STATEMENT FROM AN INDEPENDENT MH370 INVESTIGATION TEAM
Shortly after the disappearance of MH370 on March 8th, an informal group of people with diverse technical backgrounds came together on-line to discuss the event and analyze the specific technical information that had been released, with the individuals sharing reference material and their experience with aircraft and satellite systems. While there remain a number of uncertainties and some disagreements as to the interpretation of aspects of the data, our best estimates of a location of the aircraft at 00:11UT (the last ping ring) cluster in the Indian Ocean near 36.02S, 88.57E. This location is consistent with an average groundspeed of approximately 470 kts and the wind conditions at the time. The exact location is dependent on specific assumptions as to the flight path before 18:38UT. The range of locations, based on reasonable variations in the earlier flight path result in the cluster of results shown. We recommend that the search for MH370 be focused in this area.
We welcome any additional information that can be released to us by the accident investigation team that would allow us to refine our models and our predictions. We offer to work directly with the investigation team, to share our work, to collaborate on further work, or to contribute in any way that can aid the investigation. Additional information relating to our analysis will be posted on http://duncansteel.com and http://blog.tmfassociates.com. A report of the assumptions and approaches used to calculate the estimated location is being prepared and will be published to these web sites in the near future.
The following individuals have agreed to be publicly identified with this statement, to represent the larger collective that has contributed to this work, and to make themselves available to assist with the investigation in any constructive way. Other members prefer to remain anonymous, but their contributions are gratefully acknowledged. We prefer that contact be made through the organizations who have published this statement.
Brian Anderson, BE: Havelock North, New Zealand;
Sid Bennett, MEE: Chicago, Illinois, USA;
Curon Davies, MA: Swansea, UK;
Michael Exner, MEE: Colorado, USA;
Tim Farrar, PhD: Menlo Park, California, USA;
Richard Godfrey, BSc: Frankfurt, Germany;
Bill Holland, BSEE: Cary, North Carolina, USA;
Geoff Hyman, MSc: London, UK;
Victor Iannello, ScD: Roanoke, Virginia, USA;
Duncan Steel, PhD: Wellington, New Zealand.
Following up on the previous post, here is an endpoint sensitivity test, based on propagation of the trajectory from the equidistant point until 00:19 UTC:
http://bitmath.org/mh370/sensitivity-equidistance.pdf
The model is the usual linear integration of L(t), and this particular computation takes constant altitude into account.
We all know it already, but here are numbers to back it up: the timing of the southern part of the flight makes a tremendous difference, and so does altitude. I believe these two factors are the main differences between the various contributions to this site.
Henrik
Here is the endpoint latitude as a function of doppler distance (L):
http://bitmath.org/mh370/doppler-distance.pdf
This graph is constructed by finding the angle along the final ping ring (00:19) for which L is a given value. Since L(00:19) can be found by integrating the L-band doppler contribution from the zero point, the problem boils down to finding the best integration of L, taking any assumptions of flight mode and altitude into account. The latitude can then be read off the graph above.
There is no solution for L larger than 49 km or so, which may (or may not) be significant.
The integration of L(t) is what reveals the difference between a “straight” path and the curved ones, even turning upwards, that we have seen example of (from Byan C, Ken S, rLya, Stevan G, myself and probably others). My own calculations show a maximum in L(t) at around 400 minutes after 16:30.
Henrik
Henrik, for those of us in the back of the class, would you mind laying some ground work on what you’re discussing here? What is L(0) and what is the signficance of integrating this function?
Hi Jeff,
Thanks for your question. Here is one way to look at it: we have two unknown values which we are trying to pin-point. One is the distance from an imaginary center point, and the other is the angle around that same center point. The BTO value gives use the distance. The BFO gives us the angle.
The reason why the BFO gives us the angle is because the BFO contains a partially compensated L-band doppler component that depends on the direction towards or away from the center point. The exact form of the doppler-plus-compensation amounts to a value which, when integrated, becomes the difference between the distance between the aircraft and the satellite on the one hand, and the aircraft and the “geostationary point” on the other hand. The latter is an imaginary point, programmed into the AFC on the aircraft.
Now, this is all well, but high-school math teaches us that an integrated quantity is undetermined up to a constant. If we follow the flight from the very beginning, at KUL, the constant, L(0), can be determined. However, the uncertainty in the flight path from there on has made this approach lacking in accuracy. The recent posts have to do with the fact that there are other points along the flight path where the constant is known. In particular, it turns out that the zero point, i.e., L(t_start) = 0, can be determined if we know exactly where the flight path crosses the “calibration curve”. In effect, this means that L(t) can be determined with much higher accuracy.
And this means that the end point can be determined with higher accuracy. The remaining uncertainties are:
1) Where *or* when did the flight path cross the calibration curve
2) What underlying assumptions are used to interpolate the L-band doppler from that point to the end
These are the unknowns. Now, this is in itself not very surprising; the ATSB has come to this conclusion, and this website has collectively come to this conclusion. However, it has so far not been formalized, nor quantified. With the calibration curve, we can clearly see that there are two branches of solutions: one early turn south, and one late turn south, for instance. We can also quantify the error in L(t) based on the assumptions made. To me, this is a positive step. I am looking forward to further analysis based on this.
Thanks,
Henrik
“that depends on the direction towards or away from the center point.”
This did not come out right, sorry about that. It should read “that depends on the direction towards or away from the geostationary point”.
Henrik
A new calibration line
———————-
Last night it dawned on me that the aircraft is likely to have passed a certain “calibration curve” at least once. The curve in question are the points along the ping rings for which the aircraft-to-satellite distance is the same as the aircraft-to-geostationary-point distance.
Mathematically, this is the curve along which L = 0 [1]. Starting from the intersection of this curve with the actual flight path, the end point can be obtained with much higher accuracy, since all uncertainty in the integration up to that point vanishes.
It also means that “when” can, in this respect, be related to “where”. Here is a skyvector plot of the curve:
http://skyvector.com/?ll=6.861349019776775,95.35180664439639&chart=304&zoom=3&plan=G.5.997305,102.757662:G.6.056519,102.219465:G.6.110627,101.790224:G.6.162084,101.358033:G.6.211055,100.922776:G.6.257694,100.484333:G.6.300735,100.056882:G.6.341459,99.606621:G.6.377637,99.144268:G.6.413402,98.681847:G.6.448753,98.219359:G.6.483688,97.756806:G.6.518204,97.294188:G.6.552298,96.831504:G.6.585969,96.368756:G.6.619200,95.906625:G.6.644010,95.675054:G.6.662141,95.497027:G.6.680202,95.318984:G.6.698200,95.140923:G.6.716134,94.962845:G.6.734004,94.784749:G.6.751810,94.606635:G.6.769552,94.428504:G.6.787230,94.250355:G.6.804843,94.072189:G.6.822392,93.894005:G.6.839875,93.715804:G.6.857293,93.537585:G.6.874646,93.359349:G.6.890250,93.233801:G.6.900066,93.288514:G.6.909872,93.343311:G.6.919673,93.398110:G.6.929467,93.452911:G.6.939255,93.507715:G.6.949036,93.562521:G.6.958812,93.617329:G.6.968581,93.672140:G.6.978343,93.726952:G.6.988100,93.781767:G.6.997850,93.836589:G.7.008628,93.993963:G.7.019974,94.216128:G.7.031217,94.438310:G.7.042355,94.660508:G.7.053388,94.882721:G.7.064317,95.104951:G.7.075140,95.327196:G.7.085859,95.549457:G.7.096472,95.771733:G.7.106980,95.994025:G.7.117382,96.216332:G.7.127709,96.438901:G.7.152108,96.775449:G.7.177270,97.120186:G.7.202175,97.464973:G.7.226823,97.809811:G.7.251213,98.154698:G.7.275344,98.499634:G.7.299214,98.844620:G.7.322824,99.189655:G.7.346172,99.534739:G.7.369257,99.879871:G.7.392079,100.225051:G.7.440022,100.586634:G.7.540932,100.982689:G.7.641493,101.378939:G.7.741695,101.775383:G.7.841532,102.172021:G.7.941000,102.568857
As can be seen, there are two general solutions, which corresponds to the “early” and “late” turn south. Here is a table with some points along the curve:
112.000000 6.601036 96.159752
119.000000 6.640130 95.709632
133.000000 6.689499 95.227084
140.000000 6.713823 94.985824
150.000000 6.748369 94.641110
160.000000 6.782674 94.296331
170.000000 6.816738 93.951486
180.000000 6.850558 93.606575
190.000000 6.884132 93.261680
191.166666 6.888013 93.222072
192.000000 6.889613 93.230369
195.000000 6.895318 93.262000
200.000000 6.904812 93.315028
220.000000 6.942726 93.527162
230.000000 6.961648 93.633242
240.000000 6.980547 93.739330
250.000000 6.999422 93.845485
260.000000 7.021067 94.237629
270.000000 7.042712 94.667676
280.000000 7.063966 95.097782
290.000000 7.084826 95.527947
300.166666 7.105630 95.965341
Time in minutes since 16:30.
Analysis of the implications is ongoing, but I thought it might be of interest to share this right away.
[1] See mh370-path.pdf for how L(t) relates to the L-band doppler.
Hi Henrik,
Fascinating, as always!
If I interpolate your curve to find the position at 19:12 mentioned in the ATSB report, the result I get is 6.78944N 94.22750E.
This matches the BFO data for an aircraft in this location, track 216 degrees true, ground speed 473.5 knots, assuming you accept an interpolation of the BFO curve between 18:40 (88 Hz) and 19:41 (111 Hz) giving 100.47 Hz at 19:12.
Richard
Hi Richard,
Yes, it looks reasonable to me. Personally, I am in favor of an even later crossing time, but that is of course only conjecture.
I am working on a complete separation of the altitude and distance-covered (L(t)) errors, which is possible if working in the ping plane, i.e., the plane that cuts out the great circle, aka the ping ring. It should give as a firm handle on how much difference we can really expect between a straight and a slightly curved path. The time of ascension remains the principal source of error, though.
Thanks!
Henrik
Err, “time of ascension” should of course be “time of descension”, which refers to the time of the crossing of the calibration curve. Not a very good description to begin with…
Henrik
Hi Henrik,
My comment is regarding
“I am working on a complete separation of the altitude and distance-covered (L(t)) errors, which is possible if working in the ping plane, i.e., the plane that cuts out the great circle, aka the ping ring”
First up an admission: I am not across the details of the L(t) integration subject, but spotted an implied potential source of error in the wording of the envisaged method above.
In my under standing, the ping rings are intersections between satellite centered ping spheres – their radii determined by the BTO – and a chosen earth centered surface, either ground level or some other altitude. In that context, “Ping rings cut out by planes” sounds a little wrong.
Accordingly, work to separate altitude and distance errors should be performed in the ping spheres. Admittedly the maths becomes more complicated.
From your wording above, it is not clear, which plane you are choosing. If choosing an (earth-)vertical plane, altitude errors could be rather large. I apologize if I state the obvious to you here (you may well be way ahead of me ;o), if choosing a plane to formulate the maths, I would choose the local tangent plane to the satellite centered BTO sphere at the point of interest. This plane is normal to the sat to airplane vector, i.e. inclined with respect to the earths surface (related to elevation angle).
Cheers
Will
MuOne,
“First up an admission: I am not across the details of the L(t) integration subject, but spotted an implied potential source of error in the wording of the envisaged method above.”
The L(t) subject is actually quite simple. By definition, it measures the difference in distance from the airplane to the satellite and the geostationary point, respectively. Because of how the AFC TX correction of the airplane works, L(t) happens to be simply related to the resulting L-band doppler: D(t) = -(f/c) dL(t)/dt. Hence, in order to know L(t_end), it is enough to integrate D(t) from a time t_start when L is known.
Each ping ring lies in a plane, and those are the planes I refer to, nothing else. They cut through the earth just like a great circle plane, although a great circle plane is defined to always go through the center of the earth. I did not think words like ‘frustum’ or ‘spherical cap’ would sound any less confusing. 😉
Henrik
Hi Henrik,
Can you explain more in detail how you derived the curve? (I don’t get the part: “..are the points along the ping rings.. “)
I guess that not all possible relevant flightpaths have a point L(t)=0. Even not if they cross the lines in space (?). Can you comment to that?
Nevertheless, my first impression is that for “delayed” flight paths (i.e. no direct turn south after last radar contact) this could be very interesting.
Niels.
Niels,
Thanks for the questions.
“I guess that not all possible relevant flightpaths have a point L(t)=0. Even not if they cross the lines in space (?). Can you comment to that?”
