So What's Up with the French ?

People almost always do things for a reason, even French people. So why have the French not made public any information regarding the damage forensics of the flaperon recovered on La Reunion? There seems to be little if any discussion about this lack of disclosure. How the flaperon was damaged would seem to be important relative to whether the forensics support aerodynamic damage and in-flight separation (consistent with a high speed dive) or whether the forensics support damage and separation from impacting the water while extended (consistent with a controlled ditch).

As everyone knows, the French have opened a criminal investigation relative to the disappearance of 9M-MRO. This formality allows the French to claim that the forensic information is "sealed" as part of an ongoing investigation. OK, but why - unless the forensic information points to a scenario that involves parties that may be guilty of a criminal act even if that act was simple negligence? Withholding of information allows investigators maximum freedom to probe the periphery of this disappearance. Releasing information that does not support the status quo would alert guilty parties, and increase their sense of caution. It is difficult to postulate a reason for withholding information that supports the status quo.



















My sense is that there may be evidence from the flaperon forensics that suggests something is or was going on that is inconsistent with publicly available information.

What this "something" might be is subject to speculation. Suppose the flaperon forensics support a controlled ditch. Suppose further that barnacle analysis makes the current search area even less likely than the drift modeling already suggests. If the forensics supports a controlled ditch well North of the current search area, the landscape surrounding this mystery would be altered substantially. Questions regarding that flight path would certainly be raised, and areas of inquiry would be expanded. Perhaps the French do not want this to happen, at least not yet.

Weapons of Math Destruction

The 30 November 2015 book draft, "Bayesian Methods in the Search for MH370", authored by members of the Australian DSTG (Defense Science and Technology Group) is an interesting document. Hereinafter I will refer to it as the BM. It is especially interesting to me. This short document addresses two issues in the BM that have received commentary, without clarification, by a number of independent investigators. I say without clarification since I am not aware of any published attempts to clarify them. Of course, I may have missed them, and apologies in advance if I did miss them.

The first issue has to do with measured BFO errors. There has been quite a lot of discussion relative to the accuracy that might be expected from the BFO data contained in the Inmarsat logs for the last flight of MH370. These discussions have been primarily between myself and Mike Exner of the Independent Group, IG. Until now there has been no way to quantify these errors directly since no data was available. The BM changes that, and Figure 5.4 from the BM is reproduced (without permission) below.











The BM comments on Figure 5.4 as follows:



The BM offers no additional data to support the claim of "geographic dependency" such as repeated flights exhibiting a pattern correlated with the data in Figure 5.4.

When I first read the BM, the data in Figure 5.4 did not really surprise me at all, and had questions not been raised by others, I would have probably not have given it further consideration. Without supporting data I mentally discarded the "geographic dependency" explanation, and applied my own explanation which is simply drift in the AES -> 3F1 -> Perth oscillator chain. I have long estimated this drift to be on the order of +/- 5Hz over the duration of the MH370 flight. Cut and paste below from a much earlier post in this blog, "BFO Errors (again)".

















The errors shown in Figure 5.4 of the BM are certainly this order of magnitude. My estimate was based on a few decades of experience with oscillators of the type used in the Inmarsat chain. It was not based on a knowledge of specific part numbers and manufacturer's specifications of the oscillators used in the hardware associated with the MH370 BFO data. There is not much doubt in my mind relative to the source of the errors in Figure 5.4, but I stand ready to retreat from my explanation should the DSTG present data supporting their "geographic dependency" claims.

As a parting comment relative to this first issue it important to realize that BFO errors on the order of 1 Hz produce position errors along a range ring on the order of a degree of latitude per Hz (some 60 nautical miles of error).

The second issue has to do with the "anomalous" paths show in Figure 9.2 of the BM, and reproduced below.



































The commentary offered in the BM relative to these anomalous paths is pasted below.



Basically if one draws a radial from the sub-satellite point to the aircraft flight path, the BFO data becomes ambiguous relative to a continuation along the flight path and a continuation at an angle equal to and on the "other side" of the radial to the sub-satellite point. While this statement is not quite true for satellite positions far from the extreme ends of the satellite "dither" (where the Doppler associated with satellite movement is significant), it is exactly true for times such as 19:40 data point in the MH370 log when the satellite was virtually standing still at the extreme end of its wobble. As some readers might recall, I pointed this phenomenon out on the Wise blog some time ago. It was met with the howls of protest normally associated with my blogs there. No matter. It is what it is (or is not).

