# Inmarsat analysis for missing flight MH370

1. Mar 24, 2014

### yuiop

Initially the pings from Malaysian airlines flight MH370 could only determine the distance of the aircraft from the satelite based on round trip times of the pings sent at one hour intervals. Taking the fuel range and estimated speed of the aircraft into account this confined the possible location of the missing aircraft to two arcs, the so called North and South corridors. What is the physics behind the claim of the satellite company to have narrowed the location to the Southern corridor? Does anyone have any idea what mathematical analysis they used?

I can see how a Doppler analysis of the pings would indicate whether the plane was going towards the satellite or away from it, but that still gives no indication of whether the aircraft was going North or South.

2. Mar 24, 2014

### nsaspook

The probable physics behind the claim is that they had help and information from other sources that proved the northern track was impossible at the speed and altitude needed to travel that far north without detection once they refined the likely travel arc path to less than 3 percent of the possible arc using detailed signal analysis.

http://www.inmarsat.com/news/washington-post-tracks-inmarsat-role-hunt-mh370/
That said I guess it's possible to use a changing north/south satellite offset from the equator to generate some additional position information if the satellite is also moving in respect to the plane if you have precise reference data to known paths using GPS fixes from another plane(s) and their ping data.

http://www.bbc.com/news/uk-26720772
https://www.physicsforums.com/showpost.php?p=4698717&postcount=161

Last edited: Mar 24, 2014
3. Mar 24, 2014

### yuiop

Everyone had already assumed that, assuming all the countries involved were competent and honest about their military radar data. The Inmarsat claim implies they pinpointed the aircraft independently of any radar information, using mathematical analysis of the satellite pings only (and analysis of pings from other aircraft flying at the time).

The Inmarsat satellite is supposed to be geostationary and so stay above the same point on the ground, but I guess there 'might' be some North/South wobble. I just get the impression there is something they are not telling us, like additional data from an independent military satellite not on the equator that helps triangulate the location. At the moment they are claiming to locate the aircraft using a single geostationary satellite. That is a bit like pin pointing a phone using a single mast when it normally takes 3 masts not in a straight line to triangulate the position, if there is not GPS data encoded in the signal.

4. Mar 24, 2014

### yuiop

You might be right about the North/South wobble. This map showing the last 4 ping arcs of MH370 shows the satellite is not exactly on the equator. Therefore the satellite cannot remain above the exact same spot on the ground over 7 hours and therefore the position of the satellite shown on the map is not accurate but just an average position. Given that additional information (exact varying latitude of the satellite at each ping) combined with the Doppler shift for each ping, I guess it is possible to narrow the aircraft location to the South corridor.

5. Mar 24, 2014

### sophiecentaur

I saw a map in some newspaper which showed a circle of possible positions around what was presumably the centre of the satellite footprint. I can only assume that would refer to the locus of locations with a given signal level (based on the satellite radiation pattern). But that would imply they could tell what the level was at the centre of the footprint. I guess there may be something clever they could do to correlate signal levels at various points on its path history, which assume a straight line (rhumb line or great circle (?) ) course. It would all be pretty speculative I think.
The North / South issue could be resolved if there were significant wobble in the orbit. But one thing bothers me and that is the beam pattern is pretty flat in the service area (sinc function) so what sort of accuracy are they dealing with?
I guess people (governments) want closure and will pick the evidence to suit them.

6. Mar 24, 2014

### nsaspook

This is the position, zoom in to see the N/S movement. http://www.n2yo.com/?s=23839

They do have at least 6 sets of timing data over at least 6 hours on the plane to generate a good pattern of distance and possible speeds to match a flight path if the first ping was close to known good fixes heading south before it was lost on radar but I would expect some sort of 'cover' if classified sources and methods are being used to determine a location.

Last edited: Mar 24, 2014
7. Mar 24, 2014

### sophiecentaur

What is meant by that expression? Does it really involve measurement of actual distance between satellite and transceiver? I wonder what use that very approximate measure would be (think of the trigonometry involved). Rescue beacons always send GPS coordinates of the casualty (from the casualty's equipment) and they are received and relayed to the rescue services via the satellite. Afaik, the Inmarsat system doesn't attempt to locate the casualty. Is there another layer to this system that I don't know about? It would be nice to know if there is.