Yes, this is the really crucial part. Here is the logic and a proof:
If the actual flight path is known, a priori, to not contain any zero point (point in time and space where L = 0), then if such a path crosses the calibration curve, we cannot deduce anything, because we simply pass that point in space at another point in time.
However, if the flight path is known, a priori, to contain exactly one zero point, then that point must coincide with the crossing of the calibration curve (!).
Proof: Assume that the zero point of the flight happens somewhere where it does not cross the calibration curve. Because it is part of the flight, that point is found along the ping arc at that time. But there is a unique zero point [1] for every ping arc, so the zero point of the flight must be the same as that unique one. Since every unique zero point is part of the calibration curve, there must a crossing. The assumption is hence false, and we conclude that the zero point of the flight and the zero point of the calibration curve must be the same. In particular, the times must be the same.
Regarding how to construct the curve: For every time of the flight, find the ping arc from the BTO. Find the angle along the arc for which the distance to the satellite is the same as the distance to the geostationary point (placed at 0N 64.5E, 35786033 meters above sea). This distance can be seen to lie roughly at half the latitude of the satellite at that time. Work out the lat/lon coordinates of the point along the arc. For every time (well, a suitable discrete set), plot the coordinates on the globe.
Thanks,
Henrik
[1] There are two zero points along the circle, one westward and one eastward. We are only interested in the east arc, so the point is really unique.
the turn south happened later if we are to believe indonesian officials that MH370 didn’t stray into their airspace
I think I have mentioned that once (with links provided) but the comment was not approved… it would be nice if we could get general advice of what is allowed to post here and what is not (and why), if moderators think that thai&indonesian officials are conspirators then I’m outta here
This website is for serious science and evidence based discussion of the tragedy of the missing airliner, and it is fully apparent that you do not understand what that implies. A previous comment from you cited the popular media early on after the aircraft was lost, and that most certainly does not constitute ‘evidence’. Even your first sentence above indicates that you do not understand what is evidence, and what is not. The Indonesians have stated that they did not identify MH370 crossing their airspace, and that is not the same thing as saying that they can be sure that it did not. You might do others the courtesy of perusing the many, many previous comments on the same specific topic, whilst making statements yourself which display your ignorance and insult other people. This website is different from others because of the rather strict rules of logic, word and text meaning, and acceptable evidence, that I choose to apply.
oh please, Jakarta Post is indonesian newspaper citing indonesian officials and I don’t understand what’s the difference if they are popular or not?
again – “The Indonesian Air Force has also repeatedly said that none of Indonesia’s military radars detected a flying object that could have been MH370.”
while there is a theoretical possibility it could fly over Indonesia undetected, at the first place the PIC (whoever it was) didn’t have any reason to do so and risk interception when he could just go around so it’s up to you to show us the evidence of going across their airspace it being very unlikely, not the contrary
BFO&BTO are simply not reliable enough to draw the flight path across their country, it’s something even ATSB admits and it’s not the good science sticking to unreliable data.
As you wrote, you don’t understand.
Please take your ideas elsewhere.
Hi Henrik,
I have a few thoughts about the curve (thanks for explaining more about it!):
– Maybe it is helpful to graphically indicate the points in the curve which belong to “measured” pings (and their time)
– By connecting points to form the curve you implicitly assume a forward flightpath between measured pings (I’m not sure: flying a circle, so messing up the order in imaginary ping rings could induce a loop in the curve?)
– I think it is possible to construct similar calibration curves for other values of L
– L(t) is a continuous function, so in that light I’m curious what is the sign of L at the official point of last radar contact
Regards,
Niels.
Hi Niels,
I agree, the curve does contain interpolations between the BTO values that may not be perfect. That can be improved, agreed, and I am in fact working on the BTO right now. However, I do not expect any big changes. In any event it will not change the idea as such.
Flying in a circle… something would change I presume, but I will leave it to you to figure out exactly what. 😉
Yes, it is possible to construct similar curves for other values of L. I actually tried this a bit already. The uncertainties that emerge are largely connected to the question: did the flight pass this value of L? At large values of L, the curves start to look a bit funny. That said, they do say something about the possibilities at the end, but I think we already know about those. Let’s see what I can do, time permits.
Regarding L(t), I never did publish such a curve, sorry about that. Here is the one for the ‘pristine’ path:
http://bitmath.org/mh370/pristine-L.pdf
Thanks, as always, for your questions.
Henrik
Here’s my latest attempt at modeling the flight. I did not match the BFO as well as Richard, but it’s still pretty good. The main enhancements this time around are :
a) the EAFC/Satellite calibration from Table 1 of the ATSB report;
b) a wind model (borrowed from Richard and parametrized);
c) a spheroidal earth. When you are matching to 1 km and 1 Hz accuracy, it matters.
d) attention to geodetic v. geocentric coordinates.
e) elevation of aircraft included (but not descent at end)
Because the Earth is spheroidal, the concepts of ping radius and ping angle no longer make sense; I focus directly on matching the BTO data, although I do include elevation angle calculations for comparison with the ADS-B positions and ping rings in Figure 18 of the report as explained in a previous post.
https://drive.google.com/file/d/0B7YQpAH4JIN5N0RUSUdUZkJRMmc/edit?usp=sharing
My path ends up at the South end of the new high-priority search zone. However, I do not make any claims or recommendations about where the search should be conducted.
sk999… it might be useful to some to be explicit about what you mean by a spheroidal, rather than spherical, Earth shape. What shape? MSL? WGS84? Some other assumed shape?
It’s an oblate spheroid with parameters from WGS84, but we are still at a level of accuracy where the differences among the different Earth models are unimportant.
Hello sk999, Yap,
Over the past weekend I made some improvements (hopefully) to my model with regard to the Earth geometry: from spherical shape to WGS’84 oblate spheroid. I also ‘played’ a bit with altitude, which affects wind. The terminal point 00:19 found as a result of the minimization of the error function appears to be closer to your estimates:
Heading: 176.5 deg; Air Speed 883.6 km/h (477.1 knots).
Trajectory:
Time(UTC); Longitude(degE); Latitude(degN); Ping_distance_error(km); BFO_error(Hz)
2014-03-07 19:41:03 93.63, 4.42, 3.82, 2.06
2014-03-07 20:41:05 94.11, -3.47, -6.26, -1.93
2014-03-07 21:41:27 94.59, -11.43, -3.51, -0.41
2014-03-07 22:41:22 95.09, -19.38, 9.06, 1.51
2014-03-08 00:11:00 95.89, -31.25, -3.12, 0.12
2014-03-08 00:19:29 95.97, -32.38
Here BFO_error column is the same thing as BFO residual in sk999. The “best” found altitude is 12300 m so far, but again, results are not very sensitive to it. In my understanding, one of the principal differences between my and sk999’s models is that I do not impose the requirement on the exact matching BTO data.
The aircraft’s location 19:41 is, however, quite different. I can imagine ‘hook’-like trajectory from the last known location (18:22) towards the cluster of Islands: Car Nikobar, Batti Malv, Chaura, Teressa, etc. (93E, 9N), and then southward. The last known direction (I mean radar) is consistent with the direction towards these Islands. Post-hook direction is consistent with the constant heading theory. The distance along such a ‘hook’ from the known 18:22 position to the estimated 18:41 position would be around 1100 km – consistent with the distance the aircraft could travel. Such a trajectory would also be on the edge of the Aceh radar coverage, which explains why the aircraft remained undetected. Sorry, but I am not convinced how the Indonesian air defense radar in Aceh could miss Boeing 777 flying just above it. They would better use it to cook “Nasi Goreng” with chicken sate if it is the case… But I think it was not.
Oleksandr,
Here are my results for a constant course (rhumb line) path with minimal BFO error and exact matching BTO. The altitude is constant at 10.7 km from 19:41 to 00:11 UTC, but I allowed for a drop from 00:11 to 00:19 UTC. Position at 00:19 is almost -36 deg. latitude.
https://drive.google.com/file/d/0B6gvsOWO81hTdjIydXY0Q08zazg/edit?usp=sharing
I’ll be interested to see your results for the same simulation. Thanks.
@sk999 On the subject of using non-spherical earth modelling and the BFO – I’m wondering if the aircraft’s Doppler compensation code itself uses a spherical or non-spherical earth model? If the SDU just gets given numbers for latitude, longitude and speed by the navigation system (so *not* actual fixed-frame 3D positions or vectors) then it must presumably calculate something like a 3D position and a 3D (tangent) vector – or equivalents – in order to then be able to calculate the appropriate Doppler compensation (based on the assumed fixed satellite position) – and presumably in order to turn latitude, longitude and speed into 3D positions and a velocity tangent vector it has to make an assumption about the shape of the surface of the earth? You (and others) may very well have already considered this, but – though I haven’t done any calculations – I’m assuming that if you are getting into levels of accuracy at which a non-spherical earth model makes a difference then presumably the nature of the model (spherical or non-spherical) being used by the Doppler compensation itself will also likely have an effect of a similar order, if not larger, as the BFO is a ‘difference between large(ish)’ numbers kinds of thing (though I admit I’ve not attempted to quantify this). I’d be interested to know how you’ve approached this.
Skwosh,
That’s an interesting thought. I have tried it out and the difference (between using a spherical and a non-spherical earth model for the aircraft’s Doppler compensation code) in the end point at 00:19 UTC is about 1 deg latitude, which is significant.
Skwosh, Yap,
Ah yes, this is not at all given. On the other hand, what would the difference be in the BFO? Our calculations (mine at least) for the AFC calibration have been based on everything in the same coordinate system, meaning the AFC radial cancellation is perfect. This is backed up by comparisons to the ADS-B data. I presume the difference would be easily detectable in that data set. Victor, any thoughts on this?
Henrik
Hi Duncan
Here is a new version of my model (meanwhile V10). Many thanks to Annette, Warren, Dr. Bobby Ulich, sk999 and others who have pointed out various errors. Many thanks to Brian for suggesting I recalibrate the Bias Offset, which I have done. Many thanks to Mike Exner for suggesting that I should not blindly continue at an altitude of 35,000 feet as you will see MH370 started descending at 23:14. The implications of this have not escaped me!
Here is a model that fits all BTO data to +/- 0.5 km and all BFO data to +/- 0.1 Hz. It confirms the search area originally proposed in this post by the Independent Group.
https://www.dropbox.com/s/l53h153adhecs5k/MH370%20Flight%20Path%20Model%20V10%20South%20Independent%20Group%20Constant%20Heading%20Summary.pdf
https://www.dropbox.com/s/e8o2qbwabnuodpg/MH370%20Flight%20Path%20Model%20V10%20South%20Independent%20Group%20Constant%20Heading%20Summary.xlsx
Here is a constant Track as opposed to constant Heading solution that ends up 12 km away but does not fit the BTO and BFO data quite so well.
https://www.dropbox.com/s/yfoa99wxl4uis21/MH370%20Flight%20Path%20Model%20V10%20South%20Independent%20Group%20Constant%20Track%20Summary.pdf
https://www.dropbox.com/s/qsxoggwnxhp3cq8/MH370%20Flight%20Path%20Model%20V10%20South%20Independent%20Group%20Constant%20Track%20Summary.xlsx
Richard
Nice. I would like to see more emphasis placed on a probabilistic interpretation of the data as opposed to a “dot on a map”. The next step, IMHO, is to incorporate the uncertainties in the observables, and form an extended area with probability contours. This is the reality of what we are dealing with here, and it would greatly aid the searchers in developing a search strategy i.e. Bayesian.
I am still be very much interested in how Inmarsat actually measured the BFO values using a snapshot of RF energy – very very difficult. I am skeptical of even 2 Hz accuracy.
BTW, ATSB mentions 100nm per Hz. My analytics are closer to 150nm per Hz.
Thanks for sharing this data. It is a useful check on what I’m doing. I can’t quite duplicate your BFO values. I’m assuming we are using different satellite velocities. Could you share these or your model you are using to calculate these values? I use the visual basic platform in excel to do all of my calculations because it makes it easy to share functions/subroutines with others. Out of curiousity, what platform are you using?
Hi, Richard, Oleksandr, SK999,
Thanks for sharing your work. As a number of us are now reporting different results, it will be good to find out why there are differences. I could think of at least three reasons:
1) Our input data are different.
2) Our analytical models and/or assumptions are different.
3) There are some mistakes in the calculations.
