BTO Error Scatter Plot

From "Bayesian Methods..." page 27. The computed standard deviation value of these R1200 samples is 29 sec. So 4-sigma would be ~120 usec.  At least 11 samples below exceed 4-sigma.

A scatterplot of 30,000 Gaussian distributed samples was created and is shown below. The probability of a 4-sigma sample is a little over one in 15,000. It is not known how many samples are in the DSTG BTO scatter plot, but it is surely not more than a thousand or so. In the 30,000 Gaussian sample below only one sample exceeded 4-sigma and the 3-sigma values are in the range of 3 in 1,000 samples. The probability of a 3-sigma value is about one in 370.

So basically the BTO is not strictly Gaussian distributed, and large BTO values are over represented in the sampled data.

MH370 Position at 18:25:27

This document...

...has this to say about the 18:22:12 radar position.

On this page.

This location is 6.6N 96.3E (I use an accuracy of tenths of a degree because that is what the data merits, IMO.)

Based on the time of the cell registration near Penang and the distance to this last radar point the aircraft is traveling at an average speed of ~500knots.

If that speed and track is maintained for another ~3.5 minutes a position of 6.8N 95.9E is reached. This position is the position the BTO ring at 18:25:27 crosses N571. The BFO of ~142Hz, while not understood relative to its accuracy near a logon, is compatible with the track of 296T (direction of N571), the location of 6.8N 95.9E, and the speed of 500knots.

Data Used by the DSTG in "Bayesian Methods..."

Any BTO difficulty between 18:25:27 (12520us) and 18:28:06 (12500us) is not discussed in the text. The time separation is actually 2 minutes and 39 seconds. At 500 knots the aircraft would have traveled about 22 nautical miles (41 kilometers) essentially toward the sub-satellite point. This would involve a range change to the satellite of about 4 kilometers. Well within the BTO measurement error.

Vector Distances at 18:25:27 and 18:28:06 @296T 500knots

satellite to GES distance at 18:25:27

39271.5 km

satellite to GES distance at 18:28.06

39271.9 km

satellite to aircraft at 18:25:27 (6.8N 95.9E 30000')

36903.2 km

satellite to aircraft at 18:28:06 (7N 95.6E 30000')

36885.5 km

39271.5 + 36903.2 = 76174.7 km (total distance aircraft to GES @18:25:27)

39271.9 + 36885.5 = 76157.4 km (total distance aircraft to GES @18:28:06)

change in distance 18:25:27 to 18:28:06 = 17.3 km (round trip 34.6 km)

34600 meters / C = 115 usec

Looking Again - Another Way

Use an 18:22:12 point of 6.6N and 96.3E (precision adequate for the 10nm past MEKAR description)

Propagate path at 296T and 500knots to 18:28:06.

Position is 7.158N 95.558E

satellite to GES at 18:28:06 = 39271.9 km

satellite to aircraft at 18:28:06 = 36884.1 km (WGS 84 used for lla to xyz)

total distance = 76156 km (2x total distance = 152312 km)

BTO = 12379usec (using equation(1) in Inmarsat paper  page 6)

measured BTO = 12500usec

BTO error = 121usec  (error standard deviation is 29usec)

Conclusion is that 296T 500knot from 18:22:12 location does not work. Or maybe not. See post above on the error statistics.

Full Response from DST MH370 Search Team

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.

http://tmex1.blogspot.com/2017/02/from-bayesian-methods.html

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.

Turnover Point OCXO

The labeled point is the target set point for the oven temperature control loop.

Crystal Oscillator Frequency vs Temperature

Correlations??

Doppler Residual (Fup + Fcomp) vs Time

Ground track = 169 degrees

Ground speed = 480 knots

As is my custom, the values are plotted for 19:40 to 00:11.

Numbers next to the plotted points are computed values in Hz.

Red line is best linear regression fit.

Second order polynomial fit below.

My version of Holland's Figure 6 below. Nothing remarkable.

From "Bayesian Methods..."

Stop the Madness

Totally off topic (off the MH370 topic) rant to follow.

A truly great article appears in this month's (February 2017) Scientific American. The article ("Pop Goes the Universe") addresses recent data gathered by the European Space Agency Planck Satellite. This satellite measured the cosmic background radiation with greater precision than ever before. A poor camera capture of the basic thesis is presented below.

Article pdf linked below.

Pop Goes the Universe

These guys are heavyweights, and what they say obviously took a great deal of courage. Basically they are telling the entrenched cosmology establishment that they are likely to be full of shit.

I have been a critic of the "big bang" for quite some time.  My doubts were based entirely on the missing mass needed to make the theory hang together. These people, the cosmology community, have been looking for dark matter and dark energy for almost 50 years now without any success whatever. A reasonable person might well conclude that neither exists. That is certainly my conclusion.

In any case, it is a great article IMO, and well worth picking up and reading. I was particularly struck by comments at the end of the article that suggest that scientists, in particular cosmologists, now appear willing to discard one of science's key properties. That is empirical testability, in exchange for immunizing the "big bang" theory from experiments that seem to suggest that it is incorrect. A sign of the times I suppose.

Going on with my irreverence I will transition to evolution and AGW. It is easy to show that the rate of genetic mutation and the known age of the earth are more than an order of magnitude incompatible with the diversity and specialization of the creatures occupying the earth.  You can show this disconnect on the back of an envelop, yet no one seems to be terribly bothered by it. AGW falls in the same category. No one really knows if the prevalent conjectures are true. I am inclined to believe Duncan Steel's view (brilliant paper that he wrote, BTW).

So we are busy teaching our young people that the "big bang", evolution, and AGW are established scientific facts. Never mind that the average California high school graduate reads at the fourth grade level. Why are we educating youngsters to participate in "party conversations" instead of emphasizing basic skills like reading and math. It drives me crazy. Is it any wonder that the US ranks about 17th in tests that evaluate language and math skills worldwide?