Background Information on the Pinging of MH370 by Inmarsat-3F1 _ Duncan Steel.pdf

5/4/2014 Background Information on the Pinging of MH370 by Inmarsat-3F1 | Duncan Steel

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Background Information on the Pinging of MH370 by

Inmarsat-3F1

Duncan Steel, 2014 April 03. duncansteel.com

In this post I am just giving some information that followers of this saga might/need want to

know.

The Inmarsat briefing to the AAIB thence the Malaysian Government

In a comment following a post of March 23rd a correspondent ‘Andy’ wrote, several days later

(2014/03/29 at 2:03 am), to say the following :

There was a PDF document on the Inmarsat site which gave some details of the work involving the

doppler effect:

http://www.inmarsat.com/wp-content/uploads/2014/03/Inmarsat-Differential-Doppler-Study.pdf

It does not appear to be there any longer, but the document is present in internet archives.

Andy sent me the PDF. I present it below as images (screen grabs from the PDF). The second,

third and fourth pages are the pages that formed the ‘Annex I’ issued by the Malaysian

Government on March 25th (see also this web page). The cover sheet (page 1) shows that the

origination of those three pages was a briefing by Inmarsat to the UK AAIB. Nothing new there,

but I put it in for completeness.

BACKGROUND INFORMATION ON THEPINGING OF MH370 BY INMARSAT-3F12014/04/03 | DUNCAN | 24 COMMENTS

Duncan Steel

http://www.duncansteel.com/some-comments-on-the-final-ping-of-mh370-by-the-inmarsat-3f1-satellite

http://www.malaysiaairlines.com/content/dam/mas/master/en/pdf/Annex_I_images.pdf

http://www.malaysiaairlines.com/content/dam/mas/master/en/pdf/Information_provided_to_MH370_investigation_by_UK_Air_Accidents_Investigation_Branch_Updated.pdf

http://www.duncansteel.com/archives/526

http://www.duncansteel.com/archives/author/duncan

http://www.duncansteel.com/



http://www.duncansteel.com/wp-content/uploads/2014/04/p1.png



Everyone will surely have seen the above three images previously; but likely not the first of the

four.

Deciphering the Burst Frequency Offset (BFO) graph to get Doppler shifts

The three contributions to the BFO are explained in p.2 above. The idea here is that component

D3 can be calculated, knowing the satellite ephemeris and the location of the ground station;

D2 is derived from the BFOs (i.e. is time-dependent); and values of D1 can then be inserted and

tested against possible paths and speeds of the aircraft. The fact that the initial path and speed

of the aircraft is known (including being stationary on the ramp at KL) allows a calibration to be

achieved.

Mike Exner, with some assistance from Ari Schulman, has deciphered all this and so derived

time-dependent values for the Total Doppler, as in the first diagram below. I calculated the LOS

speeds (hence time-dependent Doppler shifts D3) between the satellite and the Perth ground

station and supplied those to Mike for incorporation in his analysis.

From the Total Doppler Mike pulled out just the L band Doppler (red dots in the first diagram)

as shown in the second diagram below. From those Doppler shifts Mike calculated speeds of the

aircraft relative to the sub-satellite point (i.e. Range-Rates in usual ground-based radar




observations) and based on an assumption that the elevation angle from the aircraft to the

satellite was 40 degrees. That is what is shown in the third diagram below.

At the time he was doing these calculations shortly before going on vacation, Mike only had

that angle (40 degrees: the ping ring elevation at 00:11 UTC) to use. We now have others (which

I will be posting on this webpage in a while). Anyone with a calculator should be able to derive

the aircraft speeds relative to the sub-satellite point for any other elevation angle by back-

calculating, using an assumed altitude for the satellite (35,790 km is near enough).

Mike inserted comments regarding his method and assumptions into each diagram. His time

frame was MYT = UTC + 8 hours. Following are the three pertinent graphs that result; Mike

Exner specifically asked me to make these public here.

http://www.duncansteel.com/wp-content/uploads/2014/04/All_Doppler_2014-04-02.jpg



http://www.duncansteel.com/wp-content/uploads/2014/04/L-band_Doppler_2014-04-02.jpg

http://www.duncansteel.com/wp-content/uploads/2014/04/MH370_Radial_Velocity_2014-04-02.jpg



Time (minutes) LOS Speed (km/sec)

0990 –0.000341

1003 0.007443

1015 0.014936

1027 0.011022

1105 0.043419

1107 0.025610

1109 0.020462

1180 0.020136

1240 0.031279

1300 0.041077

1360 0.051776

1451 0.064485

Please, I am simply unable to explain anything further about these plots. If you don’t

understand them, apologies. Let me close by repeating the line-of-sight speeds that I gave

(based on Mike Exner’s analysis) in my previous post. In my own analysis, this is all I need.

http://www.duncansteel.com/archives/507



24 THOUGHTS ON “BACKGROUND INFORMATION ON THE PINGING OF MH370 BY

INMARSAT-3F1”

2014/04/03 AT 11:43 PM

You can still find the PDF (or something very like it) here:


There is also the Inmarsat ‘Newsroom’ page which essentially reproduces the same

information here:

http://www.inmarsat.com/news/malaysian-government-publishes-mh370-details-uk-

aaib/

2014/04/03 AT 11:59 PM

As I wrote, I am sure that everyone has seen the later 3 pages already; but not the first

(cover) page.