I would like to check if I could replicate your results. Victor and I have started using a common form to share our data, so hopefully it will allow us to quickly identify the source of any discrepancy. Here’s the Excel form:
https://drive.google.com/file/d/0B6gvsOWO81hTdFp1OFNMdGcySVU/edit?usp=sharing
And here I’ve filled it with my data for an optimized curved path with minimal BFO error. I’m using a spheroidal earth model (WGS84).
https://drive.google.com/file/d/0B6gvsOWO81hTVEtLU1hUVHY5amc/edit?usp=sharing
It’ll be helpful if you could do the same and share your data using the form. Any suggestions are welcome. Thanks very much.
Yap
Yap,
Will work on it. Question – for latitude, do you use geodetic or geocentric?
The satellite orbit is definitely a big source of error here. The NORAD/Celestrak TLE set gives positions that differ from Inmarsat by up to 4 km and velocities that differ by 1.1 Hz equivalent BFO. My orbital fit to Inmarsat’s numbers is 4x better than that but still could use improvement.
sk999,
For latitude of the aircraft and the ground earth stations, I have used geodetic. For the satellite, I have simply used the ECEF data given in the ATSB report.
I’ve also tried the satellite models that Henrik and yourself published (thank you), and they are all in good agreement with each other. In Henrik’s model, geocentric latitude is used.
If anyone is interested, here’s the spreadsheet implementation of the two satellite models:
https://drive.google.com/file/d/0B6gvsOWO81hTWThuaWJhSE5hdDQ/edit?usp=sharing
Hi Yap.
I think our estimates of the terminal point converge. Over the past weekend I switched to WGS’84 shape, and as I see our models are pretty close in terms of the terminal location @00:19:
http://www.duncansteel.com/archives/826#comment-8027
At a glance there are many small differences between our models, so no wonder we have slightly different results. For instance, assumed altitudes are slightly different. In the latest models I found the best fitting corresponds to 12,000-12,300 m altitude when wind is accounted. Wind itself is another source of discrepancies. Sk999’s model considers one additional BFO sample (@ 23: 14), which is not yet in my model (it does not seem to be accounted in your model either). I agree with sk999 – satellite orbit is another significant source of errors and discrepancies (I used linearly interpolated ATSB data). There is also some uncertainty in how aircraft’s terminal corrects Doppler effect:
1. Does it consider WGS’84 shape or spherical? Skwosh’s comment (http://www.duncansteel.com/archives/826#comment-8028).
2. Does it consider redshift correction (in current version I assume it does not).
3. Does it assume ground speed or air speed for the correction?
4. What is the accurate position of the assumed geostationary satellite?
Finally, the results are dependent on an error function to minimize. I do not have any priority over BTO / BFO errors (residuals), whilst sk999’s model requires matching to exact ping distances at corresponding times (i.e. priority to BTO over BFO).
In order to assure that we are on the same page in terms of input data, may I suggest Duncan to consider creation of a summary page (that can be edited by everybody, but upon requests/approvals only), which would summarize all known facts and assumptions most accurate up to date?
Yap FF,
If you are still following this thread, here is a spreadsheet, mostly in the format you are using.
https://docs.google.com/file/d/0B7YQpAH4JIN5M3ZUNHh6Nzc4Ums/edit
I just took the times and positions from your sample spreadsheet and made my own computations of the remaining quantities. There might be some errors in assembling it (since I don’t use spreadsheets natively, and some of the numbers are translated from what I keep internally). There could also be errors in computing the numbers in the first place – but that is what we are trying to catch.
sk999,
Thanks. I’ve discovered some minor errors in my calculations, and after making the correction, my numbers are now almost identical to yours.
Richard,
I have compared some of your results with mine, and I noted several differences:
1. With respect to wind, the best information I have found so far can be found at:
http://earth.nullschool.net/#2014/03/07/2100Z/wind/isobaric/250hPa/equirectangular=95.29,-30.72,1024
For instance, at your 22:41 point (17.53S, 91.20E for ~ constant heading), I get 70 degrees at 6 knots, whereas your spreadsheet shows 323 degrees at 34 knots. That’s a large difference that would have a significant impact on the predicted terminus. If you don’t get the wind right, you won’t get the end right.
2. With respect to handshake arc radii, your values are anywhere from 4 to 31 km larger than mine. That is also a pretty surprising difference. I used the ATSB Report formula and offset, plus an elliptical earth model with an effective radius integrated from approximately the sub-satellite point to the aircraft latitude. In other words, the radius of the arc in terms of distance over the Earth’s surface is actually not a constant value, but it depends on the aircraft latitude. I compared our sub-satellite positions, and they match closely, so that is not the problem. Which model are you using for the earth radius?
3. I also noticed you allowed the BTO bias to change. What is the rationale for this?
Bobby
Frankly, I am a bit mystified over worries about wind speed, geodetic vs geocentric coordinates, earth model, and the like. The accuracies we are dealing with here simply put these considerations in the domain of second order effects. I still maintain the best one can do is model the observables during the initial phase of flight, and apply those models to the observables at the end of the flight (at the time of the 7th ping ring). Does anyone really care how the aircraft got there (not meaning to sound like Hillary here) in terms of locating the airplane? Those things are probably of interest relative to causation, but not location.
Dennis,
“The accuracies we are dealing with here simply put these considerations in the domain of second order effects. I still maintain the best one can do is model the observables during the initial phase of flight, and apply those models to the observables at the end of the flight (at the time of the 7th ping ring). ”
Modeling the observables is precisely what people are doing. Are you not forgetting that it is the *measurement* that exhibits random errors – not the physical mechanisms behind what is measured?
“Does anyone really care how the aircraft got there (not meaning to sound like Hillary here) in terms of locating the airplane? Those things are probably of interest relative to causation, but not location.”
Since there is apparently little measurable difference between, for instance, a straight path and a curved path, I would say that knowing how the plane got onto the southern path may very well be the *only* thing that can help us find the plane.
Rational realism is good. However, we need more than that to solve this puzzle.
Thanks!
Henrik
Hi Richard
Some observations on the consistency of your track summaries V9 & V10, in particular the columns headed Decimal time, (aircraft) Latitude & Longitude, Calculated Leg speed. I calculate each leg independantly using spherical earth (6371km, cosine rule). Mostly all fine!
1. All of the spreadsheets have a row with a timestamp of 17:08:10. I calculate the speed from the previous location (17:07:04.406) as 548 knots whereas you have 469 knots (in V10). I failed to find the source of your 17:08 data. Perhaps it is interpolated from here? http://www.reddit.com/r/MH370/comments/28otnj/adsb_data/
2. The speeds are higher from Pulau Perak (18:02 to 18:22, 18:22 to 18:25 I calculate 493 & 470 respectively whereas you have 445 & 451 [in V9, but corrected in V10])
3. I note that the leg distance & speed can’t be calculated from 18:39 to 19:41 as the aircraft’s movements are unknown.
4. In Model “V9 South Indep Group” I calculate the speed at 19:41 to be 565 knots and at 00:19:29 to be 606 knots
5. In Model “V10 South Indep Group Constant heading” I note that the longitude for the aircraft at 18:25:27 has changed from the V9 model but not the latitude giving rise to a speed of 550 knots.
6. Your Model “V10 South Indep Group” labelled “Constant heading” looks to me like “constant (air) speed”.
I also note that Yap is using 17:07:18.906 (132) from the data logs rather than your 17:07:04.406 (131). The ATSB 26th Jun report uses 17:07 (132)
Duncan & all,
It’s been nearly one month that your independant team produced a statement urging to focus the search means around 36°S around the last ping ring.
A report describing the assumptions & models you used to estimate this priority search area was to be released in a near future: is it still on the agenda ?
Jeff
Yes, still on the agenda, although there is a (healthy) disparity of analyses and opinions; plus, since then the analyses and outcomes have been refined. There is no official report from this non-official group, but there have been many inserts here from a variety of very proficient people both working in the group, and outgroups, and individually. See for example comments from Brian A, Richard, Don T, Henrik, Yap, and many others deserving of note. See the useful entries from Cheryl, and LGHamilton, and others. I think that wise readers can soon see who has useful insights, and who do not.
I don’t think people mind disparity, but are more interested in seeing the workings and methods—a similar concern I recall hearing in regard to the earlier releases of probabilistic location results without accompanying methods. Is there anything myself or others can do to assist those listed with their names above in helping to write-up or present the methods; for example some recent publications:
If it’s of use for others as a starting reference, the LaTeX source for the last one is available in revision control at the usual location:
Hi Duncan ~
At this point, what information is still missing specifically from Inmarsat? For example, do you and your esteemed colleagues still require the six missing lines from the signalling unit log?
~LGH~
Since April 01, I have written about a northerly excursion for MH370 that takes it over the Andaman Islands and back down into the Indian Ocean. Radar data and eyewitness accounts that we have ignored do support a flight to the north. I have laid out a plausible scenario here:
https://www.dropbox.com/s/vmxqnijjd10goq8/First%20Last%20Hours.pdf
https://www.dropbox.com/s/of7qdmh05ximmy4/MH370nautilus.bmp
Sorry that it’s light on rigorous calculations but those will come once we gather together a few more data points.
Bruce
So it is OK to ignore the rigorous calculations based on the BTO (and indeed BFO) values?
It remains fastidious to follow & extract the useful information from this ever growing thread, even if we know who its primary contributors are (an external viewer may easily be lost here !). It is not always obvious to distinguish between the information endorsed/backed up by the independant team and the one which is not, or the degree of consistency of the varied hypothesis explored. I tried to follow this thread (and the others) and beyond the GES or AES frequency compensation fine modelling (eclipse effect incl.) a few points related to your early statement are still not clear to me:
Has the independant team been able to reproduce one of the 3 analysis conducted in the ATSB “search areas definition” report ? (which shows that the most probable candidate or the best fit trajectories end between 28° and 32°S). The degree of consistency of the varied hypothesis/trajectories in the report (mapped into a color scale) is measured as a BFO error, an n hybrid BFO and BTO criteria can be used too.
OleOle suggested on PPrune that the C-Channel BFO measure (around 90 Hz) around 18:40 could be a valid one (as well as the later C-Channel BFO measures which seem to fit the R-channel BFO profile) suggesting that the A/C was already flying south at 18:40:
The indpt team 470 kts trajectory seems to avoid the Indonesian airspace: when/where does the south turn occur in your simulation ? (injection point)
Do you take into account this 18:40 C-channel BFO value ? (which may constrain the south turn/the injection point to the last south leg)
Did you choose a 470 kts true ground speed because it leads to the straightest trajectory from your injection point or because it leads to the lowest BTO/BFO errors (versus the observed profile) ?
About the AES fixed frequency bias:
On a methodological point of view, we know that the MH370 AES frequency bias is around 150 Hz but there is an uncertainty on it (the ATSB report modelled this as a uniform distribution between 150-5 and 150+5 Hz) and we know that the end results of the simulations are highly sensitive to this value:
Instead of fixing the AES fixed frequency bias, be it randomly or a priori, why not estimating it, given the available data and knowledge ? When all the other BFO contributors (except the AES frequency bias) have been carrefully modeled (naming this knowledge/model BFOpred), why not estimate the AES frequency bias as the minimizer of
||BFOobs(t) – (BFOpred(t)+bias)||² ?
This is a very simple case of linear regression of BFOobs – BFOpred versus a constant time serie ! (the practical estimation of this bias only involves a correlation coefficient calculation between BFOobs and BFOpred). When I do this for each simulated flight in the MC simulation and I get an AES frequency bias distribution which seems reasonnably valued (concentrated between 150 and 153 Hz though, not uniformly between 145 and 155 Hz).
http://www.cnn.com/2014/07/12/travel/united-flight-boeing-777-diverted/index.html?hpt=hp_t1
Is this relevant?
http://www.duncansteel.com/archives/826#comment-7950
Hi Duncan ~
CXL my request/offer regarding the missing six lines from the ISUL. Since the 26 June 2014 ATSB report contains Appendix G which provides an analysis of the BTO measurement, I think you guys have what you need. Carry on!
~LGH~
LGH,
There is a lot more information in the Inmarsat data logs that would be very useful. The analysis done by Paul Sladen, in his Briefing Note 3 July, illustrates . It would be really interesting to see the whole lot – – but that might be wishful thinking.
Does anyone know if a 777 autopilot has selectable rate turns less than 0.5 degrees per second (= 1/2 BANK Autopilot Mode)?
Also, if a new true/magnetic course is selected, will the aircraft come back to the true/magnetic course line that passes though the aircraft position when the new course was selected?
I would suppose that if a new “heading” were selected, the aircraft would simply turn from its current heading to the new heading without regard to any particular track, but if a new “course” was selected, the autopilot would turn past the new bearing direction in order to fly down the line (at the desired bearing) that passes through either the next waypoint or the current aircraft position.