8. Mar 24, 2014

### AlephZero

According to http://www.bbc.co.uk/news/uk-26720772 the new features of the analysis seem to be
(1) developing a new analysis technique using the Doppler shift in the signals received, and
(2) comparing the signals with previous Malaysian Airways flight data, going back several weeks (presumably to validate the new method).

9. Mar 24, 2014

### nsaspook

The round trip time is measured very accurately as it's used to assign data time slots for future transmissions in the protocol for Inmarsat satellite users due to the long latency times.

Location methods.
http://www.cisco.com/c/en/us/td/docs/solutions/Enterprise/Mobility/WiFiLBS-DG/wifich2.html#wp1049497

Last edited: Mar 24, 2014
10. Mar 24, 2014

### phyzguy

I think it involves viewing the track of the airliner in three dimensions. If I plot the velocity toward or away from the satellite as a function of time, there should be a big difference between the north track and the south track, since on the north track it was always north of the equator, while on the south track it had to cross the equator. So on the north track the z-component (away from the satellite, towards the center of the Earth) would be steadily increasing, while on the south track it would decrease, go through zero, and then begin increasing.

11. Mar 24, 2014

### nsaspook

The problem is it's so near the equator at the beginning so the z-component change is small until it's very far away. It might be detectable but it really looks to be in the distance noise level.
http://tmfassociates.com/blog/2014/03/17/locating-satellite-pings/

http://www.telegraph.co.uk/technolo...lite-company-Inmarsat-tracked-down-MH370.html

It's inclination is 1.7 ° , that's pretty big when compared to a fairly new 'stationary' bird like this one near the USA http://www.n2yo.com/satellite/?s=28884

Last edited: Mar 24, 2014
12. Mar 24, 2014

### yuiop

I think I have figured it now. The diagram below shows the principle of how the North/South motion of the satellite allows the North/South corridors to be differentiated.

The diagram is not to exact scale but exaggerated to show the principle. The satellite is here assumed to be moving North over the time period. Successive pings are shown as dashed circles from red -> green -> blue -> brown. Starting from the last known military radar detection, segments of constant length are drawn going North and South that assume constant flight speed. Successive pings from the North going route have progressively less Doppler shift as they get progressively more parallel to the the ping arcs. By contrast, successive pings from the South going route have progressively more Doppler shift. This is presumably what the Inmarsat team detected.

Additionally, the South going route follows a great circle which is what you would expect from an aircraft on auto pilot going on a fixed heading. The North going route on the other hand is clearly not on a geodesic and requires continuously varying change of direction from a pilot with detailed knowledge of what would be detected by detailed analysis of the Inmarsat data.

It seems the possibly unintended 'imperfection' of the satellite's geostationary position is what made location of the aircraft possible with a single satellite. If that is the case it would seem to be good idea to increase the North/South wobble of the satellites or add some non-geostationary satellites to the Inmarsat satellite constellation. That way, satellites could track aircraft across oceans (or anywhere else) in near real time, using the current technology already installed in most commercial aircraft. The additional safety and chance of being rescued in a timely manner would surely be worth the cost. In fact, it is a bit shocking to me, that most aircraft on oceanic routes or on overland routes far from airports are "off radar" most of the time. See http://planefinder.net/

NOTE: The ping arcs are shown as perfect circles in the above diagram, which is an approximation. This is only valid for a satellite position exactly in the centre of the map. For perfect accuracy, the ping circles should become increasingly elliptical as the satellite position deviates from the centre of the map. (Some of the maps published by the press do not take this into account.)

#### Attached Files:

• ###### pings.jpg
File size:
29 KB
Views:
379
Last edited: Mar 24, 2014
13. Mar 24, 2014

### yuiop

Most of the Doppler effect is due to the movement of the aircraft (in flight) which is much greater than the movement of the satellite relative to the ground, but nevertheless, you were right that the key ingredient to differentiating the North route from the South route is the movement of the satellite itself.