2014/04/04 AT 12:55 AM

Agreed that it is potentially interesting that the ‘Inmarsat cover page’ appears to have

been removed. Sorry about the duplicate link, I was just trying to give a bit of wider

context.

2014/04/04 AT 1:02 AM

My intent in putting that in is more a matter is establishing a chronology as this sorry

saga continues.

The guys were working on a Sunday, credit to them; similarly the information was

conveyed from AAIB to the Malaysian Government promptly.

Skwosh

Duncan

Skwosh

Duncan


http://www.inmarsat.com/news/malaysian-government-publishes-mh370-details-uk-aaib/





2014/04/04 AT 1:13 AM

Ah – I get you – the *date* is on the cover page. Yes – I see what you mean (I was

thinking that it might be something to do with the ‘politics of attribution’ and/or

not wanting the word ‘Inmarsat’ to appear on it for some reason – though why

that would be I can’t think – your explanation is much simpler!)

2014/04/03 AT 11:56 PM

Many thanks.

As I understand Total Doppler received at LES is just sum of those Dopplers at every step:

C band Doppler (3615MHz) + S/C induced Doppler (1643MHz) + Total L band Doppler +

Net AER Doppler

The last is the one of our interest.

And here is one thing to point… when you calculate Doppler shift for part of recorded track

with 900Mhz of initial frequency it fits almost perfectly presented BFOs of Net AER

Doppler.

At least with Hamster3null’s spreadsheet.

2014/04/04 AT 5:28 AM

AndRand said,

April 3, 2014 at 12:41 am

if you use 900Mhz of AES frequency to calculate doppler shift it quite matches the BFOs

from the recorded part of track.

I have to update this statement: it fits the planned flightlog

https://flightaware.com/live/flight/MAS370/history/20140307/1635Z/WMKK/ZBAA/t

racklog

With flightlog updated to this guestimation http://skyvector.com/?

ll=4.746514696181505,98.71435545889493&chart=302&zoom=9&plan=A.WM.WMK

K:F.WM.GUNBO:G.5.7530039670591675,103.1850585976314:F.WS.IGARI:F.WM.GU

NIP:F.WM.VAMPI there is significant difference:

[img]http://i.imgur.com/LAUjjoR.png[/img]

Skwosh

Andrand

AndRand

https://flightaware.com/live/flight/MAS370/history/20140307/1635Z/WMKK/ZBAA/tracklog

http://skyvector.com/?ll=4.746514696181505,98.71435545889493&chart=302&zoom=9&plan=A.WM.WMKK:F.WM.GUNBO:G.5.7530039670591675,103.1850585976314:F.WS.IGARI:F.WM.GUNIP:F.WM.VAMPI



My version of Hamster3null spreadshet here: https://docs.google.com/spreadsheet/ccc?

key=0AhvpxNRGOuapdERwQ0hPdzlnVDE4djRBWVM2dURVMXc&usp=sharing

2014/04/04 AT 12:51 AM

Duncan, I have just posted my long ranty *alternative* take on the ‘D1 D2 D3′ diagram at

TMF Associates.

2014/04/04 AT 1:09 AM

Thank you for the above. I really don’t understand all the technical know-how \or know-

what about the loss of the air craft. But can I ask one Q.

If this plane was on a mission to no where, with no guidance, since it seems it was

transmitting nothing, so assume it couldn’t also receive anything.

Why would it be assumed << probably not the right word that is kept to a 'air corridor' why

not just fly off randomly to anywhere?

2014/04/04 AT 1:37 AM

Thanks for that, Lea. Honest questions (like your own) are good.

Actually, the aircraft could transmit one thing (or perhaps I should say, *did* transmit one

thing). And that was responses to pings, or handshakes. Computers do just this over the

internet: it’s like a brief signal that asks “Are you there?” and if an automated response

comes back (from the aircraft, here), then it means it is still “there” in that it is functioning

and ‘conscious’ in an electronic sense.