Bobby
Boeing uses bank angle controls, not rate of turn for it’s aircraft. In transport category aircraft turn rate is not used as a way of controlling the aircraft, rather, bank angles are used with a limit of 25° to 30° of bank while on autopilot.
Hi Ed! How are you?
FYI a NYT article estimated a banking angle of 20° for the westward turn back, while Don Thompson has estimated that 25° is the most likely banking angle that fits various constraints in his analyses.
http://mobile.nytimes.com/2014/03/18/world/asia/malaysia-airlines-flight.html?_r=0&referrer=
~LGH~
You are correct about the Autopilot – but the actual control reference target is either a heading or track angle set digitally with a turn knob to integer (one degree) settings. These settings can be either Magnetic or True as set by a toggle switch.. Using Track Select mode infers that the system will deal with the winds aloft in that the heading of the aircraft nose will be adjusted so as to keep the actual path parallel to the Mode Control Panel setting. There is no attempt though to follow an actual line over the earth by using GPS corrections. This is true for the Autopilot by itself – the FMS system is a higher level control system that does fly great circle routes between lat/lon waypoints.
Dale C.,
Thank you for that explanation but could you further explain where the triple redundancy comes in regarding the SDU. I thought I read where the communication path was designed to be triple redundant? Are you saying that by isolating the left AC bus and right AC bus then that denies the triply redundancy factor of a third power source to take over?
Cheryl #1
I thought you might find this conversation interesting — it is regarding a FAA AD for IFE systems in t7’s built before 2007. Be nice to know if this work was ever done by MAS. Be nice to know all sorts of things.
http://www.airliners.net/aviation-forums/general_aviation/read.main/5760243/
Hi,
Thank you Ole, Henrik, and Dennis for your feedback on my comment 7738
So if I understand correctly it is the missing ac velocity vector at 00:11 which prevents direct (accurate) solution of position (from eq. 6 in Henrik’s June 3rd summary combined with “ping ring” location)
And why under the constant heading and speed assumption, the position and time of turn south is essential.
In this light, and back to the beginning: is there consensus about the point of last primary radar contact. I noticed initially it was given between GIVAL and IGREX on route P628, see:
http://www.smh.com.au/world/malaysia-airlines-flight-mh370-may-have-been-deliberately-diverted-to-andaman-islands-20140314-34sp1.html
Apparently it has shifted but I don’t know why and when.
Furthermore, In the June 26th ATSB report there is made reference to “a distance further NW of Sumatra” (p. 6), a “north western limit at 1912” (p. 21) and a “NW point at 1912” (p. 46). How could we get more info on this?
Niels.
Hi Niels,
I think you are spot on with your analysis. We could still figure out why, mathematically, the equations show such a large span of near-possible solution, through.
Regarding the last known radar point, that is the crux, isn’t it? I think everyone is wondering if there has been a revision to the flightpath. The total silence from Malaysia is… not good.
Point further NW: there was a discussion here, quite long time ago, about a possible ‘fifth pin’ in the official map. It would take a bit of digging to find it, but it could be related to this new point (IGOGU or NOPEK?).
Henrik
Hi Henrik,
I was thinking a bit more about the large span of near-possible solutions. First of all, is it correct that r(t) is BTO based and p(t) BTO+BFO based?
When you intersect dynamic and stationary ping rings: these have large radii compared to their displacement. Note that towards 00:11 they come closer to really overlapping. So the point of intersect must be very sensitive to small error in p(t) (error in radius of stationary ping ring).
This is just a first very qualitative thought and one way of looking at it, feel free to shoot at it!
In this light, if you can get rid of the integration in L(t), of part of it as you suggest today …
Niels.
Point further NW:
To me it looks like the origin in fig. 28 in the ATSB report (1000 random unconstraints paths) is west of Sumatra
(maybe one of my biased sights ;-), so please check)
Niels.
Hi Niels,
“is it correct that r(t) is BTO based and p(t) BTO+BFO based?”
The difference (r – p) is purely BFO-based, which is the difference that really matters.
” So the point of intersect must be very sensitive to small error in p(t) (error in radius of stationary ping ring).”
Spot on. The cancellation error is the reason why we have been extra careful in modeling the distance between the satellite and the geostationary point. This is also the reason why the aircraft altitude matters. That said, the resolution is not a problem when performing the calculations. That is, the computed angle is correct to machine precision.
It may be noteworthy that there is no way around this. The sensitivity of the solution simply becomes apparent when knowing that it involves the difference between two large numbers. This is, ultimately, why the end position has such a large error bar attached to it.
Henrik
Hi, Niels44
Another thing, how can the ping arch 19:40 UTC line up with any other ping rings, if mh370 had not continued to the NW before turning to the south?
Don Baker
Here are my routes, if anyone is interested.
https://www.dropbox.com/s/wi2jicz7n73o5bt/Google%20map%20of%20turn%20to%20the%20south.%20%281%29.pdf
https://www.dropbox.com/s/ph2pcg5a75fyrqf/Google%20map%20of%20turn%20to%20the%20NW.pdf
Hi Don,
I’m not sure I understand your question fully right. But please have a look at comment 7967 by sk999 to see an example of a path that does not continue NW after last radar contact, but which is consistent with the “ping rings”.
Note also that the point of last radar contact officially has shifted more south, though I agree with your remarks that the initial report through Reuters was quite detailed, so indeed a bit strange this description of flightpath was suddenly “dismissed”.
Regards,
Niels.
Oeps, the example I refer to does continue NW for <= 18 min. Sorry for that inaccuracy!
But in general I don't see why you cannot reach 19:41 ping ring with turn SW/South directly after 18:22
(Not implicating that this is necessarily what happened)
Niels.
Don Baker said.
2014/07/13 at 18:14
Just one other point. If you measure between ping rings, you will find the same values of distances.
Duncan said.
Not QUITE true, but yes the near-consistency of ring separation is one thing leading many of us to use an assumption of a single great circle constant speed path rather than the curving path seen in the ‘official’ report. In fact we have been using that as a basis for a couple of months, maybe more.
You are correct Duncan, I was under stress when I inserted that statement. The distances are close, but not precise. I leave the math to the experts.
I don’t have a college degree and with ADD and being dyslexic with no memory, I never learned anything. However my IQ is over 130, for what that is worth.
Like I’ve said before, I would hate to see that, that initial report of military radar contact of possible flight MH370 that was close to waypoint IGREX be totally ignored.
I don’t know anything about BFO’s, BTO’s or UFO’s My intent is to stimulate thinking and that is all. I also sent ATSB my thoughts. Thank you all for your thoughts.
I’m sorry that I keep coming back, but I just thought of another thing. I appears to me that the maximum fuel range white circle is centered on waypoint IGREX. Why was that? I don’t really want to know. Something to think about.
Just stimulating thought.
How does from N9 Deg. 42′, E94 Deg. 27′ to S31 Deg. 9′, E95 Deg. 36′ fit in the ping arch’s time (Distance) line and in the maximum fuel range?
Hi, Niels44
Another thing, in order to line up ping 18:27UTC close to last known military radar contact @ 18:15UTC, flight mh370 would have to be on a NW heading toward waypoint IGREX.
Don, please explain why you believe that to be the case. i.e. what is the evidence explanation for what you are asserting.
Don, please get real. I see no sign that you have tried to obtain any match against the BTO and/or BFO data. This website is for people trying to make a serious contribution to the understanding and analyis of such information as is available regarding the flight of MH370. Perhaps 25 people gathered here have been applying their best efforts and intent to this aim for the past 16 weeks. We like signal, but we do not like noise. Enough.
Just one other point. If you measure between ping rings, you will find the same values of distances.
Not QUITE true, but yes the near-consistency of ring separation is one thing leading many of us to use an assumption of a single great circle constant speed path rather than the curving path seen in the ‘official’ report. In fact we have been using that as a basis for a couple of months, maybe more.
One other thing, I see that ATSB has the flight circling. Possibility to get the possible flight time to within a 7 and 1/2 hour time limit. My flight time in my suggestion is approx. 7 hours and 40 min. No need to respond to any of my post, because, I don’t know anything anyway and it would not help the team. I’m just attempting to stimulate though, so as to not let any possibilities pass by.
What puzzles me and this is why I mention this, is why was the last military radar contact even mentioned to be close to waypoint IGREX? It must have gotten someone’s attention. However why would they withdraw that claim? Was it a weak, short duration blip and they was afraid that they would be criticized, if it proved wrong later? No way of knowing.
I apologize in advance if this has already been mention ( I do not see any reference after reviewing comments here for the past few days). It is an FYI as I do not understand all the analysis complexities involved in this excellent and rational blog. On the pprune.org site, I just now found comment No. 199 by “sk999” posted July 09, 2014 saying “…Duncan Steel is wrong…” I read his reasons, but neither understand them nor know how to convey their import or veracity, if any, to this group.
A post that matches the description, appears to be:
I believe sk99 was referring to an earlier derivation of the ping rings. In the process of interpreting the scant (and sometimes inaccurate) data available, we have all at one time or another made incorrect assumptions, which we have progressively corrected as new data, knowledge, and insight have become available. Now that we have the ATSB report with its clear definition of how the BTO relates to the aircraft-satellite range, we are all on the same page about the BTO and ping rings. (I think!)
Bruce Lamon,
Thanks for the links regarding the IFE and fires. Since the IFE disabling event was around the same time as the other loss of comms at 17:21, was that a “load shedding” process of some kind? Disabling the IFE would mean disabling it’s satcom link or the SDU. Where is that done, in the FMS or by pulling the AC buses? What I don’t get in the ATSB Report, they speak of the SDU and if there is a loss of power to both AC buses, left and right, then the RAT is deployed and the APU, auxilliary power unit, kicks in for power to the SDU? So how did this not happen when the SDU was disabled in the first place at 17:21, about an hour prior to the 18:25 log-in request rebooting? And is the 18:39 handshake then the Ground initiated satphone call, the “one hour” time slot that the ATSB speaks of when the SDU is offline for one hour that the ground will inquire about it?
From page 33: “To experience a power interruption sufficiently long to generate a log on request, it was considered that a loss of both AC buses or, a disabling of the automatic switching, would be required.”
Basically, isolating the bus (in other words “disabling of the automatic switching” to other power sources) is needed in order for the SDU to be unpowered for extended periods of time. Both the SDU and IFE get their power from the left main AC bus, and it was re-powered at around 1825 Z based on the satellite communication logs.
The electrical buses can be configured from the flight deck through the electrical system control panel:
http://meriweather.com/flightdeck/777/over/elect.html
Does the SDU have any sort of holdover battery? If so, how long does it run on battery alone?
LG HamiltonUSA,
Hi LG, yes of course, the Lists are right within this blog on Duncan’s last article, I believe on or about 2014/6/20. I have since posted additions to them throughout the blog, just referencing the updated number on the list.
As it grows more, perhaps by Duncan’s next article, I will again retype it out in it’s entirety here in one place. As it stands now, we have a small handful of additions since 6/20, which have been noted here.
Cheryl #1
Hi Cheryl ~
I’m sorry I missed your reply. Rather than hunting around for multiple URLs and risk piecing together a preliminary, incomplete list I’ll just wait for the updated presentation.
~LGH~
For those trying to solve the set of 10 equations:
The algebraic trick appears to be:
Solve the equation for Rs^2 to get x as a f(y,z)
Substitute the other equations into the expressions for Vsp and Vps in the velocity equation. Square the velocity equations and then solve for Vpr^2 (We only have an expression for Rr^2, not Rr). The square root of the velocity equation can now be solved and yields an expression for y as a f(z). Substitute this into x as a f(y,z). Using x^2 + y^2 + z^2 = r^2, solve for z. This now yields a quadratic equation for z (latitude).
If others are working on this solution, let me know. Perhaps we can share results for constants at some point. To make it easy at this time, I’m using a constant value for satellite height and I am not adding the plane altitude to r. These are easy substitutions that we can make later. The number of constants that must be gathered together into new constants is so large, I’m running out of names for constants. If I was not retired, this would have been a great exercise for some student interns. Ah well! This may take a few more weeks, but getting a closed form solution is possible. I hope it is not a waste of time. I don’t believe Inmarsat was using the exact solution based on the ATSB report. They indicate that they checked flight paths between ping rings with different speeds and headings. But, it is not clear to me if they allowed for both a northern and southern heading between points.
Hello,
I was reading your comment and found the list below I think that is corresponding the comment above??
Why is there 10 equations? I reviewed your interest and was able to complete a solution in only 2 steps?
Maybe I misunderstand what it is you seek for a solution?