Note: 12 February 2016

The text above was "struck" because it is incorrect. The bifurcations in the path for BTO are, as stated, about a radial to the sub-satellite point. The bifurcations in the paths for the BFO values are not about a radial to the sub-satellite point. They are about a N-S line, a meridian. My apologies to anyone who was misled or wasted time due to this error on my part. 

The explanation from the BM above could have been worded better, but suffice to say that the three examples of flight path deviation are simply illustrative samples from a continuous "fan" of possible paths - "the true underlying pdf has support all the way around the arc. Without dynamic constraints the location of the peak of the pdf is simply a function of the measurement noise".  What the quoted snippet in italics means is that without the assumption that the aircraft is flying in a straight line ("dynamic constraints"), the plane could be just about anywhere on the last arc while satisfying BTO and BFO.

Summary

The Inmarsat system was not designed to be a navigation system. It was designed to be a communication system. While I acknowledge the huge amount of effort put forth by various parties (including myself), that effort does not change the physics of the system. The simple truth is that this huge effort is akin to turning a sow's ear into a silk purse. It is certainly a very worthwhile effort, but it would be a mistake to think that the Inmarsat data can, in and of itself, be used to accurately estimate the terminus of MH370.

The DSTG BM adds little new to boost confidence in a terminal location. It is very "IGish" - assume a flight dynamic,  find a path for your assumed dynamic that satisfies the ISAT data, and then conclude you have high confidence in the terminal location.














Duncan Steel

Sherlock Holmes

'Eliminate all other factors, and the one which remains must be the truth.'

Sherlock Holmes Quote

-The Sign of Four

When one considers what may have happened relative to the disappearance of MH370 there are four broad categories of possibilities.

1> Suicide by someone on board - a not so broad category.

2> Downing by a sovereign state - intentionally or unintentionally.

3> Technical issue - fire, mechanical failure, explosion, decompression,...

4> Highjacking which may or may not involve a spoof or remote control. 

5> Alien abduction, black hole, alternative dimensions, or the like.

I can't think of any other scenario or know of any scenario proposed on the WEB that does not fit into one of the above categories. I will eliminate 5> by fiat. Consider the others one by one.

Suicide

Neither the pilot nor the copilot have been assessed to have had suicidal symptoms. Numerous people in the mental health profession have weighed in on this possibility, and I have not read one opinion that would indicate suicide by either pilot. Background checks have not revealed that there was anyone else on board who could fly the aircraft. Suicide appears contra-indicated.

Downing by sovereign state

Possible, but a coverup of the magnitude required would be an incredible undertaking. Also, there is strong evidence to support that the aircraft flew until fuel exhaustion. Fuel exhaustion and intentional or unintentional downing are not compatible.

Technical issue

All of the explanations I have read in this regard are implausibly complex. While a technical issue cannot be ruled out, it would require a sequence of events that is three sigma or more improbable. Technical issues historically account for 20% of aircraft crashes. That probability is lowered in this case by the additional failure of all communication systems, and then lowered even further by the fact that the plane continued to fly until fuel exhaustion. Also, the flight path simply does not support this notion. Rather it supports an aircraft under the deliberate control of conscious pilot. A technical issue is a non-starter IMO. 

Hijacking

The only explanation that has any credulity. What could be the motive for hijacking? The only ones I can think of are listed below.

1> To obtain something or someone on the aircraft.

2> To obtain the aircraft itself.

3> To architect a 911 type event.

4> To use as a "bargaining tool".

An aircraft has never been hijacked to obtain something or someone on board the aircraft in the history of aviation. MH370 could be a first, but it is far easier to obtain that someone or that something before it was placed on the aircraft or after the aircraft landed.

The aircraft itself is not the least bit unique. The same or comparable aircraft can be obtained from a number of online brokers. Orchestrating a hijacking for the purpose of obtaining the aircraft is perhaps the most complex way to do it. Not to mention the murder of more than 200 people in the process. It just does not hold together.