All the analyses you will find here is about the pings. The point is that the ping returns (to

the satellite, thence the satellite ground station) can tell us two things about the aircraft

at the times of the pings: (a) The distance between the satellite and the aircraft, from the

time delay in the ping (due to the travel time of the radio signal); and (b) The relative

speed of the satellite and the aircraft, from the Doppler shift in the radio frequency; look

that up on Wikipedia (Doppler effect). In the case of *sound* (not radio waves) you hear it

often, for example the change in the pitch of a siren as an ambulance whizzes by.

Skwosh

Lea Meadow

Duncan

https://docs.google.com/spreadsheet/ccc?key=0AhvpxNRGOuapdERwQ0hPdzlnVDE4djRBWVM2dURVMXc&usp=sharing




That covers your second sentence. Now the third one.

An assumption being made is that the aircraft flew on under the control of an autopilot

with no ongoing human control, for whatever reason. That may have been a default of the

B777, it may have been an autopilot setting entered by the crew, we don’t know. But the

autopilot (I am told by aviation people including some very experienced B777 pilots)

would have been set, one expects, to follow: (i) A constant speed and altitude (we know

neither for sure); and (ii) On a direction that has been set as being either a great circle

route to or towards some waypoint (e.g. the South Pole) or following a specified magnetic

bearing (which varies with latitude and longitude). The first of those (great circle) you can

think of as being a straight line, except that the Earth is not flat; a great circle is the

shortest distance between two points. The second would mean that the aircraft would

keep changing its heading slightly, from minute to minute.

My understanding is that during long flights the autopilot is flying the plane for most of

the time. With two pilots (captain plus co-pilot) one would be resting/eating/whatever

whilst the other was in the seat in front of the controls but not with his/her hands and

feet doing anything. He/she would just be checking progress.

Whatever route the aircraft *did* take, the intent in the analysis here is to determine that

route based on the information available from the pings, and the known locations of the

aircraft earlier in the flight.

Hope that answers your questions,

Cheers,

Duncan

2014/04/04 AT 1:48 AM

Many thanks. I had gathered the bit about the pings (a bit like cookies on the

computer) and that this was how it was tracked to have taken the Southern Corridor (I

believe that is what is is called).

So the bit about the Autopilot makes complete sense. But (sorry always a but) thought

that if all systems were down\disabled – would indicate surely amiss with the aircraft.

Then it begs the Q – no need to answer Why did the autopilot continue to work, i.e.

part of the computer system, but all else apparently failed.

Lea Meadow



Again, many thanks.

2014/04/04 AT 1:22 AM

Duncan,

It occurs to me that one could derive the ping ranging from the red track and then check to

see if the sub satellite issue has been covered by Inmarsat by trying to reproduce the yellow

track with and without satellite motion. Might be too degenerate, or the image not detailed

enough but perhaps it is worth a try.

2014/04/04 AT 1:44 AM

Hi Chris.

In fact a back-engineering of the ping rings from that fuzzy Google Earth image (have

those people no shame?) has been done in a quite beautiful study which I recommend all

to look at:

http://www.reddit.com/r/MH370/comments/21xw2a/mh370_reverse_engineered_ping_

data/

http://www.reddit.com/r/MH370/comments/21jla4/mh370_flight_waypoints_timing_an

d_speed/

Right now I am putting the ping ring information (for different times) into my STK

scenario so as then to search for possible paths that fit.

Cheers

Duncan

2014/04/04 AT 3:28 AM

You can recover quite precise information from such images. It is not hard to pin down

the centers of those tracks and also fit the coordinate grid to great precision owing to

its mathematical nature. That is some pretty nice work going on there in that link.

Here is a question that might be revealing: in the last three pings, there are three

ranges from the satellite and three LOS velocities relative to the satellite, so six

Chris Dudley

Duncan

Chris Dudley

http://www.reddit.com/r/MH370/comments/21xw2a/mh370_reverse_engineered_ping_data/

http://www.reddit.com/r/MH370/comments/21jla4/mh370_flight_waypoints_timing_and_speed/




independent data points. If we assume a great circle course, is there a unique solution

in each hemisphere for speed, heading and position that can be derived? If so, that may

give rather specific information on where to look. The red track seems to indicate that

changing speed required avoiding a great circle course, which might be an odd way to

fly.

If thee pings is enough, then trying again with the three prior to those and checking to

see if the dots can be connected between the third and fourth pings back at constant

speed might be a test of the constant speed assumption in the South, though working

with the sixth ping back may be problematic.

2014/04/04 AT 6:02 AM

Chris: Well spotted.

Basic answer is yes, and that’s what I am now trying to do. But first I had to get the

initial (pre-18:22 UTC) part of the flight path correct (see other answers). All takes

time.

Thanks

Duncan

2014/04/04 AT 4:01 AM

Glad you were able to use the data, and great work here. Your satellite data was crucial

to the analysis of course. If I get time I will check that the yellow track BFO calculation

matches their published estimate.