Could you please be more specific, or just remove the chaff and leave the wheat with what you seek?
Okay now, I am goodwillhunting so I will check back soon. thank you!
I solved the equation for Rs^2 to get an expression for x as a f(y,z) since a know Rs^2. Then I try to solve the velocity equations to get an expression for y as a f(z) after substituting x as f(y,z) into this equation. The velocity equation is:
V = Vsp + Vps – Vpr
Substituting:
V= ((x-xs)Vsx/Rs + (y-ys)Vsy/Rs + (z-zs)Vsz/Rs) + ((x-xs)Vpx/Rs + (y-ys)Vpy/Rs + (z-zs)Vpz/Rs) + ((x-xr)Vpx/Rr + (y-yr)Vpy/Rr + (z-zr)Vpz/Rr). Vsx, Vsy, Vz are known. Vpx, Vpy, and Vpz are a f(x,t) and these expressions must be substituted. Rr is an unknown. To make it worse I only have an expression for Rr^2. Therefore, I must do the following.
(V – ((x-xs)Vsx/Rs + (y-ys)Vsy/Rs + (z-zs)Vsz/Rs) – ((x-xs)Vpx/Rs + (y-ys)Vpy/Rs + (z-zs)Vpz/Rs))^2 = (((x-xr)Vpx/Rr + (y-yr)Vpy/Rr + (z-zr)Vpz/Rr))^2 and substitute Rr^2 = (x-xr)^2 + (y-yr)^2 + (z-zr)^2. As you can see when you substitute the expressions for Vpx, Vpy, and Vpz, and Rr^2, this gets very messy. If there is a easier way let me know.
The reason I why think this is important is that we are fitting a curve (flight paths) to BFO data points. BFO is a complex function of f(x,y,z, t, Vs, Vp). As in most curve fitting, it is useful to know the expected shape of the function you are fitting a curve to. For a simple function where y = f(x) we would either fit a linear, exponential, or a 2nd, 3rd, 4th order polynomial as appropriate. In this case, all we know is that the BFO data defines some flight path. This could be a defined flight path to a compass heading or a great circle. Or, these points could define a flight path that changes direction and speed at each data point. A defined great circle flight path heading due south appears to match the BFO data well. To check this, I thought I would solve an estimate of the exact solution of the BFO function to check if the BFO data would allow any significant deviations to this path. My estimated solution indicated that there may be deviations and we may have a less defined flight path. One possible deviation on the last leg of the southern flight path, I’ve been able to verify. However, given the complexity of the BFO function, I will not be certain of all of the possible impacts until I have an exact solution.
σAT
σCT
σh
σA
where
σAT= 3σ along track error
σCT = 3σ cross track error
σh= 3σ altitude error
σA = 3σ heading error
Navigation equipment accuracy constraint is specified by the above vector. Throughout the derivation of the navigation requirements, the along track, cross track and altitude components are derived from the following equations:
σAT = 1/10 sAT
σCT =1/10 sCT
σh = 1/10 sh
where
sAT = an along track distance
sCT = a cross track distance
sh = an altitude.
The 1/10 factor is used to define navigation equipment errors which will be insignificant with respect to:
(1) flight technical errors
(2) human blunders
(3) display instrumentation, control, and guidance errors
This constraint was made significantly stringent so the requirements would be maximum, and safety factors could be incorporated.
Methodology used to derive the system requirements is documented stated below
The navigation requirements are:
General aviation GA 1, GA 2
σAT = 1.5 nmi, 5 minutes
σCT = 0.2 to 1.0 nmi
Military and Air Carrier (low altitude)
σAT = 2.5 nmi, 5 minutes
σCT = 0.5 – 5 nmi
I would not substitute anything, I would get the values…
BTW… what happened to my reply to Bruce L, It disappeared ” is there a tech support for that??
Let me know if you need interpretation and make suitable citation to goodwillhunting if you decide to apply in your application.
Thx!
Goodwillhunting: I appreciate that you are trying to contribute, but your comments are almost unintelligible and vague. Either you can post things that assist, or else I will need to trash them so as not to confuse people or waste their time.
To all prospective commenters: there many been many, many comments over the past 3 months. Most of what is being suggested by people now has been stated and discussed previously.
Uh Oh, something happened on the post, all my superscript fell level???? any suggestions or may I suggest a dropbox to send it too. May I drop it in your box, let me know, that superscript must be displayed, that should be fixed here, oh well..
Ladies and Gentlemen,
I don’t have any college education, however I am a thinker. Most think that I am also a stinker. I admit that is true. Now I’ll get serious. I’ve been looking for a straight line of flight from the last possible known northern location of Flight MH370 to the last known plausible southern location. If we start at N9 deg. 35′, E94 deg. 37′ and fly south @ 496 Knots ground speed, we end up before the final partial ping and @ the maximum range radius. General heading 179 Deg. Intersecting ping rings 19:40 UTC through 21:41 UTC close to the 496 Nautical miles between ping rings. I don’t know what a 40 knot, out of the east cross wind at altitude for an aircraft heading as above and at full throttle of aprox. 510 knots would result in the ground speed. However that seems irrelevant to me, because it is the ground speed that is relevant.
Sorry, if I am out of line, by posting my opinion. Don’t mean to take up anyone’s time unless I thought it was important. The last thing that I want is to be a hindrance. My obsession is to find this for those who it means the most to.
Don Baker.
PS. I failed to mention that a heading of 180 deg. would be most logical in my mind, because programing a heading of odd number of degrees into the auto pilot, would not fit my nature.
I understand that the autopilot of an Airbus will stay engaged during an engine failure due to fuel starvation, however Boeing does not, except for perhaps the later models like the 777. I have read that Boeing has changed something with the autopilot software on newer models, but don’t understand their lingo. Also I understand the importance of the angle between the satellite and aircraft. It would seem to me that angle would only be significant in locating the final good ping location of the aircraft.
Hi Don,
Many thanks for your posting. Your “last possible known nothern location” is close to waypoint IGREX on P628. I think this is is quite northerly compared to most reports about last possible radar “sighting”. Can you please explain your source / how you came to this position?
Regards,
Niels.
If you was to simply take a Drafting Compass and place needle point in a ball, tennis ball or whatever Bal you have that is round is example use only,
Then flex the Drawing point outward 40 degrees, making this your distance point,…
Now mark that point on the Ball keeping your Drafting Compass at point, Then simply hold the ball still and your Compass steady being the ball is stable and rotate from center axis needle point……
Notice the Marking point comes off the ball unless you “manipulate” the compass to drag and rotate around…
The point is simple, The curvature of the radius for earth truly changes and does not allow you to simply pick any point you choose, being it’s not truly a great circle. To be further South, much more distance would be needed to apply.
Hi, Niels44.
Thank you for asking. I was worried that I didn’t have that info, but I did keep my sources or at least, most of them. It is my uneducated opinion that the ping rings are not precise enough to get a straight line track of this aircraft.
http://ogleearth.com/2014/03/flight-mh370-search-data-in-google-earth/
On the above website there is a white zig-zag line on the second Google earth picture on the right side of that pic., that represents the first part of the flight from military radar data. I had found this on a website that let me download the white lines to Google earth, however I can’t find that info. At this time. Sorry. If I do find it, I will post it.
http://opennav.com/waypoint/IN/IGREX
http://en.wikipedia.org/wiki/Malaysia_Airlines_Flight_370
http://www.reuters.com/article/2014/03/14/us-malaysia-airlines-radar-exclusive-idUSBREA2D0DG20140314
The Satellite ping ring integrity.
http://www.slate.com/articles/technology/future_tense/2014/06/inmarsat_releases_data_showing_mh370_definitely_went_south.2.html
Niels44
PS, I forgot to mention that, after their initial claim of a military radar contact at that location, they withdrew from that statement. However of my 74 years upon this planet, I have learned that, if something gets our attention, but later seems insignificant, it should not be forgotten. The aircraft was headed in that general direction and any slight blip on the radar screen at that location should be considered.
Niels44, I’m no longer considering the final partial hand shake, because, I can’t get it to fit any possible flight path.
Niels44
This is why I considered this position.
People are fearful that if they make a claim, (Go out on a limb) even implying that it may not be anything of significance, someone may later say why did you even mention it? They will do anything to protect their ego’s. It is my opinion that this personal pride may have already affected this investigation. Only my opinion. We need to find two constants and sometimes we must think outside the box.
I really think that this team needs to rethink the early claim by Malaysia of the last known military radar eco approximately at waypoint IGREX, because the aircraft was heading in that direction and a heading from that approximate location of 178-180 degrees does line up closely with all ping rings except for the last one.
Assuming an aircraft vector of 510knots airspeed at 180deg heading and a wind vector of 40knots at 270deg, in an hour the aircraft would fly 510nm southward and be blown 40nm westward… i.e. ground speed would be sqrt(510*510 + 40*40) = 512knots, and ground track = 180 + atan(40/510) = 185 degrees
From Cheryl #1:
An update to #8 on the Wish List. I reread the Preliminary Report (not the ATSB Report) for the sake of fine tooth combing it yet again and came up with another flight (MH386) that was asked to establish contact with MH370:
#8. Original Audio Recording of MH88 or any other flight (JAL750?) that was asked to establish contact with MH370, including MH386 that was asked by HCM ATC and KL ATC to try to establish contact on Lumpur frequency and emergency frequency at 2:53:51 (on report).
An update to #11 on the Back Shelf for further clarification:
#11. In Four Corners show, it stated that “someone tampered or interfered with the IFE, in-flight entertainment system.” How is this known and due to it’s technically unique and independent set up apart from the main processor, how does it act after a power failure or a power surge? What are it’s self-sustaining capabilities?
I was puzzled about the IFE tampering implication as well. How could that possibly be known?
A passenger tweet or text message sent shortly after take off saying that the IFE system had been turned off seems to me like the most likely possibility (assuming of course it is “known” and not just a reporting error). (Big assumption.)
Not that you asked, but turning off the IFE system to fight an IFE-based in-flight electrical fire is precedented, e.g.:
http://www.runwaygirlnetwork.com/2014/02/04/air-france-confirms-a380-ife-smoke-incident/
http://www.runwaygirlnetwork.com/2013/12/08/british-airways-not-ruling-out-new-ife-for-747s/
In the case of a cellphone lithium ion battery fire aboard a 777-200, the crew turned off the IFE system pending finding the cause.
http://www.bea.aero//docspa/2010/f-pk101208.en/pdf/f-pk101208.en.pdf
It seems that an intentional disabling of the IFE is a telltale sign of possible fire onboard.
Hi Cheryl #1 ~
I ‘d like to read the Wish List. Would you please tell me the URL where I can find it?
Thanks, LG
Hi All ~ Would anyone here kindly advise the URL for the “Wish List”. Thanks, LG
http://www.duncansteel.com/archives/826#comment-6560
That’s the last version that Cheryl #1 gave in toto. There have been subsequent additions and slight revisions: find those by searching the website on “Cheryl” (to whom much appreciation is due).
Running out of gas on this endeavor, and my better half is escalating the rhetoric relative to the futility of the effort.
Still, a parting shot is in order relative to what I expected the ATSB report to be, and what I actually got.
Considering the resources available what I would have done is:
1) Carefully modeled all the sources of error relative to BFO and BTO, and developed a probability density function for each. A source of BFO error not even mentioned anywhere is the accuracy of the Doppler compensation algorithm in the mobile terminal. Apparently it is assumed to be perfect. Likewise the measurement accuracy of the BFO values.
2) With these models in place I would have performed a Monte Carlo simulation which would result in a probability distribution in the Indian Ocean, not some colored patches on a map. The Monte Carlo would include other variables appropriately weighted such as fuel range and terminal glide path.
3) Armed with this result, it would be easy to construct a Bayesian search algorithm for the millions of dollars on the expense horizon.
Maybe this is what the internal report actually looks like, and the published search map was created for ease of public consumption. I have to believe this is the case.
WAVING MY HAND FURIOUSLY!!!
Exactly my point, how accurate is the SDU BFO Bias? What about temperature extremes of a fire or decompression or fire followed by decompression? Is this simply a TCXO? There are temperature limits. If it is a VCTCXO with AFC. there are still temperature limits regarding analog circuitry, op amps resistors, diodes, etc.
The oscillator in the mobile terminal is an SC cut single oven. Should be very good after a couple hours of warm up. Expect about two parts per billion drift in the first two to three hours from turn on. I do not know if the mobile terminal is powered by an APU when the aircraft is at the gate. I also do not know the previous flight history of MH370 that day prior to the Beijing departure. It may well be that the oscillator was very close to it’s stable operating point before takeoff. This information should definitely be considered relative to the BFO offset derived from the initial phase of the flight.