A 911 event requires a target. There were no plausible targets within the fuel range of the aircraft. A heading to Perth would require a speed that is incompatible with ever reaching Perth and simultaneously satisfying BFO and BTO.  A heading to Perth at a BFO and BTO compatible speed would terminate well short of Perth. The 7th ping ring arc is a very long way from Perth.

That leaves the "bargaining tool" scenario. The only candidates I can think of are Chinese terrorists negotiating with the Chinese government or captain Shah negotiating with the Malay government. Take your pick. An argument can be made for either candidate. Personally, I lean toward Shah on the basis of background checks which are said to rule out the PAX. If this scenario is true, it is plausible that the aircraft was flown along the Southern coast of Sumatra and Java where there are several airfields that could accommodate a 777. Certainly a flight path to the ATSB search area in the SIO is not a path anyone would select for this scenario. It is also true that all the drift models associated with the flaperon finding greatly favor the area below Sumatra as a terminus. 

I have a very difficult time understanding how the ATSB and their collaborators can possibly assess the primary search area identified in any incarnation of their analytics as an area of high confidence. It is simply not sensible. 

/// Clusterfuck ///

From the Wiktionary:

Noun[edit]

clusterfuck ‎(plural clusterfucks)

1. (slang, vulgar) A chaotic situation where everything seems to go wrong. It is often caused by incompetence, communication failure, or a complex environment.  

Google defintion:

..and so it goes with the search for MH370.

History has taught us, or as Duncan Steel might say - should have taught us, that any product resulting from a group effort is subject to far more flaws than the output from a single well-qualified contributor or a small group of such contributors. This fact is especially true in an age where rapid electronic communication produces a segregation of ideas (lots of papers on this subject) and a polarization of thought (lots more papers) far more rapidly than a weekly or monthly face to face meeting.  The current US political situation is a good metaphor. According to Pew Research, America has never been more polarized except perhaps (data not available) in the period preceding the US Civil War.

Among my favorite books is a relatively obscure effort by Dr. Frederick Brooks (Harvard PhD), "The Mythical Man-Month: Essays on Software Engineering". Basically Brooks chronicles his experiences and failures as manager of a large software project (Operating System for the IBM360) while employed at IBM.  One of my favorite quotes from the book describes the evolution of a complex software system (and is applicable to any system or undertaking, IMO):






Does the above sound applicable to the current state of affairs in the quest for the terminus of MH370 - "Worn out as a base for progress."? The recent book draft, "Bayesian Methods in the Search for MH370", represents the high water mark in the evolution of the ATSB official search strategy. BTW, the authors claim that Springer-Verlag, which no longer exists (now simply Springer), will be the publisher. Springer has gone far down hill from their once respectable publisher position, and has been forced to retract a number of recent offerings due to flawed peer review and faked source material.  Not trying to imply the DSTG effort is anything but sincere, it is simply based on the same tired assumptions that have not yielded any positive results, and are contradicted by lack of debris (surface or subsurface), drift models, and plausible causality.

Let's look at the starting definition above a little more closely to see how the terms fit.

Incompetence

Certainly a lot of that to go around. The principal contributors being the journalists supplying the conduit for disseminating information to the public. It is difficult to find an article in a mainstream channel that is not burdened by errors, misrepresentations, and attention grabbing tabloid style headlines. It is truly a pathetic  reflection on the state of the journalistic profession today.

Communication Failure

The whole MH370 undertaking has been severely hampered by the refusal of virtually every party involved to release pertinent source information - be it radar data, flaperon forensics, cargo manifests, unredacted Inmarsat data,... The list goes on and on. I don't think anyone would dispute this point.

Complex Environment

No doubt. There is little to guide us, and it is a big ocean. The interpretation of the meager data we do have is subject to a lot of guess work and assumptions in order to derive a terminus. I could write a very long treatise on this aspect alone.

So, we have all the ingredients for a monumental clusterfuck.  Is it any wonder we have reached the point where progress has halted (for some time now), and a restart (or serious consideration of alternatives) is both necessary and warranted as Brooks concludes above? What have we learned, and what could we have done better? My own opinion is that the search effort was "corrupted" by unfortunate timing. Had the flaperon been found before substantial expense was incurred searching what is now called the high priority area, events may well have evolved very differently.  Sunk cost, both real and intellectual, is notoriously difficult to abandon. People will fabricate all sorts of reasons to continue down a path they have invested in long after it has become obvious that things are not working out according to plan.