2014/04/04 AT 6:07 AM

GlobusMax you are a star.

Great work, great write-ups. Exemplary.

Many thanks,

Duncan

Duncan

GlobusMax

Duncan





2014/04/04 AT 1:46 AM

Also: Inmarsat *did* use the satellite motion in this later study (March 23). It was their

earlier attempt leading to the map issued by the Malaysian Government on March 15

that assumed a truly ‘geostationary’ satellite and started me on this whole chase…

2014/04/04 AT 2:23 AM

Hi, interesting site although I don’t understand it!! One thing I don’t understand, shouldn’t

your flightpaths follow the published radar tracks?

http://ogleearth.com/2014/03/mh370-updated-route-final-radar-plot/

2014/04/04 AT 6:00 AM

Answer = fundamentally yes, and that is what I have been addressing in the past 24 hours

or so.

Thanks,

Duncan

2014/04/04 AT 3:37 AM

Hello,

please take into consideration this image of the flight path up to 2:08 Malaysian Time, it

was shown to the Chinese relatives.

http://www.themalaymailonline.com/uploads/gallery/2014-

03/mh370_china_screen_press_briefing_20140322.JPG

2014/04/04 AT 6:04 AM

Stefan: Thanks for the message.

Duncan

dave

Duncan

Stefan

Duncan

http://ogleearth.com/2014/03/mh370-updated-route-final-radar-plot/

http://www.themalaymailonline.com/uploads/gallery/2014-03/mh370_china_screen_press_briefing_20140322.JPG






My answer: No, because I do not KNOW this path to be correct. I am working only on

what I know, or think I know, is true.

Duncan

2014/04/04 AT 4:40 AM

Hi,

I’m puzzled ….

My understanding of Mike Exners charts is that the BFO in the inmarsat graph actually

represent the Total Doppler. From there Mike subtracts D3 (C-Band Doppler) and D2 (S/C

induced L-Band Doppler) and gets to D1. The red circle in the inmarsat slide suggests

somehow that only D2 is plotted in the inmarsat graph while actually the Total Doppler

appears to be plotted.

The D2 contribution (S/C induced L-Band Doppler) is very small i.e. in the range of 5Hz.

With my primitive vector algebra and the sat position/velocity data Duncan provided, I

calculated LOS speed (S/C) – (position of A/C) :

a) 0.0010 km/s at 16:30 at the ramp in KUL (=> 5Hz L-Band doppler)

b) -0.0087 km/s at 0:11 at an estimated final position -32° 92° somewhere close to the

Australian search area west of Perth.

b) also is a good match for the LOS velocity S/C – Perth at 0:11 which I calculate as -0.0084

km/s. That LOS velocity matches the C-Band doppler of 100Hz Mike puts for that time in

his graph.

Maybe Duncan and Mike can double check the absolute LOS velocity of the S/C in the

direction of the aircraft’s estimated position for times after 19:30 UTC (3:30 local).

According to my calculations the S/C induced L-Band doppler should rise to ~40Hz and not

to only ~5Hz as per Mike’s graph. That is backed up by the consideration that the C-Band

doppler rises to 100Hz (=>8.4 m/s LOS velocity). Because at the end of the flight aircraft

position is close to Perth, the LOS velocity (S/C )- (position of A/C) should be similar to LOS

velocity S/C – Perth .

The next mystery: According to Mike’s conclusions the asymmetries between north and

south track can only be introduced by the S/C motion and position. Everything else is

Ole



independent of the aircraft’s position. At the times when the S/C induced L-Band Doppler

is smallest in Mike’s graph, the asymmetries between predicted north and south track are

biggest. How can that be?

Regards

Ole

P.S.:

My way to calculate the LOS velocities of the S/C is:

- Convert lat,long,alt to ECEF

- get LOS vector by subtracting pos vector from sat_pos vector in ECEF coordinates

- normalize LOS vector

- calculate inner product of normalized LOS_vector * sat_velocity vector.

2014/04/04 AT 6:14 AM

Thanks Ole:

(1) “at 0:11 at an estimated final position -32° 92° somewhere close to the Australian

search area west of Perth.” – We do not KNOW that; we do not KNOW that it took a

southerly course.

(2) ” Because at the end of the flight aircraft position is close to Perth, the LOS velocity

(S/C )- (position of A/C) should be similar to LOS velocity S/C – Perth .” – see above.

(3) Quoting myself: “Please, I am simply unable to explain anything further about these

plots. If you don’t understand them, apologies. ”

Haelsingar,

Duncan

Duncan


Background Information on the Pinging of MH370 by Inmarsat-3F1 _ Duncan Steel.pdf

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