I have found a patent or two relative to Doppler compensation of mobile terminals using the received satellite downlink frequency as a reference. The mobile in MH370 definitely does not use this technique. As Henrik pointed out, the incomplete Doppler compensation during the climb out of KUL is strong evidence of a compensation algorithm that only compensates for horizontal velocity (velocity being a vector) relative to the satellite. Inputs for the compensation calculation are either GPS or inertial or a blended combination.
Why the mobile does not use three dimensional compensation is a mystery to me. It seems simpler than compensating in two dimensions. My guess is to allow the use of the terminal in an aircraft that can only supply airspeed and heading info (no GPS or inertial).
Hi Dennis,
“Why the mobile does not use three dimensional compensation is a mystery to me. It seems simpler than compensating in two dimensions. My guess is to allow the use of the terminal in an aircraft that can only supply airspeed and heading info (no GPS or inertial).”
I have been wondering about this too. My guess is that the compensation is an approximation based on a fixed radius, which will simply leave no place to input the rate of climb. Since both the position and the velocity are needed, it makes sense; the altitude is not likely to be accurately known.
Henrik
Bryan9
With regard the point you made. The FDD is “defaulted” to “open” should you wish to pull the CB.
Duncan
The reason I remain “slightly” confused re the INMARSAT data is I cannot see a “log off” on the system.
A “forced” log off is possible in flight, but I don’t see a record of this.
Thanks to the efforts of many including some members of the Independent Group, Inmarsat were forced to release some data in late May (the 47 page document). However, certain data have been withheld ( first several entries, many data fields etc) as many including Richard have pointed out. We should make another concerted effort to obtain the withheld data before the momentum fades. Perhaps the Independent Group can lead the way, just like some of its members did previously. All entries from start to end with all data fields, at the minimum.
Rand Mayer,
So my idea in principal is right, it is going to be through their non cockpit controlled Classic Aero? I remember in the early stages of this Inmarsat saying that the handshakes were never meant to be a tracking application, however that doesn’t state that they can’t make or enhance them into one. The demand wasn’t there but the supply would have been available, and now the demand exists since there is one missing plane. So all they have to do are modifications to the ground stations not the planes themselves and voila, we have tracking via Classic Aero. I’d call it
“AeroTrax.”
Cheryl #1
The ATSB Report left me pessimistic that MH370 will be found as a result of the planned effort it outlines, and not just because the search area is so far from the area identified by the Independent Team.
The Report’s analysis seems to rest on twin foundations: 1) that the primary radar location at 18:22 is reliable, and 2) that the 7th arc is quite close to the final location.
With profuse apologies if I have missed intervening clarifications, I understand that whether the 18:22 location relates to MH370 or UAE343 (or even is within the range of the Butterworth primary radar) remains unsettled. E.g., http://www.duncansteel.com/archives/730#comment-2966 (If the 18:22 location was not within Butterworth’s range, I infer that the 18:22 location is from Indonesian primary radar. The ATSB report is so agnostic as to the probable route from 18:22 to 19:41, I further infer that, with the possible exception of the traces after the “blip gap” leading to 18:22, ATSB has available no Indonesian radar to help determine the search area.)
Then there is the question of glide (or not) after 00:19, leaving aside the questions of how well the 00:19 arc can be defined via extrapolation or the seemingly anomalous BTO/BFO information from Inmarsat. http://www.dca.gov.my/mainpage/MH370%20Data%20Communication%20Logs.pdf at 41.
The Report acknowledges “a maximum glide distance of 100+ NM” but says the decision to search a width of 50 NM is to “avoid an impractically large search area” and because the “uncertainty in the width of the search area should be in balance with the uncertainty in the length of the search area.” http://atsb.gov.au/media/5243942/AE-2014-054_MH370_SearchAreasReport.pdf at 35. This width uncertainty is compounded by the realization that “MH370 may not correlate well with the case studies and the 20 NM distance suggested from the study may not be applicable.” Id. at 36 (“Comment” column).
The sequence of events upon fuel exhaustion described in the Report at 33 does not agree with Dave Whittington’s simulation (which showed a 17 minute glide). http://www.duncansteel.com/archives/826#comment-7052 The Report has a loss of power to both buses, followed by ram air turbine deployment and APU “auto-start” leading 3 minutes and 40 seconds later to an SDU logon. Dave’s simulation has a loss of power to both buses, simultaneously with activation of “backup elec sys” which deactivates after about three minutes, and then ram turbine deployment. So, the Report seems to suggest an SDU log-on several minutes farther into the descent than does Dave’s simulation.
I’d chalk up these differences to shortcomings in Dave’s simulation pretty much reflexively except that the Report seems to be imprecise on points that ATSB seemingly should have locked down. E.g., with the ACARS fuel data transmission at 17:07, shouldn’t ATSB be able to be more definitive than to say at 00:19 “fuel exhaustion was a distinct possibility”? Id. at 33. And shouldn’t ATSB be able to be more specific than the “RAT provides limited hydraulic and electrical power for instrumentation and flight controls”? Id. “Limited” in what way? I.e., what, if any, power does the RAT provide that would help an unpiloted aircraft stay aloft? E.g., hasn’t Boeing simulated this flight ad infinitum? Did it not share results with ATSB? The Report does not seem too sure-footed about the operational and performance characteristics of the aircraft under the assumed circumstances.
Speculation alert. The more I look at the Report, the less credence I give to diversion/suicide/shadowing/conspiracy theories, and not at all because the Report shies away from them. Human malfeasance theories deflect blame from the airline, the aircraft manufacturer and the component manufacturers, because, after all, no one can stop all the crazy and evil people in the world. If this plane is not found for years, it’s unlikely that anyone will be able in the meantime to persuasively lay blame on such things as improperly stowed or wrapped batteries in the cargo hold, or an electrical cockpit fire, or even my favorite, an ELT lithium battery fire. I suspect the corporate parties are relatively knowledgeable and regard human malfeasance as a long shot, which means that finding out what actually happened to MH370 might not be in their best interests.
My overall point is, ATSB may have the wrong 18:22 point, the wrong ending point and precious little technical help besides the unappreciated (by ATSB) Independent Team to get back on track.
wasnt this just changed yesterday in a press release, i mean the 7th arc, they said that the search is narrowed along the refined 7th arc??
like previous searches, is located along the seventh arc – “a thin but long line” “that marks where the missing aircraft last communicated with a satellite.”
they basically was stated that the 6th no longer determines the #7 curvature and the search is now focused on a thin but long line??
Did I read that correct? I will wait for the experts to say, I am just goodwillhunting.
Pending an expert response, as far as I know, the location of the 7th arc has not changed since it was first plotted publicly on April 7 (then called “Satellite Handshake Calculation #7). http://www.jacc.gov.au/media/releases/2014/april/mr012.aspx
I did not notice any discussion of the 6th arc or refinement of the 7th arc in yesterday’s press release. http://atsb.gov.au/infocus/posts/2014/cautious-optimism-in-search-for-mh370.aspx
The most notable thing to me about yesterday’s release was Thales getting I think its second official mention. This time they are listed before Boeing as among the “technical advisers.” Does anyone have a comment on what Thales’s role is? Perhaps it is doing project management? The most suggestive thing I have found is that Thales supplied the pitot tubes that malfunctioned on AF447. http://www.aviationtoday.com/regions/sa/Pitots-Being-Replaced-on-A330-Fleet_32766.html#.U77CmvldXxY
Meanwhile yesterday’s release continues ATSB’s ambivalence about the BTO data. When they want us to be in awe of Inmarsat’s prescience, ATSB says, “BTO was . . . added at the suggestion of the satellite operator following the AF447 accident to assist in geo-locating an aircraft.” http://atsb.gov.au/media/5243942/ae-2014-054_mh370_searchareas.pdf at 19. But yesterday, when the occasion called for ATSB to be seen as struggling valiantly, ATSB tells us that, “[t]hose handshakes were never intended to provide information about the location of the aircraft . . . .”
Hello Bruce L.
Those are not the precise updates I was referring in my comment, so let me clarify and maybe someone else may see what I have read;
This week, The SAR has been Dramatically refined since the release of the 6/26 report….
6/26 Original consist of 200,000km Square
The breakthrough is so overwhelming, the World Team was summoned; and theirs alot more where thats coming from
as I was informed. The New Robust Satellite Data and information along with the entire flight path Data received,
is refinement to its utmost integrity.
Also, there has been confirmed intelligents from an Independent Analyst somewhere in the USA that has been summoned;
apparently this enlightened information is a Game Changer, or is so overwhelming and interesting all parties were needed to fully tackle the massive amounts of Data being robust in nature, and quantity as well as clarification on Inmarsat and what is actually the standard over Inmarsat. There is much going on as my back channels have stated and publically, it shows. I am on my toes waiting to see what they revised so quickly since the earlier release on 6/26 and the speed-up on the SAR.
This week, SAR is now No larger than 60,000km Square as noted and discussed and Hyped by the officials;
for example see here::: http://www.financialexpress.com/story-print/1259088
As for all “Original” Media Releases By ATSB and DepPM Truss, I refer to the Updates released this week in direct relation to an apparent massive breakthrough that they had received at the end of last week.
“Just for Reference H2O placed the alert readiness for a fleet of ships and rov’s to be dispatched and arrive no later than 8/15 whereas the schedule was not to even leave before that date as it was pushed to September at the earliest”
DepPM Truss and Comm. Dolan made such request and the following links to the media “Updates” although Dated 6/26, they was released as Dolan has dated them in his Blog, also I refer to the JACC statement by Chief Air Marshal Angus Houston;
From AYSB Home page click on the “Update” by DepPM Truss http://www.atsb.gov.au/ that links here http://www.atsb.gov.au/newsroom/news-items/2014/mh370-new-high-priority-search-area-announced.aspx
that was reported Tuesday in AUS media and
noted in Dolan Blog here http://atsb.gov.au/infocus/posts/2014/cautious-optimism-in-search-for-mh370.aspx
This released today here http://www.atsb.gov.au/mh370/search-area-map.aspx
Compare Language to Original Release here and discussed by Dolan and Truss
http://www.atsb.gov.au/mh370/mh370-definition-of-underwater-search-areas.aspx
Sometimes “You Must Read Between the Lines, or even read the lines themselves”
If I have not read that correctly, please clarify for me as I am anxious and goodwillhunting.
Bruce,
Thales is the designer/manufacturer of the aircraft Satcom box. Thales is a subsidiary of Honeywell. The really interesting contribution that they can make is describing exactly how the system does the enhanced automatic frequency compensation, which in turn leads to a better understanding of the BFO calculation.
The little devil in me cannot resist pointing out the peculiarity of the eclipse of the satellite perhaps affecting the accuracy of the calculations being made by a company called Thales. (If you find this note mystifying, google on ‘Thales eclipse’.)
Thanks, Brian. No good deed goes unpunished: I have another question.
This link suggests that Thales also makes the IFE. http://www.airframer.com/aircraft_detail.html?model=B777#Navigation Aids (Airborne) (under “Airframe Systems/Cabin Interiors). Might the 17:07 ACARS transmission included data about the status of the IFE (and thus be a possible source for the 4 Corners comment)?
Brian, the MCS series of SDUs (originally 3000/6000) was jointly developed by Honeywell and Racal. Racal was later bought over by Thales (then Thomson-CSF). Thales is not a subsidiary of Honeywell. Most of the avionics on the 777 come from Honeywell. The question is why was Thales consulted but not apparently Honeywell. The bigger question is why the authorities have seen fit not to disclose any information about the Satcom equipment, given the whole Indian Ocean crash theory is premised on signals transmitted by such equipment. The pictures of MH370 on the net (see the link provided by Bruce) show MH370 had 2 Satcom antennas, a low gain antenna on top of the rear fuselage and dual side mounted high gain antenna above the door between the middle and rear fuselage (visible as a patch in the higher resolution pictures). A dual antenna configuration usually means dual SDUs, with the primary SDU linked to the high gain antenna and the secondary SDU linked to the low gain antenna which acts as a backup.
Whoops ! Let me try again – –
Thales and Honeywell partner to provide Satcom systems for aircraft, including the SDU and antennae etc. I think it is Miteq who made the EAFC unit which is also used in the satcom installation, and for which it would be interesting to have a precise understanding of the compensation system.
A Q&A site (Aviation Beta) suggests that what Thales is doing is to try to put, I quote, “ADS-B receivers on satellites. This concept is being developed by Thales Alenia Space and Iridium (Aireon) at the moment. The first satellites will launch next year, the system is expected to be operational in 2018.”
