Here is my explanation of the Nominal Terminal concept, why it is used in the calculating the log values and how to utilise it with it in data analysis.
The Inmarsat notes say: “The BTO is a value (in microseconds) relative to a terminal at a nominal fixed location.”
It is the difference between a) the round trip from the ground station to the aircraft and b) the round trip from the ground station to the Nominal Terminal at some fixed location (with respect to the Earth). So:
BTO = 2 x [ (ground station to aircraft path) – (ground station to Nominal Terminal path) ]
As the Inmarsat notes say, each of those paths involves a ground station to satellite leg, and a satellite to terminal leg. The legs between ground station to satellite cancel in the calculation above (as they are the same for any single time), hence:
BTO = 2 x [ (satellite to aircraft path) – (satellite to Nominal Terminal path) ]
It has been stated by Inmarsat that the reason for logging BTO numbers was to assist in locating aircraft, so a measure that includes the ground station to satellite link delay element would be counter-productive. To be clear, the Nominal Terminal is a ‘virtual’ terminal which just exists in the Inmarsat processing system to allow them to log (in real-time) some meaningful (and short) numbers. The simplest assumption is the Nominal Terminal is at a fixed altitude above the equator at longitude 64.5E. I show a schematic of the Nominal Terminal idea below. The length of the green line segment in the diagram is that determined by the individual BTO values as shown.
https://www.dropbox.com/s/85ymzzaj6i...l_terminal.jpg
BTO values so defined can be used immediately to give a rough ping-arc using just the average satellite position. With the actual position of the satellite the full accuracy is possible. If only the full round-trip time to the aircraft was logged then more processing would be needed to get even a rough ping-arc, particular for aircraft positions close to the sub-satellite point at 64.5E.
The distance of the Nominal Terminal from the satellite can be calculated from the pings before take-off (where we know the aircraft position and hence the satellite to aircraft distance) using the formula above; this gives the satellite to Nominal Terminal distance as 35079km and hence a Nominal Terminal altitude of 718km. The choice of this altitude value is entirely at the convenience of Inmarsat. It can’t be zero as that would give negative BTO values for aircraft overflying the sub-satellite point. Also they would want some margin to allow for noisy measurements without giving negative BTO numbers.
On this basis, the fixed Nominal Terminal position determined as above (including the fixed altitude) has to be used in calculating the satellite to aircraft ranges from the later BTO values, allowing for the changing position of the satellite. There must be a small constant term in the BTO calculation that corresponds to the response time of the aircraft terminal but that can’t be differentiated from the altitude of the Nominal Terminal determined earlier.
The ping-arcs derived from this technique match those that follow from the ‘fuzzy’ photo of a satellite elevation graph shown to the families some months ago. The distances on the ground of the key ping-rings are as follows, using a 'average' aircraft height of 15000ft:
18:29UT 3630km
19:41UT 3375km
20:41UT 3436km
21:41UT 3692km
22:41UT 4096km
00:11UT 4819km
The Nominal Terminal concept does not apply to the BFO data.