The channel dependent calibration term T_channel is assumed to be constant over a single flight but can vary between flights. A fixed value for each flight assessed was empirically derived by comparing the communications logs with known aircraft positions: the calculated value of T_channel was the mean difference between the measured BTO and the expected BTO calculated using the known aircraft location.
The so-called T_channel calibration term is a component of the BTO bias used to convert the BTO log data to total range (Perth GES to satellite + satellite to aircraft) from the ground station to the aircraft. This range is then used to produce the "ping rings" denoting a locus of possible locations of the aircraft at the "ping" times.
If the T_channel calibration changes ("can vary") from flight to flight, what is to prevent such a variation occurring as a result of an SDU reboot? There is no way to determine the value of the BTO bias after the aircraft went dark near IGARI. The ACARS data which provides aircraft position remained off, and the radar information (such as it is) does not overlap any ping rings.
Another statement from page 26 of "Bayesian Methods..." below.
A fixed value for each flight assessed was empirically derived by comparing the communications logs with known aircraft positions: the calculated value of T_channel was the mean difference between the measured BTO and the expected BTO calculated using the known aircraft location. For the accident flight this calibration is only available for the time when the plane was at the tarmac and for the first half hour of flight.
The so-called T_channel calibration term is a component of the BTO bias used to convert the BTO log data to total range (Perth GES to satellite + satellite to aircraft) from the ground station to the aircraft. This range is then used to produce the "ping rings" denoting a locus of possible locations of the aircraft at the "ping" times.
If the T_channel calibration changes ("can vary") from flight to flight, what is to prevent such a variation occurring as a result of an SDU reboot? There is no way to determine the value of the BTO bias after the aircraft went dark near IGARI. The ACARS data which provides aircraft position remained off, and the radar information (such as it is) does not overlap any ping rings.
Another statement from page 26 of "Bayesian Methods..." below.
A fixed value for each flight assessed was empirically derived by comparing the communications logs with known aircraft positions: the calculated value of T_channel was the mean difference between the measured BTO and the expected BTO calculated using the known aircraft location. For the accident flight this calibration is only available for the time when the plane was at the tarmac and for the first half hour of flight.
There is really no way to know if the assumption of a constant BTO bias is a valid assumption, particularly after an SDU reboot. Any device with multiple counter chains can initialize in a number of different states. Synchronizing all the counter chains can certainly be done, but it does require some overhead in the design, and is not usually done unless there is a functional reason for doing so. Note that the 18:25:27 BTO is derived from an R600 channel whereas all the other BTO's are derived from R1200 channels. The clock timing ambiguity associated with a simple divide by two is shown below. There are two equally likely possibilities based on how the counter chain initializes. The two states differ in phase by one clock period of the reference. See figure below.
The radar information (note I am not using the word data because radar data has never been placed in the public domain) we have adds more confusion to this situation than clarity. In particular, consider the radar graphic below presumably captured by the Malay radar on Penang Hill. This graphic was shown to the Chinese NOK in the now infamous Beijing LIDO Hotel presentation.
This graphic has been used extensively by independent analysts in an attempt to characterize the flight path of 9M-MRO after it crossed the Malay Peninsula. Of particular interest is the time stamped information in the box at the upper left of the figure. The time 02:22 is 8:22 UTC. The 295R is the azimuth angle from Penang Hill, and the 200nm is the range. Analysts were quick to recognize that this figure, in particular the information in the box at the upper left, could not be reconciled with the Inmarsat data (the 18:25 ping ring) nor did the track conform to normal air "corridors". As a result, the data in the box was declared to be in error, and the graphic was morphed in various ways to conform to air corridors in the region. The area inside the white circle has been the subject of various conjectures relative to why the track is missing in that region.
Consider the Google Earth graphic below which shows the above area along with labeled range rings, in particular the 18:25 ring. The graphic also includes a 295R/200nm radial from Penang Hill (the yellow line, and various points of interest such as the Kota Bharu "sighting" location, and the position of Kate's (the saucy sailoress) boat. The white horizontal line connecting the end of the Penang Hill radial to the 18:25 range ring has a length of 145km (78.6nm).