Voices there are guessing the costs of building adn maintaining such as a system would be significant. I read in some haste.
I reencountered this Guardian article from 25 March, which could be found valuable to reread: http://www.theguardian.com/world/2014/mar/25/airliners-should-broadcast-location-every-15-minutes-says-inmarsat-expert
The Inmarsat stock is apparently rising, literally. Should it be doing that, figuratively?
Hi Duncan,
Is Inmarsat right?
Yes, but …
They forgot to tell us a small detail. After MH370 left the last known location at the end of the Malaysian Military Radar trace heading toward waypoint NILAM, it then turned south toward Banda Aceh, but it overflew the Airport at 35,000 feet and 454 knots.
But instead of continuing south on this heading of 173 degrees true, MH370 circled off the coast of Sumatra for 57 minutes until then continuing the journey south.
The flight path ends exactly where Inmarsat predicted at 30S 98E.
Here are the details:
https://www.dropbox.com/s/q678p7whxwdqbne/MH370%20Flight%20Path%20Model%20V9%20South%20Summary.pdf
Here is a map:
https://www.dropbox.com/s/bu7ajeqvhedf37i/MH370%20Flight%20Path.pdf
Richard
The statement from the Independent Group on June 17th indicated that there was general agreement among several computer models that there was a specific area to search for MH370. Now I see that there are at least two different camps of results. It would be helpful if the rest of us could be clued in to why the major variance from our position three weeks ago and what particular element – either the ATSB report, the released Inmarsat data, or just new numerical models have led to the differences. It would also be great if the different groups would crosscheck each other and make sure that as much common data was being utilized as possible (BTO, BFO, ping radii, LOS, winds, magnetic declination, etc).
I felt previously that our strength was the willingness to approach from different directions but come to similar conclusions. The need for a large NW excursion from the last radar contact or a circling over Banda Aceh in order to fit the data is a new, unexplained concept.
Dave
just to aid understanding:
The ‘Independent Group’ contains members that do not all necessarily (still) post comments here, but communicate via email (and I have over 700 *unopened* email messages sent by those to the other members, plus many hundreds that I have opened).
There are others also working together by email, and at least three groups of those, although I see frequent posts by them here (which are welcome).
There are other people working independently on their own lines of attack on the problem, and posting comments and questions and requests for information here.
Should they not all be brought together? No, because disparity of opinion and approaches (and capabilities) make that undesirable.
Dave,
One of the necessities in doing a dispassionate assessment of the data is to recognize where assumptions have been made and to question them until we believe that the possibilities have been exhausted. When the Australian analysis was published it provided additional information not previously released and a new set of conclusions. We would be remiss if we did not try to rationally understand how the conclusions were released. This includes minor differences in the BFO model and more particularly the flight path after 19:41.
The lack of a definitive analysis of plausible paths between approximately 18:40 and 19:41 in the Australian report is a serious concern, and some of the group are working on an attempt to rationalize the situation. There appears to be a need for an unexplained “delay” in reaching the 19:41 point from the loss of primary radar contact in order to make any plausible flight path model work and lead to the conclusions in the Australian report. So, some possible path scenarios are being explored. The Australian authorities can put an end to our work in this area by clearly explaining their reasoning for starting the analysis at 19:41 rather than at, for example 18:22.
There s other information regarding the formulation of the BFO model that could be released, including whether the data used to determine the BFO model was all recorded during the event, or whether some of the L-band data was measured subsequently etc… The data redacted from the “raw” communications data may be of use in determining which transmitting antenna was being used for each set of measured “ping” data. We recognize that some of the data may not be releasable for various reasons, but it is unhelpful to refuse to release purely technical data.
The lack of wind models is a handicap to our efforts (other than the nullschool) and we welcome data from governmental agencies who may have such data.
So, we continue to try an keep an open mind towards the problem even if it may sometimes appear that we disagree.
Sid
WOW Richard, where did that come from?
We need irony alerts as well as conspiracy alerts…
Hi Richard
Your persistance with the revised tracks is laudable, many thanks for sharing your work.
Following Warren’s comment on your version 8 here: http://www.duncansteel.com/archives/826#comment-7621
I looked at a few examples (in version 9) of the columns headed Decimal time, Lat, Lon & Ground speed. Mostly they are fine but the leg between 19:41 & 20:41 takes c.56mins at your declared speed rather than an hour. Is that correct?
Hi Annette,
You are right, I had made a mistake. Many thanks for spotting my errors.
Here is a revised version of the Inmarsat flight path for your checking.
https://www.dropbox.com/s/2xm5vt77n996s74/MH370%20Flight%20Path%20Model%20V9%20South%20Inmarsat%20Summary.pdf
By comparison, here is the flight path of the Independent Group also for your checking.
https://www.dropbox.com/s/v0m7p8wjkfx2hfw/MH370%20Flight%20Path%20Model%20V9%20South%20IG%20Summary.pdf
Many thanks for your efforts. Any errors, inconsistencies, stupidities, etc. that you detect are very welcome.
The model, data, calculation methods, assumptions, etc. are always being questioned and updates are frequent.
Richard
There is an airstrip at Padang Panjang west coast Sumatra near the area where the plane was reported to be circling and Langkawi International airport approach from that point as well. If there were a fire, circling and burning off fuel prior to landing would be a priority. How a crippled aircraft goes from circling to a bee line south as puzzling.
Might I also point out that the reported seismic event in the Gulf of Thailand, which was quickly discounted came from observations of only two seismic stations. This means that there is an ambiguity in that the west coast of Sumatra at approximately 3°42’17.45″N, 96°37’1.25″E could have been a real location for that event.
Joe, you are repeating things that have been discussed here many times.
For example. “circling and burning off fuel prior to landing would be a priority” – No, it wouldn’t. Safe landing weights are for protecting an aircraft from damage. To protect passengers, in the case of a fire or similar the pilots get the aircraft onto the ground ASAP, regardless of weight. There have been several pilots commenting on this, early on, on this website.
Similarly ‘seismic events’ are a furphy. SE Asia is very noisy, in this respect; and a crashing aircraft involves almost zero energy compared to earth tremors. I live in NZ, where we get quakes every day, of far higher energy that a B777 crashing.
This website is my attempt to consider things solely on the basis of evidence, and science. Please let’s keep it that way. I hate needing to trash the many off-the-wall comments that come in.
Well, I guess I didn’t expect a “smackdown”
Still, why is nobody considering the operating temperature range of the SDU oscillator that may have had a cabin fire or decompression? It seems to my poor head that the BFO Bias is merely an assumption.
Dear Duncan,
I took a short “study break” hoping to understand better the BFO based modelling (still struggling ;-))
So I apologize in advance if i missed important comments on the following:
Inspired by Ole’s simple estimate for the 19:41 z-velocity component and following a remark by Dennis Workman (comment 7551) I’m now checking if the 00.11 UTC plane position can be determined from satellite motion only, given a certain BFO and proper corrections applied.
I use the first term in eq. 6 in Henrik’s “MH370 BFO Models” explanation; for relative large satellite motion at 00:11 it seems to dominate.
The first order approx. gives:
D/F = p_unit dot v_sat
Note that for a given D this returns an angle between p_unit and v_sat, where v_sat is fully known. In combination with ping ring / elevation angle I think it could indeed give a unique position.
Question I would like to ask to Dennis and Henrik or anyone else who can help, before I dive into detailed calculations:
– What is a reasonable value for D to be used at 00:11?
– Did anyone (Dennis?) already try this, what are opinions about such approach?
Regards,
Niels.
Hi Niels,
Henrik is the best person to respond to the values associated with variables in his math. He is always forthcoming. Relative to treating each BTO/BFO pair as determining a position it is analogous to the GPS 2D solution using three satellites. The third observable is need since the user clock bias needs to be eliminated unless the user is walking around with a cesium which is generally inconvenient. Clocks in the GPS user segment are generally far too imprecise to not require a third pseudorange for a 2D solution.
Best,
Dennis
Hi Niels,
I followed the same line of thought in this post on pprune:
http://www.pprune.org/tech-log/541472-mh370-resolving-inmarsat-data-6.html#post8542092
In Richard Cole’s paper
http://mh370.bookofresearch.com/Documents/MH370%20data%20analysis%2016-06-2014%20issue%201.pdf
he provides plots of the BFO components on pages 43 and 44.
40Hz -45Hz seems a reasonable value for D at 0:11, which corresponds to a line of sight speed of ~8m/s
Actually the line of sight speed of the sat towards the GES in Perth was also ~8 m/s at 0:11 so a “0th order” approximation (or maybe “minus first order” approximation ) can be made that the aircraft position at 0:11 was on a line between the sub-satellite point and Perth.
Problem is that 1Hz in BFO error translates to ~100km position error and that the remaining BFO component which is caused by the mis-compensation depends heavily on the the heading at that time, so that it is not easy to isolate the BFO component that was caused by the sat’s velocity.
Regards
Ole
Hi Niels,
“Did anyone (Dennis?) already try this, what are opinions about such approach?”
This was among the first things I tried, back when we were still struggling with the sign of the BFO model [1]. The resulting angle dependency resolves to the towing area, more or less.
Sadly, once adding the speed to the mix, it is possible to move a long way along the arc; hence, the much smaller aircraft velocity constant (0.03) is not sufficiently small to rule out other solutions.
If think you will find all the values and constants you need as you dig through the links in the summary. 😉
Henrik
[1] http://www.duncansteel.com/archives/751#comment-3647
May I ask a very basic question, as an non-expert in this field but one who shared tremendous interest in it.
WHY do the plane and ground station correct for doppler effects? Perhaps the answer to this question may help to explain HOW they correct for it???
For “doppler effects” read “Doppler shifts” (in frequency) I think.
The answer, fundamentally, is to keep the (radio) carrier frequency being used within allowable limits. That is, close to the allocated frequency, and not shifted off into a frequency that is allocated to other channels or other users.
For some background, look up TDMA (Time Domain Multiple Access), and related topics.
On the EAFC correction and the Eclipse effect
———————————————
Ever since the release of the ATSB report, and after running comparisons to
the best-to-date EAFC correction models (Victor, Yap and myself have been
through quite a few over time), I have had the nagging feeling that we
still have not gotten to the bottom of this. Until yesterday, the three of
us were in agreement that the best fit was obtained for a setup with the
pilot at Burum, and the EAFC programmed with Burum and AntiPerth as pilot
and ground station, respectively.
However.
It appears we can obtain a perfect fit to the ATSB data, 0 Hz offset, using
the simplest possible interpretation of the Miteq EAFC description [1]
– if we source the pilot signal from Fucino, but keep the EAFC
programmed at Burum. Victor and Yap has been through these calculations as
well, and agree that this is quite likely it.
So, here is my EAFC model.
A1. Let D be the total doppler shift on the pilot signal, measured at
Perth. Satellite effects will be dealt with further down.
A2. Let D0 be the average doppler measured over a (sidereal) day, aka
long-term effect. This value captures both the frequency translation error
and non-periodic effects in the orbit. The latter can contribute as much as
3-4 Hz to the correction.
A3. Let p and g be the pilot and ground positions, respectively, in ECEF coordinates.
A4. Let L and C be the L-band and C-band frequencies, respectively.
A5. Let M be a geometric constant, determined by
M = (C g_z / g) / (L p_z / p + C * g_z / g)
A6. The EACF approximation of the true C-band (D3) doppler is then
D3_EACF = M * (D – D0).
This model is obtained by assuming the satellite follows a simple inclined
orbit, and then evaluating the doppler contributions to first order. The
inclination (and ascension time) are the parameters on display on the Miteq
device, although in this model, they are indeed not used to produce the
correction itself.
The term p_z / p is essentially sin(LAT_BURUM), but to allow for a WGS84
model, the ECEF coordinates have been used instead.
With the above model, and setting D0 = -3 Hz from the previous day (slight
unknown here; the 14066.96754476 epoch yields -3.5 Hz, but earlier epochs
seem smaller), I get the table below:
TIME EAFC ATSB DIFF
0 29.07 29.1 0.0
12 27.54 27.6 0.0
25 25.80 25.8 0.0
37 24.11 24.1 0.0
115 11.61 10.7 -0.9
191 -2.02 -0.5 1.5
251 -12.67 -1.5 11.2
311 -22.33 -18.0 4.3
371 -30.27 -28.5 1.8
461 -37.78 -37.7 0.1
469 -38.16 -37.8 0.4
The ATSB value includes the eclipse effect, which happens between 169 and
236 minutes after 16:30, on March 7 2014.