No matter.  Changes will not be made. The search will continue "in good faith" until people tire of tossing money into the ocean, and the whole affair quietly loses public interest.  My own belief is that the aircraft will never be found. Blogs and tweets will go on in perpetuity, of course.

Controlled Ditch ??

The Australian Defense Science and Technology (DST) Group claims (see AE-2014-054) the evidence from the Inmarsat data "is inconsistent with the plane making a controlled ditch".  They offer no compelling explanation for that claim other than the assertion that engine power is needed to execute such a maneuver, and the evidence strongly indicates a dual flame out. Wow. How did Scully manage the "miracle on the Hudson" with both engines inoperable due to bird impacts? Does the DST not read newspapers or do they know something we don't know?

My guess is the latter. What would it take to make such an outrageous claim that flies in the face of a very recent and well-publicized event? The only answer I can come up with is that the French have provided flaperon forensic data to the Aussies, and have not shared it with the rest of the world. If the French have concluded that the flaperon damage is consistent with aerodynamic flutter, as originally suggested by Mike Exner, then the DST assertion makes perfect sense. The damage forensics would be THE key piece of information needed to rule out (or support) a controlled ditch.

Also the implicit DST rejection of a long terminal glide associated with an assumption of pilot control inputs is consistent with a flutter damage scenario.

Edit 12/14/2015:

On second thought, it really is conceivable that the DSTG pulled their conclusion out of some place other than their brains. Nothing would surprise me anymore relative to the MH370 "science".

Christmas Island Revisited

Christmas Island Revisited

A great deal has been written about the terminus of MH370 by "experts" of all persuasions, some very good and some not so good. The prevailing theory among the cognoscenti is that the plane travelled pretty much directly South into the Southern Indian Ocean, SIO.  Problems with this scenario arose almost immediately. There is no plausible motive or causation hypothesis, and no debris from the aircraft has been found there. That did not deter the expenditure of tens of millions of dollars searching the ocean floor in that region. As we all know, nothing has been found. What most people do not realize is that the SIO hypothesis is flawed - the major flaw is the assumption relative to the fixed AP flight dynamics after the turn South. This turn is often referred to as the final major turn, FMT.

This fixed AP flight dynamic assumption has taken on a life of it's own. Too much has been invested to retreat from it. A few people, Dr. Victor Iannello and Jeff Wise among them, have proposed viable alternatives. However, they have not been seriously regarded by the people advising or conducting the search operation. The reality is the plane could be virtually anywhere on the last range ring. A competent analyst can create a set of flight dynamics to support a location North or South of the equator. While these flight paths might seem contrived, they are certainly not far removed conceptually from the flight dynamics used by the ATSB and "consensus" IG.  The observables suggest that MH370 was actively piloted prior to the FMT.  To assume that everything was "hands off" after the FMT is logically unsustainable (for me).

I have taken a somewhat more holistic approach to the problem. An approach that invokes the notions of motive, lack of radar sightings, and lack of debris. When one considers the totality of information, some of it nuanced, it becomes clear that the SIO terminus is tenuous at best. Neither pilot displayed any suicidal tendencies. Suicide is usually not the result of a spontaneous decision. It evolves over a long time period (i.e. the German Wings case), and warning signs are almost always evident.  It is more likely that Captain Shah simply wanted to make a political statement or negotiate a political concession from the Malaysian government. Shah had several landing locations available with a more Northern flight path depending on the status of "negotiations" going on in Malaysia between the government and his co-conspirators - Banda Aceh, Cocos, Christmas Island, Bandung,... Certainly flying into the SIO toward the current search area provided no opportunity to land the aircraft. Flying along the Southern coast of Sumatra/Java offers a diverse set of landing opportunities.

With that as background, I have constructed a revised flight path below which satisfies all the BTO and BFO data after and including the 19:40 handshake. The revisions from earlier postings are based on:

• Carefully derived BTO range rings using a WGS84 ellipsoid and correct sub-satellite centers. My original rings were made in haste using a spherical earth and centered at the nominal sub-satellite location over the equator.

