As a follow-up to my post on understanding satellite pings, I thought it would be helpful to give a bit more detail on how the location of a ping can be identified. In my previous post I indicated that you could potentially measure range (based on timing) or angle (based on power). After some further thought, it is likely that the range measurement would be much more accurate, not least because a change in angle (e.g. a plane banking) would throw off the power measurement significantly. The determination of a “measurable distance” is also what David Coiley of Inmarsat described in an interview with the New York Times last week.
How does this measurement happen, and how accurate is it? The first thing to understand is that the pings are sent to the satellite in a specific “time slot”, which has a given frequency and start time, but the burst of energy in the signal might not always be exactly in the center of the slot. This is illustrated very well in a recent Inmarsat patent, which shows the variation between three different bursts B1 to B3 which are scheduled in the same frequency (f1) and successive time slots (T1-T3).
How much the burst is offset in time relative to the center of its designated timeslot gives a measurement of range, since the further the terminal is away, the longer the energy will take to reach the satellite. How much the burst is offset in frequency relative to the center of its designated timeslot gives a measurement of speed, since if the terminal is traveling towards the satellite, the frequency will get higher and if it is traveling away from the satellite, the frequency will get lower (this frequency offset is the Doppler effect).
So in the illustration above, B2 is shifted both in time (range) and frequency (speed), whereas B3 is shifted in frequency (speed) but not in time (range).
UPDATE: One complicating factor is that if the Doppler correction takes place only in the terminal itself, then it is possible that the network may not see much if any frequency shift for the ping that is returned from the terminal. I am trying to confirm how this aspect is handled.
I should also note that it would not necessarily be expected to be standard operating procedures for a satellite operator like Inmarsat to save the precise time/frequency offset associated with each burst received by its satellites. But since the precise time data appears to have been used in the range calculation, it seems logical to conclude that this information (and potentially the associated frequency offsets as well if these are available, although this was not mentioned in a CNN interview today) must have been recorded.
Key point 1: It is likely to be feasible to calculate the range and possibly also the speed relative to the satellite from the ping information via the time/frequency offset method described above.
What we’ve seen in terms of the arcs of possible locations so far just represent the range component of this measurement. It seems that there is no triangulation involved (which is consistent with the CNN interview), because in this particular coverage region the specific frequencies involved are only used on the Inmarsat 3F1 satellite and not on any other satellites.
Its much harder to interpret the speed component (if it is available), because it is the speed relative to the satellite. So if the terminal was moving along one of these arcs, it would not be getting closer to or further away from the satellite and there would be no frequency shift. So in that situation the signal would look the same as from a plane that was stationary on the ground at the time of the transmission. If this information is actually available would expect Inmarsat to have been able to interpret the frequency shift as well as the time shift, but even then there would be no easy way to illustrate “relative speed” on a chart like the one given above.
Key point 2: Speed relative to the satellite is not the same as absolute speed, so (even if this information were available) it would not be possible to determine with certainty if the plane was on the ground and stopped.
Similarly, comparable data has not been released for previous “pings” before the last one. Whether or not the frequency/speed data is available, I would expect that it should be possible to determine that some points on the arcs above are more likely than others, but even with both pieces of information it is unlikely to eliminate any points completely unless other information is known (or assumed). For example, if one assumed that the plane flew at a constant speed and bearing then it would be possible to narrow down the locations quite significantly (because the speed and range would change in a predictable way, although north/south ambiguity would remain). However, that may or may not have been the case.
UPDATE: Similarly, one could test the theory about “following another aircraft” because the track of the other aircraft is known and its position would have to coincide with the arcs calculated for intermediate pings while this “following” was in progress.
Key point 3: The combined information from multiple pings would potentially be fairly dispositive as to whether the plane flew at a constant speed and bearing (i.e. on autopilot), although there might still be some uncertainty in the ultimate location (and north/south ambiguity) unless speed information was also available. The intermediate pings would also determine whether the “following another aircraft” theory is feasible.
So now for the big question, how accurate is the location of this arc. Without the ability to triangulate between multiple satellites, then geolocation accuracy (i.e. the ability to identify where on Earth a signal is being transmitted from) is considerably reduced, but a single satellite geolocation detector from Glowlink is said to have an accuracy of 40-60 miles. However, that detector may use more measurements (of a static source) than is possible with this limited number of pings from a terminal that is moving around. So I would expect my initial estimate of say 100 miles is still fairly reasonable. Its also important to remember that the plane could have had enough fuel onboard to have flown as much as a couple of hundred miles after the last ping.
Key point 4: The range accuracy is unlikely to be much better than 100 miles, and perhaps more because the plane could have continued flying after the last ping.
UPDATE: This is the latest search area, as shown by Reuters Aerospace News, including up to 59 minutes of potential travel after the final ping (i.e. the full period before the next hourly ping, regardless of remaining fuel).
UPDATE (Mar18): The Australian Maritime Safety Authority has held a press briefing today at which they described exactly the procedure outlined above for the southern route, i.e. assuming a constant speed and heading and correlating the results from all of the pings. They have produced the following map based on NTSB analysis showing that there only two paths consistent with the set of arcs and a constant speed/heading assumption. They declined to speculate on the northern route but indicated in the press briefing that similar analysis had been conducted. Presumably therefore it is now known whether or not the “following another aircraft” theory is feasible.
UPDATE (Mar 19/20): This evening, CNN put the image below on screen, showing purported ping arcs and the overlap with one of the projected southern tracks. It is not known if these are accurate locations, or if the image was purely illustrative. However, if the arcs are accurate, then (if the debris is a false lead) the “shadowing” hypothesis can be ruled out because the plane would not have gone far enough out into the Bay of Bengal. Moreover, if the plane is found in the southern search area having traveled along one of the projected paths, then it was flying in a straight line at constant speed (as AMSA and NTSB previously assumed in making these projections) and so was not likely to have been under active pilot control when it crashed. In addition, if the plane is found in the identified search area so quickly, it will intensify the scrutiny of the delays in making use of the ping information which Inmarsat provided very early in the investigation.
UPDATE (Mar 20): As noted by a commenter, the Washington Post published 3 of the earlier ping arcs in a graphic shown below. These are quite similar to the ping arcs depicted by CNN, suggesting that if the 4.11am ping arc is as close to the 5.11am arc as suggested by the CNN graphic, the “shadowing” hypothesis for the northern route is likely to be infeasible.