**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, writes TMF Associates’ Tim Farrar.**

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) 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 clear that there is no triangulation involved (i.e. the signal was not received by many different satellites), because the ends of the arcs have been determined (according to this figure released by the Malaysian government today) based purely on the maximum and minimum flying speed of the plane. That is not surprising (and 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).

** Read More: Malaysian MH370: SATCOMS 101 (Part One)**

So why hasn’t Inmarsat (or Air Malasia) released any info about the earlier pings? And why aren’t reporters raising a bigger stink about it? It is incredibly frustrating to have to listen to a bunch of wild speculation, when this data should dramatically narrow the range of possiblities.

Shouldn’t the satellite ping arc really be continuous? There should be no ‘break’ over Thailand, Vietnam and Malaysia as the ‘range at minimum speed’ limit surely assumes that the plane was flying in a straight line.

Alexander is correct because during the early part of the Burst Offset Frequency chart we know the frequency was plotted increasing (towards the satellite) yet we also know the aircraft was under radar surveillance flying away northeastwards.

There are only two rational explanations, either the signal processing inverted the BOF data or somebody intentionally and subjectively inverted the data to make it appear to support a theory the plane flew west.

Extremely interesting stuff. However, has anyone explained why the plane would follow a flight path of an arc for over 3000 miles?

From a CNN article, the arc only represents the last ACARS transmission.

If the aircraft route was changed in the FMC when it hit the last fix on the route the auto pilot would have entered a wings level flight mode and maintained that with no pilot intervention. If this is the case the distance to the satellite would change. If they have 6 pings that give them 6 arcs if you input approximate speed and the distance between the arcs someone better at math that I should be able to W>A>G a fair flight path?

Thank you for putting this together. I was wondering about ACARS and this helped clear up several questions. But I still have one, if anyone can help. I did some rough calculations and found that directly underneath the satellite, nadir, the time delay is around 119 milliseconds. Along the arc everyone is pointing to, the delay time is 125 milliseconds and the larger areas are between 123 and 127 milliseconds. I am wondering, how good is the ACARS clock? A clock that is slow by 1 millisecond would move the arc toward the satellite by over 500 kilometers. Any thoughts?

As i understand it, the ping arcs are a collection of possible locations at a point in time. My question is, why do the ping arcs not extend in a complete circle?

thank you for your reply.