• More care relative to speed and heading selection to better match the BTO and BFO data without the need to include arbitrary altitude variations.

• The conclusion that the PIC intended to land from North to South instead of South to North. This change was the result of considering surface winds from the Southwest at that time.

• The conclusion that the PIC did a flyby South of the Island to verify a clear runway before turning North for the final approach.
• It has been pointed out to me by a very sincere source that it is also possible that the PIC turned North to land at Bandung, and the intention was not to land on Christmas Island.

The Inmarsat BTO and BFO data were used in accordance with the vector diagram below.

The revised flight path is shown below along with the supporting data in spreadsheet form. The spreadsheet continues to be shown in two parts. The upper part calculates Doppler residuals based on the known observables. These residuals would be the same for any flight path. The lower part of the spreadsheet shows the aircraft location, speed, and heading used to match the residuals. The area inside the white circle will be the subject of additional discussion below.

Note that no altitude variations were used to reconcile the BFO data with the aircraft position, speed, and heading.

Edit 2/23/2016 to table below:

A 23:15 data point was added at the request of Oleksandr. No other changes were made.

In the table data above D2 refers to the aircraft and satellite Doppler, and D1 refers to the Doppler compensation produced by the AES. The heading lag is associated with the turn North and the Doppler change associated with this lag is quantified in an earlier post in this blog. A three degree per second turn was assumed with an inertial update interval of 0.25 seconds. Two values are shown for the 00:10 Doppler - one with no ROC or heading lag, and one with an ROC of +2 meters/sec OR a heading lag of 0.7 degrees (either accounts for the additional 7Hz of Doppler).

The aircraft speed at 19:40 was based on a calculation made in another post in this blog "Mid-flight Speed - MH370" below.

The conclusion is that the aircraft ran out of fuel during or shortly after the turn North, and went into the ocean almost due East of Christmas Island. Please take a look at "Coincidences - Are You a Believer ??" elsewhere in this blog.

The graphic below shows an enlarged version of the white circle area in the first graphic above.

The area inside the circle (with the exception of the 19:40 location) represents residual confusion. The radar data presented by the Malaysian government showed a last contact at a range of 200nm on a 295 degree radial. This contact was time tagged at 18:22 UTC. This location and time are not compatible with reaching the 18:25 UTC range ring location. The aircraft could not fly that fast. Other analysts have concluded that the radar data presentation was made in haste, and that the labeling was incorrect. They have used overlays to infer a last radar contact range of 250nm on a 285 degree radial toward Mekar.  An "official" correction to the radar data has never been made. It is also true that the GM400 radar at Butterworth has a manufacturer specified detection range of slightly more than 200nm, and that the radar data showed by the Malaysians did not come from a GM400 display. Until revised and officially certified data is available, I won't speculate on the flight path prior to 19:40.

A final comment is that the flight path associated with my analytics lies too far West to have been the sighting described by Kate Tee.  Kate could have seen the plane, but at a distance of some 70nm.

Of course, the usual disclaimers apply. While I believe the calculations above are correct, history has shown that making errors is virtually inevitable.

Update 20 November 2016

The flaperon found on Reunion Island has been confirmed by the French to have come from 9M-MRO (MH370). This finding and confirmation allows drift models to be created in an attempt to narrow down the likely terminus of the aircraft on the last ping ring. The most credible such model has been created by  Geomar, a Research Institute in Germany.

Dr. Jonathan Durgadoo and Prof. Dr. Arne Biastoch from GEOMAR Helmholtz Centre for Ocean Research Kiel used a state-of-the-art ocean model in combination with observational data. This provides a coherent realistic dataset for their drift analyses to determine the possible origin of the flaperon. To do so, they release virtual particles around La Réunion and compute their trajectories back in time. "Of course it does not make much sense just to track only a few particles within the model," Dr. Durgadoo explains. "We have traced back almost two million 'virtual' particles over a period of 16 months," Durgadoo continues. "For each month back, we subsequently calculated the probable region of the particles positions."

The Geomar model shows that the most likely origin of the flaperon is far to the North of the current search area, and compatible with the Christmas Island region terminal hypothesis.  The Geomar probability map is shown below. Other models such as the CSIRO model are suspect, IMO. There is virtually no probability (see map) that the flaperon originated from the current search area.

