considered by the author of the article, and is discussed in the last line of the left column of page 6 of the article, and the first 14 lines of the right column on page 6 of the article.