14. Mar 25, 2014

### sophiecentaur

I looked at the link and it deals mainly with ground level location. It does suggest a timing accuracy of around 100ns, which corresponds to a distance error of around 30m. There is the added factor of the trigonometry involved with the satellite at a distance of 35000km but, surprisingly, that only seems to increase the error by a factor of about 20, for distances of 1700km from the satellite lat and long. That's less than 1km error - which surprised me - but I think it's right. The advantage this system has, over the personal rescue beacon system is the timing measurement. For EPIRBs, the casualty's position is found by a local GPS receiver and (I think) the LEO satellites are used to relay that information to the rescue services. A 1km error would not be good for finding a sinking yacht in bad conditions, even if the system used by the aircraft were used.

15. Mar 25, 2014

### yuiop

The chart below for the "MH370 burst frequency offset analysis" seems to agree with the assumption of progressively increasing Doppler shift for the South going route in post #12.

http://en.harakahdaily.net/images/stories/mh2.png [Broken]

Last edited by a moderator: May 6, 2017
16. Mar 25, 2014

### nsaspook

It wasn't a complete 'WAG' as we had to handle birds in some pretty crappy orbits 'stationary' orbits when I was a young GAPFILLER/SATCOM system hacker in the 1970s Navy. The station-keeping fuel budget for N/S alignment must have been an afterthought for some of the early FLTSATCOM designers that made our job of tracking them at sea a pain with old gear like this.

http://electronicstechnician.tpub.com/14092/css/14092_42.htm
http://www.fas.org/spp/military/program/com/fltsat.htm

Last edited: Mar 25, 2014
17. Mar 25, 2014

### yuiop

I have just noticed that the diagram I posted in #12 has the arrow indicating the satellite motion pointing the wrong way. Here is the corrected diagram with some minor refinements:

#### Attached Files:

• ###### pings2.jpg
File size:
32.9 KB
Views:
346
18. Mar 25, 2014

### nsaspook

These guys seem to be using a similar technique to locate 'interference' using single satellite technology at <100 miles but that's with a stationary target.
http://www.satellitetoday.com/publi...-to-solve-interference-geolocation-obstacles/

19. Mar 26, 2014

### yuiop

In post #17 I assumed the satellite was going South as the was the best fit to the information I had available. This diagram captured from this video confirms that was in fact the case.

The diagram shows the satellite started heading South back towards the Equator at around 03:30 AM not long after Malaysian Airways flight MH370 also started heading South into the Indian Ocean. The data for the diagram comes from a much more detailed account given by http://www.duncansteel.com/

03:30 hrs (19:30 Hrs UTC) is also when the chart in post #15 for the Doppler shift of MH370 changed from decreasing to increasing.

#### Attached Files:

• ###### wobble.jpg
File size:
17.3 KB
Views:
342
Last edited: Mar 26, 2014
20. Mar 26, 2014

### nsaspook

It's looks like we got lucky they were using INMARSAT for data links in the Indian Ocean.
Almost all of their birds except the newest have usable wobbles for single-satellite geolocation.

91018A INMARSAT 2-F2 -142.0 9.3
08039A INMARSAT 4-F3 -97.6 3.0
97027A INMARSAT 3-F4 -53.9 3.5
96053A INMARSAT 3-F2 -15.5 0.1 : Mainly broadcast services in that slot so better station keeping? http://www.satbeams.com/channels?norad=25949
98006B INMARSAT 3-F5 24.6 0.3 : Last of the 3 series launch date 1998.
05044A INMARSAT 4-F2 25.1 2.3
13073A INMARSAT 5-F1 62.7 0.0
96020A INMARSAT 3-F1 64.6 1.6
05009A INMARSAT 4-F1 143.5 2.7
96070A INMARSAT 3-F3 178.2 1.0

http://www.satsig.net/sslist.htm

I monitor KU band satellite broadcasts over NA on a 1M movable dish as a hobby using several DVB PC cards in a Linux server, most are pretty stable in orbit but a few are getting long in the tooth and have the 'shakes'.

#### Attached Files:

• ###### P8250058.jpg
File size:
30.7 KB
Views:
53
Last edited: Mar 26, 2014