There is still no word from the French relative to the flaperon damage forensics or the pathology of the barnacles.

Mid-flight Speed - MH370

Mid-flight Speed - MH370

A mid-flight speed estimate for MH370 was made by Brian Anderson using a time of flight methodology. Brian's method can be found at the link below.

http://www.duncansteel.com/archives/1330

Since it is a slow week, and I can't stand to look at any more Maldives posts without getting upset, I decided to revisit this calculation using a different method than Brian. My method refers to the Doppler diagram below.

At 19:40 the satellite is virtually standing still at the extreme end of the "dither". V_s is essentially zero, and the Doppler shift associated with satellite movement relative to both Perth and the aircraft is negligible. All of the residual Doppler is the result of aircraft motion, D2 - D1 above.

Setting V_s = 0, V_p = V_pt, and | R_s - R_p | ~ | R_e - R_p | in the expression for D2 and subtracting D1 results in the following:

D2 - D1 ~ V_pt dot (R_s - R_e) x FL / | R_e - R_p | x C

R_s - R_e  is a vector in the North - South direction of magnitude 1206 km. 

| R_e - R_p | is 36, 738 km (by calculation from satellite to 19:40 range ring)

Using the values above and the values for FL and C we have:

D2 - D1 = (V_pt dot z) x 0.18 (approximation valid near equator)

where V_pt dot z is the scalar component of aircraft tangential (to the earth) velocity in the North - South direction.  

Using a residual Doppler value at 19:40 of 37.8 Hz (D2 - D1), and solving for V_pt dot z yields:

V_pt dot z = 210 m/s = 756 km/hr = 408 knots.

408 knots is the slowest speed that the aircraft could have been traveling to produce a residual Doppler of 37.8 Hz at the 19:40 range ring. That speed would be at a heading of 180 degrees. Headings on either side of 180 degrees would require a higher speed to produce the 37.8 Hz residual Doppler, limited by the aircraft performance envelop.

This value is in general agreement with Brian's calculation. 

Update: 08/05/2016

The graphic below shows the mid-flight speed probability distribution calculated by the DSTG and published in their book "Bayesian Methods..." Figure 5.7. The highest probability speed calculated by the DSTG corresponds exactly with the 408 knot value calculated above.

It should not be inferred that the DSTG result and my result somehow reinforce  each other - although the most probable DSTG speed corresponding to zero BFO error at 180 degrees is identical to my result. The DSTG result is a probability distribution. My result is simply a determination of the minimum speed necessary to produce the 19:40 BFO observation. In fact, I would regard speeds below 400 knots in the above graphic not only to be unlikely, but physically impossible if the 19:40 BFO value is valid. It would require a significant bias drift to account for speeds less than 400 knots at 19:40. A vertical line at 180 degrees in the above figure would depict the probability function the DSTG used for BFO error.

Update: 9/11/16

Given the calculation of speed and heading required at 19:40 it is reasonable to ask what combination of speed and heading, if maintained, would produce an arrival time at 20:40 consistent with the distance to that range ring. The answer is about 425 knots at a heading of about 168 degrees. This answer assumes a late FMT with a latitude at 19:40 of about 8N.

It turns out this heading is directly at the Cocos waypoint. 168 degrees is also consistent with the recent work of Iannello and Godrey which postulates a terminus on the 7th arc around 27S using McMurdo Station, Antartica as a programmed destination.

Update: 9/12/16 

If one carefully extracts the likelihood relative magnitude vs speed in DSTG Figure 5.7 above it is possible to derive the BFO probability density function used by the DSTG in their modeling. This information is displayed graphically in the figure below. The data extraction yields a standard deviation (sigma) of approximately 5Hz. Track maintained at 180 degrees true. Speed is ground speed.

BFO Errors (again)

BFO Errors (again)

Note: The original post contained errors in the M matrix (NEU to ECEF conversion). The matrix has been corrected as of 25 September 2015)

There are many ways for errors to creep into the BFO data:

- Drift in the AES, satellite, and ground station oscillator chain (my estimate +/- 5Hz).

- Unknowable rates of climb/descent which are not included in the AES Doppler compensation algorithm (~  +/- 4Hz/m/sec).

- Heading errors (the subject of this post) - caused by sensor lag and sensor drift.