The eclipse effect is somewhat complicated, because it will be partially
compensated by the EAFC algorithm, and it will also affect the long-term
value. There is a little room for error here, depending on how and when the
long-term value is swapped out. That said, this is the stand-alone eclipse
model:
B1. Let t be the time, measured in minutes since 16:30.
B2. Let tx = t + n S, where n is an integer and S is the sidereal period,
such that (tx – 169) denotes the number of minutes since the most recent
eclipse start.
B3. Let T denote the temperature relaxation time after the eclipse. The fit
yields T = 65 minutes, which may seem surprisingly high. There is at least
one study, on the Telstar satellite [2], supporting this kind of times.
B3. Then E, the bare eclipse contribution, is given by
if (tx < 236) then
E = E0 + k (tx / (236 – 169))^2
else
E = E0 + k exp((236 – tx) / T)
endif
Here k = 34.17 and E0 = -1.066 Hz. The constant term, E0, is somewhat of a
fix; it allows for minor overshoot effects in the real data.
The model is based on two significant phases. The first phase is a linear
rampup (or rampdown) in temperature, driven by a large temperature
difference (eclipse or applied heat). The traditional frequency correction
to an oscillator is quadratic in the temperature offset from optimum
performance, hence the square. The second phase is an undriven temperature
relaxation phase, which simply approaches the ambient temperature at a rate
determined by the physical properties of the bodies involved.
I was half expecting the temperature effect to be negative (k < 0), but
without knowledge of any details regarding the system setup, optimal
temperatures and heater effects, a positive contribution seems just as
likely. I would very much appreciate input from people in the know here.
With this model, the effect of EAFC plus eclipse becomes
TIME EAFC+SAT ATSB DIFF
0 28.91 29.1 0.2
12 27.39 27.6 0.2
25 25.65 25.8 0.2
37 23.97 24.1 0.1
115 11.46 10.7 -0.8
191 -0.63 -0.5 0.1
251 -1.48 -1.5 0.0
311 -17.96 -18.0 0.0
371 -28.62 -28.5 0.1
461 -37.48 -37.7 0.2
469 -37.91 -37.8 0.1
The negative value at 115 is somewhat perplexing still. It could very well
be connected to the "reset/reboot" event.
It should also be noted that here, only the 14066.96754476 epoch has been
used, which produces a reduced D0 of -2.5 Hz in the EAFC data. This should
possibly be handled slightly differently.
In conclusion, there is a simple EAFC model that, given the "right"
settings, produces the ATSB data almost exactly (apart from one still
unexplained data anomaly). Furthermore, the EAFC correction allows for the
remining eclipse contribution to be extracted and analyzed, and for a model
of the true eclipse effect to be constructed.
To my knowledge, this is the best correspondence to the ATSB data from a
model, so far.
Henrik
[1] http://miteq.com/docs/23TEC.PDF
[2] Hutchison, P. T. and Swift, R. A. (1963), Results of the Telstar
Satellite Space Experiments. Bell System Technical Journal, 42:
1475–1504. doi: 10.1002/j.1538-7305.1963.tb04041.x
“The negative value at 115 is somewhat perplexing still. It could very well be connected to the “reset/reboot” event.”
No, the only reboot event here was inside my head. Please disregard this statement.
Henrik
Hi Henrik,
your model seems plausible to me and describes the EAFC as I would expect it to work, yet I’m not expert enough to give a real judgement.
What still puzzles me:
Inmarsat logs should contain thousands of BFO measurements of communication messages between other aircraft and Perth at the time around the eclipse. Position and speed of these other aircraft should be well known which allows for a backward calculation of (δf sat + δf AFC) . So this is a rich source of data that can be used for ex-post calibration of (δf sat + δf AFC), yet in their latest report ATSB doesn’t mention explicitly it was done this way.
If it were done this way, any modeling of the EAFC would only be for finding a best fit to the data and for sanity checking.
Ole
Hi Ole,
Thanks for your comments.
“So this is a rich source of data that can be used for ex-post calibration of (δf sat + δf AFC”.
Indeed, that would be very clever and would yield very good calibration. And if they shared it with us, that would be even better.
“If it were done this way, any modeling of the EAFC would only be for finding a best fit to the data and for sanity checking.”
There is a third reason for doing this, perhaps the most important one from my perspective: articifial enhancement of the data. As a note to readers: this is not so far from the sciene-fiction-style command “enhance!” that always seems to exist when people need to see clearer in a picture. The difference is that this method actually works; by accurate physical modeling of the observables, one can move the measurement errors over into systematic errors, governed by a handful of parameters.
Alas, this will not find the plane for us, but it makes it easier for us to comfortably focus on the L-band contributions.
Henrik
Henrik,
I’m confused by ” source the pilot signal from Fucino, but keep the EAFC programmed at Burum”. Do you mean that the pilot signal is generated at Fucino and beamed up to the satellite from there? Is Burum the sole ground station? Or is the ground station in Perth but is programmed for Burum’s location? Is the AFC done in Burum and sent digitally to Perth? Put another way, is p at Fucino or Burum? Is g at Burum or Perth? We seem to have Fucino, Burum , and Perth all in play but only two variables (p and g) to describe them.
Dave, glad to have you aboard, but you need to read previous comments and replies about pilot waves, virtual terminals, where Inmarsat’s ‘correction’ algorithms incorrectly assume Perth to be, and the like.
Henrik,
I’m not a math whiz here, as Duncan can attest to – tag yer it Duncan!!! – but there may be one hiccup in your formula, although this has probably already been addressed in previous posts.
It assumes, I think, that the Inmarsat satellite has a “wobble” factor (sorry – I can’t think of a more correct definition or term) that remains constant through a sidereal day, or a series of sidereal days depending on the amplitude and frequency of the total “wobble”.
If the satellite moves through the wobble at a constant rate through a complete cycle, then ok. But if that wobble varies in speed amplitude throughout a cycle, then may tend to throw off a calculated point.
Just thought I’d ask this question.
Cheers and keep up the great discussion!!!
Colin: ah, yes. One can calculate the ephemeris of the satellite (which I and others have done) across the time of the flight of MH370, using the latest set of orbital elements for the satellite as of March 7, from what is often called the NASA TLEs (two-line elements), although they are actually derived using capabilities if the US DOD. In fact there was an updated set of elements at an epoch during the MH370 flight. This tells you, rather precisely, where the satellite was at each instant of time. Henrik knows all this very well. But what he is addressing here is not that. What he is investigating is how the overall satellite communications system was making a first order correction for how the Doppler effect would be shifting the frequencies of the carrier waves between the ground station near Perth (especially since the correction algorithm apparently used the wrong sign for the ground station’s latitude) and the satellite, and also between the satellite and the aircraft. The correction, when applied, would minimise the difference between the actual frequency and the desired frequency (i.e. the middle of the allocated bandwidths). A complete, automated correction is obviously impossible unless the aircraft position and velocity is known at all times. Similarly it is not feasible to know in real time the satellite positions and velocities for use in the correction algorithm, because the age of that satellite means that it does not have a GPS receiver on board. What Henrik is modelling – rather successfully – is what Inmarsat’s correction algorithm might be doing under these circumstances, given that we are not privy to that information. That is, he is using the form of simplified, approximate motion of the satellite that he thinks that Inmarsat likely is using. And it looks like he is correct.
Colin,
Thanks for your comment. Duncan already said it all very well, but it does not hurt to repeat: We know the real satellite movement very well, to within a hundred meters or so. The EAFC device, sitting in Perth and making adjustments to the incoming signals, approximates this movement in a particular way, that leads to a particular doppler correction. That is what is sought in this particular post.
Thanks,
Henrik
BTO and BFO – Again!
I have been critical of how the BFO and BTO values have been handled in the ATSB report. Those prior posts have been met with little or no commentary. So I will try again.
First BTO – Reference is made to Table 2 on page 55 of the ATSB report.
Consider simply the first seven values in Table 2 when the satellite to aircraft range is constant at 153037 kilometers (this value is actually twice the range to account for the round trip measurement time). The last column (error) is obtained by subtracting the bias value for that measurement from the average bias and multiplying by the speed of light. What troubles me is that these errors are intrinsically in the direction of the line joining the satellite to the aircraft. The error on the surface of the earth will be much larger.
For example, consider the very simple flat earth model below.
H = height of satellite above surface of earth
R = distance from aircraft to satellite
L = distance from point on earth below satellite to KUL
In the simple flat earth model R^2 = H^2 + L^2 (a simple right triangle).
Differentiating with respect to L and rearranging yields:
dL = (R/L)dR.
This result shows that errors in R ( the values in Table 2) should be scaled by the ratio of R to L to get the corresponding errors in L which is what we are really concerned about. The ratio of R to L is approximately 9. So I state that the width of the error band on the ping rings should be +/- 100km not +/- 10km. This dilution of precision (DOP) is a direct result of simple geometry, and is very commonly used in the GPS vernacular. The use of a flat earth model has little loss of generality, and makes the math trivial.
Second BFO.
I speculated in an earlier post that the BFO values were suspect due to unaccounted drift in the oscillator in the mobile terminal during the first 6-12 hours of operation. I used a value of 2 parts per billion as being typical of an ovenized SC cut crystal oscillator. I have subsequently learned that this is the type of oscillator used in the mobile terminal of MH370. So my speculation of errors on the order of 4Hz at L band over the time of the flight was appropriate.
I would expect smaller errors in the satellite oscillator since it is powered on continuously. Still the eclipse is an unusual situation. On earth temperature changes tend to be gradual due to the thermal inertia of the environment. An eclipse is like taking the satellite from your kitchen table and sticking it in the refrigerator. I have no idea how to model the thermal inertia of the satellite or the agility of the temperature controlled oven surrounding the oscillator. This modeling should definitely be done by someone who has the information and the skill to do so.
Lastly, no mention is made of how the BFO values are actually measured. It is no small task to perform a frequency measurement on a sub-second burst of energy at L band (or any other frequency for that matter). The most accurate method I know of is counting cycles over a gated precise time period. One would need to count cycles for an entire second at L band to get 1Hz measurement accuracy. Is the transmission from the aircraft that long? Don’t know.
Dennis,
I think you need to look at the description of the BTO measurement earlier in the document, and also at the data logs released by Inmarsat about 27 May, where the formula is given for the BTO calculations. [Indeed it is the formula proposed in this blog by Mike Exner many months ago.] The figure you quote, 153037kM is actually the total path length from the Perth GES to the satellite then to the aircraft on the ground at KUL.
The point of Table 2 is to illustrate the process that Inmarsat used to calibrate the calculation and derive a fixed value for the constant “K” [called the Bias], in order to then use this for the calculated LOS range at later times. As you can see the precise fit to KUL is not that good, but errors can be explained by possible multi path transmissions, and system warm-up during these times.
It is also possible to check the calibration of “K” at later points in the flight, noting that the satellite is moving continuously and its precise position needs to be taken into account too. Having done this it is indeed possible to match ground positions to within 2kM, and also to show that the Inmarsat derived constant is satisfactory.
The BTO numbers are rounded to 20usec. By reverse engineering the range calculation it is also possible to show that the an exact match to the ground position can be obtained within the rounding of the BTO. Hence the width of the error band for the “ping radii” is conditional on the rounding error in the BTO and perhaps the assumptions made for the precise satellite location at each handshake time. It is certainly within +/- 10km.
The figure I quoted is actually twice the total path length. I knew that from the start, but this blog has no edit feature. I also knew that people would get hung up on that. I stand by my conclusions relative to the interpretation of BTO and the expected accuracy on the surface of the earth. In any case I used the number (153,000 km) simply to bookmark which measurements I was talking about. It was not used to form any numerical conclusions.
GPS also uses L band, and while multipath is always a concern, it is small relative to the accuracies we are considering in this nvestigation.
I am actually pretty satisfied with the ATSB conclusions as mapped. My own estimate is that search area should be 200km wide and 2000km long centered on the 7th ping ring directly West of Perth. The length and width correspond to an error budget consistent with my own estimates, and the center location fits the location I had calculated, and stated here, before the ATSB report was published.
What if the BFO oscillator circuit is subjected to temperature extremes of fire or decompression or fire followed by decompression. Then the SDU specs are out the window. The BFO Bias is one variable that will topple this house of cards.
Joe,
Let’s say this is what happened: at 18:25, there was a drastic temperature drop, from 20 degC to -20 degC or so. What would the approximate temperature drop be at the oscillator? How big would the frequency change be? That would be useful to know. If it is very big, we can discard this theory right away, for instance. If it is within the plausible range, then that is very useful info too. What is your estimate?
Thanks!
Henrik