The precise time of the 18:25 ring is 18:25:27. Suffice to say that a 777 cannot fly 145km in 3 minutes and 27 seconds (18:22 to 18:25:27). So obviously the time stamped information in the Lido Hotel graphic must be wrong since the range ring is assumed to be correct. I also believe this interpretation of the information is probably correct.
However, there is an alternative explanation. The alternative binary is that the 18:25 range ring is incorrect as a result of a change in BTO bias induced by the SDU reboot. What value might be assigned to the BTO bias is the next obvious question. Again resorting to "Bayesian Methods..." page 26:
For some communication messages, typically during initial log-on, there was a very large difference between the measured
BTO and the nominal delay. Analysis showed that rather than simple outliers, these
anomalous BTO measurements could be corrected by a factor of N × 7,820 μs
where N is a positive integer.
What if the BTO bias was increased by 7820us, and that this increase persisted for the remainder of the flight up to the 19:xx reboot where another bias change opportunity would present itself? That would move the 18:25 range ring in the direction of end of the 295R/200nm radial, and the new distance to the range ring might be compatible with a flight time from 18:22 to 18:25:27.
A detailed calculation for the 18:25 range ring radius was performed elsewhere in this blog. See link below:
Calculation of 18:25 ring using KL BTO bias
The calculations in the link use the BTO bias of 495679us derived from tarmac measurements prior to take-off at Kuala Lumpur. What if this calculation were done again with 7820us added i.e. with a BTO bias of 503499us? A 18:25 range ring based on this BTO bias has radius of 5184km compared to the unmodified BTO bias range ring radius of 3526km. A radius increase this large is clearly not at all compatible with the radar information. Looking at other possibilities in the absence of data from previous flights, one is tempted to use a bias increase corresponding to one symbol of the IOR-R1200 slotted Aloha protocol used in the R-channel. All packet channels use 1/2 rate forward error correction, so the symbol period is 1/2400. This choice results in delay increase of 417us to a BTO bias of 496096us versus the KL measured bias of 495679. See clock phase ambiguity figure shown earlier. The resulting 18:25 ping ring radius is 3634km or about 108km larger. This value is a promising candidate.
The graphic below depicts the Google Earth view as above with the 18:25 and 19:40 range rings based on the 496096 BTO bias drawn in green. The distance to the revised 18:25 range ring (7N 96.8E) is 23nm along a 295 degree azimuth from the 200nm stated radial range end point. To cover this distance in 3.5 minutes would imply an aircraft speed of approximately 411 knots. This speed coincides with the most probable speed derived by the DSTG for the Southern track after the FMT at 19:40. See also the Mid-flight Speed post elsewhere in this blog.
mid-flight speed MH370
Note the the revised 19:40 range ring goes just about over the top of Kate's boat. Kate's boat is at approximately 6.5N 94.5E in the graphic below. It certainly reinvigorates the possibility that Kate could have seen the aircraft at very close range. Additionally this location is very close to locations posited for the late FMT needed to support terminal locations further to the North and East of the current priority search zone.
What if the BTO bias was increased by 7820us, and that this increase persisted for the remainder of the flight up to the 19:xx reboot where another bias change opportunity would present itself? That would move the 18:25 range ring in the direction of end of the 295R/200nm radial, and the new distance to the range ring might be compatible with a flight time from 18:22 to 18:25:27.