Sensor lag refers to the fact that the heading sensors, GPS or gyro, have a fixed update rate. The heading values which the AES uses to pre-compensate Doppler are never current. They will always lag the current heading by some amount depending on rate of turn (if any) and the sensor update rate.

The BFO graphic below serves as a useful starting point.

The BFO graphic includes a number of vectors associated with the locations and velocities of the aircraft, the satellite, and the ground station. These vectors are directly coupled to the problem physics. Some are known, such as the location of the LES, and some are unknown, such as the location and velocity of the aircraft. One vector, however, is estimated from sensors on the aircraft - V_pt, the velocity of the aircraft in the local tangent plane. The AES pre-compensates the L-band signal sent to the satellite by subtracting the Doppler associated with V_pt relative to the nominal position of the satellite over the equator. Vertical aircraft velocity is not included in V_pt.  Clearly, any errors associated with the estimate of V_pt will find their way into the Doppler compensation, D1. The purpose of this post is to estimate D1 errors associated with an incorrect heading.

Parameters and relationships are defined below:

The error vector contained in V_pt is quantified above. Matrix M is simply a conversion matrix used to generate velocities in the ECEF coordinate system when the NEU velocities are known. Note that most people use ENU rather than NEU. The matrix above is anticipating a velocity vector in the NEU format. 

Continuing using the D1 equation from the BFO graphic:

Note: A heading error of +1 degree corresponds to an actual heading of 179 degrees. 

The values used in the example should be familiar. The location, speed, and heading were selected to be in approximate conformity to a location and speed in the SIO favored by the ATSB and IG.

The D1 compensation is clearly quite sensitive to heading. More sensitive than I would have guessed before attempting to quantify it.  So, in addition to ROC, the BFO values will be corrupted by rate of turn (sensor lag) and sensor drift. In the ATSB and IG models the aircraft never turns (after the "Final Major Turn"), so drift is the primary consideration. 

It might be that heading errors (along with oscillator chain drift) are the major sources of error in the tracking examples in the ATSB report. 

Edit 3 February 2017

Graphic below added at request of a collaborator. It allows the effect of tracking and speed errors in the vicinity of an assumed FMT to be estimated.

Added graphic below is the "Doppler Residual", the sum of D1 + D2 in the BFO graphic above at the time 19:41 UTC. The Doppler Residual is the total Doppler due to aircraft motion relative to the satellite and the Doppler Compensation applied by the AES. It includes motion of the aircraft relative to the actual satellite position (aircraft and satellite motion), D2, and the Doppler Compensation applied by the AES for aircraft motion relative to the nominal satellite position over the equator, D1. Note longitude change to 93E.

The dashed line in the graphic above is the Doppler Residual measured by the ground station in Perth after all other sources of frequency variations have been  accounted for (AES offset, satellite motion relative to Perth, and GES correction term). The residual shown by the dashed line was derived at 19:41 UTC. 

Coincidences - Are You a Believer ??

Coincidences - Are You a Believer ??

I am generally not a believer in coincidence - been burned too many times in my career by following a data trail that seems compelling only to be jerked back to reality. So it goes.

The following essay was brought to my attention by StevanG (Jeff wise blogger) a couple of weeks ago. I had not seen it before, and I doubt many people have since it has not been referenced anywhere that I normally go relative to MH370. The author has a style that appeals to me - humble and unassuming. I have no opinion relative to his pedigree. I have not tried to validate his analytics. I present the essay as is. Link below. Please give it a careful read. It deserves that, IMO.

https://sites.google.com/site/mh370tibet/updates/05june2014

I will jump to the conclusion terminus with the graphic below (from the linked reference). The graphic shows the location of the wave height data collection sites.

A close up view of the terminus is shown below (from linked essay).

Contrast the above with my latest Christmas Island scenario (on this blog "Christmas Island Revisted"). I would "humbly" recommend reading that as well.

My speculative scenario was published prior to my awareness of the wave height essay referenced above provided to me by StevanG.  I think it is interesting. Certainly not anywhere near what I would categorize as compelling, however. Where is the f'ing debris?

Food for thought, in confusing times.

Added July 13, 2015

Tsunami wave speed as a function of ocean depth.

The height of the disturbance is small in deep water.