Don't really know the answer to the post title, but I have been absorbed by a conceptualization related to BTO and Doppler compensation. Doppler compensation refers to the frequency offset put on the L band carrier by the AES. This compensation only uses velocity components in the local tangent plane. No adjustments are made for vertical components of velocity. Also this compensation is performed by assuming that the Inmarsat satellite is stationary at its nominal position over the equator.
Consider, for example, the BTO values at 19:41 and 20:41 which are 11500 usec and 11740 usec respectively. The difference being 240 usec. The path difference associate with this time difference is 240usec * C/2 = 35975 meters (where C is the speed of light). The average Doppler shift between 19:41 and 20:41 must accumulate 35975 meters of L band cycles. A cycle or wavelength of the L band frequency is 0.182 meters. So the number of cycles is 35975m / 0.182m = 197665 cycles. These cycles are accumulated over a time period of one hour. The associated frequency is 197665 cycles / 3600 seconds = 55 Hz. So the average Doppler needed is 55 Hz.
If one plots the Doppler compensation for various trial paths it is clear that it is very linear. Meaning that the average of the Doppler compensation at 19:41 and 20:41 is a reasonable estimate of the Doppler average over the path. My suggested flight path scenario via the Cocos has an average Doppler compensation in the vicinity of 35Hz between 19:41 and 20:41. Likewise with the McMurdo path recently suggested by Ianello and Godfrey. This deviation seems too large relative to the expected 55 Hz.
So I asked DrB for his most recent path parameters at 19:41 and 20:41. The reply was:
19:41 => 0.018N 93.719E 452.7 knots
20:41 => 7.540S 93.191E 452.1 knots
DrB warned me to be careful about determining a heading since the heading is variable and effected by several different parameters. So I did the best I could, and estimated the heading at 19:41 at 183 and the heading at 20:41 at 182. I think these values are close (DrB can refine them for himself).
So, using the above values one computes the Doppler compensations as:
19:41 = -37.7 Hz
20:41 = 143.6 Hz
The average Doppler is 53Hz which is amazingly close to the required value. Much closer in fact than any path I had examined prior to DrB's path, and well within the errors associated with the BTO measurements. I should also point out that the average Doppler computed as above is extremely sensitive to position, speed, and heading. Others will agree when they try the method for themselves.
So, my conclusion is that the 19:41 and 20:41 points derived by DrB seem to pass this test.
Someone will say that using the nominal satellite position is not correct. In fact, I believe it is the right thing to do. This notion needs more work. It might be that for small changes in BTO that the actual satellite position is an important consideration.
I would encourage others reading this post to try this method for themselves. I think the conclusion will be that it is a very very sensitive test of path parameters. Of course, I could be very wrong. Turn on the flame throwers. I welcome aggressive feedback.
I do expect something to be incorrect about the approach presented above. I simply do not see what it is.
Edit 3/14/17
My suspicion is that for small BTO differences that the contribution of satellite motion to the BTO is not insignificant.