A detailed calculation for the 18:25 range ring radius was performed elsewhere in this blog. See link below:
Calculation of 18:25 ring using KL BTO bias
The calculations in the link use the BTO bias of 495679us derived from tarmac measurements prior to take-off at Kuala Lumpur. What if this calculation were done again with 7820us added i.e. with a BTO bias of 503499us? A 18:25 range ring based on this BTO bias has radius of 5184km compared to the unmodified BTO bias range ring radius of 3526km. A radius increase this large is clearly not at all compatible with the radar information. Looking at other possibilities in the absence of data from previous flights, one is tempted to use a bias increase corresponding to one symbol of the IOR-R1200 slotted Aloha protocol used in the R-channel. All packet channels use 1/2 rate forward error correction, so the symbol period is 1/2400. This choice results in delay increase of 417us to a BTO bias of 496096us versus the KL measured bias of 495679. See clock phase ambiguity figure shown earlier. The resulting 18:25 ping ring radius is 3634km or about 108km larger. This value is a promising candidate.
The graphic below depicts the Google Earth view as above with the 18:25 and 19:40 range rings based on the 496096 BTO bias drawn in green. The distance to the revised 18:25 range ring (7N 96.8E) is 23nm along a 295 degree azimuth from the 200nm stated radial range end point. To cover this distance in 3.5 minutes would imply an aircraft speed of approximately 411 knots. This speed coincides with the most probable speed derived by the DSTG for the Southern track after the FMT at 19:40. See also the Mid-flight Speed post elsewhere in this blog.
mid-flight speed MH370
Note the the revised 19:40 range ring goes just about over the top of Kate's boat. Kate's boat is at approximately 6.5N 94.5E in the graphic below. It certainly reinvigorates the possibility that Kate could have seen the aircraft at very close range. Additionally this location is very close to locations posited for the late FMT needed to support terminal locations further to the North and East of the current priority search zone.
Obviously displaced ping rings after the reboot at 18:xx completely change terminal locations derived by everyone to date. I am not suggesting that this conjecture is anything but conjecture, but it does support the range and azimuth numbers shown in the Beijing Lido Hotel graphic.
It is also possible that only the 18:25:27 range ring is corrupted since subsequent range rings are derived from R1200 channels where the additional divide by two ambiguity does not exist, at least relative to that counter chain.
Once again, data from the previous flights would be enormously helpful to determine if the variation in BTO bias on R600 channels observed in those flights is quantized near a symbol period of the R1200 channel. Recall that with 1/2 rate FEC encoding the symbol period is 1/2400 second.
EDIT 10/31/16
Checking the BFO value at 18:25:27 for the location, speed, and track derived above.
The measured BFO of 142Hz has an associated BFO residual of 17.6Hz
Using:
speed = 411knots
track = 295 @ 7N 96.8E
yields a BFO residual of 13.5Hz or a predicted BFO of 138Hz (4Hz error).
EDIT 11/1/16
Graphic below was created from Figure 4.1 of "Bayesian Methods...". The DSTG final radar contact was carefully estimated as 6.6N 96.3E by overlaying the image in Google Earth. The DSTG last contact shown is at ~250nm (maximum range of RAT31DL radar at Penang Hill) on a ~287degree radial. The Penang Hill radar horizon at 250nm corresponds to approximately a 23,000 feet aircraft altitude. The standard 18:25 range ring is located 27nm further along the 287 degree radial (black line). Implied aircraft ground speed compatible with reaching the 18:25 ring on time is is ~463 knots. Approximate location of ring crossing is 6.7N 95.8E.
Again the measured BFO of 142Hz has an associated BFO residual of 17.6Hz
Using:
speed = 463knots
track = 287 @ 6.7N 95.8E
yields a BFO residual of 10Hz or a predicted BFO of 134.4Hz (7.6Hz error).
Alternatively, the aircraft may have turned slightly to the North at Mekar to follow the air corridor to Nilam. This turn would result in a heading of 296 degrees.
Using:
speed = 510 knots (DSTG ground speed estimate)
track = 296 @6.8N 95.9E
yields a BFO residual of 17.7Hz or a predicted BFO of 142Hz (virtually no error).
This scenario would seem to be the most likely.
It should be noted that at the DSTG estimated ground speed of 510 knots the aircraft will over-shoot the 18:25 range ring by about 25km (probably no big deal).
